Balancing theory

Balancing Theory and Applications (Rev. 2.1) Ing. G. Manni

Mandello del Lario, 30.07.99

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Note from the writer The following text reports the main arguments discussed during the balancing courses proposed by CEMB and are a record for the participants and a guiding path for the teacher . During the courses ,the different arguments are more widely explained and enriched with practical examples. The explanation ,even if correct ,is simple and full of useful examples , and so understandable to all the people (with different culture level ),interested in the balancing technology .. By mentioning the source , reproduction of parts are possible .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

INDEX CHAPTER 1 BASIC PRINCIPLES 1.2

Balancing requirement

1.3

Unbalance(definition)

1.4

Unbalance measuring unit

1.5

Centre of mass (definition)

1.6

Mass eccentricity (definition)

1.7

Axis of inertia (definition)

1.8

Unbalance classification

1.9

Static unbalance (definition)

1.10

Couple unbalance (definition)

1.11

Dynamic unbalance

1.12

Equivalent total unbalances (equal)

1.13

Vector relationship between unbalances

1.14

Dynamic balancing

1.15

Examples of dynamic balancing

1.16

Unbalance effect

1.17

Balancing speed

1.18

Common frequent words

1.19

Criteria for deciding the number of balancing planes ( 1 or 2 ) for rigid rotors

1.20

Static balancing without the use of a balancing machine

CHAPTER 2 BANANCING TOLERANCES 1.21

Foreword

1.22

Balance quality grades for various groups of representative rigid rotors

1.23

Balancing tolerance

1.24

Examples of calculation of the residual unbalance according to ISO 1940/1 Standards for rigid rotors .

1.25

Evaluation of the balancing quality G (The total residual unbalance is known)

1.26

Balancing tolerances according to API 610 standards Balancing tolerances calculated according to the maximum admitted load on the bearings

1.27

Allocation of permissible residual unbalance to each correction plane according to ISO 1940/1

1.28

Static / couple unbalance with narrow balancing planes

1.29

Balancing tolerance / balancing planes

1.30

Balancing certificate

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. 3 CHAPTER 3 MOUNTING ADAPTERS 3.1

Foreword

3.2

Coupling accuracy evaluation

3.3

Basic principles to design a mounting adapter

3.4

Examples of mounting adapters

3.5

Common errors caused by the Adapters

3.6

Electronic compensation for mounting adapters errors.(eccentricity compensation)

3.7

Manual compensation for mounting adapter errors (eccentricity correction)

3.8

Example for evaluating the error caused by a coupling sleeve mounted eccentric

3.9

Basic concepts for adapter eccentricity correction

3.10

Balancing of rotors shafts without fitments ;rotor shaft key convention

3.11

Balancing the fitment (flywheel ,coupling , etc.) with an adapter having a full key

CHAPTER 4 ON FIELD BALANCING Foreword Necessary equipment Theory Test mass calculation method Two planes balancing on service conditions Not linear response Manual unbalance calculation with the graphic vector method Evaluation of the optimum angle position of the test mass during calibration Manual balancing with the use of a simple vibration meter CHAPTER 5 FLEXIBLE ROTORS BALANCING Foreword Shaft critic (natural ) speed evaluation methods Calculation of the critic (natural ) speed Natural frequencies of a beam calculation Rotors classification Rotor flexibility measurement on a balancing machine Basic criteria for flexible rotors balancing Rotors classification according to balancing requirements Quasi rigid rotors Examples of low speed balancing Flexible rotors Number of balancing planes

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Modal balancing Modal balancing test masses set Influence coefficients method Balancing tolerances for flexible rotors Flexible shaft bending evaluation (Whirl) CHAPTER 6 THE BALANCING MACHINES Industrial balancing machines classification Unbalance transducers and support mechanics Horizontal axis balancing machine support Horizontal axis hard bearing balancing machine support equipped with piezoelectric transducers Vertical axis dynamic balancing machine equipped with piezoelectric pick ups. Unbalance calculation mode Main differences between hard and soft balancing technology Error occurring when using a soft bearing machine for static unbalance measuring Hard bearing balancing machine proper use Working range of a variable speed hard bearing balancing machine Specific calibration balancing on a hard bearing machine (Self learning of influence coefficients) Different types of cradles used for rotors balancing CHAPTER 7 BALANCING METHODS FOR MOS COMMON CASES Crankshafts Propeller shafts Propeller shaft body balancing (No flexible joints) Fan impellers Pump impellers Paper rolls Vehicle turbo chargers Hydraulic couplings Tools and toolholder balancing Car wheels Plough shafts Centrifugal separators Electric armatures Textile machines components Relationship Unbalance-drill depth CHAPTER 8 BALANCING MACHINE CONTROL

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Test rotor Calibration control Balancing machine test according to ISO 2953 Balancing machine control according to ISO 9000 standards . CHAPTER 9 REFERENCES

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 7

CHAPTER 1 BASIC PRINCIPLES

1.1

Balancing requirement

Unbalance control and measure of rotating bodies is today more and more important for different reasons:

1) Higher and higher operating speeds (more production) 2) Lighter frames (lower production costs) 3) Service speed near to critical speeds (technologic or space reasons do not allow more rigid frames) 4) Longer life for each parts (bearings for instance) for a reduced load

5) Lower maintenance costs (for repair and change) 6) Longer machines availability (less production stops)

It is important to point out that the measure of the unbalance is an overall control placed at the end of the production line (it reveals errors on dimension tolerances,casting faults,uneven parts) and it is an index for the quality of the final product.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 8

1.2

Unbalance(definition)

Not uniform mass distribution around the axis of rotation A Rotor is unbalanced when its mass is not evenly distributed around the axis of rotation From definition it is clear that it makes no sense to speak of unbalance without defining the axis of rotation, that is the ideal line around which the mass distribution is considered Example:

Balanced section

Unbalanced section

Every rotor can be divided into different sections (perpendicular to the axis of rotation) having each one its own unbalance. As consequence we call local unbalance (of the section i) the value

U i = ∑ m j ⋅ rj where U i is the unbalance of the section i (described by a vector normal to the axis of rotation),

m j are the single masses belonging to the section i r j are the distances of the component masses to the axis of rotation The symbol

∑

means vectors addition.

From definition it is clear that the unbalance of a section is the mass static moment calculated with reference to the axis of rotation Total unbalance U t is the set of local unbalances and is mathematically described by the following formula

{ }

Ut = U i

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 9

1.3

Unbalance measuring unit

Please refer to the following drawing which shows a perfectly balanced section (U = 0), on which a disturbing mass m has been added on point P at a distance from the axis of rotation equal to r Added mass m causes an unbalance U, (vector with direction P-O and value equal to m·r.)

Unbalance measuring unit is:

gr ⋅ mm

mass

distance from the axis of rotation

U = m ⋅ r = 10 gr ⋅100 mm = 1000 gr ⋅ mm Same value for U = 1000 gr·mm can be obtained with a mass of 20 gr on a radius of 50 mm (placed in the same angular position) In fact we obtain U = 20 gr · 50 mm = 1000 gr·mm 50

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 10

1.4

Centre of mass (definition)

Point around which the mass static moment is equal to zero. With regard to the centre of mass following relationship is valid

∑m r = 0 i i

where

mi = generica massa ri = distanza massa - centro di massa

Calculation example

We obtain:

m1 ⋅ r1 = 3 × 25 (Vettore orientato a sinistra) = 75 gr ⋅ mm m2 ⋅ r2 = 1× 75 (Vettore orientato a destra) = 75 gr ⋅ mm

(The words mass centre or gravity centre are used indifferently The centre of mass of a system is important because its motion can be described as the sum of the mass centre plus the motion of the single parts around it.

From unbalance and centre of mass definitions it follows that , if the mass centre of a section lays on the axis of rotation, the section is perfectly balanced;, that is: U = 0.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 11

1.5

Mass eccentricity (definition)

Distance between the centre of mass and the axis of rotation Please refer to next picture where an unbalance U , mounted on a perfectly balanced section ,moves the position of the mass centre . The added mass moves the centre of mass position ,which was originally on the geometric centre (axis of rotation), to the right side

The distance between the centre of mass and the axis of rotation (Eccentricity) is calculated with the following formula

E[ μ: microns] =

U [ gr ⋅ mm] 1000 = = 100μ M [ kg ] 10

where M = massa in kg del rotante, U = squilibrio in gr·mm, E = eccentricità in microns (To be more precise value M+m should be placed in the denominator)

From the previous formula it is clear that:

1) The unbalance of a body U [gr·mm] is equal to the product of its mass M [kg] times its eccentricity E [μ] A pulley which is mounted not concentric (eccentric) on the motor shaft, generates ,under service conditions , high vibrations caused by the unbalance;). Following formula is valid U [gr·mm] = E [μ] · M [kg]

2) Eccentricity E (ratio between the unbalance of a rotor and its mass) is also called specific unbalance (that is unbalance per unit of mass).

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 12

1.6

Axis of inertia (definition)

Line around which the mass static moment is equal to zero From the definition it follows:

∑m r = 0 i i

where: m = generica massa elementare

i r = distanza della generica massa elementare dall' asse di inerzia i

From the definitions of axis of inertia and unbalance of a rotor it follows that a rotor is perfectly balanced (U t = 0 ) if its axis of rotation is the same axis as the axis of inertia the meaning is that a rotor is balanced if its mass is evenly distributed around the axis of rotation which is at the same time axis of inertia

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 13

1.7

Unbalance classification

The unbalance of a rotor (set of local unbalances) can be drawn as a set of parallel vectors starting from the axis of rotation

{ }

Ut = Ui

where

U t = squilibrio totale U i = squilibri locali (delle varie sezioni)

Each vector of the above figure describes the unbalance of a single section of the rotor. It is worth to point out that it is impossible to measure the total unbalance of a rotor ,because it requires the measure of the unbalances for each section (which ,in the most cases it is not possible)

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 14

1.8

Static unbalance (definition)

The total unbalance is called static if it is equivalent to a single unbalance vector placed in a section which contains also the centre of mass of the rotor. (The axis of inertia is parallel to the axis of rotation)

if the equivalent vector U t is not located in one section containing also the centre of mass , we call it quasistatic unbalance. (In the practice most people call static unbalance the total equivalent unbalance when it is placed in a single plane only)

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 15

1.9

Couple unbalance (definition)

The total unbalance is called as couple unbalance if the equivalent unbalance is made by two vectors,placed on two different planes. having equal values (amplitudes) and opposite directions (The axis of inertia cuts the axis of rotation passing through the centre of mass) The measuring unit for couple unbalance U c is by definition equal to U ⋅ d = [ gr ⋅ mm ⋅ mm = gr ⋅ mm 2 ]

Of course values Us e Ud (unbalance value in the two sections) are equal. For example ,if the declared couple unbalance value is 6000 gr.cm.cm ,and the distance between the two balancing planes is 15 cm , then the unbalance per plane is 6000/15 =400gr.cm (4000 g.mm ) .If ,the balancing radius on each plane is 20 cm ,then the unbalance per plane is 400/20=20grams .(the two unbalances on each plane are equal in value ,but opposite in the angle position )

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 16

1.10 Dynamic unbalance

{ }

It is possible to demonstrate that total unbalance U t = U i (set of local unbalances U i ) is always equivalent to two vectors U1 + U 2 placed in two different and arbitrary planes. The set of two vectors U1 + U 2 is called dynamic unbalance (amplitudes of U1 e U 2 depend on the position of the planes where they are applied) The simple demonstration of the above sentence is obtained by considering that a rigid rotor ,with different unknown unbalances in each section,,rotating free in the space ,can be kept fixed by placing only two bearings at arbitrary axial positions.on it Each one of the bearings generates a rotating force .The two reacting forces at the bearing position compensate all the unknown rotating forces (inertia forces) which are generated by the distributed local unbalances along the rotor The load on the bearings is a function of their axial position (distance) ;in the same way the values of the dynamic unbalances U1 e U 2 depend on the axial position for the balancing planes. Please note that balancing machines are called dynamic ,because they are capable of measuring the dynamic unbalance of a rotor (it is almost impossible to measure the distributed local unbalances) Considering the rules of vectors summing ,the demonstration is still simpler One vector can always be split into two parallel vectors which are properly positioned according to the lever law. As consequence each local vector can be substitued by two parallel vectors placed in the same two arbitrary planes.The unbalance components on the two planes can after be summed to originate the dynamic unbalance U1 e U2 as it is shown by following figure.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 17

Rotor having a total unbalance Ut = just one vector placed on the right hand side Example Nr.1: Equivalent dynamic unbalance placed on narrow planes at the same side

The rotor is mounted overhang and cosequently high load on the bearing is generated . The dynamic unbalance equivalent to Ut located on the two selected planes is U1 = 2Ut , U2 = 3Ut Example Nr.2: Dynamic unbalance placed on two different places

Placing the bearings at long distance at rotor ends,lower loads are generated The equivalent dynamic unbalance calculated for the new planes (bearings), is: U1 = 0 , U2 = Ut

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 18

1.11 Equivalent total unbalances (equal)

The total unbalance of a rotor U t is the complete set of local unbalances The rules for vector summation (composition) are valid

We can say that two total vectors U ta (unbalance of rotor a) and U tb (unbalance of rotor b) are equivalent (equal) if: 1) they have the same resultant vector , placed in the centre of mass (static unbalance) and the same couple vector (couple unbalance) or , which is the same: 2) they have the same dynamic unbalance (two vectors) placed on two same planes The rule 2 is equivalent to the rule 1 because the dynamic unbalance U1 + U 2 is on its side composed by a static unbalance plus a couple unbalance

The above mentioned concepts are described by the following mathematic relationships 1) 2)

∑U ∑M

ia ia

= R = ∑ U ib

= M = ∑ M ib

This means that two total unbalances Utb e Uta are equivalent if they have the same vector risultant (equation Nr. 1) and the same moment (equation Nr. 2) of local unbalances Ui with reference to the same arbitrary point. Since the dynamic unbalance U1, U2 is equivalent to the total unbalance Ut,the consequence is that:

U1 + U 2 = R M1 + M 2 = M where:

R = Resultant vector ( sum) M = Resultant moment vector (sum of single vector moments )

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 19

1.12 Vector relationship between unbalances The next figure shows the vector composition of the two vectors U1 , U 2 (dynamic unbalance). The resultant vector U S ,sum of the two vectors is the static unbalance. Following the rules of composition of vectors, acting on different planes, it comes out that: 1) the static unbalance (resultant vector) is not dependent from the plane where it is placed (Normally the static unbalance is placed in the same plane containing also the centre of mass 2) Couple unbalance value depends on the position where the static unbalance (resulting vector) is placed In the following example of vector calculation the static unbalance is placed in an intermediate plane between two planes containing the two vectors forming the dynamic unbalance.

where

U1, U2 = Dynamic unbalance applied in the planes 1, 2 Us = Resulting unbalance (static unbalance if positioned on the centre of mass plane) Uc = Couple unbalance (arm equal to the distance between planes 1 e 2) l/2 = half distance between the planes containing vectors U1 e U2

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 20

1.13 Dynamic balancing

•

Dynamic balancing a rotor means to reduce its dynamic unbalance to zero or better to acceptable levels

•

The dynamic unbalance is by definition U1 + U 2 , ;so it is necessary to operate on two different planes

•

Since the dynamic unbalance equivalent to the total unbalance U t can be calculated with reference to two arbitrary planes, the consequence is that the two balancing planes (where material can be added or removed)can be arbitrary chosen

What above reported is valid only for rigid rotors , where mass distribution (local unbalances) does not vary with the speed.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 21

1.14 Examples of dynamic balancing a) Original unbalance placed in one plane only a).1 One plane bala ncing

a).2 Two planes ba lancing

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 22

b) Couple unbalance balancing b).1 Balancing on t wo distant planes

b).2 Balancing on n arrow planes

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 23

It is easy to verify that ,after the balancing operation ,both the resultant vector both the moment of vectors ,calculated with reference to an arbitrary plane, are equal to zero From the above reported examples ,it is clear that a rotor can be balanced in different ways depending on the elected balancing planes In order to balance doing the minimum effort two rules are valid

1) To choose balancing planes as far as possible 2) To choose balancing radius as large as possible

Important note: by the dynamic balancing, acting on two different planes, the total unbalance ( set of local unbalances )is not reduced to zero ; only the dynamic unbalance (on two planes ) equivalent to the total unbalance U T is reduced to zero

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 24

1.15 Unbalance effect

An unbalanced rotor generates an inertial force (centrifugal) which increases with the square speed.

F = m ⋅ r ⋅ ω2 = U ⋅ ω2 where

ω=

2π ⋅ N 60

where

N=

revolutions minute

F = Centrifugal force in Newton The vector unbalance U (multiplied by the factor ω , square of the angular speed ) originates the centrifugal force F ; this means that the load caused by the unbalance increases with the square of the speed (doubling the running speed the centrifugal force ( inertia force ) becomes four times greater); 2

Note: In the MKSA system distance is measured in meters [m] ;as a consequence the unbalance should be measured in kg·m. following relationship is valid 1 kg·m = 106 gr·mm.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 25

1.16 Balancing speed The unbalance of a rotor is caused by the radial distribution of its masses along its axis of rotation; the consequence is that ,if the rotor is rigid and this means that the values and relative positions of its masses do not change ,the unbalance does not change with the speed. In a rigid rotor the operating speed does not modify mass distribution and consequently has no influence on the unbalance. By adding a 20 gr mass at a defined radial position on a perfectly balanced disc an unbalance is generated ; this unbalance does not change with the speed because in order to reset the original conditions , it is just necessary to remove the added 20 gr mass, and this independently on rotor speed For rigid rotors the balancing speed is not to be specified ; because it is related only to machine sensitivity and not to the rotor unbalance which is under measurement. Modern hard bearing balancing machines have the capability to measure the dynamic unbalance starting from 70 RPM The unbalance effect (centrifugal force) increases with the speed ;the electric signal increases at the samr time , so machine sensitivity tends to increase, because of a better ratio signal to noise Depending on the model and manufacturer ,optimum sensitivity values are obtainable starting from 400 600 RPM. Note Not expert people make confusion between the cause (unbalance) with its effect (centrifugal force or vibration). The effect increases with the speed ,while the cause (unbalance) ,in a rigid body does not change.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 26

1.17 Common frequent words

Static balancing :

Unbalance measuring and correction is done in one plane only.

