DIN-Merkblatt: Flexible structures that support machines with rotating elements

UDC 62-218 .2 :62-13 :001 .4

April 198 8

DEUTSCHE NORM Machine foundations

~-

DI IV

Flexible structures that support machines with rotating elements

402 4 Part 1

Maschinenfundamente ; elastische Stützkonstruktionen für Maschinen mit rotierenden Massen

Supersedes DIN 4024 , January 1955 edition .

In keeping with current practice in standards published by the International Organization for Standardization (ISO), a comm a has been used throughout as the decimal marker. The DIN 4024 series of standards currently comprises the following Parts : DIN 4024 Part 1 Machine foundations ; flexible structures that support machines with rotating element s DIN 4024 Part 2 (at present at the stage of draft) Machine foundations ; rigid structures that support machines wit h periodic excitatio n In this standard, the term'load' is used for forces acting on a system from the outside ; this applies equally to compoun d terms that include the component 'load' (cf . DIN 10rß,0 Part 1) .

c

Contents Pag e

Pag e

1 Scope and field of application

2

2 Concepts 2 .1 Vibration 2 .2 Types of vibration 2 .3 Damping 2 .4 Action-effects 2 .5 Model 2 .6 Machinery 2 .7 Types of foundation

2 2 2 2 3 3 3 3

3 Materials and ground 3 .1 Reinforced concrete 3 .2 Steel 3 .3 Ground 4 Loads 4 .1 Machinery 4 .1 .1 General 4 .1 .2 Static loads 4 .1 .3 Dynamic loads 4 .2 Foundation 4 .2.1 Permanent loads 4 .2.2 Imposed loads 4.2.3 Creep and shrinkage of reinforced concrete 4 .2 .4 Effects of temperature, wind and earthquakes 5 Design 5 .1 General 5 .1 .1 Objectives 5.1 .2 Static analysis 5 .1 .3 Dynamic analysis 5 .2 Model study 5 .2 .1 Principles 5 .2.2 Requirements

5 .2 .3 Simplified representation 5.3 Natural vibration 5 .3 .1 Natural frequencies and modes of vibration 5 .3 .2 Assessment of vibration behaviour on the basis o f natural vibration 5 .4 Analysis of vibration due to unbalance 5 .4 .1 General 5 .4 .2 Foiced vibration 5 .4 .3 Natural modes of vibration 5 .4 .4 Equivalent-load method 5.5 Analysis of transient vibration 5.5 .1 General 5 .5 .2 Short-circuit 5.6 Loads on the foundation and ground

5 6 6

6 Further design criteria 6.1 Design action-effects 6.2 Reinforced concrete foundations 6.3 Steel foundations 6.4 Ground

8 8 8 8 8

7 Detailing 7 .1 Reinforced concrete foundations 7 .1 .1 Table foundations 7 .1 .2 Spring foundations 7 .1 .3 Slab foundations 7 .1 .4 Platform foundations 7.2 Steel foundations 7 .2 .1 Table foundations 7 .2 .2 Spring foundations 7 .2 .3 Platform foundations 7 .2 .4 Corrosion protection

9 9 9 9 9 9 9 9 10 10 10

Standards and other documents referred to

10

6 7 7 7 7 7 7 7 8 8

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Beuth Verlag GmbH, Berlin, has the exclusive right of sate for German Standards (DIN-Normen) . 12 .90

DIN 4024 Part 1

Engl,

Price group 8 Sales No . 0108



Page 2 DIN 4024 Part 1

1 Scope and field of applicatio n This standard specifies requirements for steel or reinforce d concrete structures that support mechanical system s ('machine foundations', for short) . Such mechanical systems are understood to be machinery with mainly rotatin g elements, the foundations of which are capable of generat ing flexural vibration in at least one plane . For the purpose s of this standard, a distinction is made among the followin g types of machine foundation : a) b) c) d)

table foundations ; spring foundations ; slab foundations ; platform foundations .

Figure 2 . Periodic vibratio n

The requirements specified here are intended to preven t the static and dynamic loads from transmitting unacceptable vibration to the environment or causing damage to th e machinery and its foundation . This standard establishes criteria for determining vibration behaviour, deals wit h design action-effects, and covers principles of constructio n based on experience to date with machine foundations .