Dynamic balancing :

Unbalance measuring and correction is done in two different planes.

Correction planes :

è It is the section (plane? Normal to rotor axis where unbalance correction is performed by adding or removing masses.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 27

1.18 Criteria for deciding the number of balancing planes ( 1 or 2 ) for rigid rotors From the previous explanation it is clear that the total unbalance of a rotor is equivalent to a dynamic unbalance ( two unbalances placed on two arbitrary planes) ; only in special cases the total unbalance is equivqlent to a single unbalance placed in one plane (static unbalance).). The consequence is that a rotor is to be balanced dynamically on two planes). Notwithstanding , in the practical application ,good results are obtained sometimes acting on one plane only. The selection (one or two planes )is made according to the following table .. With reference to the following table , where l and d are respectively rotor length and diameter reported criteria are valid .Exceptions are possible according to the acquired experience . Please note that the speed plays a big role ; higher the speed better balancing (dynamic) is requested

Useful table to decide ,(as function of the speed and rotor geometric dimensions) the necessity of balancing in one plane (static ) or in two planes (dynamic Service speed (RPM)

l d

Number of balancing planes

< 200

whichever

1

da 200 a 1200 da 200 a 1200

< 0,5 > 0,5

1 2

da 1200 a 3600 da 1200 a 3600

< 0,15 > 0,15

1 2

> 3600

> 0,05 Disc shaped rotors

2 1

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. I - 28

1.19 Static balancing without the use of a balancing machine The static balancing can be obtained by simply supporting the rotor on two free rollers (or flat knives) having low friction values. The heavy part of the rotor moves by gravity ito the lower position; for static balancing it is sufficient or adding masses on rotor upper side or removing material from its lower side

A good static balancing level is obtained when trying to slowly rotate the rotor it maintains its position (does not rotate any more by gravity) When a dynamic balancing machine is not available ,the above mentioned operation may grant acceptable service conditions, exemption made when big couple unbalances are present,; only the static unbalance is corrected, couple unbalance still remains. In order to reduce to a minimum the residual couple unbalance ,the balancing: plane or planes are to be properly chosen with following criteria : 1) distributing the unbalance on two planes symmetrical with respect to the centre of mass position 2) distributing the correction over the rotor length, especially when the original unbalance is uniformly balancing plane containing the centre of mass 3) balancing plane where we know that the most of original unbalance is concentrated 4) correcting the unbalance on two planes , located at the same distance with respect to the axis of rotation , distributed along the rotor axis of rotation

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. II - 29

CHAPTER 2 BALANCING TOLERANCES

2.1

Foreword

The balancing of a rotating body has different goals: 1) reduced load on the bearings (low centrifugal forces) 2) long bearings life 3) acceptable vibration levels (a good vibration level does not create any problems to the comfort or to component life. From previous point 3 , it is clear that the optimum value for the residual unbalance can be evaluated in an experimental mode , by considering that: a) The inertia force generated by the unbalance can be calculated using the formula reported on paragrath 1.15; b) On service vibrations levels can be easily measured with a simple vibrometer. For each application an acceptable value for the admitted residual unbalance (which grants good performances ) can be defined.. ISO 1940 standards gives a rule in order to calculate an acceptable residual unbalance ,having following features: 1) gross unbalance deficiencies are avoided, 2) useless and excessive balancing works are avoided For each rotor type,(depending on its maximum service speed) the acceptable total residual unbalance per unit of mass is calculated ⎡ gr ⋅ mm ⎤ (specific residual unbalance). ⎢ ⎥ ⎣ kg ⎦ The calculated value is the same mass eccentricity defined on paragraph 1.5; so following relationship is valid:

E [μ] =

U M

where: E = Mass eccentricity [microns] U = Unbalance [gr·mm] M = Rotor mass [kg] According to ISO 1940 standards ,all rotors are classified (grouped) ,depending on their balancing requirements (look at following table). Balancing quality G is anumber which defines the balancing accuracy required ; for instance G = 2,5 means that a fine balancing is requered, G = 6,3 means that a normal balancing is accepted. Please note that the measuring unit for G is mm/s, because this value represents the vibration speed assumed by the body rotating freely in the space at the real service speed. The same value of vibration speed ( G=mm/s) is achieved by the rotor ,when it rotates mounted on a soft bearing machine at service speed. Following relationship is valid:

G=

E ⋅ω 1000

where: G = balance quality (grade) [mm/s] E = eccentricity [microns] ϖ = angular speed ] [rad/s]

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. II - 30

2.2

Balance quality grades for various groups of representative rigid rotors

Note:

Balanci ng quality grade G mm/s

Some groups of rotors ,not included in official ISO table , are added and reported in Italic types ..

ROTOR TYPES

0,4

Gyroscopes Spindles, discs and armatures of precision grinders Textile fuses

1,0

Small electric armatures with special requirements Tape recorder and phonograph (gramophone) drives, cine projectors Grinding machine drives Turbines and Compressors with special requirements

2,5

Gas and steam turbines, including marine main turbines (merchant service) Turbine driven pumps Rigid turbo generator rotors Turbo compressors High speed compressors and aeronautic compressors Medium and large electric armatures with special requeriments High quality household electric armatures ,dentist drills .textile components Small electric armatures not qualifying for one or both of the conditions specified for small electric armatures of balance quality grade G6,3 Machine tool drive Air conditioning fans for Hospitals and concert halls High speed gears(over 1000 RPM) of marine turbines . Computer memory drums and discs

6,3

Small electric armatures ,often mass produced , in vibration insensitive applications and / or with vibration isolating mountings Medium and large electric armatures (of electric motors having at least 80 mm shaft height ) without special requirements Machine tool and general machinery parts Parts of process plant machines , Centrifuge drums, decanters, washers Hydraulic machine rotors Fly wheels , Fans ; Pump impellers Marine main tuebine gears (merchant service ) Paper machinery rolls ; print rolls Assembled aircraft gas turbine rotors Individual components of engines under special requirements

16

Drive shafts(propeller shafts , cardan shafts ) with special requirements Parts of agricultural machinery, parts of crushing machines Individual components of engines (gasoline or diesel) for cars ,trucks and locomotives Crankshaft / drives of engines with six or more cylinders under special requirements Low speed separators Light boat impellers) Motor bicycle and car wheels Normal transmission pulley Wood machine tools

40

Car wheels ,wheel rims ,wheel sets .drive shafts Crankshaft / drives of elastically mounted fast four cycle engines (gasoline or diesel ) with six or more cylinders (pistons speed greater than 9 m/s Crankshaft /drives of engines of cars , trucks and locomotives

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. II - 31

2.3

Balancing tolerance

The following drawing defines the required tolerance according to ISO 1940/1.standards

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. II - 32

the previous table defines the required balancing quality G according to each rotor type. The maximum service speed is reported on the orizontal x axis , while the acceptable specific unbalance (acceptable unbalance per unit of mass or acceptable residual mass eccentricity ) is reported on the vertical y axis The following formula can be used instead of previous diagram: Et (μ ) =

9550 ⋅G N

where: Et [μ] = total acceptable mass eccentricity N [RPM] = Maximum service rotor speed G [mm/s] = Balancing quality or grade Total residual accepted unbalance: U [gr·mm] = Et·M where: M [kg] = Rotor mass Total residual admitted unbalance in grams is m =

U where R [mm] is the compensation radius. R

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. II - 33

2.4

Examples of calculation of the residual unbalance according to ISO 1940/1 Standards for rigid rotors .

Example N°1 – Fun impeller

Maximum service speed = 1500 RPM Mass M = 200 kg Left , right side correction radius Rs = Rd = 800 mm Balancing quality G = 6,3

From previous diagram we obtain: Tatal acceptable residual eccentricity et = 40 μ Total acceptable residual unbalance Ut = M·e = 200 kg x 40 μ = 8000 gr x mm 8000 gr x mm (Total acceptable unbalance)

4000 gr x mm (acceptable unbalance for left plane)

Per plane acceptable unbalance in grams =

4000 gr x mm (acceptable unbalance for right plane)

4000/800 = 5gr gr ⋅ mm =〈 4000/800 = 5gr R

Note: The acceptable unbalance per plane has been calculated by simply dividing by two the total acceptable unbalance ; this operation is correct because the two balancing planes have almost the same distance from the centre of mass position .,which is at the same time almost in the centre of the rotor.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. II - 34

Example N°2 – Turbine

Maximun service speed = 3000 RPM Rotor mass M = 500 kg Left side balancing radius Rs = 500 mm Right side balancing radius Rd = 400 mm Balance quality G = 2,5

From previous diagram we obtain: Total acceptable residual eccentricity et = 8 μ By using the formula Et (μ ) =

9550 9550 ⋅ G we obtain: Et = ⋅ 2.5 ≅ 8μ N 3000

The total acceptable unbalance Ut = M·e = 500 kg x 8 μ = 4000 gr x mm

4000 gr x mm (Squilibrio totale ammissibile)

2000 gr x mm squilibrio ammissibile piano sinistro

2000 gr x mm squilibrio ammissibile piano destro

2000 = 4gr (1,7 ) 500 2000 The accepted unbalance value for the right plane is U d = = 5gr ( 2 ) 400 The accepted unbalance value on the left plane is U s =

Values within brackets are valid for the quality G = 1 (quality g 1 is nowadays commonly required for turbines )

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. II - 35

Example N°3 – Impeller of a centrifugal pump

Maximum service speed = 6000 RPM Mass M = 10 kg Balancing radius R = 100 mm Required balancing quality G = 6.3

From previous diagram we obtain: Total acceptable residual eccentricity et = 10 μ By using the formula Et (μ ) =

9550 9550 ⋅ G we obtain: Et = ⋅ 6.3 ≅ 10μ N 6000

The total acceptable unbalance Ut = M·e = 10 kg x 10 μ = 100 gr x mm

The total acceptable unbalance in grams (for the correction radius of 100 mm) is = U = 100gr ⋅ mm = 1gr R 100mm

Note: Since the impeller is thin (reduced axial dimentions ) it is balanced in one plane only ( Static balancing)

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. II - 36

Example N°4 – Tool holder dynamically balanced

The tool holder has a useful length L bigger than 2D (where D is the cone diameter ). Considering its length it is advisable to balance it on two planes.

Maximum service speed = 24'000 RPM Tool holder mass M = 5 kg Correction radius on balancing plane 1 R1 40 mm Correction radius on balancing plane 2 R2 20 mm Required balancing quality G = 2,5 (ISO standards specify quality G=2.5 for machine tools spindles and driving systems) Total acceptable residual eccentricity E = 1 μ Total acceptable residual unbalance Ut = M·E = 5 kg x 1 μ = 5 gr x mm 5 gr x mm (Squilibrio totale ammissibile)

2,5 gr x mm (squilibrio ammesso nel piano sinistro)

2,5 gr x mm (squilibrio ammesso nel piano destro)

2,5 gr ⋅ mm = 0,06 gr 40 mm 2,5 gr ⋅ mm = 0,125 gr Acceptable unbalance on plane 2 U2 (in grams) = 20 mm Acceptable unbalance on plane 1 U1 (in grams) =

Note: The total acceptable unbalance has been divided by two because we assumed that tool holder mass is more or less symmetrical with regard to the centre of mass position ,and that the two correction planes contain the centre of mass almost in the middle position.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. II - 37

Example N°5 – Tool holder balanced in one plane only

Let us consider a tool holder which is to be balanced in one plane (static balancing). Normally the tool holder is balanced in one plane only , if its length L is lower than 2D.(D is cone diameter)

Maximum service speed = 12'000 RPM Tool holder mass M = 1 kg Balancing radius = 20 mm Balancing quality G = 1 (ISO standards specify quality G 1 for grinding machine spindles) Total acceptable eccentricity E = 2 μ Total acceptable residual unbalance Ut = M·E = 1 kg x 2 μ = 2 gr x mm Total acceptable unbalance in the correction radius U (in grams) =

2 gr ⋅ mm = 0,1 gr 20 mm

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. II - 38

2.5

Evaluation of the balancing quality G (The total residual unbalance is known)

In the assumption that the total residual unbalance is known , we it is possible to calculate the corresponding value for the balancing quality G according to ISO standards 1940/1.

Example of calculation: Rotor mass M [kg] = 6 Maximum service speed N [RPM] = 5000 Total residual unbalance U [gr mm] = 180 Total residual eccentricity E [μ] = 180/6 = 30

Using the diagram at paragrath 2.2 two lines are drawn ;one line ,normal to the x axis ,passing through the maximum service speed value ,(5000 in the example) the second line ,normal to y axis, passing through the residual eccentricity (30 in the example). The inclined line , passing through the intersection point of the two drawn lines , defines the balancing quality (grade)..

As option ,the following formula can be used:

G=

E ⋅ N 30 × 5000 = = 15.7 mm/s 9550 9550

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. II - 39

2.6

Balancing tolerances according to API 610 standards

The following formula is valid:

U = 6350

W N

where:

U [gr mm] = Admitted residual unbalance referred to the bearing journals W [kg] = Static load on the considered bearing(mass) N [RPM] = Maximum service speed Modifying previous formula , we obtain:

6350 U = E [ μ] = (total acceptable eccentricity = acceptable unbalance per mass unity) N W The equivalent ISO formula is :

E [μ] =

G ⋅ 9550 N

Important notes: 1) Unbalance tolerance according to API standards is more severe than ISO grade G=1;it is 1,5 more precise and it seams sometimes not obtainable. 2) It is important to point out that the required tolerance ,according to API standards, is referred to the bearing journals and not to the two balancing planes ,(look at the paragrath 2.8) 3) The unbalance tolerance measured in microns, (Eccentricity = unbalance per unit of mass) is related to the required mechanical precision , especially when adapters are necessary to mount the rotor on the machine spindle.(the used adapter shall have a mounting precision below the required tolerance 4) For balancing qualities equal or below G 1 ISO standad recommends to balance the rotor complete with its own bearings .(The eccentricity between the inside and the outside bearing race can be of the same level as the requested eccentricity)).

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. II - 40

2.7

Balancing tolerances calculated according to the maximum admitted load on the bearings

The goal of balancing is to reduce loads /vibrations on the supporting frames , in order to achieve an acceptable life. The unbalance introduces internal couples and rotating forces on the bearings As a consequence , the residual acceptable unbalance can be calculated by stating a maximum acceptable value for the rotating (centrifugal forces )generated by the unbalance in service conditions A possible rule is to state that the rotating force is kept below 10 percent of the static load.(USA navy standards)

Fr [N] (Rotating force caused by the unbalance) = m ⋅ r ⋅ ω2 = Fg [N] (Static load on the bearing) = M ⋅ g where M = body mass related to the bearing [kg];

U ⋅ ω2 10 6

g = gravity acceleration = 9.8 m/s2

According to the above mentioned rule

Fr =

1 Fg 10

that is

1 m ⋅ r ⎛ 2πN ⎞ ⎟ = ⋅ M ⋅ 9.8 6 ⎜ 10 ⎝ 60 ⎠ 10 2

it follows:

m⋅r 9.8 3600 10 6 1 1 = E (eccentricity or acceptable specific unbalance) = ⋅ ⋅ 2 = ⋅ 896 ⋅ 2 ⋅ 10 6 2 M 10 4 ⋅ π N 10 N It is worth to point out that according to API and to ISO standards the accepted residual eccentricity (unbalance) varies with

1 ;,the relationship is linear while with the last rule (USA navy standards ) it varies N

with the inverse of the square of the speed.(as the speed increases the accepted residual unbalance decreases rapidily)

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. II - 41

2.8

Allocation of permissible residual unbalance to each correction plane according to ISO 1940/1

ISO 1940/1 standards calculate the total acceptable unbalance of a rotor (static unbalance ) referred to the plane (rotor section)containing the centre of mass The acceptable residual unbalance on the two balancing planes (dynamic unbalance) is calculated taking care of the position of the centre of mass with regard to the position of the correction planes..

a) Distance between correction planes less than the bearing span It is valid:

L 3000 RPM) with the possibility of running near some critical speed (during start up or cast down ), it is advisable to calculate the test mass as a function of the accepted residual unbalance ,by using the following formula :

m⋅R = k ⋅ Ea M where:

m [gr] = Test mass R [mm] = Radial position of the test mass M [kg] Rotor mass Ea [µ] = Residual eccentricity according to ISO 1940/1 k = Factor varying from 4 to 10

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. IV - 78

4.5

Two planes balancing on service conditions

Balancing on one or two planes is the most frequent application in the practice. Reference is made to the next sketch where S1, S2 are the rotor supports (where the vibration is measured) and P1, P2 are the balancing planes (where material is added or removed for unbalance compensation).

The two vibration pick ups are placed on the rotor bearings (supporting the centrifugal force caused by the unbalance) preferably in horizontal position and fixed by a magnetic base . The magnetic base is used in order to obtain repeatable readings (the pick up is tied to the same point ) A reference mark for the photocel is used as origin of the angle division (look at par. 4.2). Spin Nr.1:

vectors V10 , V20 are measured (original vibrations caused by the unbalance in values and angles ).

A test mass m is added on a known angle position (it is advisable to put the test mass in the angle position defined by the reference mark , zero position) at a radial position R1 on the correction plane P1. Spin Nr.2:

vectors V11 , V21 are measured (vibrations caused by the unbalance and by the test mass placed on the balancing plane P1 ). on the support Nr. 1 (V11 ) and on the support Nr. 2 (V21 ).

The test mass m is removed from the correction plane P1 and placed on the balancing plane P2.at the radius R2 in a well known angle position (better on the angle defined by the reference mark ). Spin Nr.3:

vectors V12 , V22 are measured (vibrations on supports 1, 2 caused by the unbalance and by the test mass placed on the balancing plane P2.

The test mass is removed from the balancing plane Nr.2 The measured data ( 6 vibration amplitudes and 6 angle values ) are input in the software program which ,solving the two equations with complex variables reported on the previous paragraph ,calculates the unbalance on the two planes P1 e P2.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. IV - 79

When balancing overhung rotors , the relationship balancing planes /vibration measuring planes is shown by the next sketch..

Notes: On field balancing is possible only when the synchronous vibration values are constant and repeatable in value and angle.

If the balancing weight ( grams ) is applied to a different radius , in comparison with the radius used during the calibration procedure ,its amount varies in the reverse proportion , with regard to the actual radius , as R0/R..(R0= calibration radius , R= correction radius)

Normally ,when balancing on two planes ,after the first correction on both planes , it is necessary to check the residual vibration level and to perform an additional trim balancing.

Modern portable analysers ( CEMB N402 for example ) show, on the display, clear instructions about the balancing operations , automatically acquire the vibration values and directly calculate the amount and the position of the balancing weights .

It is convenient to proceed with the balancing operation only if the synchronous vibration is relevant (>10% total vibration) ,otherwise with the balancing operation , the vibration level cannot be reduced by a significant factor . In order to obtain a precise balancing ( good evaluation of the original unbalance an ,as consequence , good estimation of the correcting weight ) the filtering bandwith is to be lower than 10% (standard value =5%). Even better results can be achieved by using , in addition , the vector synchronous averaging method .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. IV - 80

4.6

Not linear response

In the case of high vibration levels (machine with dampers ,with high mechanic clearances or with sleeve bearings ) the relationship vibration versus unbalance may be not linear (look at following curve ).

In this case it is advisable to repeat the calibration process several times by using each time lower test masses ,as the vibration value tends to decrease . This is necessary because otherwise , by following the previous calibration and the calculated compensating masses , the vibration level reduces only a little and does not better any more .

Example: Original vibration = 15 mm/s Test mass = 100 gr Calculated unbalance = 300 gr A correction mass of only 200 grs is added at the calculated angle . Residual vibration , after the first balancing operation = 8 mm/s The calibration procedure is repeated with a lower test mass of 30 grs. Calculated unbalance = 80 grs. A correction mass of only 50 grs. is added at the calculated angle . Residual vibration level , after the second balancing operation = 5 mm/s A new calibration procedure is now performed with a lower test mass, for instant = 10 gr, etc..

Sometimes it is necessary to completely close the supporting dampers , before starting the balancing process ; this way the system is made linear because of two reasons : the vibration level is reduced (lower the vibration more linear the system) and the negative effect of the dampers ( on phase and linearity ) is removed .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. IV - 81

4.7

Manual unbalance calculation with the graphic vector method

The manual graphic vector method is normally used only when balancing on one plane ,because it does not take care of the plane interference . The procedure is fully described in the following : Vibration pick up mounting The vibration pick up is to be placed as near as possible to the shaft supporting frame (better if on the supporting bearing ) in radial direction (horizontal or vertical ) perpendicular to the rotation axis . Reference mark for the angle A reference mark (piece of reflective tape or pen stroke ) is to be placed on a visible part of the rotary shaft. The angle numbering ( increasing ) is opposite the sense of rotation , with the zero position corresponding to the reference mark . It is also possible to define the zero (beginning of the angle measurement scale) as the position where the test mass is applied during the calibration process .(the angle always increases opposite the sense of rotation ).

Tuning the filter 1) If the portable Balancer is equipped with a photocell , it is sufficient to fix a portion of reflective tape on the rotor shaft and to verify that the LED placed on the backside is lighted when the reference mark is placed in front of the cell . This control can be done (if possible ) by rotating the shaft slowly by hand . 2) If the portable Balancer is equipped with a stroboscopic light , it is necessary to manually rotate a potentiometer until the rotor ,under service speed and light by the lamp, appears in a steady condition ( as if it were fixed and not rotating ), it is important to not touch the rotor which appears at standstill while really it is rotating . 3) In order to verify the correct filter tuning it is necessary to turn the potentiometer until the stroboscopic light shows a shaft with two reference marks on the opposite angles .(if the previous measured speed is correct ,in this condition the stroboscopic light must measure a speed value double than the real one , because the stroboscopic light is using a frequency which is double than the rotor speed ; here the reason for the appearance of the two marks ).

Measuring the original vibration The rotor is spun at the service (balancing ) speed and the filtered original vibration (caused by the unbalance ) is measured . CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. IV - 82

Measuring the vibration with the test mass applied

A test mass is applied on the balancing plane and the new filtered vibration is measured .

Vibration value The amount of the filtered vibration (vibration related to the unbalance ) is directly shown by the instrument . Vibration angle (phase )

When using a vibrometer equipped with a photocell, the angle of the vibration is immediately shown on the machine display. When using a vibrometer equipped with a stroboscopic light ,the angle is seen directly on the rotor surface(top point ) by the stroboscopic light placed on a fixed position (vertical or horizontal for instance). Before starting the balancing process the angle division is marked directly on the rotor .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. IV - 83

Practical instructions (step by step operations) for manual unbalance calculation

Reference is made to the table reported on the next page , for a rotor having the following features : correction radius R = 1000 mm and mass M = 2000 kg. For a proper unbalance calculation , the measuring instrument should use a filter with a band with lower than or equal to 5%.

1) Fill the annexed table with: - Original vibration (value and angle) – New vibration with the added test mass (value and angle) 2) Draw points A and B (see the example). 3) Connect point A to B ,measure the distance A-B and write its value in the pre set position. (For evaluating this value take care of the used reduction scale ,for instance 1 cm = 10 microns or 1 cm = 1 mm/s) 4) Draw a line starting from O parallel to the segment AB from B to A ;this line defines the angle ϕ. 5) Remember to remove the test mass. 6) By using the reported formula , calculate the correction mass (compensating for the existing unbalance ) and its angular position . 7) Measure the residual vibration and if it is still not acceptable , proceed with a new balancing operation following the reported procedure

Notes: 1) The calculated angle is for balancing by adding weight ; in case of balancing by removing , the angle is in the opposite position (+180°). 2) When the calculated angle is negative ,add 360° to make it positive.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. IV - 84

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. IV - 85

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. IV - 86

4.8

Evaluation of the optimum angle position of the test mass during calibration

High original vibration values (almost dangerous), requirements to reduce the number of balancing spins (electric motors with a reduced number of start up cycles for thermal reasons ) draw the attention to carefully evaluate the value and angle position of the test mass used during the calibration process . If, during the calibration spin , the test mass is placed on the correct angle (that is in an angle opposite the position of the original unbalance) the machine bearings are not suffering higher vibration values and the balancing process is shorter (less spins ). In order to evaluate the best angle position for the test mass different angle addendum are to be considered : F1:

Angle depending on the used measuring unit Measuring unit

Angle F1

Despacement Velocity Acceleration F2:

0 –90 -180

Angle depending on the position of the relative position rotor speed (N) and rotor critic speed

(Nc )

F3:

F2

F2 (recommended)

N < Nc

0÷45

45

0,7 Nc N 1,3 Nc

45÷135

90

N Nc

135÷180

135

Angle depending on the relative position of the photocell with regard to the vibration pick up

F3 = Angle between the photocell and the pick up. This angle is positive if the vibration pick up has to be moved in the same sense of rotor rotation in order to reach the photocell (on the contrary it is negative ). For the example drawing F3 = -50°

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/731384

Cap. IV - 87 The estimated position of the original unbalance is: α 0 = α + F1 + F2 + F3 where: α is the measured angle of the original synchronous vibration The test mass is to placed (on the balancing plane ) at the opposite angle: α 0 + = α 0 + 180° Notes:

4) The method is valid under the condition that the angle of the original vibration is properly measured 5) If the calculated angle is negative , make it positive by adding 360°. 6) If the calculated angle is bigger than 360° remove 360°.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/731384

Cap. IV - 88

Example 1: Rotor service speed lower than the critic speed (N < Nc )

Vibration measuring unit [mm/s] F1 = -90° (measuring unit mm/s) F2 = 45° (under critic speed) F3 = 90° (angle photocell –pick up) α = 65° (measured original vibration angle) Optimum angle for the test mass

α 0+ = α + F1 + F2 + F3 + 180 = = 65 − 90 + 45 + 90 + 180 = 290°

Example 2: Rotor service speed bigger the critic speed (N > Nc )

F1 = -90° F2 = +135° F3 = 30° α = 306°

(measuring unit mm/s) (over critic speed) (angle photocell-pick up) (measured original vibration angle )

α 0 = 306 − 90 + 135 + 30 = 16° This is a real case where the original unbalance was on the angle 0 The optimum position for the test mass is :

α 0+ = 16 + 180 = 196°

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/731384

Cap. IV - 89

4.9

Manual balancing with the use of a simple vibration meter

When the vibration value ,caused by the unbalance , is relevant (>60% of the total vibration) it is possible to balance, on service conditions, by the use of a simple vibrometer (having no filtering capacity ) .

a) Four points method Four points are marked on the rotor balancing surface at 90 degrees .

Vibration values V0 (original vibration ) and VI , VII , VIII , VIV ( vibrations obtained by moving the test mass m on the angle positions I, II, III, IV at 90° on the balancing plane ) are measured . A sine curve (connecting all points ) is then drawn .

2⋅ m =E Vmax − Vmin V + VII + VIII + VIV The averaged measured value is Vm = I (it should be equal to V0). 4 The original unbalance (calculated ) U is E ⋅ V0 . The frame rigidity is

The angle position of the unbalance is evaluated from the curve (distance Vmax from point I) In the example the angle is

2 ⋅ 90° ≅ 30° 6

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/731384

Cap. IV - 90

b) Three points method Vibration values V0 (original vibration ) and VI , VII , VIII (obtained by moving a test mass m on the angle position I, II, III at 120°on the balancing plane ) are measured. A circumference with radius a V0 is drawn. Points I, II, III at 120 degrees angle position are marked. The measured vibration values are filed in a decreasing order (for instance VIII > VII > VI). With the centre in point III a circumference with radius VIII is drawn. With the centre in point II a circumference with radius VII is drawn The two common points of the circumferences define the two possible unbalance positions . A third circumference , with the centre on point I and a radius VI , defines the correction position (in the example P1). The unbalance angle is defined by the line connecting point P1 to the centre O of the original circumference (direction P1 O). The unbalance value is:

Example:

V0 = VI = VII = VIII =

m × V0 O P1

4 mm/s 2 mm/s 5 mm/s 6 mm/s

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/731384

Cap. V - 91

CHAPTER 5 FLEXIBLE ROTORS BALANCING

5.1 Foreword A professional approach to flexible rotors balancing requires the knowledge of: 1 ) Rotor critic (natural ) speed (at this speed high vibrations occur even in presence of small unbalances or other causes ) 2) Rotor bending mode at the critical speed (it is the geometric shape assumed by the rotor running near its critic speed ). Let us consider the following example with a shaft having an original unbalance (static type) concentrated in the middle and compensated by two equal masses placed at its ends . By increasing the rotating speed , the centrifugal forces related to the three concentrated unbalances increase together with the inside shear forces and bending couples ; the overhaul frame is still in equilibrium (the exerted forces on the bearing supports is null).

When the rotating speed approaches the rotor first critic speed the shaft bends. The bending causes itself a big unbalance which even more increases the shaft deformation according to the first modal bending shape . With bending the rotor mass distribution changes , while the axis of rotation ( defined by the two supporting bearings ) does not change .

If the rotating speed increases again ,over the critic speed value , the shaft shape becomes again straight .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 92

5.2 Shaft critic (natural ) speed evaluation methods The measurement of the real rotor critic (natural ) speed is very important , because it gives the possibility to evaluate if the rotor ,on the service conditions , is running near its critic speed , that is : it is to be considered as a rigid or a flexible rotor .

a)

Impact test method By the use of a proper hammer impulse the rotor is exited to vibrate and its natural vibration frequency in CPM (cycles per minutes ) is measured with a vibration transducer .

Natural vibration mode of a frame exited by an impulsive shock

Natural waveform (over the time ) of the transient vibration caused on a shaft by an impulsive shock

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 93

b)

Bode diagram

It is necessary to use an instrument capable of storing and displaying the synchronous vibration or the displacement as a function of the rotor speed . For a paper roll ,for instance , the bending value in the middle is registered ,in value and angle , as a function of the speed . This way ,the response of the assembly (rotor plus supports ) is measured as a function of the rotary centrifugal force (caused by the unbalance ) acting on the frame with increasing angular speeds ( at different frequencies ). The following typical diagram is obtained :

Near to the critic speed the vibration level increases a lot and its angle changes by 90° , while above the critic speed the angle changes by 180°.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 94

5.3 Calculation of the critic (natural ) speed If the rotor mechanic features such as : Rigidity K [N/m] Inertia I [m4] Material density [kg/m3] and the rotor boundary conditions are known , the different rotor natural (critic ) bending frequencies can be calculated by numeric computation . The finite element method is today commonly used and standard software packages are available to be easily used on every process computer . The theoretical calculation of the rotor critic speed is outside the scope of this course ; nevertheless it is important to know the next formula which points out the main parameters which contribute to determine the value of the first critic speed (every frame has different critic (natural ) speeds , with different related vibration shape modes ).

fn =

1 ⋅ 2π

K M

where: fn = first critic speed in CPS (cycles per seconds) K = rigidity [N/m] M = rotor mass [kg] (The frequency in cycles per minutes is obtained by multiplying fn x 60 ) From the formula it is clear that the critic speed increases with the rigidity and decreases with the rotor mass . These are the two parameters which are to be changed in order to modify a disturbing critic speed (do not forget that , near to a critic speed , even small unbalances can generate high vibrations or bending ). A formula which calculates the first critic speed of a uniform beam in term of revolutions per minutes is :

Vc =

60 ⋅ 2π

g fs

where:

g = gravitational acceleration = 9.8 m/s2 fs [m] = static bending in the middle section In the case of a uniform beam simply supported at the ends the centre bending is :

fs =

5 l4 ⋅m⋅ g ⋅ 384 E⋅I

where: m = mass per unity of length [kg/m] E = Beam elasticity [N/m2] l = distance between supports [m] By introducing the value for the centre bending fs into the previous formula we obtain :

Vc [CPM] =

60 8,76 E ⋅ I ⋅ ⋅ 2π l 2 m

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 95

5.4 Natural frequencies of a beam calculation

By solving the general differential equation for the lateral vibrations of uniform beams ,the different natural speeds ( frequencies ) are calculated by the next formula :

ωn = n2 ⋅

E⋅I m

(1)

where: ωn = Natural frequency for the n vibration mode [rad/s] E = Beam elasticity [N/m2] ( for the steel E = 21’000 kg/mm2 =

21'000 ×10 = 21× 1010 N/m 2 ) 10 −6

I = Beam inertia [m4] m = Mass per unit length [kg/m] ( m = ρ A , with A = area [m2] and ρ = mass density [kg/m3] ; for the steel ρ = 7.8 g/cm3 = 7.8·1000 kg/m3) n2 = Factor depending on the boundary conditions ,on the different natural vibration modes and on the beam length l [m] according to the next table :

Boundary conditions

1a speed

2a speed

3a speed

(n1 ⋅ l )

( n2 ⋅ l )

(n3 ⋅ l ) 2

Simply supported

9.87

39.5

88.9

Cantilever

3.52

22.4

61.7

Double clamp

22.4

61.7

121.0

Clamped/hinged

15.4

50.0

104.0

2

2

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 96

We develop now the previous formula (1) for a very common case of a paper roll with a ( cylinder ) uniform section . For a simply supported condition at its ends , the fist natural frequency is :

V1[CPM] =

60 9,87 E ⋅ I ⋅ ⋅ 2π l 2 m

( The same value with the formula reported on the previous chapter ,based on the static bending in the middle , is lower of about 10%) For a uniform (cylinder ) section with D = outside diameter [m] and d = inside diameter [m]:

π m [kg/m] = 7.8 ⋅103 kg/m 3 ⋅ ⋅ D 2 − d 2 4 π I [m 4 ] = ⋅ D 4 − d 4 64

(

(

)

)

The first natural speed of a ,simply supported ,uniform steel cylinder beam (roll ) can be calculated with the next formula :

V1[CPM] =

122263 ⋅ D2 + d 2 2 l

Calculation example with:

l=5m D = 450 mm = 0,45 m d = 350 mm = 0,35 m we get : V1 =

122263 ⋅ 0,45 2 + 0,35 2 = 4890,5 ⋅ 0,2025 + 0,1225 = 2788 giri/minuto 25

According to the formula of the previous chapter V1 =

2788 ⋅ 8,76 = 2476 giri/minuto 9,87

From the comparison of the measured and the calculated values for the first natural speed of uniform steel paper rolls , simply supported on its end journals ,it seems that this last formula (of the previous chapter ) gives better results. It is reported down for an easy use :

V1 [CPM] =

110037 ⋅ D2 + d 2 2 l

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 97

5.5 Rotors classification Depending on its maximum speed a rotor is classified as Rigid rotor The maximum service speed is lower of 30% of the first natural bending speed. (that is V< 0,7 Vc where V = maximum service speed and Vc = first natural rotor speed) It can be dynamically balanced on two arbitrary planes. It can be balanced at an arbitrary speed ,below or equal to the service speed. Its masses distribution around the axis of rotation remains constant .

Flexible rotor

The maximum service speed is bigger than the previously specified value ,that is V> 0,7 Vc. A flexible rotor is to be balanced a) In well specified planes (sometimes more than two). b) At special speeds (sometimes at more than one speed ). Near to the critic speed the rotor mass distribution changes due to the bending .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 98

5.6 Rotor flexibility measurement on a balancing machine In order to measure the rotor critic (natural ) speed on an industrial balancing machine it is necessary to spin it at different increasing speeds . The unbalance vector is measured and recorded as a function of the speed. It is necessary to pay attention to the safety of the operation and to increase the speed slowly , because , near to the critic speed , the rotor deformation causes an high unbalance (high centrifugal force ) which may cause the rotor jumping out of the balancing machine . A Nyquist diagram is obtained similar to the following one .

In the example the critic (natural ) speed is 900 RPM ; at the same speed change (100 RPM) the maximum change on the unbalance measure is found .