2 .2 .2 Harmonic vibratio n Harmonic vibration is a periodic vibration process in whic h a quantity, q, is a sinusoidal function of time (see figure 3) , this being expressed by the following formula :

t

q( ) = 4 sin (wt + (po)

2n

2 Concept s

w=,

2 .1 Vibratio n For the purposes of this standard, vibration is a process i n which a mechanical quantity,q,varies as a function of tim e (see figure 1), alternating at least once between a minimu m negative and a maximum positive (peak) value .

(2 )

,where r1 is the amplitude ; w is the angular frequency based on the equatio n

=

2nf ;

ro o is the zero phase angle .

Figure 3 . Harmonic vibratio n 2 .2 .3 Transient vibratio n Transient vibration is a temporary state during which th e peak values or the duration of vibration are not stead y (e .g .when the machine is turned on or off,when a vibratio n process starts or ends, or during short-circuit) .

Figure 1 . Vibratio n

The mechanical vibration quantities of concern are : a) displacement (e .g . deflection, deformation) ; b) vibration velocity ; C) vibration acceleration ; d) restoring forces and moments (associated with dis placement) ; e) damping forces and moments (usually associated wit h vibration velocity) ; f) inertia forces and moments (in proportion to the vibration acceleration) ; g) external forces and moments ('excitation') . 2 .2 Types of vibratio n 2 .2 .1 Periodic vibratio n Periodic vibration is a process in which the magnitude o f a quantity, q, periodically varies with time (see figure 2) , this being expressed by the following formula : q(t) = q(t+nT)

(i )

where n is a whole number and T is an increment of tim e The reciprocal of T, in s, is the frequency, f, in Hz .

2 .2 .4 Free vibratio n Free vibration is that which results when a linear system i s excited once, i .e . any loads varying with time cease to act on the system . This process involves system-related natura l modes of vibration and the associated natural frequencies , the lowest of which being referred to as the fundamenta l natural frequency. 2 .2 .5 Forced vibratio n Forced vibration is a state of vibration caused by externa l forces that vary with time . 2 .3 Dampin g Damping is a system characteristic by which kinetic energ y is dissipated and either irreversibly converted to othe r forms of energy, particularly heat, or conducted away to th e environment . The forms of damping of concern are : a) material damping,where the damping force is given by : Po =

~~x

(3)



DIN 4024 Part 1 Page 3 or, when allowing for stiffness : FD = kB c •

x

(4)

b) viscous damping,where the damping force is given by : FD =dv•z

(5 )

or, when allowing for stiffness :

j'u = kv•c•,z

(6 )

The quantities used to characterize the damping are : a) damping factor (Lehr damping factor), D 1 ) dB

D=

(7 )

2•Sl c• m k13

D

C

2 ~

m

D=

dv 2 c• m

D=

2

m

(8 )

(9 ) (10)

b) logarithmic decremen t A=

2rL• D

(11 )

1•-D 2 where, in equations (3) to (11) , is the excitation frequency, S2 dß, dv'), kn t) and kv are damping characteristics (quantities with different units) , c is the elastic (spring) constant (of a single-degree-of-freedom system) , in is the mass (of a single-degree-of freedom system) , is the vibration velocity. z

2.4 Action-effect s

2 .6 .4 Balanced quality The balanced quality of a system is a measure, Q, of the roto r unbalance, expressed as Q = e • Q,where a is the eccentric ity of the rotor (cf.VDI 2060) . 2 .6 .5 Driving momen t The driving moment is the torque at the input of a drive n machine (e .g . a turbine) . 2 .6 .6 Output momen t The output moment is the torque at the output of a drivin g machine (e .g . a generator) . 2 .6 .7 Vacuum forc e Vacuum forces are static loads that result when vacuum i n the condensor of a steam turbine is produced . 2 .6 .8 Terminal short circuit and loss of synchronisatio n Terminal short circuit and loss of synchronisation ar e transient malfunctions that occur as a result of a rapi d change in the magnetic forces in the air gap of an electri c machine .

2.7 Types of foundation 2 .7.1 Machine support A machine support is a flexible structure in the form o f a slab or a configuration of beams on which the machin e systems rests and is anchored . 2 .7.2 Table foundatio n A table foundation consists of a slab placed on props tha t are usually arranged in pairs. The props usually rest on a reinforced concrete base, the latter resting on the ground . 2 .7.3 Spring foundatio n A spring foundation is made up of spring elements, usuall y consisting of several prefabricated springs having defined spring constants, and the supporting structure, which i s defined as the structure beneath the spring elements , including the ground .