Note : during the test on the balancing machine , all the system natural frequencies (balancing machine plus rotor ) are measured. As a consequence it is necessary to use rigid supports (whose natural frequencies (speeds ) are higher than the test rotor frequency ) or to use soft bearings having lower frequency values In normal applications ,before the test at different increasing speeds , it is useful to measure the rotor critic speed , while it is simply supported on the machine , with the method of the impact test (look at 5.2a) with a hammer impacting the rotor on the vertical direction (where the machine is more rigid ). This way we can know in advance the rotor critic speed and do not take care of the possible critic speeds introduced by the balancing machine itself ..

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 99

5.7 Basic criteria for flexible rotors balancing The goal of flexible rotors balancing is to obtain acceptable operating conditions in term of vibration levels or bearing life , which is possible only if the rotor mass distribution around the axis of rotation does not change over the all speed range . To obtain the goal it is necessary to reduce to a minimum the forces inside the rotor (bending moments and shear forces caused by concentrated unbalances along rotor axis ) which increase with the speed and may cause rotor deformations .

Example of a rotor (having an original unbalance concentrated in the middle section ) and balanced with two masses at its ends .

.

Inside moments diagram ,caused by the rotary forces ,related to the previous example

The bending moment is maximum in the middle and its value is

U l 2 ⋅ ⋅ ω [N ⋅ m] 2 2

If we balance the rotor section by section ,that is , if we remove any concentrated unbalance ,the inside forces (bending moments and shear forces ) caused by the centrifugal forces are reduced to a minimum and the rotor is not forced to bend .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 100

Example of rotor divided into different sections individually balanced

The centre of mass of each rotor section lays on the axis of rotation . By increasing the speed the inside moments caused by the centrifugal forces are reduced to a minimum . The above mentioned balancing procedure is commonly used in the practise . Let us mention ,for instance ,the balancing of steam and gas turbines where each blade ring is individually balanced (each blade is scaled before mounting it on a ring ) and the balancing operation is repeated at each ring mounting on the shaft (the unbalance correction is made on the ring itself ). Another example is the balancing of cars turbochargers where the turbine shaft and the compressor are separately balanced .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 101

5.8 Rotors classification according to balancing requirements

According to ISO standards , for balancing purposes ,all rotors can be classified as : 1) Rigid rotors 2) Quasi rigid rotors 3) Flexible rotors 4) Rigid rotors with flexible or not rigid connections 5) Flexible rotors to be balanced at the service speed only

5.9 Quasi rigid rotors

The maximum service speed is near to the critic speed but they can be balanced at low speed by acting on well known planes They are classified as: 1) Rotors with known axial unbalance distribution ( pulley on a flexible shaft, f.i.)

2) Rotors with unknown unbalance distribution ,but in fixed planes (multi stages centrifugal pumps f.i.)

Quasi rigid rotors balancing procedure 1) The separate parts are pre balanced as rigid rotors . The mounting tolerances are kept within specified values .After assembling , the complete rotor is dynamically balanced again on two or more planes . (The static unbalance correction is distributed on the shaft length while the couple unbalance is corrected at the ends) 2) The separate parts are balanced ,step by step ,during the assembling (sometimes two parts are mounted and balanced at the same time and the correction is made on the two planes defined by the two parts ). The shaft alone is balanced first then a ring is mounted and the balancing is made by acting on the ring itself . (It is evident that ,if the shaft has been previously balanced ,the new unbalance is caused by the new part that has been lately mounted ). After each mounting , the unbalance compensation is made on the lately mounted component . 3) The single components ( pre balanced or not ) are assembled on the main shaft and the balancing process (on the specified planes ) goes on only if the measured unbalance is below a certain maximum admitted value . (50% of the static unbalance is corrected on the central plane ).the balancing operation is performed only if the original unbalance is relatively low so that , even balancing on two planes ,the inside moments , caused by the rotary centrifugal forces , are kept within low values . (the rotor is born with a reduced unbalance value .)

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 102

5.10

Examples of low speed balancing

a)

API Standards: Multiple stage pumps

One plane (static ) balancing at each ring mounting step

Two planes (dynamic) balancing at each mounting step (Two impellers are mounted at the same time)

Final balancing (finishing )of the complete assembly ;the static unbalance is corrected on the centre while the couple unbalance is corrected at the ends .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 103

b)

Paper rolls

In the paper rolls , the original unbalance is mainly static , because it is caused by a different wall thickness on two opposite angle positions ,all along the shaft. The low balancing speed on the roll ends creates an inside bending moment ,which at a high speed can deform the roll (see 5.7). If the original unbalance (mainly static ) is not too high and the balancing speed is not too near to the first critic speed ,it is possible to balance , at low speed , in two ways : 1) Placing the correction masses at 0,22 L. The balancing planes placed at 0,22 L reduce to a minimum the residual inside bending moments caused by the original uniform distributed unbalance together with the correction masses placed on the two balancing planes .

2) Correcting 60% of the original static unbalance in the centre of the shaft and correcting then the residual unbalance on two planes at the ends . (The compensation is distributed on three planes in order to reduce to a minimum the inside bending moments caused by the rotary inertia forces .

. Notes: 1) The low speed balancing validity can be verified by increasing the rotor speed , in the balancing machine , up to the service speed and by checking that the balancing conditions do not vary (no deformation occur ) 2) Normally the balancing of paper rolls ,which have a low rigidity ,is to be adjusted and verified at the service speed . 3) It is easy to verify that a roll is rigid by simply measuring ,at its centre position ,the bending value ;if the dynamic run out (bending ) does not vary with the speed , the roll is balanced at all speeds .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 104

5.11

Flexible rotors

1) The balancing planes are to be selected properly and are more than two (3, 5 etc.). 2) It is better to simulate , on the balancing machine ,the rotor service boundary conditions (supports rigidity and resting positions ) 3) They require the balancing at different speeds (more than one and at high speed ).

Important note : When there is the doubt that a rotor has a service speed near to its first critic speed , it is advisable to define a third balancing plane in a centre position or in a position where the rotor experiences the maximum deformation ., so that a proper balancing ( on more than two planes can be achieved )

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 105

5.12

Number of balancing planes

Let us consider a paper roll simply supported on its ends ;when spun near its first critic (natural speed ) it bends. The first bending mode assumes the shape reported on the next sketch with zero bending at the ends and with a maximum bending in the centre position .

The balanced conditions obtained at low speed balancing on the ends is no more maintained at high speed (the roll bends ). In order to avoid the bending in the centre position , it is necessary to place a proper mass also on the centre plane . As a consequence ,from the example , it is evident that a proper balancing requires three planes (2 for the low speed balancing ,one the centre for reducing the bending at high speed). After the balancing , if the rotor speed is increased near to the second rotor critic speed ,the roll bends again and assumes the shape corresponding to the second bending mode ,which is shown on the next sketch.

In order to balance the rotor at the second critic speed ,from the figure it is clear that two more planes are necessary like planes P4, P5. The next general formula is valid to establish the number of balancing planes for a rotor running near its N binding mode : The number of balancing planes for a flexible rotor are : 2N+1 where N = bending mode (1 = first, 2 = second) From the above reported examples , it is clear that the optimum balancing plane positions are placed where the rotor experiences its maximum bending at the critic speed .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 106

5.13

Modal balancing

It is the balancing method ,for flexible rotors, which takes care of the rotor bending shape (mode ) near to the critic speed in order to find out the correct balancing planes position and the correct set of the test masses capable of exiting only the bending mode under consideration. Step by step instructions are : 1) Pre balance the rotor at low speed (Rigid balancing on two end planes ; it is necessary in order to spin with safety at high speed ) 2) Increase the speed slowly up to the first critic speed (15 ÷ 30% distance) 3) Record value and angle of the instrument measurements ( vector V0 ) (repeatability is to be verified ) 4) Add a set of testing masses capable of exiting only the first bending mode .( better if the previous balancing conditions are not destroyed ).Look at following examples . 5) Spin the rotor to the same balancing speed (point 2) and record value and angle measured by the instrument (vector V1 ). 6) Calculate the unbalance with the use of the vector method (as reported at chapter 4.3 and shown by the next sketch) 7) Continue the balancing for the second bending shape repeating points 2, 3, 4, 5 8) Repeat all the balancing procedure for the three balancing speeds : low speed near to the first critic (natural ) speed near to the second critic rotor speed (at each balancing speed the previous balancing conditions must not be changed ).

where: V0 = Original measurement V1 = Measurement with the applied test masses set Up V1-V0 = Test masses set effect The masses set capable to eliminate the original unbalance is : U 0 = Note:

Up V1 − V0

⋅V0

It is a vector relationship and the test masses set is composed by different masses placed on different planes , as shown on the next page .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 107

5.14

Modal balancing test masses set

A modal test masses set is composed of different masses , placed on different planes , capable of exiting the bending mode under consideration only , as shown on the next examples .

I° bending mode

one mass placed in the centre

this set does not change the previous unbalance

II° bending mode

this set does not change the previous unbalance

Notes: 1) Sometimes ,for safety reasons ,it is necessary to repeat the high speed balancing (at the first and second critic speed ) at two speeds ,that is at a distance from the critic speed of 30% and then of 15% . 2) The coefficient influence values are automatically calculated by the standard CEMB measuring units , and recorded in order to be used for similar rotors ..

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 108

5.15

Influence coefficients method

It is a method of general use allowing to balance a rotor at different speeds and on different balancing planes .It is always convenient ,if possible , to place the correction masses where the rotor bending is bigger . At each balancing speed the measurement values are recorded (amount and angle ) at each support for : Rotor alone Rotor with a test mass placed in sequence on each individual balancing plane . The matrix of influence coefficients is built and a system of linear equations define a unique solution (set of masses on the different balancing planes ) capable to balance the rotor at all the speeds . (The way to built the influence coefficient matrix is similar to the one described in chapter 4 regarding the balancing in the service conditions )

Vijk = ∑ K ijk ⋅ U jk where

K = 1, n = different balancing speeds Vij = point i vibration caused by the test mass placed on the balancing plane j j = 1, m = number of balancing planes i = 1, k = number of measuring points

Sometimes the equations system has not a unique solution because the number of equations is different from the number of unknown unbalances .In this case the system is solved trying to calculate, among all the possible solutions , the correction masses which: •

make the residual vibrations values as low as possible over the all speed range . (minimum square root method )

•

make the residual vibrations values as low as possible at the service speed by accepting a certain vibration level near to the critic speed . This is the case of a standard power steam turbine ; near to the turbine critic speed that is during the start up and the cast down transients a relatively high unbalance value is accepted because it lasts only for a short time , while on the operating speed the vibration

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 109

5.16

Balancing tolerances for flexible rotors

a)

Foreword The actual true critic (natural ) speed of a rotor varies from one individual rotor to another even of the same type ,so the unbalance tolerance is to be specified (on well defined planes ) over a speed range containing the rotor critic(s) speed(s) and if necessary also on specified speeds where the rotor may be considered as a rigid one . The dynamic behaviour of a rotor changes a lot , even by changing its speed of a few revolutions , when it is running near to the critic speed . (a small speed difference can cause high vibration levels change .). The balancing machine supports , or in general the balancing bench , must not introduce any additional critic speed which can generate fault readings . The used balancing bench must have its critic speed (s) outside the measuring range or , when this is not possible , the ( known ) supporting balancing bench critic speeds are to be excluded from the measuring field . The measuring unit must be capable of recording the measured values versus the speed . Different criteria for specifying the unbalance tolerance for flexible rotors are given ; the best one to be used is chosen after an experimental confirmation . For some flexible rotors , an additional finishing balancing on service conditions is to be made after the balancing on an industrial balancing machine .

b)

Residual unbalance tolerance specified (in gr.mm) on the two supporting journals (a = c = 0, b = distance between supports) The tolerance ( in gr·mm ) is specified on the two rotor journal planes (a = c = 0, b = distance between machine supports ) It is the most precise method , even if it is not commonly used , because it is difficult to keep the machine calibration constant over the all balancing speed range containing the rotor critic speed . Normally an acceptable unbalance (in gr.mm ) is specified for the low speed (rigid ) balancing and the acceptable residual unbalance , on all the speed range , including the critic speed , is requested to be lower than x times (10÷20 the specified value for the rigid tolerance )

c)

Maximum acceptable dynamic load on the supports (in Newton )

A low speed dynamic residual unbalance ( in gr.mm ) is specified , together with the balancing planes . The maximum acceptable value for the rotary inertia force ( in Newton ) is specified on the balancing machine supports , for all the speed range. Since the piezo electric pick up output is directly proportional to the rotary inertia force , generated by the unbalance ,this method can be easily used .

d)

Maximum dynamic run out (bending ) acceptable in one or more rotor sections

Reference is made to a paper roll , simply supported , running near the critic speed . A maximum value for the dynamic run out , in the centre section , is specified over the all speed range . It is evident that the paper roll ,despite being straight , is to be balanced over the all speed range (low speed included ) and an acceptable unbalance value is specified on the two balancing planes . In special cases , only a maximum dynamic run out value is specified ,near the critic speeds , at certain sections , without any requirement for the residual acceptable unbalance .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 110

e)

Maximum acceptable machine supports vibration (mm/s)

The accepted tolerance for the unbalance is specified for the rigid conditions (low speed balancing ), and the maximum balancing machine supports vibration is specified for the all the working range (mm/s) . Of course the maximum vibration levels are obtained around the rotor critic speed , which can be different, even for rotors of the same type . This method ca be easily applied on semirigid type machines which use velometers as transducers , under the condition that the machine itself does not introduce any critical speed , or the machine critical speeds are clearly known ... The acceptable value for the machine support vibration can be directly measured by spinning several rotors having good service conditions or by calculating the acceptable vibration on the balancing machine multiplying the on service vibration by a factor which takes care of the main differences between mchine s and real rotor s support parameters (rigidity and damping ). The disadvantage of this method is that the accepted tolerances are valid only for a certain machine type (frame of the support and rigidity ).

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. V - 111

5.17

Flexible shaft bending evaluation (Whirl)

Reference is made to the next figure ,where the most important items are pointed out

M is the mass of the centre disc , equal to the mass value of the complete shaft having a specific unbalance E [μ] = U / M If the shaft bends, its shape is shown by the previous figure where G is the centre of mass position , S is the geometric centre of the disc and OS is the bending value R (peak). When the shaft is rotating at the angular speed ω [rad/s] around the axis O, the equation regulating the motion is :

M ⋅ ω2 ⋅ ( R + E ) = K ⋅ R Setting ωn =

where K = shaft rigidity [N/m]

K as the shaft natural speed, by modifying the previous formula , we obtain : M 2

⎛ ω⎞ ⎜⎜ ⎟⎟ ω R = ⎝ n ⎠ 2 ⋅E ⎛ ω⎞ 1 − ⎜⎜ ⎟⎟ ⎝ ωn ⎠ Assuming a fixed value for the specific unbalance E [gr⋅mm/kg] , the bending value R is a function of the distance between the rotation speed and the shaft natural speed . Some values are reported on the next table . ω = ωn ⎛ ω ⎜⎜ ⎝ ωn

⎞ ⎟⎟ ⎠

⎛ ω 1 − ⎜⎜ ⎝ ωn

0,5

0,6

0,7

0,8

3

0,33

0,56

0,96

1,78

-1,125

2

⎞ ⎟⎟ ⎠

2

=

For values of ω much greater than ωn (shaft speed bigger than its natural speed ) , the bending value R is equal to the shaft eccentricity E ; this means that the shaft bends with the same value as E but on the opposite direction. (negative value = -1)

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 113

CHAPTER 6 THE BALANCING MACHINES

6.1

Industrial balancing machines classification

The industrial balancing machines are classified according to the measuring system and to other important features, as reported on the following table .

Balancing machines classification ( according to the measuring system) NOT ROTATING (GRAVITATIONAL) Only the static unbalance is measured

Disadvantages

Lower measuring accuracy (sensitivity)

Long cycle times

ROTATING (DYNAMIC) The dynamic unbalance is measured (static plus couple )

Force measuring (hard bearings)

The centrifugal force caused by the unbalance is directly measured (permanent calibration)

Soft bearings

Supports vibration (displacement)is measured

Advantages

Completely Semirigid rigid (electrodynami c pick up) Big diameters heavy rotors can be balanced without (piezo pick up) any power supply (f.i. helicopter blades, huge flywheels etc.) Not completely pasted rotors can be balanced (grinding wheels not yet hardened)

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 114

Balancing machine classification according to the working mode. Orizontal Axis of rotation Vertical Fixed Balancing speed Variable End drive Belt drive (no external part is added to the rotor during the measure) Spinning device Compressed air (for turbochargers) Electromagnetic fields (X rays sources ) Manual Operation mode Automatic By removing material (drilling, milling) mostly used for high speed rotors Balancing method

By adding material (welding, riveting) pls.note that welding can introduce additional unbalance because of thermal deformations

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 115

6.2

Unbalance transducers and support mechanics

The following flow chart points out the main elements Parameter to be measured

UNBALANCE (By spinning the rotor)

Effect caused by the unbalance

CENTRIFUGAL FORCE

Piezo pick up

Movement caused by the rotary force

SUPPORT MOVEMENT

Seismic (displacement) pick up

The balancing machine support behaviour is described mechanically by the following sketh, where :

M = Rotor mass [kg] k = Support rigidity [N/m] F = Rotary force caused by the unbalance [N] x = Displacement [m] c = Damping factor [N/m/s]

The governing equation is : F = M&x& + kx + cx& The active force F (component, along the x direction, of the rotary force caused by the unbalance) is a periodic force (sine wave) tied to the rotation speed The horizontal motion of the support is a sine wave with a frequency (RPM) equal to rotor speed ; its amplitude, for a give value of F, depends on M (rotor mass), and on K (support rigidity ) . Normally, on balancing machines, the value for the damping factor c is zero, because any damping may cause errors in the measuring of the angular position of the unbalance.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 116

Machine support displacement (oscillation) is described by the next figure, as a function of the rotation speed., for a given unbalance value .The diagram represents the graphic solution for the previous equation of suppots motion . A (in microns) is the amplitude of the oscillation, V (in revolutions per minutes, RPM ), is the rotor speed

From the drawing it is clear that for a certain value of the rotation speed (machine critical speed ) oscillation amplitudes become high. The balancing machines are classified according to their operational speed with regard to the critical speed.

•

Soft bearing balancing machines (over critic ) ;the working range is above the support critic speed. The balancing speed V is 2 ; 3 times bigger than. the critic speed.

•

Hard bearing machines (under critic) . the working range is under the support critic speed. The balancing speed V is below 0.7, 0.5 the support critical speed .(support oscillations are small and linear with the unbalance )

Note : In the most modern hard bearing balancing machines, equipped by piezoelectric transducers, the support displacement is zero, because the piezoelectric sensor picks up directly the rotary force caused by the unbalance . An electric charge is generated on the two surfaces of a piezoelectric element submitted to pressure and the piezo element is a rigid crystal ) .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 117

6.3

Horizontal axis balancing machine support

The rotary force generated by the unbalance causes a periodic oscillation of the roller cradle supporting rotor journal. Note:

The hard bearing balancing machines using a velocity transducer (semi rigid machines) have basically the same type of supporting frame where the oscillating thin plate is replaced by a more rigid plate and the displacement caused by the unbalance is very small(one or two microns). .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 118

6.4

Horizontal axis hard bearing balancing machine support equipped with piezoelectric transducers

The rotary force generated by the unbalance causes a sine wave pressure on the piezoelectric crystal, which reacts with an electric charge having the same oscillation over the time .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 119

6.5

Vertical axis dynamic balancing machine equipped with piezoelectric pick ups.

The next figure shows a vertical axis balancing machine equipped with piezoelectric transducers. The two transducers (CEMB patent )are placed at 90°. The radial sensor mainly measures the static unbalance, while the axial sensor measures the couple unbalance

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 120

6.6

Unbalance calculation mode

To simplify, let us consider an horizontal axis balancing machine

a - Hard bearing machine An unbalance placed in one plane distant a from the left hand support, when the speed is constant, causes a centrifugal force F which acts on the machine supports. The forces acting on planes 1, 2 can be easily calculated by applying the laws of statics .They are :

l −a l a F2 = F ⋅ l

F1 = F ⋅

In the measuring process, F (inertia force caused by the unbalance ) is unknown, while the values of F1 e F2 (forces exerted on the two supports by F ) are directly measured By vectorial summing F1 e F2 the value of F (amplitude and angle ) is obtained The unbalance vector U is directly calculated by dividing F ratio the square of the angular speed(look 1.12)

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 121

b - Soft bearing machine Under constant speed conditions the unbalance generates a rotary force which causes aperiodic oscillation on the two supports 1 e 2. The oscillations X1, X2 of the two supports are related to the axial position of the unbalance (distance a) and to the axial position of the rotor centre of mass (rotor equivalent mass on support 1, 2 ) Normally on a rotor, the position of its centre of mass is unknown, so the measure of the oscillations X1, X2 does not immediately gives the value and the axial position of the unbalance (a calibration cycle is necessary for different rotor types).

For one rotor type, the calibration can be obtained in two ways

1) By the influence coefficient method (look 4.4). Three spins are required . After the first reference spin with the rotor alone, two additional spins are performed applying a known calibration mass, in sequence, on the two balancing planes .The influence coefficient values can be memorized and recalled when a similar rotor is to be balanced (in this case the dynamic unbalance is measured at the first spin .) With the rotor mounted and kept in a standstill position, a known unbalance [gr mm] is generated in sequence on the two supports. The microprocessor unit directly measures the relationship existing between an unbalance, placed in the support plane, and the related support oscillation . 2) The calibration is obtained by placing on machine support a motor having a known unbalance value ; of course the calibrating device is to be smaller compared to the rotor mass. The unbalance , in the two balancing planes, is then calculated with the same method used for the hard bearing machines

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 122

6.7

Main differences between hard and soft balancing technology

A comparative analysis is given between soft and hard bearing balancing machines with special emphasis to the practical applications

Features

Hard bearing technology

Soft bearing technology

1) Permanent calibration

Standard. By simply setting up geometric rotor data, in only one spin, the machine measures the unbalance on both planes (values and positions ) and this independently of the rotor centre of mass position.

Three calibration spins are required when the rotor is mounted the first time, at the fist spin the planes separation and the unbalance values are unknown

No problem with the use of a simple reverse thrust roller cradle the complete rotor can be mounted as it is in the service conditions.

An additional mass or a heavier adapter are used in order to move the rotor centre of mass within the supports .The plane separation is poor .

2) Over hang balancing

.

. 3) Ventilation effects

No problem, it is also possible to balance at low speed (70 RPM).

The air movement can cause noising oscillations in the supports. (fan pump turbine impellers ). The reading can be influenced by any barrier to the created air flow . The axial thrust may create fluctuation ( motion)in the thin supporting plates.

4) Flexible rotors balancing

No problem if system rigidity (machine supports and foundation ) is greater than the rotor critic speed .The machine better simulates service conditions .ISO standards for flexible rotor balancing recommend the use of hard bearing supports

The soft bearings can influence rotor vibration modes . The advantage of soft bearings is that they isolate the rotors from any noise (critical speed ) originated by machine supports and base .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 123

Features

Hard bearing technology

Soft bearing technology

5) High vibration values during transients (start and stopping ) through the supports critical speed .

No problem

It can cause support breaking . The problem is overcome by keeping the supports locked during transients ; they are unlocked when the steady running condition is reached .

6) High level original unbalances

No problem, just reduce the balancing speed

High vibration which can cause support damages can be originated . The balancing is impossible, unless a preliminary gravitational unbalance (look 1.19) or a pre balancing (locked supports ) are made . .

7) Static balancing on a dynamic (two pick ups) machine

The true static unbalance is calculated and displayed

One support has to be locked, the display is not the true static unbalance (look 6.8)

8) Foundations

Rigid foundations and a good Special foundations are not required concrete floor is required. .Relatively . The balancing speed is relatively slow speed is used high .

9) Working environments

Suitable to operate in working in working spaces characterized by : dust, chips, swarf etc. cutting forces (drilling thrusts etc.)

The protection against dust or chip is a must , any friction in the pick up movement can cause a bad reading . .A reaction to every external force is necessary otherwise the pick ups are damaged .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 124

6.8

Error occurring when using a soft bearing machine for static unbalance measuring .

Normally people, using a soft bearing balancing machine, when the rotor is to be balanced only in one plane (static), lock the support near to the end drive and reduce the unbalance following the readings coming from the free support .the balancing goes on until the support vibration is reduced to zero. This way the rotor is not statically balanced, also the couple unbalance, which contributes to the support oscillation, is corrected, as shown by the following sketch.

The machine support S1, end drive side is locked, while the other support S2 is free to oscillate The oscillation of the support S2 is caused by : •

Original static unbalance Us

• Original couple unbalance Uc As consequence the balancing process which takes place following the oscillation of the support S2, even if obtained by correcting in one plane only, is not a pure static balancing. The error made is greater if: •

The original couple unbalance is high.

•

The ratio l/d is small

(In order to reduce the error it is necessary to increase the ratio l/d , this way the couple unbalance has a lower influence on the oscillation of the free support ) To confirm our theory is simple . After the balancing in one plane only, as described, it is sufficient to verify that the free support does not oscillate even if a couple unbalance is mounted (the display has to measure no variation on the static reading). This same test can also be performed on a rigid machine and it is recommended by ISO standards 2953.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 125

6.9

Hard bearing balancing machine proper use

For properly using an hard bearing balancing machine, it is necessary to comply the following items .

a - Rotor mounting The rotor journals are to be placed directly on the balancing machine rollers in order to grant, on the balancing unit, the same axis of rotation that the rotor has in the service conditions .If, by any reason, (to avoid journals marking f.i. ) the rotor is not laid on the machine rollers, in correspondence of its bearing position, it is necessary to verify with a dial that the supporting section is concentric enough with the bearing section (admitted diameter run out 0.01, 0,02 mm). It is a good rule to avoid the use of couplings placed on the rotor journals .(two possible errors can be introduced :eccentricity external /internal coupling diameters, eccentricity inside coupling diameter /external journal diameter .)

b - Rotor data set up These data are used to process sensors signals transforming it into unbalance data . With reference to the next figure, it is necessary to set up :

a = distance left support-left left balancing plane (mm) b = distance between left and right balancing plane R1 = left plane balancing radius R2 = right plane balancing radius

Set up errors causes unbalance measure errors; by setting up, for instance, R1 = 50 instead of 45, the measured unbalance (in grams ) will be lower of 10%. The values R1 e R2 non do not change the measured unbalance in gr·mm; only an incorrect setting of a, b, c parameters has a negative influence in the unbalance measure . (Be aware that by multiplying a, b, c times a common constant factor the displayed unbalance value does not change )

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 126

Horizontal axis balancing machine set up parameters

Vertical axis balancing machine set up parameter:

a = upper machine plane – lower balancing plane distance b = balancing planes distance

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 127

c - Unbalance measuring The balancing machine measures directly, in one spin, the dynamic unbalance on the two balancing planes :

U1 , α1 and U 2 , α 2 where:

U1 , U 2 = valori di squilibrio in the two balancing planes 1 e 2 α1 , α2 = posizioni angolari corrispondenti Following machine readings, by adding or by removing masses, the dynamic unbalance is corrected and the rotary forces on the machine supports are reduced to zero .

d - Correction and check spin After the correction, a check spin is performed in order to verify if the required tolerance has been achieved.

Example of unbalance display in polar form (spot) with value and angle display . The polar display is useful to immediately verify the type of unbalance (static if the two spots have the same angular position, couple if the two spots are opposite), nearer is the spot to the centre lower is the unbalance . In the example, the two unbalances have opposite angular positions .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 128

6.10

Working range of a variable speed hard bearing balancing machine

The working range of a general purpose, variable speed, hard bearing balancing machine is defined by a curve, which is normally reported in the instruction manual. As a function of rotor weight (vertical axis ) the line shows (on the horizontal axis ) the minimum and maximum usable balancing speed. Within the working range the machine is permanently calibrated (maximum error about 10 percent)

•

Above the reported maximum balancing speed the machine is no more calibrated.

•

For balancing values between 0,6 ÷ 0,9 Vmax, the machine has its optimum performances (sensitivity); for lower values the machine sensitivity decreases

•

With the use of the self learning mode, if safety allows, CEMB balancing machines can be used above the speed limit values . 2

The hard bearings machines Manufacturers normally, instead of the curve, declare a value for Pn , that is the product of the rotor mass (in kg ) times the square of the maximum usable balancing speed for that rotor 2 mass. The measuring unit for Pn is kg·RPM2 where RPM is the maximum balancing speed measured in revolution per minutes. 2 If, on a balancing machine, the declared value for Pn is 700·106 kg·RPM2, it means that a rotor, whose mass is 700 kg,, can be balanced using a maximum balancing speed of 1000 revolution per minutes. 2 The product Pn is 700 kg x 10002 = 700·106. A rotor whose mass is 1400 kg can be balanced on the same machine with the maximum speed of 1000 / 2 , that is 710 RPM . 2 The value Pn is a way to measure machine supports rigidity ; bigger is its value more rigid are machine supports.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 129

6.11

Specific calibration balancing on a hard bearing machine (Self learning of influence coefficients)

The hard bearing balancing machines are permanently calibrated because they measure the unbalance in the two balancing planes (dynamic unbalance ), in one spin ; it is only necessary to set up the rotor geometric parameters a, b, c (look 6.9). The permanent machine calibration is obtained by the manufacturer which uses a standard rigid rotor ( ISO test rotor ), with known masses applied to well defined balancing planes . In many applications when: •

The balancing planes are very near ( narrow planes)

•

The balancing planes are overhang (outside supports)

•

It is necessary to balance an assembly (motor and fan together)

•

The required balancing. speed is outside the machine working range

It happens that the permanent calibration does not permit an ease and satisfactory balancing (the calibration and the planes separation is not good enough ) . In all these cases a specific calibration for the particular rotor under balancing is possible. The calibration method is similar to the balancing method under service conditions (look 4.5). The calibration factors (influence coefficients )can be memorized and recalled for balancing similar rotors ; of course the rotor is to be mounted in the same calibration conditions (mounting conditions and speed ). This method gives to possibility to obtain low values for residual unbalance with a precise machine response, which is not possible using the permanent calibration method unless special mounting adapters are used.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 130

6.12

Horizontal axis balancing machine components

The next figure shows the main parts of an horizontal axis balancing machine .As a principle, we refer to hard bearing type balancing machines .

•

It is necessary that all parts are rigidly fixed (base to the ground, supports to the base, roller cradles to the support) ;otherwise the readings are not stable.

•

During the measuring cycle the rotor must not move axially (even small axial displacements cause the change of the axis of rotation and of unbalance readings.

•

When using roller cradles, the rotor journal diameter is to be different from the roller diameter or from its half value, otherwise the unbalance readings are not stable (a different diameter roller cradle or a V cradle is to be used .

The rollers are lightly crowned for two reasons : - To avoid a too precise supports alignment, - To avoid rotor journal marking, due to .rotor bending or misalignments

The alignment of the two machine supports is to be as best as possible: alignment errors cause axial thrusts which may cause nor real couple unbalances. In order to align automatically the supports, the rotor is kept under rotation al low speed,(the supports being not completely connected to the base ) for a certain time and small shocks are applied to the supports until the axial thrust is reduced to a minimum, then the two supports are rigidly fixed to the base. In order to obtain a good measuring repeatability it is better if the rotor has a light axial thrust only in one side ;this way we are sure that from one spin to another the rotor axial position is always the same, so that the axis of rotation does not change.(a change, even small, in the axis of rotation, causes a change on the unbalance )

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 131

6.13

Different types of cradles used for rotors balancing

During unbalance measuring, the rotors are laid on supporting frames (cradles 9 of different types

Normal rollers cradle: it is used to balance rotors on its journal, when the rotor centre of mass is within the two supports. The two rolls are crown and its diameter eccentricity, should be below .01mm. Rollers diameter is to be different from the journal diameter

φr ≠ φ p

φr ≠

φp 2

Reverse thrust roller cradle ; it is used, on one support side, to balance rotors whose centre of mass is out board the opposite support.,(a vertical force is generated ) the contact rotor journal / upper rollers is to be constant and stable(constant load upwards).

Over hang roller cradle ; it is used to balance special electric motors having inside journals .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 132

V flat cradle ;it is used to balance a rotor complete with its own bearings . It is advisable to use a relatively high speed (1400 ÷ 2500 CPM) so that the ball s bearing can reach the same position they have under service conditions .

Self aligning V cradle: it has the same use as the previous cradle, with the advantage of permitting rotor alignment during balancing .

Sleeve bearing cradle: it is used to balance very heavy rotors (turbines, armatures etc.) having soft journal ; the risk of marking is eliminated because the rotor supporting surface is bigger and the local pressure is reduced.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VI - 133

End flanged cradles ; they are used to balance cardanic shafts .They reproduce, in the balancing machine, the same mounting conditions the propeller shafts have in its service conditions. Sometimes, the inside part of the cradle is axially movable in order to facilitate the mounting of the shaft . The two end flanged cradles must be perfectly aligned., otherwise an axial thrust can be generated with a anoice on unbalance measuring .

Antifriction material V cradles: they are used for: – Balancing small armatures – Balancing small crankshafts (the risk of journal marking, because of the lubrication hole is reduced ) A system for static electricity discharging , is required.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 135

CHAPTER 7 BALANCING METHODS FOR MOST COMMON PRACTICAL CASES The balancing methods for some common rotor types are briefly reported on the next pages, together with an explanation of the basic concepts.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 136

7.1 Crankshafts They are , in the most of cases , balanced by drilling or milling on the webs and can be classified into two categories .

a)

Crankshafts classification

I° category All the cranks having its mass (pistons included ) evenly distributed around the axis of rotation belong to the first category (the axis of inertia is equal to the axis of rotation ) .The reciprocating forces of the first order , caused by the pistons acceleration are self balanced . They can be directly mounted an a balancing machine as a common rotor . II° category The mass is not evenly distributed around the axis of rotation. The reciprocating forces caused by the pistons motion are not balanced For this types of rotors the balancing on a machine is only an acceptable compromise , because a rotating force ( like the one originated by the unbalance associated with a web ) cannot counterbalance a reciprocating force ( like the one originated by the pistons ) acting on one plane only . Proper masses (Bob weights ) , are to be applied to the shaft cranks ,before mounting the crankshaft on the balancing machine .

A crankshaft belongs to category I° if the two following conditions are verified : 1) The mass is simmetrically distributed around the axis of rotation (

= axis of rotation )

2) There is an axial simmetry of the masses around an axis perpendicular to the axis of rotation and passing through the centre point

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 137

b)

Balancing speed

The balancing speed should be not too high in order to avoid that the shaft itself could bend because of its weight or because of the local rotating forces caused by the concentrated unbalances (web masses ). The right balancing speed is simply verified by measuring the unbalance at different speeds ( ± 100 RPM ) ; the measured values should be the same in order to confirm that the shaft keeps rigid (in the case , the balancing speed is to be reduced ).The balancing conditions shall reproduce the service conditions. Note: under service conditions the shaft is surely rigid because it is supported on all its journals , while on the balancing machine it is supported only on two positions and is subject to bending because of its weight or because of the high rotating forces caused by its webs .

c)

Balance quality

For agricultural tractors or trucks crankshafts the required quality is G = 40.according to ISO Standards. The most used quality is G = 16. Only for shafts belonging to the first category sometimes quality 6,3.is requested .

d)

Bob weights

The compensation masses , which simulate the piston masses , for the shafts belonging to the II° category ,(to be applied to each crank during the balancing process ) are calculated in order to compensate 100% the rotating mass (connecting rod big end ) and 50% the reciprocating mass (piston ) by using the following formula .The value 0.5 is a compromise ; for some application a different factor comprised between 0.4 and 0.6 is used .

m = mr + 0, 5ma

where:

m = compensating mass value (bob weight or bush ) mr = part of the connecting rod having mainly a rotary movement (about 2/3 of rod mass) ma = piston + pin and segments + connecting rod small end (about 1/3 of rod mass ) 0,5 =

compensation factor for the reciprocating mass (this value is comprised , depending on the motor boundary conditions on the two radial axis , between 0,4 and 0,65)

Bob weights shall have an equal mass (maximum admitted mass difference below 1/10 the admitted residual unbalance ) , shall be balanced and perfectly centered on the crank journal . It is to be pointed out that , in the case of crankshafts belonging to the II° category, the balancing is a compromise ; a rotary force caused by the concentrated web unbalance is used to compensate the piston reciprocating inertia force . Without any piston compensation (no webs on the cranks) a reciprocating force , acting on the vertical plane , is generated by the piston , while with a compensation at 100% (compensation factor equal to 1 ), the vertical force is cancelled and a new horizontal force is generated ;the compromise of 50% (compensation factor equal to 0.5 ) the vertical force is reduced by 50% while a same reduced force is generated on the horizontal direction .The only way to compensate a vertical force is to use two unbalanced counter rotating shafts , the two counter rotating centrifugal forces generate a force acting only on the vertical plane opposite to the reciprocating force caused by the piston .