Forthe purposes of this standard, action-effects are forces , moments and quantities of displacement that occur as a result of static or dynamic loading .

2 .7.4 Slab foundatio n A slab foundation is made from reinforced concrete an d rests directly on the ground .

2.5 Mode l

2 .7.5 Platform foundation A platform foundation is a construction that is made o f slabs or beams,on which the machine system directly rests , and that is integral with a multi-storey structure .

For the purposes of this standard, a model is a representation of the actual mechanical system, used for the calcu lation of essential system characteristics . Each possibl e independent displacement of a material point or a model element, within a spatial configuration, is defined as a degree of freedom . Where vibration in any one coordinat e influences vibration in other coordinates, the system may be represented by several, mutually independent model s ('decoupling') .

2 .6 Machinery 2 .6 .1 Service frequency (rotational speed ) The service frequency is the rotational speed under servic e conditions, expressed in s -1 (or in min-1 ) . 2.6.2 Service frequency rang e The service frequency range is the range of rotational speeds under service conditions . 2 .6 .3 Excitation frequency Excitation frequency is the frequency at which dynami c loads act on the system . It is often the same as the servic e frequency.

3 Materials and .groun d 3 .1 Reinforced concrete Concrete of at least strength class B25 as specified i n DIN 1045 shall be used . For the dynamic analysis, the static moduli of elasticity a s given in DIN 1045 maybe assumed . Where precise information about the damping characteristics is not known, th e damping factor, D, of the entire system (machine plu s foundation) may be assumed to be 0,02. Where stiffness related viscous damping is a factor, kv should be selecte d so that D is less than or equal to 0,02 at the highest calculated natural frequency, f . (see subclause 5 .3) . For loa d cases that involve significantly higher loading than tha t during normal service, a higher damping factor may b e assumed . t ) in the relevant literature, the symbol0 is used forD,k or b for dv, and V for kB .

Page 4 DIN 4024 Part 1 Reinforcing steel, suitable for loads that are not predominantly static, shall be used formembers subject to dynami c loads ; the reinforcement of such members shall not b e made from smooth reinforcing steel . 3 .2 Stee l Steel of at least grade St 37-2 as specified in DIN 17 100 shal l be used . For the dynamic analysis, the static moduli of elasticity a s given in DIN 18800 Part 1 may be assumed . Where precise information about the damping characteristics is not avail able, stiffness-related material damping may be assumed , as well as a damping characteristic, hß, equal to 0,02 . For load cases that involve loading significantly higher tha n that during normal service, a higher damping factor may b e assumed . 3.3 Groun d For the dynamic analysis, the resiliency of the ground nee d only be considered in special cases (cf . subclause 5 .2) , except for slab foundations, where the resiliency must b e considered . It may, however, be advantageous to conside r the damping of the ground . The dynamic characteristics of the ground (e .g . shea r modulus and Poisson's ratio) can only be determined b y field or laboratory measurements . Since measured value s tend to be widely dispersed, calculation of the dynami c loading should be based on limit values forthese quantities , which can be found in the relevant literature, [1] to [3] ,

4

Loads

4 .1 Machinery 4 .1 .1 Genera l The machine manufacturer shall provide the following infor mation : a) erection loads ; b) loads during normal service ; C) loads during malfunction ; d) service frequency and service frequency range ; e) any thermal effects of the machine or the ancillar y equipment on the foundation . The static and dynamic loads in each of the above case s shall be given separately . If the machine manufacturer requires the foundation to b e of a particular stiffness, the above load information shall b e stated in the form of displacement values which are not t o be exceeded . If vibration is to be restricted (to prevent damage to th e machine .and its ancillary equipment), even in the case o f malfunction, the manufacturer shall provide relevant limi t values . 4 .1 .2 Static load s The following are static loads during normal service : a) the mass of the rotors and the machine casing ; b) the mass ofthe condensers, depending on howtheyar e erected and the amount of water they contain ; C) the vacuum force in a turbine whose condensors ar e connected to the turbine casing via compensator s (both vertical and horizontal) ; d) the machine's driving and output moments that act o n the foundation via the casing (vertical pairs of forces) ; e) friction loads on the bearing faces (predominantly horizontal), caused by the thermal expansion of the casing :

f)