Counter rotating masses

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 138

e)

Balancing the complete crankshaft

The complete crankshaft balancing requires that all the moving masses (pistons and connecting rods ) are equal (± 1 gr); if this is not possible it is advisable to mount the heavy piston with the light connecting rod or to mount the heavier pistons on opposite positions .

Example to calculate the compensation masses (bob weights ) for an in line two cylinder crankshaft (21 kg)

Piston

[gr]

760

+

Pin

[gr]

235

+

Segments

[gr]

88

+

Sleeve small end

[gr]

58

+

Seeger

[gr]

2

+

Connecting rod small end

[gr]

430

=

RECIPROCATING MASS

[gr]

1573

x

0,5

=

Compensation factor Compensated reciprocating mass

[gr]

786

+

ROTATING MASS

[gr]

931

=

Partial

[gr]

1717

x

1

=

N° cylinders per cranks

Note:

BOB WEIGHT MASS

[gr]

1717

Connecting rod big end

[gr]

866

+

Sleeve big end

[gr]

60

+

Oil

[gr]

5

=

ROTATING MASS

[gr]

931

the total weight of the connected rod , complete with bolts , nuts and washers is 1296 gr. Calculating the connecting rod big end with the approximate formula we obtain: Rod big end = 1296 x 2/3 = 864 gr This value is quite equal to the measured value

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 139

Example drawings for bob weights(compensation masses )

Two pieces cylindrical compensation masses Diameters D and d must be concentric .

Adjustable weight compensation masses with V shaped locking .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 140

Quick locking /unlocking compensation mass (bob weight ) .

Method for measuring the connecting rod reciprocating and rotating mass

The rod reciprocating mass ma = mb − mr

where : mb = total rod mass mr = massa rotante

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 141

7.2 Propeller shafts The balancing of propeller shafts is greatly influenced by the clearances of the existing flexible joints , which reduce the obtainable precision and sometimes make it impossible . If particularly long and thin , they can be assimilated to rigid rotors . The balancing speed is to be high enough in order to reduce the noise caused by the flexible joints and to simulate ,on the balancing machine , the service shaft radial position (values of 1000 ÷ 1500 CPM are recommended for truck shafts and values of 2000 ÷ 3000 CPM for car shafts ). A way to verify the right balancing speed is to measure the unbalance at different speeds ( ± 200 / 300 RPM) ,the measured unbalance should not vary . The unbalance compensation is obtained by welding small steel plates near shaft ends . Spot welding or projecting welding are the most used correction methods ; for the last system special steel plates having 2 or 3 protuding parts are used , as shown on the following sketch .

The small steel plates are welded on the connecting tube , near shaft ends , and on a centre position if the shaft is bending . The use of a special cradle simulating on service conditions is necessary to mount the shaft on the balancing machine (look at next figure and at paragraph 6.13). Required balancing quality Q is 16 according to ISO Standards (see Chapter 2); it makes no sense to ask for a better accuracy which is not obtainable because of the mechanic clearances of the joints . The propeller shaft connection to the machine D cradle requires the use of an intermediate mounting flange . The achievable balancing results greatly depend on the centring accuracy obtainable by the two intermediate flanges Before locking the intermediate mounting flanges , it is necessary to verify , with a dial , that the two flanges are perfectly centred and its surface are perpendicular to the axis of rotation (maximum admitted run out equal to 10 microns ) .With a modern machine , equipped with the eccentricity compensation software (see 3.6) the errors introduced by the mounting flanges can be completely eliminated .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 142

Examples of mounting a propeller shaft on a balancing machine

One piece shaft by using two D cradles

Two pieces shafts by using two roller cradles and one D cradle

Two pieces shafts by using two D cradles and one roller cradle

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 143

7.3 Propeller shaft body balancing (No flexible joints) The balancing of connecting shafts (pls. refer to the following sketch ) is not easy and several points are to be considered .

a)

Axis of rotation

The same on service axis of rotation is to be generated on the balancing machine . A machined centring surface is not available for proper mounting on the balancing machine and the axis of rotation is only determined by the holes on the two external coupling flanges .

b)

Shaft mounting on the balancing machine

Since resting journals are not available , auxiliary adapters are to be used in order to mount the shafts on the balancing machine. b).1 Using standard roller cradles Two flanges complete with journals are bolted to each shaft ends (they can also be connected by a centre body ). The two flange type adapters are to be balanced and perfectly centred by the use of calibrated bolts . (It is advisable to use the software for compensating mounting tool errors ,see 3.6.)

b).2 Using special flanged D cradles The two connecting shaft end faces may be not perfectly parallel and not perpendicular to the axis of rotation : so , by using rigid coupling flanges to connect it to the machine D cradles , an axial thrust can be generated between machine supports .This axial thrust can cause the measuring of a not real couple unbalance . It is advisable to use flexible type coupling flanges between the connecting shaft and machine D type cradle . (as an example look at the following sketch ).

Intermediate coupling flexible type flange (steel for springs width about. 2-4 mm)

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 144

7.4 Fan impellers •

They are normally balanced by adding masses (by welding small steel plates ).

•

In order to avoid fan deformation caused by the welding process , the compensation masses are fixed by rivets (the fan is drilled in the correction position ).

•

Small fan impellers are balanced by adding small clips .

•

The balancing speed is normally low in order to avoid any air effect or axial thrust on the machine supports .

•

In order to eliminate the ventilation effect , the impeller can be spun in the opposide sense of rotation or can be covered by a wide tape on its radial surface .

•

Required balancing tolerance corresponds to G 6,3.

•

When balancing small impellers mounted on car conditioning systems ( radial or axial ),it is advisable to balance the complete assembly motor plus fun .( this way the mounting coupling errors are completely corrected ).

•

A standard horizontal balancing machine can be used ; for mass production a vertical axis machine is better because of the easier and quicker mounting and desmounting .

•

If possible it is better to balance the impeller complete with its own shaft .(no errors are introduced by the mounting adapter )

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 145

7.5 Pump impellers Pump impellers are normally balanced by removing mass ; by drilling, milling or ginding on the lateral surface .If the impeller width is small compared to its diameter balancing on one plane is enough .

Required balancing accuracy corresponds to ISO G 6,3 / 2,5. The high speed centrifugal impellers (speed equl or greater than 3000 RPM ) are dynamically balanced on two planes according to quality G 2.5 or according to API Standards by grinding on the two lateral surfaces .(unbalance compensation by grinding is requested in oerder to avoid fluid turbolence .). For multistage pump impellers the balancing procedure of flexible or of quasi rigid rotors is required .(for more details look at the chapter concerning the flexible rotor balancing )

Sometimes the balancing process is completed by high speed balancing on 3 planes (at a centre plane and at the two ends .) The single stage pumps ( working overhung ) are better balanced complete with the shaft , and if possi ble , with the coupling joint. .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 146

7.6 Paper rolls The balancing of paper rolls have two goals: To reduce the rotating forces ( caused by the unbalance ) on the supporting bearings To keep the roll straight (on the contrary there is the possibility to brake the paper )

a)

Number of balancing planes

Normally paper roll unbalance is caused by a different wall thickness between two opposite lines of the tube , this results as an uniformely distributed unbalance . Almost all paper rolls , even if working away from the natural frequency , are elastic and because of the relatively high original unbalance , with the speed increase bend ; as a consequense the balancing planes are : 2 planes placed at 0,22 l (with l = roll length); 3 planes, the two end planes and a centre third plane . Only the rigid rolls (presses) are balanced on the two end planes .

b)

Balancing speed

The working speed of a paper roll is variable and it is elastic ; the consequence is that the balancing conditions shall be verified on all the working range , up to the maximum service speed . The paper roll is 2 balanced at a speed compatible with the machine Pn value (relatively low speed ) , then the speed is increased up to the maximum service speed and the bending value is recorded .(if the dynamic run out or bending does not increase with the speed it means that the balancing conditions do not change ). The use of a bending (run out ) device makes it possible to balance a paper roll at high speed with a machine 2 not eccessively rigid (low Pn value) and has the advantage of directly measuring the paper roll dynamic run out which is a parameter today required.

c)

Paper rolls classification

The following table classifies paper rolls according to the required balancing specifications Number of balancing planes

Dynamic run out measurement

2

NO

less than 1000 m/min

2

YES

Greater than 1000 m/min

3

YES

whichever

3

YES

FLEXIBLE ROLLS

RIGID ROLLS (PRESSES) Length

less than 5 meters Greater than 5 meters

Max.service Speed

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 147

d)

Unbalance tolerance

The required balancing tolerance for new paper rolls corresponds to ISO 2.5. For reconditioned rolls quality G = 6.3.is required . The next formula calculates quickly the acceptable residual unbalance (quality 2.5) as a function of the main roll data and of its maximum service speed which is , in the most of cases , specified in meters per minute . wheree: U1, 2 = Admitted unbalance [gr] referred to the roll inside radius

De = Roll external diameter [mm] Di = Roll inside diameter [mm] P = Roll weight [kg] V = Maximum service roll speed [m/min] The accepted bending value (Dynamic Run out) is also calculated by using the same ISO formula which defines the residual acceptable rotor eccentricity as a function of the max. service speed . For quality grade G = 2.5 , the acceptable bending value at the roll centre position is calculated by the next formula :

E = 150 ⋅

De V

where: E = Acceptable dynamic run out ( in microns ) in the centre position (peak to peak value) De = Outside diameter [mm]

V = Max service speed [m/min] If the calculated value for E is lower than 40 µm ,the value= 40 µm is given to E. The accepted value for the static bending (mechanic run out or roll straightness ) is about 100 µm. The roll is considered as balanceable if the total measured unbalance is lower than 1/100its total weight .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 148

e)

Flexible rolls balancing procedure

Important notes 1) Particular attention is to be paid when fixing masses on the outside diameter and increasing the speed .. 2) When a big original static unbalance is present it is convenient to reduce it by machining the roll journals out of centre . The eccentricity value can be calculated with the next formula

E= 3)

4)

U where: U = measured unbalance [gr·mm], M = roll mass [kg], E = radial eccentricity M

[µm]. When the roll wall thickness is not within the specified values (big difference on two opposite angle positions ), it is convenient to remachine the inside diameter in order to obtauin a more unifor thickness . Before measuring the unbalance , keep the rotor running for some time in order to eliminate any static bending ..

e).1 Two planes balancing 1) Define the two balancing planes at 0,22 l. 2) Pre balance at low speed (200 – 300) the roll by fixing masses on the outside diameter with a standing rope. 3) Increase the speed and , at each step correct the unbalance always in the same planes .. 2 4) When the speed is over the machine admitted Pn value , the bending measuring pick up is to be used , always acting on the same planes and using ropes to fix the provition al compensation masses . 2 5) Continue the balancing process up to the service speed untill both the unbalance (below machine Pn value ),both the dynamic run out (on all the roll working range ) are within the specified tolerances . 6) Remove the outside provisional correcting masses and apply it on the inside by increasing the value inthe ratio outside/inside diameters . e).2 Three planes balancing 1) Select the three balancing planes ; two at the end sides as near as possible to the journals and the third one at the roll centre position . 2) Pre-balance provisionally , on roll ends ,at low speed (200 – 300 RPM). 3) Spin , at the same low speed , and measure the geometric run out . Record this value and remove it (subtract ) electronically in order to measure only the dynamic run out . 4) Increase the speed , as much as possible with regard to a safety operation ,until the monitored dynamic run out increases to an unacceptable value .. 5) Measure and record the dynamic run out . 6) A known test mass is fixed , by using standing ropes on the outside diameter , at the centre roll position at an angle opposide the measured run out angle . The test mass value can be equal to 40% or 60% the masses used to pre balance at low speed (point 2 ). 7) Spin the roll at the same previous speed ,measure and record the new dynamic run out .The mass to be added , at the roll centre position , in order to compensate the original bending (dynamic run out measured at point 3 ) is calculated with the vectorial method described under paragraph 4.3. Normally the machine software calculates the correcting mass (value and position )to be applied in the centre position . 8) Remove the provisional test mass and add the calculated mass on the outside diameter by using standing ropes . 9) Measure the unbalance and correct it on the two end planes at low speed (the firstly applied masses are normally reduced ) 10) Repeat steps 3-9 untill the following conditions are obtained : – Residual unbalance on the end planes at low speed or at the maximum balancing speed permitted by 2 the machine Pn (see 6.10) is below the accepted tolerance . – The dynamic run out is within the accepted tolerance on all the service speed range .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 149

f)

Fixing the inside correcting masses

Reference is made to the next figure. 1) Calculate the length of the correcting steel rod according to the measured unbalance value and to the inside radius .It is inserted through the holes of roll ends . 2) It is advisable to use square or rectangular shaped rod 40x50 mm.max. 3) If the calculated length is longer than 800 mm ,some 4 mm. Depth notch is to be made on the rod length . 4) By using the real correcting rod placed on the external surface ,mark the position of the fixing bolts .the distance between each bolt is about 200 and 300 mm. 5) Drill and countersink the roll wall ,taking care to prevent chips entering inside . 6) Insert the correcting rod and position its threaded holes in correspondence of the roll wall threaded holes .(to facilitate the operation the roll is supported at its ends and the threaded holes are moved in the lower position ). 7) Fix the rod to the roll wall with at least two threaded bolts. 8) Rotate the roll in order to move the threaded holes to the upper position . 9) Apply LOCTITE on the bolts and screw untill its core is broken . 10) Reduce the protuding part , upset ,shape and tape grind it . Note: Do not weld the bolts to the roll wall..

g)

Semicritic speed

When the paper roll is rotating , on a balancing machine ,at a speed equal to the middle of its natural speed , sometimes high vibrations are measured (high dynamic run out values at the centre ).These vibrations have a frequency double the rotating speed , cannot be reduced by adding masses ( balancing ).and disappear by changing the rotation speed ( increasing or decreasing it ) The explanation of the experience is simple : it is sufficient to consider that a misallignment (caused by machine supports, rotor journals, support roller cradles ) or out of round rotor journals can generate a vibration having a frequency double the running speed . If the running speed is exactly equal to half the roll natural speed, a small source of vibration (at double frequency ) equal to the roll natural speed ( resonance conditions ) can excite big vibrations . Paper rolls damping factors are very low ,this explaines why low impulses can cause high vibrations . Some rolls manufacturers specify a limit to the bending value in semicritic conditions (2° order dynamic run out ) between 700 and 1400 microns. According to our opinition there is not a direct relationship , when running in semicritic conditions , between paper roll behaviour on the balancing machine and on service conditions , because the boundary and damping conditions are different .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 150

7.7 Vehicle turbo chargers The Manufacturer balances ,as separate, the turbine shaft and the compressor , as shown on the following sketch.

People repairing the turboshaft normally balance the complete shaft only by removing material on planes 1 and 2 because the single parts have alkready been balance separately . When the measured unbalance values are too high ,it is advisable to verify the mechanicsin order to avoid to remove too much material and , as a consequence ,to compromise the mechanic safety .of the turboshaft . The balancing speed depends on the rotor weight and on the type of the used machine type and generally is comprised between 2000 and 40000.. The balancing tolerance is established by the Manufacturer and varies from type to type depending on the weight and service speed (the computation formulae used for rigid rotors are not applicable ,specially for high speed compressors ). As reference value then ,consider that on a Garret turbine type TO1 (totol weight approx 100 grams and service speed of about 120000 CPM) it is requested to rech on plane 1 and 2 a tolerance of 0.25 gr.mm In case of small turbochargers running at very high speed (requested tolerance lower than 0.5 gr.mm )it may be necessary to balance the complete assembly .The compressor mounting/desmounting operation may damage the requested tolerance ,due to the fact that there may be a non repeatable mechanic centering.In case of desmounting ,after balancing , it is suggested to make a reference mark so as to minimize the remounting errors . The next table lists the required tolerance for different turbine models.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 151

Required unbalance tolerance for the most common car turbo shafts

GARRETT

KKK

HOLSET

TURBOSHAFT MODEL 3LD, 3LDZ 3LKZ, 3LEP, 3LEZ 3LKS 3LKU, 3LEU, 3LKY 3HD, 3HF, 3DB 4LE, 4LF, 4LG, 4LB, 4LGZ, K361 4HD, 4HE, 4MF, 4B, 4BD 5MD, 5MDE, 5MDZ, 5MDY K14, K16 K24 K26 K27 K28 K33 K34 K36 K37 K42 K44 K52 K54 T31 T04, T04B, T04S, TA35 T05B, TE06 T06, T07 TH08A T11 T14 T18 T18A T30 T60, TV60, TV61 TV70, TV71 TV77 TV80, TV81, TV91 TA45, TA54, TM51, TM54

COMPRESSOR TURBINE Unit( gr·mm) 2,1 1,5 2,1 1,5 2,1 1,5 4,3 3,1 4,3 3,1 4,3 3,1 8,0 6,0 0,55 0,4 1,2 0,9 1,3 1,0 1,5 1,1 1,6 1,2 3,7 2,9 4,0 3,1 4,0 3,1 4,6 3,6 8,9 7,1 9,8 7,8 12,3 9,5 13,5 10,5 0,25 0,38 0,25 0,35 0,51 0,64 0,25 0,48 0,86 1,40 0,38 0,84 1,27 2,18 1,42 1,40 1,37 1,40 1,63 2,41 0,51 0,54 0,61 0,89 0,61 0,64 0,92 1,40 0,51 0,64 / 0,76

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 152

7.8 Hydraulic couplings The balancing problem in hydraulic couplings is tied to its geometric shape ; if it is not uniform when the coupling is filled up by the oil an unbalance is generated .; another point to consider is that the two parts composing the coupling may work with different relative angle positions . If the geometric shape is good a dry balancing (no oil in ) is enough , the same unbalance is measured with and without the oil . On the contrary the balancing is complicated if the coupling shall work with different oil levels ( the oil level controls the transmitted torque ) ,in this last case the following procedure can give good balancing results .

Balancing procedure 1) Balance the coupling in dry conditions by using one or two auxiliary flanges (the measured unbalance is compensated on the two flanges ). 2) Fill up the coupling with different oil levels .At each level perform the balancing acting on decreasing diameters of the coupling . This way every single coupling ring is balanced when filled up with the oil . 3) Remove the auxiliary flanges and balance the coupling ,in dry conditions, without destroying the local balancing conditions previously obtained .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 153

7.9 Tools and toolholder balancing Foreword Today spindles in modern CNC lathes can reach very high revolution speeds (20÷25000 RPM). The high speed causes some problems : •

cutting tool cooling,

•

chips removal

• frame rigidity. The correct balancing of the tool and the tool holder plays an important role . Unbalance effect The unbalance U , generates a centrifugal force which increases with the square of the speed according to the next formula :

F = U ⋅ ω2

where: F = Rotary centrifugal force [N] U = Unbalance [kg·m] ω = Angle speed [rad/s]

As an example , an 1 gram unbalance placed at 30 mm distance from the axis of rotation , at 20'000 revolutions per minute , generate a rotary force of 120 Newton (about 12 kg) , which is a value of a certain importance . The centrifugal rotary force can cause vibrations which can be more or less high depending on the machine rigidity and on its natural frequencies . The vibrations have big influences on the obtainable surface mechanic accuracy , on the tool life and on the spindle bearing life . Balancing necessity Tool and toolholder balancing is today important in a modern manufacturing centre for different reasons: •

tool life is increased because of the better cutting conditions without vibrations;

•

spindle life is increased because of the lower charge on the supporting bearings ;

• final product quality is bettered because of the reduced roughness and tighter dimensional tolerances . The use of tools and tool holders separately balanced normally grants good service conditions even if some errors can be caused by the their coupling ; from this point of view the best way is to balance the complete assembly tool and its tool holder at each presetting. One/Two planes balancing As aprinciple , a rotor having axial dimensions bigger than its radial dimentions ( not disc shaped ) has to be dynamically balanced on two different planes . In the case of tools and tool holders , two plane balancing can be neither cheap neither practical because the second balancing plane is not available ; so , in the most of cases the unbalance compensation is made on one plane near the centre of mass position . Only the static unbalance is corrrected , but the residual couple unbalance has lower influence on the spindle bearings . As a general rule , the static ( one plane ) balancing is valid under the condition that: •

total tool holder length is limited (L < 100 mm or L < 2·D ,with L = useful tool holder lengthe [mm] and D = centring tape diameter [mm])

•

the correction plane is near the center of gravity (mass)

•

the couple unbalance is not too high (< 10 times the residual static unbalance )

•

the maximum service speed is lower than 12000 CPM.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 154

Sources of the unbalance Causes of the unbalance in a tool holder can be divided into two groups: a – Constant causes which can be fixed for ever Are generated by an asimmetric tool holder manufacturing : •

surfaces not properly grinded,

•

different recesses in the driving part ,

• not counterbalanced tool fixing bolts. All the above mentioned sources can be eliminated by a proper balancing . b – Variable causes which cannot be easily compensated A different unbalance can be generated at each mounting and can be caused by : •

Tool locking collet which can be positioned in a different angle on the mounting tape

•

Locking ring nut wich can be placed on a different radial position depending on the way it is screwed on the centering thread .(one more revolution can centre it in a different radial position )

•

Not balanced cutting tools for two reasons : not simmetric recesses for chip removal or not balanced cutting bits for its mass or position .

•

Tool not properly centred in the tool holder .

12345-

Not simmetric recesses Centring collet Unbalanced tool Unbalanced /not centred ring nut Unmachined surfaces

Considering all possible unbalance sources and , above all , those type b (not repeatable at each mounting ) , the best way is to balance the assembly tool and toolholder .. Since it bis not thinkable to balance the toolholder at each different tool mounting ( the tool holder will be destroyed ) .it is understandable that today somepeople use a tool holder with the possibility to balance it by properly moving some masses included in the tool holder itself .(rotating msses etcetera.).

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 155

Balancing tolerance calculation a - ISO 1940/1 Standards Depending on the fact we consider the tool and the toolhoder as parts of a lathe or a grinding machine , the required balancing tolerance according to ISO 1940 is equl to G = 2,5 or G = 1. The total admitted residual unbalance for a tool / toolholder is calculated , for quality grade G = 2,5 , according to the next formula :

U=

24000 ⋅M N

dove:

U = Total acceptable residual unbalance [gr·mm]

N = Maximum tool holder service speed [RPM] M = Total mass ( tool and toolholder ) [kg] For G = 1 the accepted values are 2,5 times lower and the following formula is applicable:

U=

9500 ⋅M N

At 24000 RPM the admitted specific unbalance E [µ] for the quality G 2,5 is 1 µ , while for quality 1 is 0,4 µ = 0,4 gr·mm/kg. b – Recommended unbalance tolerance We start by considering that an optimum unbalance tolerance shall have the following benefits : 1) It is easy to be obtained with the balancing machines today available in the market with acceptable production costs . (low time required). 2) It easy verified even after different mountings and desmountings . 3) The related centrifugal forces on the spindle bearings are acceptable or lower compared to the cutting forces . Considering also that the balancing of a toolholder requires the use of a mounting adapter whose mechanic centring accuracy (centring repeatability ) is not better than 1 or 2 microns, we think it right not to require a tolerance better than quality G = 2,5. Taking also into consideration the accuracy of the standard balancing machines , today available in the market , the acceptable residual unbalance for a toolholder can be calculated by the use of the following formula :

U=

24000 ⋅M N

U = 2⋅M

(valid for N ≤ 12000 RPM) (valid for N > 12000 RPM)

If the value for U , calculated by the previous formula ,is lower than 0,5 gr·mm it is accepted the value U = 0,5 gr·mm. where U [gr·mm] = Maximum admitted residual unbalance N [giri/min] = Maximum toolholder servise speed M [kg] = Total mass(toolholder and tool ) What above specified means that the minimum accepted total residual unbalance is not lower than 0,5 gr·mm and that mechanic centring repeatability of the used adapter is within 1 micron.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 156

It is better , in oder to verify the residal unbalance at each following mounting , that the measured unbalance values during the balancing process are lower that the ones calculated by the previous formula (lower by 50 %) ; this means :

U=

12000 ⋅M N

U = 1⋅ M

(valid for N ≤ 12000 RPM) (valid for N > 12000 RPM)

U ≥ 0,5 gr·mm When balancing on two planes, necessary for toolholders having long axial dimensions (L > 2D), The acceptable residual unbalance on the two different planes U1, U2 is calculated by the following formula :

U1 = U 2 = 2 ⋅ U

if the distance between the two planes ≥ 80 mm

U 1 =U 2 = 4 ⋅ U

if the distance between the two planes < 80 mm

In both cases the total residual unbalance (static ) shall be lower than U. Notes: 1) The admitted tolerance on the two different planes (couple unbalance ) is bigger , under the condition that the total unbalance (static unbalance ) is lower than U. 2) It is advisable to balance at about 50% the calculated tolerance so that at each following mounting , even with the errors introduced by the mounting adapter , the measured unbalance is within the required tolerance . Balancing speed Tools and toolholders are rigid rotors (do not deform ) and at consequence the unbalance (mass distribution around the axis of rotation ) does not change with speed . The right balancing speed depends on the type of used balancing machine . The balancing speed value or range is to be chosen in order to obtain the best balancing accuracy and repeatability .with the available balancing machine . Normally the used balancing speed varies from 1000 and 3000 RPM (higher speed for lighter toolholders ). The right balancing machine for toolholders An horizontal or vertical type balancing machine can be used . The main differences are : •

The vertical axis balancing machine is sometimes more practical (easier toolholder mounting and desmounting )

•

The vertical axis balancing machine can be suitable to balance on one ( static balancing ) or on two (dynamic balancing )

•

The horizontal axis balancing machine , normally belt driven , has some important advantages : -better sensitivity (0,1 gr·mm against 0,2 ÷ 0,4 gr·mm) - better balancing accuracy (0,1 ÷ 0,3 gr·mm/kg against 0,5 ÷ 1 gr·mm/kg) - possibility to balance on 1 or 2 planes - possibility to be used to blance other different rotors types

A good balancing machine for tools and toolholders must have the following features : •

Measuring of the dynamic unbalance (static and couple );

•

Good sensitivity (0,1 ÷ 0,2 gr·mm);

•

Including the software to electronically compensate the errors caused by the mounting adapter (unbalance and mounting eccentricities ) (see 3.6).

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 157

Mounting adapter The final balancing result of a toolholder is greatly influenced by the mounting adapter which is used . It is necessary to reproduce ( in the balancing machine ) the same conditions (axis of rotation ) existing in service conditions . Following recommendations are valid: a) With HSK type attachments it is necessary to exert a strong axial thrust so that the toolholder face completely touches the resting face (as it is on service conditions ). b) With ISO type attachments the axial thrust can be reduced because the centring is granted by the cone . It is worth mentioning that mounting adapters , copying exactly the toolhlder locking in service conditions in the machine spindle, do not grant good repeatability for the unbalance measuring becuse some mobile components (flaps ) are not sufficiently guided ( eccessive clearance ). Simpler mounting adapter can be used with easy mounting /desmounting and good repeatability in the centring . . The next sketch is an example of a good adapter used to balance HSK toolholders on an horizontal axis balancing machine .By simply screwing a side screw the toolholder is axially locked and centered. It is absolutaly necessary to use the software for compensating the unevoidable eccentricity errors caused by the adapter itself : - adapter unbalance - eccentricity in the mounting . Even if the eccentricity compensation (for the same adapter ) is valid for all the same type toolholders ( having same shape and mass ) , it is advisable to repeat it at each different toolholder ( even of the same type).

Example of a good tool holder

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 158

7.10 Car wheels a)

Wheels

The european association of wheel manufacturers define the acceptable unbalance tolerance on one plane only ( static ), according to the following figure .the acceptable residul unbalance varies only with the speed .

ES-3.04

b)

Acceptable residual unbalance fo car wheels

Tyres

An acceptable residual unbalance is specified according to the tyre weight . For new tyres the total acceptable unbalance in grams is Uta [gr] = k · M , where M = tyre mass in kg and k a factor varying from 2 to 4.

c)

Complete car wheels

Are dynamically balanced on two planes by adding lead masses on the wheels sides .. According to ISO 1940 Standards the required tolerance is G 40. Normally a beter quality ( G = 16 ) is used in order to reduce the final unbalance resulting from a not perfect centring of the wheel on its hub .. If the maximum unbalance per plane is bigger than 60grams the wheel is rejected . The required tolerance is 5÷10 grams per plane (car wheels ) and 30÷50 grams per plane for truck wheels.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 159

7.11 Plough shafts Agriculture plough shafts can be considered as rotors with variable geometry because , as a function of the speed , the position of the cutting blades can change . The high service speed (2000 – 2200 CPM) and the length ( sometimes more than 3 meters ) may cause the service speed to be near the first natural speed (it can be considered as a flexible rotor ).. Plough shafts proper balancing requires : •

Cutting blades having more or less the same mass (nominal weight ± 25 grams).

•

Simmetric distribution of the cutting blades on the shaft body ( tube ) with a proper design .

•

Cutting blades locking system which permits a free repeatable movement above a certain speed .

•

Pre-balancing at a low speed (800÷1000 RPM)., with the all blades completely open .

•

Unbalance compensation , if possible , on the all body length .

•

Balance improving at different steps by gradually increasing the speed untill the maximum service speed

Notes: 1) The balancing is easier if the centre body (tube ) is rigid at all speeds. 2) The body rigidity increases with the external diameter. The wall thickness has lower influence on the tube rigidity .. 3) If the shaft is flexible , a third plane in the centre is to be used .(v. 5.13). 4) The welding of masses can originate new unbalances because of induced tube deformations .. 5) It is better to use tubes having a constant uniform wall thickness .. 6) Sometimes , at high speeds , a good balancing is achieved just adding small masses in the centre position .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 160

7.12 Centrifugal separators The high speed centrifugal separators (4000÷6000 RPM) require a good balancing (quality Q=2,5). The right balancing procedure is: •

Dynamic balancing of all the inside parts (bell etc..);

•

Low speed dynamic balancing of the complete assembly ;

•

Hydraulic test ;

•

Vibration check at the maximum service speed and sometimes near the natural speed, under service conditions.

If the measuredvibration value at the maximum service speed is not acceptable , they are to be reduced by two possible ways : a) Low speed balancing again of all the components and of the assemble; b) On service condition balancing (normally on one plane only ). The balancing operations described at points a and b are justified by a permanent deformation or by a movement of the inside components during the hydraulic test . The balancing is normally achieved by adding masses ( welded tin ) on the inside . Some manufactures specify a thicker wall thickness on a ring to be used for unbalance compensation by milling or grinding .

The high speed , on service balancing , is obtained by placing the vibration pck up directly on the upper oscillating bearing of the centrifugal separator . The mounting on the balancing machine for the low speed balancing is made by using an adapter similar to the one shown at the item 3.4 (e).

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 161

7.13 Electric armatures a)

Balancing tolerance

Normal armatures are balanced according to quality G= 6,3 ; special armatures according to quality G= 2,5.

b)

Unbalance compensation methods

As all rotor types the electric armatures can be balanced : b.1

By adding masses ; for example: Washers are fixed on the pegs of squirrel cage armatures; Steel plates are welded on the end faces of big alternate or continous current motors ; Steel masses ( movable on circular T slots made on the rotor end faces ) are used to balance big alternators ; Two components compound , which hardens in a few minutes , is directly placed on the wires of small electric armatures ; Small bolts are screwed in the existing threaded holes ( 12 ) placed on the end face circumference of permanent magnets high speed motors .

b.2

by removing material Unbalance correction by mass removing is normally used on automatic machines for small and medium size armatures . Small armatures are milled on the polar expansions ; Cage rotors are axial drilled on the rotor body ; Small continous current motors are balanced with radial drillings on two lateral flanges designed for this purpose .

Balancing by drilling

Balancing by milling

Taking care of the balancing method which requires: •

Milling in fixed angle positions ;

•

Relevant drilling depths compared to rotor dimensions ;

the automatic balancing machine can reach optimum performances (URR between 80 and 90%) only if the software for balancing by components and by not linear drilling is available .With deep drills the correction radius varies (radial drillings ) or the balancing plane changes (axial drilling ).

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 162

7.14 Textile machines components a)

Foreword

Normally textile rotors have high service speeds and the working range containes a natural frequency . The balancing procedure is clearly specified in the maintenance manual supplied by the manufacturer because even after the change of a wear part (bearings for instance ) the rotor is to be re-balanced . Please note that the balancing operation is to be performed after a suitable running in time and that after a drilling operation the rotor shall run for a certain time for stretching . Normally the rotor is balanced by drilling or by adding masses (small screws into pre-existing holes ). The rotor is balanced only after a geometric control (admitted run out ) and only if the measured original unbalance is below an admitted value .Sometimes , for some components , a balance in service conditions is required if the measured vibrations are greater than admitted ( in this case the measuring points and the balancing planes are specified ).

b)

Motorolls

Motorolls are fed by a frequency varitor ( inverter operating at 25 ÷ 200 Hz) and are composed by a centre fixed shaft around which the external cilinder part rotates .. They can be considered as rigid rotors and are balanced at a speed between 2500 and 3500 RPM. The mounting on the balancing machine is made by resting the journals ( sometimes with the use of couplings if necessary ) on V type cradles ( look at the next figure ) and the rotation can be obtained by resting the belt on the external surface or by means of the frequency variator . The relatively high balancing speed , even it is a rigid rotor , is necessary for the bearing balls to run on the same trace as in the service conditions . The required balancing quality is G 2,5 and the two end face are used as balancing planes . The unbalance is compensated by badding small threaded bolts ( fixed by loctite ) into pre-existing holes .

1, balancing plane 2, Rotor journal; 3, Journal locking .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 163

c)

Chucks

Chucks are flexible rotors and are balanced , depending on the model in one , two , or three planes . A special mounting cradle ( simulating the service conditions ) is used to mount the chuck in the balancing machine .(see figure ).