loads due to the mass of the ancillary equipment an d the effective forces and moments (that act both vertically and horizontally), e .g . thermal expansion, flo w forces and vapour pressure ; g) thermal effects from the machine and its ancillary equipment. In the case of turbines, a difference in temperature o f 20K across the foundation cross section may b e assumed, unless otherwise specified by the machin e manufacturer. Erection loads are generally transient mass loads that d o not occur during normal servive, and include the load s resulting from erection equipment and lifting gear . 4.1 .3 Dynamic load s The following are dynamic loads during normal service : a) bearing forces (both vertical and horizontal), resultin g from rotor unbalance, depending on the rotationa l speed ; b) periodic operating loads, resulting from the particula r machine performance, that act on the foundation vi a the casing orthe bearings, e .g. forces at twice orsevera l times the rotational frequency of single-phase a .c . machines or biowers,forces from the casing at twice th e mains frequency of a three-phase machine, or slip frequency magnetic forces from an induction machine ; C) forces and moments that result from turning th e machine on or off, or other transient situations (e .g . those associated with the operation of shock converters or occurring during synchronization) . The major dynamic loads that result from malfunction are : a) an increase in the periodic bearing loads in the case o f exceptionally high rotor unbalance caused, for example , by blade breakage or rotor distortion ; b) terminal short circuit or loss of synchronization in th e generator or motor ; C) shock to pipes or fittings upon emergency shut-down . 4 .2 Foundatio n 4 .2.1 Permanent load s The design values of the self-weight of the structure shall b e determined in accordance with DIN 1055 Part 1 . 4.2 .2 Imposed load s Imposed loads need not be considered for the structure a s a whole, but the individual members shall be designed t o carry particular imposed loads, these being the subjec t of agreement among the machine manufacturer, the foundation designer and the client . Unless otherwise specified , an imposed load of 5 kN/m 2 shall be assumed . 4 .2 .3 Creep and shrinkage of reinforced concret e Shrinkage of reinforced concrete shall be considered, a s set out in DIN 1045, and no allowance shall be made fo r creep (cf . subclause 7.1) . 4 .2 .4 Effects of temperature, wind and earthquake s Where the effects of temperature, wind and earthquake s need to be considered, refer to the relevant standards (e .g . DIN 1045, DIN 1055 Part 4 and DIN 4149 Part 1) .

5 Desig n 5 .1 Genera l 5 .1 .1 Objective s Machine foundations are intended to accommodate th e static and dynamic loads from the machine .They should b e designed on the basis of machine movement during normal

DIN 4024 Part 1 Pag service (i .e . the minimum performance requirements to b e satisfied), and to prevent unacceptable vibration fro m being transmitted to the environment.This can be assesse d on the basis of the vibration amplitudes of rotors, especiall y at the bearings, and the associated vibration and forces . Any effect that malfunction has on the foundation shall no t impair subsequent machine performance under servic e conditions . To verify compliance with these general requirements, a static and dynamic analysis shall be made, instead of calcu lations . 5 .1 .2 Static analysi s The static analysis of machine foundations, i .e . analysis o f the action-effects of the system under static loading, shal l be based on specified load cases (cf .subclause 6 .1) for th e machinery (cf. subclause 4 .2.1) and for the foundatio n (cf. subclause 4 .2) . Since such an analysis is the same a s that made for similar structures, it is not dealt with here . Compliance with any limit displacement values specified by the machine manufacturer under defined load condition s (cf. subclause 4 .1 .1) shall be verified . In the case of machine foundations made from reinforce d concrete, deformation due to creep may be limited b y means of a suitable structural design (cf . subclause 7.1) . Where thermal effects are to be considered in the analysis of reinforced concrete foundations, the 2nd moment o f effective cross-sectional area may be assumed to be equa l to 0,3 1 . The static analysis of steel machine foundations ma y generally be limited to a determination of the suppor t reaction, as the vibration load on such foundations is low. 5 .1 .3 Dynamic analysis Dynamic analysis of machine foundations serves to asses s vibration behaviour and to determine the action-effect s of the system under dynamic loading. It is to be based o n a model of the entire system that has largely linear charac teristics and several degrees of freedom . The metho d of assessment of the vibration behaviour (displacement) and of determining dynamic forces will depend on whethe r dynamic excitation forces are to be considered or not . Where excitation forces are not considered, predicting th e vibration behaviour may be based on a comparison o f the calculated natural frequencies of the machine with it s excitation frequencies, and then assessing the excitatio n potential of these natural modes . The action-effects ca n then be determined by assuming analogous maximum dis placement values based on the natural modes established . Where excitation forces declared by the machine manufac turer are used in the calculation, or where such ar e assumed, predicting the vibration behaviour and determin ing the action-effects may be based on an analysis o f forced vibration, in which case natural vibration is also to b e determined . Dynamic analysis and consideration of the dynamic component in subsequent calculations may generally b e dispensed with if the mass of the rotating elements .is les s than one one-hundredth of the mass of the entire syste m (machine plus foundation) . (Note that for platform foundations, the foundation is understood to comprise only thos e members which are directly loaded .) Otherwise, in the cas e of systems whose elements run at different rotational speeds,theirexcitation unbalance at any one speed mayb e neglected if the sum of the masses of the individual elements is less than one one-hundredth of the mass of th e entire system .

5 .2 Model stud y 5 .2 .1 Principle s A model is intended to facilitate analysis of the vibrat i behaviour of the entire system (machine plus foundati c The system is represented by a linear-elastic model hav i distributed or concentrated masses on spring supports .T excitation source,as well as system characteristics suc h mass, stiffness and damping, are to be included so as permit a sufficiently accurate assessment . 5 .2 .2 Requirement s The model usually consists of beam elements in whi p shear and torsion deformation have been accounted f Rotation inertia maybe neglected . In the case of reinforce concrete, the 2nd moments of area of the cross-sectio n areas may be determined for the cross section exhibiti r no cracks (state 1) . The distribution of mass may eit h be represented realistically, or the mass assumed to t distributed at different points . It should be noted, howeV E that if calculation is based on distributed masses, t h required accuracy can be achieved with substantially few ( degrees of freedom than with concentrated masses . I the case of reinforced concrete foundations, the machi n shaft and casing may usually be seen as static ; for ste ( and steel/concrete composite foundations, a more preci s analysis should be made . Each model point (node) has up to six degrees of freedo n i .e. three translational and three rotational . The number o degrees of freedom that need to be considered in a parti c ular case cannot be specified here . The numberof nodes required and the numberof degrees o freedom 'to be assigned to them depends on sever a factors, including : a) the geometry of the entire system ; b) the type of vibration to be investigated (vertical, hor i zontal or torsional) ; c) the relevant frequency range ; d) the calculation method selected . If the system is symmetrical with respect to the vertical centre plane in the longitudinal direction, it will have sym • metric and antimetric natural modes of vibration that ca n be calculated using models that represent each half o f the system . The relevant frequency range, .i .e. the range of natural frequencies that approaches the service frequency , will affect the minimum number of translational degrees o f freedom that need not be considered .This number should be greater than twice the order of the highest natural frequency in the relevant frequency range . Damping maybe neglected when calculating natural vibration, but should be considered when calculating force d vibration . Where it is necessary to consider the resiliency of th e ground (cf. subclause 3.3), the continuous resiliency ma y be represented by a number of springs . 5 .2 .3 Simplified representatio n The foundation usualiydoes not need to be represented in a spatial configuration . Rather, it may be represented b y models of the individual components, one each for translation and rotation in the two vertical planes and in the hori zontal plane, The rotational component may often b e dispensed with . For consideration of horizontal vibration, the foundatio n may generally be assumed to be decoupled from the sup port and to be laterally retained by springs . For table foundations, the natural flexural vibration of th e props maybe calculated separately from the entire system .



Page 6 DIN 4024 Part 1 The following simplifications are permitted for the calculation of vertical vibration . a) Where the flexural strength of the spring-supporte d system is high relative to the stiffness of the spring sup ports, i .e . where 13 .

1

mo Co Model

m„ CB

ct

i

(12 )

E -1

is less than or equal to 50 (see figure 4), the n - it maybe assumed that the flexural system is rigid fo r calculation of the natural frequencies generated b y the spring supports, o r - the spring supports maybe neglected forcalculatio n of higher natural frequencies . b) In the case ofspring foundations,where the stiffness, cu , of the supporting slabs, beams or other supports is a t least ten times the stiffness, cF, of the spring elements , i .e. where CUICF is not less than 10, then the foundatio n may be assumed to be separate from the support and t o consist of a configuration of beams resting on sprin g elements . For calculation purposes, this means that the resiliency , cu, of the foundation, as well as the effect of its mass , can be neglected . C) The effect of the ground and that of the mass of th e foundation may usually be neglected, provided one o f the three following conditions is met (see figure 5) . c t : The lowest natural frequency, f t , of the foundatio n plus machine (mass rrrn) on the spring support , where the foundation (mass nij is assumed to b e rigid, is at least 20% lower than the lowest servic e frequency, fn, . C2: The lowest natural frequency, f,, of the entire system,assumed to be a rigid bodyvibrating on flexibl e ground,is at least 20%lowerthan the lowestservic e frequency, f,,, . , C3: The lowest natural frequency, f t , of the foundation a s such,assumed to be rigid, is at least 25%lowertha n the lowest natural frequency, fB , of the foundatio n as such, assumed to be rigid and on flexible ground . l Mode l

E• I Ct

r.