1, Machine bed; 2, Machine supports; 3, Mounting cradle ; 4, Driving motor ; 5, Chuck; I, II, III, IV, Balancing planes The balancing is achieved by radial drilling (in planes I, IV also by axial drilling ). The required balancing tolerance is G 2,5 and the balancing speed varies from 1200 and 2200 RPM. In order to avoid damage to the chuck with unusefull holes , it is advisable to balance it by adding plasticine on the external surface and to drill it only at the end when the required tolerance has been surely achieved . It is necessary to keep in mind that : •

Before the unbalance measurement , the rotor has to be kept running in for the time specified by the manufacturer

•

The drilling operation and the machine start up ( spinning ) causes an elastic deformation which must desappear before taking the unbalance measurement . ( the rotor is kept running until the unbalance reading is constant ). Even with a low speed balancing , acceptable results are obtainable if the measured unbalance is corrected in adistributed way (for instance 30 ÷ 40 % of the measured static unbalance is corrected on plane III and the remaining unbalance on planes IIand IV). Once pre-balanced at low speed , the chuck is tested at different speeds up to the service speed including its natural speed and the vibration ( pick up signal ) is recorded ; if it keeps within specified values the chuck is balanced otherwise a high speed balancing ( near the critic speed ) in a specified plane is to be performed as described at paragraph 4.3 . For maintenance purposes , after bearings change ,a good low speed balancing is enough . A finer balancing at low speed is obtained by using the self learning mode (see. par. 6.11). Notes: Some manufacturers specify the acceptable value for the balancing machine supports vibrations with reference to a well defined balancing machine model , so users of other types of balancing mchines must calculate , in an experimental way , what is the acceptable vibration for their machine by using a test chuck surely balanced and recording the vibration values over the speed range ... It should be better , as reported on paragraph 5.16 , if the accepted tolerance is specified in gr·mm (force exerted on the machine support ) ; this way the tolerance is not tied to a balancing machine type and model .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 164

d)

Reverse shafts

They are flexible rotors running high speed over the first and sometimes over the second natural speeds (running speed up to 24'000 RPM). The required tolerance is G 2,5 and there are 3 or 5 balancing planes depending on shaft rigidity and on its natural speeds . The balancing is obtained by following the standard modal balancing described at paragraph 5.13. Also for these shafts the machine supports acceptable vibrations are normally specified ( same comments of the previous note are valid) . It is advisable to previouly balance the reverse shaft by adding provisional plasticine and then proceed by drilling . becuase , as shown at paragraph 5.13 , modal balancing requires different steps with possible changes. Also for balancing these types of rotors it is better to use a machine with the self learning calibration mode or specific calibration .( see. par. 6.11).

Balancing planes on a reverse shft passing only through the first natural speed

Balancing planes on a reverse shaft passing through the first and second natural speeds. Notes: 1) Sometimes the shaft low speed unbalance is not important and the manufacturer specifies only the balancing at high speed near the critical speed ; in this case the goal is to reduce the shaft bending value at certain shaft positions ..( the balancing mass is calculated by the vectorial method ) 2) On a flexible rotor , even of the same type , the critic speed is different ; so the ( high ) balancing speed varies from a rotor to another of vthe same shape ..

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VII - 165

7.15 Relationship Unbalance-drill depth

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VIII - 167

CHAPTER 8 BALANCING MACHINE CONTROL

8.1

Test rotor

The quality control of a universal balancing machine, as far as concerns the minimum achievable residual unbalance and the unbalance reduction ratio, is obtained by using a standard test rotor , according to ISO 2953 standards The main features of ISO test rotors are : •

Its residual unbalance is very low

•

Its shape is simple

•

It is surely rigid

•

The positions for the applied test masses (planes and radius ) are well defined

For the same tests or only for calibration tests , a different type of test rotor ,can be used ,if agreed between the Manufacturer and the User , under the condition that it complies with the above listed features . For special purposes balancing machines (automatic machines ) the test rotor or master rotor can be a rotor similar to the ones processed (a pulley ,a brake disc ,a crankshaft ,f.i.) having the same geometric dimensions but with better tolerances (perfect ninety degrees between the centring hole and the supporting surface ) and hardened working surfaces .(of course the master rotor complies with the above reported specifications ). The ISO test rotor ,to be used on a universal balancing machine , should have a mass lower than 1/3 the maximum machine weight capacity.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VIII - 168

a - Test rotors type A ,for vertical axis balancing machines

Suggested dimensions ,masses and speed for test rotors type A (vertical machines ) RotorN°

1

2

3

4

5

kg

1.1

3.5

11

35

110

Major diameter D

mm

110

160

230

245

510

Minor diameter d = 0.9 D

mm

99

144

206

310

460

Height H = 0.5 D

mm

55

80

127

170

255

X = 0.075 D

mm

8

12

19

25

38

Y = 0.175 D

mm

20

30

45

60

90

Z = 0.175 D

mm

20

30

45

60

90

F = 0.06 D

mm

6.5

9.5

13

20

30

G

mm

M3

M4

M5

M6

M8

I

mm

50.8

50.8

114.3

114.3

114.3

J

mm

0.4 x 45°

0.4 x 45°

0.4 x 45°

0.4 x 45°

0.4 x 45°

K

mm

4.2

4.2

4.2

4.2

4.2

R

mm

76.2

76.2

133.35

133.35

133.35

O

mm

6.6

6.6

10.3

10.3

10.3

20 000

14 000

10 000

6 000

4 000

Rotor mass M

Highest test speed

giri/min

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VIII - 169

b - Test rotors type B, for horizontal axis balancing machines

Suggested dimensions ,masses ,and speed for test rotors type B Rotor N°

1

2

3

4

5

6

7

kg

0.5

1.6

5

16

50

160

500

Major diameter D

mm

38

56

82

120

176

260

380

Overall length L = 2.5 D

mm

95

140

205

300

440

650

950

Shaft diameter d = 0.3 D

mm

11

17

25

36

58

78

114

Bearing distance 2D = A+B+C

mm

76

112

164

240

352

520

760

A, C = 0.5 D

mm

19

28

41

60

88

130

190

B=1D

mm

38

56

82

120

176

260

380

E = 0.25 D

mm

9.5

14

20.5

30

44

65

95

F = 0.5 D

mm

19

28

41

60

88

130

190

P1

mm

31

46

72

108

160

240

350

H

mm

-

-

-

4

1.4

1.8

2.2

K

mm

-

-

-

7

30

42

57

P2

mm

-

-

-

30

47

62

84

mm

M2

M3

Rotor mass M

M4

M5

M6

M8

M10

Critical speed = 7 600 000/D

giri/min 200 000 140 000

95 000

65 000

45 000

30 000

20 000

Highest test speed

giri/min

9 500

6 500

4 500

3 000

2 000

N

20 000

14 000

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VIII - 170

c - Test rotor type C (over hang test on horizontal axis balancing machines)

Suggested dimensions , masses, and speeds for test rotors type C Shaft N°

1

Rotor N° kg

Mass M Bearing load

2

3

4

5

1

2

3

4

5

2.2

6.2

19.5

60

190

A

N

-3

-8

-25

-75

-230

B

N

24

70

220

700

2100

Y

mm

20

30

45

65

95

d1

mm

17

25

36

58

78

d2

mm

21

30

45

65

95

d4

mm

50

72

106

156

230

M3

M4

M5

M6

M8

Major diameter D6

mm

110

160

230

345

510

Bearing distance l

mm

164

240

352

520

760

A

mm

41

60

90

140

203

N

40

60

90

120

180

Critical speed

giri/min

mm

25 000

17 000

14 500

8 000

5 500

Highest test speed

giri/min

4 000

2 800

1 900

1 300

900

B

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VIII - 171

8.2

Calibration control

The test is performed in order to verify if the machine is properly calibrated and the measured unbalance values are the right ones . The test or master rotor is to be used . When the rotor is mounted ,the geometric data related to the balancing planes are set up (a, b, c, R1, R2). The control is composed by :

a - Electric zero control With the pick up cables disconnected ,the measured unbalance is to be zero. ;it means that no noise comes from the electronics . In the modern microprocessor machines, this control is possible only by the use of special connectors which replace sensor cable (if cables are disconnected the machine stops and gives a warning message :cables pick up disconnected ).

b - Calibration control The measured unbalance ,for the test rotor ,should be zero or very low . When using vertical axis balancing machines ,even if the master rotor is balanced ,an unbalance value can be measured , because of the error which can be introduced by the mounting adapter .(tool unbalance or eccentricity ,look at chapter 3) ; as consequence , the mounting tool eccentricity compensation shall be used . Also on horizontal axis balancing machines ,small original unbalances can be found on the master rotor caused by the driving joint or by rotor journals not perfectly grounded (by changing the supporting points , the axis of rotation can change ). The plasticine is used to reduce , if necessary , the master rotor unbalance . Known masses (for instance 10 and 50 grams )are applied on the test rotor on the available different angular positions ,first on the plane one ,then on the plane number two . The calibration test is positively passed if all the measured values , satisfy the following criteria : •

The error on the measured unbalance is : ± 10%

•

The error on the position unbalance is : ± 3°

•

Maximum residual unbalance on the opposite plane (plane separation ) : 10% of the applied mass.

The error is calculated as : (measured value-nominal value ) / nominal value .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VIII - 172

8.3

Balancing machine test according to ISO 2953

ISO 2953 standards establish a way to verify the declared machine performances measured in two units :

U mar = minimum achievable residual unbalance [gr mm] which is normally calculated as E · M; where E = minimum achievable residual eccentricity [microns], or minimum achievable residual specific unbalance [gr mm/kg], M = rotor test mass.

U rr = unbalance reduction ratio (measured in %). The unbalance reduction ratio is a way to measure the machine calibration (the error on the measured value ,taking care that the unbalance is a vector) Both parameters are used to evaluate balancing machine performances and are influenced by : •

Machine mechanic features (eccentricity /surface finishing of the supporting rollers ,bearing clearances ,driving joint noises , etc..)

•

Measuring unit features (filtering capacity ,electric noises , etc. )

The first parameter is tied to the machine sensitivity and verifies the machine capability to balance a rotor within the declared residual unbalance .In the best conditions (test rotor ) the minimum residual unbalance ,obtainable because of the machine mechanics and electronics ,is verified . The second parameter is tied to the precision of the unbalance measure (in value and angle ) and practically gives an idea of the reduction on the original unbalance if the machine measurements are followed . For example a declared value of U rr = 95% means that ,if the unbalance correction is made according to the measurement without any error ,the original unbalance is reduced by 95% It specifies the measurement error Of the balancing machine The next table shows the plane positions 1, 2, 3 for the test masses and the positions I, II for the supporting positions of the different rotor types A, B, C.

Vertical axis balancing machine

type A

Horizontal axis balancing machine Rotor within supports Over hang rotor (shaft +rotor type A) type B type C

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VIII - 173

Test for verifying the declared value of Umar •

A test mass equal to 10 U mar is required

•

4 spins can be used to reduce the test rotor unbalance to a minimum value (below 1 0r 2 Umar )

•

The test mass is placed on the balancing plane N.3.

•

The rotor is spun and the unbalance measured on the planes I, II, .is recorded .

•

Measurements are repeated by placing the test mass on the all different angular positions.

•

The next table is filled up ; with the same values the next curve is drawn.

Note :Instead of one single mass ,two masses each one equal to 5 Umar , to be placed on the two planes 1 and 2 in the same angular position , can be used . (they are equivalent to the double mass placed in the intermediate plane N.3).

POSITION FOR THE TEST MASS Measured unbalance value

0°

30°

60°

90°

120° 150° 180° 210° 240° 270° 300° 330°

Left plane (lower plane) Right plane (upper plane)

Table containing the measured values obtained during the sensitivity test (Umar test ) on horizontal and vertical machines. (lower plane and upper plane refer to the vertical axis balancing machines).

Curve of the values registered on the previous table . The test is passed if all the sine curve points are kept within a range of (0,88 ÷ 1,12). Instead of drawing the above curve ,it is possible to calculate the average measured unbalance : Au = (Sum of the unbalance values )/12 The sensitivity test is passed if the maximum measured value is lower than 1.12xAu and the minimum measured value is greater than 0.88xAu

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VIII - 174

Test for verifying the declared value of Urr Twin double masses are required •

2 equal stationary masses Ustat having each one a mass value between 20 and 60 Umar

•

2 equal travelling masses Utrav having each one a mass equal to 5 Ustaz

•

The two stationary masses (Ustaz) are placed each one on an arbitrary and different angle ,one on the left one the right balancing plane .

•

The same thing is done for the two travelling masses (Utrav).

•

On the annexed table the following values are registered : positions of the test masses on the two planes and the related measured unbalance.

•

The unbalances values are measured after moving (clockwise direction for plane 1 and anticlockwise direction for plane 2) the travelling masses .

•

The unbalance measured values (11) ,together with test masses angular positions are recorded in the above mentioned table

•

The unbalance measured values (amplitudes )are then divided by Umar and the new calculated values are reported as single points in the annexed drawing .

•

The vector position reveals the achieved value for (URR) Please note that a not acceptable value for URR can be caused even only by an error on the measured unbalance angle position .

Note :

With over hang test rotors (type C) the stationary masses Ustaz are equal to 60÷100 Umar.

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VIII - 175

Table for URR test data

Date

Balancing machine model____________________________

Test rotor N°_________

Mass P = ________kg

Over hang test rotor N°_______________

Min. achievable eccentricity

e = _______μm

Unbalance radius

r = _______mm Stat.mass

Umar per plane = P ⋅ e

= ________gr

Mass

P= __________kg 25 Umar = __________gr 125 Umar __________gr =

Trav.mass

2r

Test mass angle Spin

Left plane

Right plane

Stationa Travelli ry ng

Stationa Travelli ry ng

Left plane Measured unbalance value g

Angle

Right plane

g S rmo

Measured unbalance value g

Angle

1 2 3 4 5 6 7 8 9 10 11

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

g S rmo

Cap. VIII - 176

Drawing to verify the obtained value for URR for two balancing planes .

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VIII - 177

8.4

Balancing machine control according to ISO 9000 standards .

A lot of companies ,using balancing machines ,are quality certified according to ISO 9000. The balancing machine , as every measuring instrument ,is to be checked and the quality manual clearly specifies all the steps required to verify the balancing machine and the time interval between each check.. The quality manual can require :

a - Calibration check made by the machine manufacturer or by a certified company

The company quality control manual must specify : 1) The name of the company taking care of the machine calibration control; 2) The procedure currently used for calibration check; 3) The time interval between each control (normally once per year , in special cases ,for instance nuclear or aeronautic industries ,every month or every six months ) . The technician verifies the machine calibration , if necessary makes the required modifications ,puts on the machine a stick certifying the calibration and its validity ,and provides an official calibration certificate .

b - Calibration check self made by the company quality control section

The quality control manual must specify :

1) The test rotor to be used , It ca be : 1.1) ISO test rotor (look 8.1),normally used for general purposes machines .. 1.2) Rigid rotor similar to the produced pieces (for instance a fan:, or a pulley or a brake disc ,etc. ). The used test rotor must have the following features : - Grounded and hardened supporting journals. - Test masses can be added on clear and fixed positions - Low value original unbalance. 2) Test masses to be used

The used test masses must be : - Certified as amount - Easily mounted and removed 3) The mounting position of the test rotor on the balancing machine supports The machine set up parameters a, b, c, R1, R2 are clearly specified together the value of the balancing speed to be used for the test ,if the machine is a variable speed one . On the modern balancing machines , the test rotor parameters are saved in a special program and recalled when necessary ..

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VIII - 178

4) Step by step operations , for example : -

Mount the test rotor on the balancing machine

-

Recall set up data from memory position N°1

-

Verify that the set up data are: a =100, b =300, c =100, R1= R2=100

-

Verify that the actual mounting position of the test rotor on the balancing machine is in agreement with the set up data

-

Spin the rotor slowly up to the demanded balancing speed

-

Verify that the test rotor original unbalance is very low ,if necessary using the eccentricity adapter compensation

-

Add the test mass n°1 (f.i. 10 grs. ) on the left balancing plane , on the radius R1 (on a random angular position )

-

Spin the rotor and write the unbalance measured values on the test table

-

Move the mass in the next available angle position ,and take a new reading

-

When all left positions have been used ,move the test mass on the right plane and repeat all the measurements

At each reading ,the measured values are written in the test table

5) Actions to be done , in case of negatives results (to call the manufacture after sale service ,for example )

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

Cap. VIII - 179

6 )Test certificate module An example is shown :

Balancing machine : Serial Nr. Test rotor Balancing speed Set up data

CEMB ZC 20/TC/6V 3000 ISO N.2 800 RPM a=28, b=56, c=28, R1=28, R2=28

Left plane

Right plane

Value [gr]

Angle

Value [gr]

Angle

0,2 0,4

28 –

0,1 0,4

33 –

9.9 9.8 9.8 10.1

1 89 181 270

0.3 0.4 0.3 0.2

24 80 160 200

10 ± 1

α±3

1

–

0.3 0.2 0.3 0.1

10 80 170 280

9.8 9.9 9.9 10.1

0 89 181 271

1

–

10 ± 1

β±3

Measured test rotor original unbalance Admitted values Measured unbalance values ,with the test mass N°1 (10 gr) placed on the left plane ,in sequence on the angular positions :. α =0 α =90 α =180 α =270 Admitted values Measured unbalance values with the test mass N°1 (10 gr) placed on the right plane , in sequence on the angular positions : β = 0 β = 90 β = 180 β = 270 Admitted values Test result :positive

Date : 30.11.98

Operator : Caio

Depending on the used test rotor ,the measurement points can be more ,because more angle positions are available . The same test measurements can be repeated with a different test mass ;in order to check machine calibration with a different unbalance The selected values for the two test masses can be related to the required tolerances (10 or 5 times ) and to the averaged measured unbalance . If all the measured values ,included in the above table ,are processed by using the normal statistic rules , in the case that the original test rotor unbalance is a small percent of the test masses and the number of readings are sufficiently high , the evaluation of the machine incertitude is possible (for statistic reasons it is possible to repeat the measure several times so that machine repeatability can be better evaluated .)

CEMB S.p.A. - Via Risorgimento, 9 - MANDELLO DEL LARIO (LC) - ITALY - tel. 0341/706111

REFERENCES

1)

ISO 1940 / 1, 2. Standards Balance quality requirements of rigid rotors.

2)

ISO 11342.Standards Methods and criteria for the mechanical balancing of flexible rotors.

3)

CEMB N. 3 technical book “Technical elements in balancing”, L. Buzzi

4)

CEMB N. 8 technical book “Balancing accuracy of rigid rotors”, L. Buzzi

5)

CEMB N. 19 technical book “Crankshaft balancing”, L. Buzzi - G. Manni

6)

Vibration theory and applications. W.T. Thomson

7)

CEMB N. 18 technical book “Cars wheels balancing”, L. Buzzi

8)

CEMB N. 23 technical book “Controllo delle vibrazioni nelle macchine in servizio”, L. Buzzi - G. Manni

9)

Dispensa tecnica CEMB “Wheels unbalance control”, G. Manni

10)

EUWA Standards ES 3.04 “Definition of static unbalance for car wheels”