C2

C3

i

. f

t

---------- --- - - -

.~

When calculating ft and f2, E • I shall be assume d to approach infinity.

~.

\

r~'

f3

When calculating fn,with larger than 2, c ; shall be assumed to be zero .

`'~ - - -~

f4

Ct )

f

t

=

t -~ V I.

2~n

f

f

m

f >02fm C2)

t

fj= 2n

CB

m,•m

fm

ft

f

~ Z02fm

C3)

j

= 2-I-~

f

~,

m,

1 fB= 2; n

Ce

m

f

+---

? 0,25 fB Figure 5. Simplification c)

ft

fB

5.3 Natural vibratio n 5 .3 .1 Natural frequencies and modes of vibratio n The natural frequencies ft to & and the modes associate d with them shall be calculated in ascending order. The number of natural frequencies and modes to b e established shall be selected so that the highest natura l frequency calculated is at least 10%higherthan the servic e frequency. This requirement may be dispensed with in th e case of foundations for machines with high service frequen cies (i.e . where fn, > 75Hz) ; however, depending on th e analysis model, the number of natural frequencies to b e calculated, n, shall comply with the following : a) n =10 for two-dimensional models in which onlyvertica l displacements are considered and in which symmetri c and antimetric vibration are not decoupled ; b) n = 6 for two-dimensional, symmetrical models in whic h onlyvertical displacements are considered and in whic h symmetric and antimetric vibration are decoupled. 5 .3 .2 Assessment of vibration behaviour on the basis of natural vibratio n An assessment of the vibration behaviour of a machin e foundation, in respect of the objectives given in sub clause 5 .1 .1, may, as a simplification, be based on the rela tionship of the natural frequencies, fn, to the servic e frequencies, fm . If both conditions land 2below are met for each decouple d model, subsequent analysis may be dispensed with , 1. First order natural frequency ft z 1,25•fm (13 ) or (14 ) ft s 0 8 • fn, 2. Higher order natural frequencies a) Higher order natural frequencies that approach th e service frequency : 1

A

S 0 . 9 -/m and

Figure 4 . Simplification a)

fn + 1 Z 1,1 • f m

(15 )



DIN 4024 Part 1 Page 7 b) if condition 2a is not met,it shall suffice that fn is less than f,,, where n is equal to 10 or 6 (cf. sub clause 5.3 .1) .

the two adjacent natural frequencies, provided that they li e within the specified range and that the magnitude of th e excitation force is kept constant .

Where conditions 1 and 2 are not met, a more precis e assessment of vibration behaviour can nonetheless b e attained by analyzing the excitation potential of the natura l modes of vibration . For this purpose, the highest natura l modes, assuming they lie within the frequency rang e defined by conditions 1 and 2 above, may be analyzed fo r the magnitude of the relative displacement, xi , ,, at th e bearings, i, of the machine shaft . Each natural mode ofvibra tion shall be checked separately for each bearing, i, for fulfilment of the following condition :

5.4 .3 Natural modes of vibratio n if calculating the displacement can be dispensed with, th e forces may be determined on the basis of the natura l modes of vibration adjacent to the service frequency, thi s being intended to simplify the analysis that would be required for forced vibration . On the basis of the natura l modes and the associated action-effects, for each membe r that incorporates a bearing, maximum amplitudes an d forces for the operative and malfunctioning states shall b e assumed, and the forces obtained by conversion . Fo r members that do not incorporate bearings, the action effects shall be determined by superimposing load dis placement curves . The following amplitudes, effective at the bearings, may b e assumed for the particular machine. group in accordanc e with VDI 2056 . a) Operative stat e The value associated with the operating frequency fo r the assessment criterion given in VDI 2056which is on e grade higher than that guaranteed by the manufacture r shall be taken as the amplitude under service conditions at the particular bearing . b) Malfunctioning stat e The amplitude in the case of malfunctioning shall b e assumed to be six times that values used for the opera tive state .

I xin •

2 fn 2

1

2