18424933 Metrology and Measurements
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Standards of Measurements The different types of standards of length are 1. Material Standards (a) Line Standard – When length is measured as the distance between centers of two engraved lines. (b)End Standard – When length is measured as the distance between to flat parallel faces. 2. Wavelength Standard The wavelength of a selected orange radiation of Krtypton-86 isotope was measured and used as the basic unit of length. International Prototype Meter International Prototype meter is defined as the straight line distance, at 0’c between the engraved lines of a platinum irridium alloy of 1020 mm of total length and having a tresca cross-section as shown in the figure. The graduations are on the upper surface of the web, which coincides with the neutral axis of the section. The sectional shape gives better rigidity for the amount of metal involved and is therefore economic in use for an expensive metal. Line and End Standards and differentiate between them. Line Standards – When length is measured as the distance between centers of two engraved lines, it is called Line Standards. Both material Standards, yard and metre are line standards E.g. Scale, Rulers, Imperial Standard Yard. Characteristics of Line Standards : (i) (ii) (iii) (iv) (v) (vi)
Scale can be accurately emblemed, but the engraved lines posses thickness and it is not possible to accurately measure Scale is used over a wide range Scale markings are subjected to wear. However the ends are subjected to wear and this leads to undersize measurements Scale does not posses built in datum. Therefore it is not possible to align the scale with the axis of measurement Scales are subjected to parallax errors Assistance of magnifying glass or microscope is required.
End Standards – When length is expressed as the distance between centers of two flat parallel faces, it is called End Standards. Slip Gauges, End Bars, Ends of micrometer Anvils. Characteristics of End Standards (i) (ii) (iii) (iv)
Highly accurate and used for measurement of closed tolerances in precision engineering as well as standard laboratories, tool rooms, inspection departments. They require more time for measurement and measure only one dimension. They wear at their measuring faces They are not subjected to parallax error.
Differentiate between Line and End Standards Sl no
Quick and easy
Effect of wear
Wear at only the ends Cannot be easily aligned low cost
Line Standard Length is expressed as distance between 2 lines Ltd. To ± 0.2mm.
Subjected parallax effect
End Standard Length is expressed as distance between 2 ends Highly accurate of closed tolerances to ±0.001mm Time consuming and requires skill wear at measuring surfaces easily aligned high cost not subjected parallax effect
Slip Gauges Slip Gauges are universally accepted end standards of Length in industry. Also known as Johnson gauges. Slip gauges are rectangular blocks of high grade steel with close tolerances. They are hardened throughout to ensure maximum resistance to wear. For successful use of slip gauges their working faces are truly flat and parallel. Most slip gauges are made from constant alloy which is extremely hard and wear resistance.
Wringing of slip gauges Wringing : Success of precision elements which can be made with slip gauges either by using it alone or in conjunction with other sample apparatus such as rollers, sine centers, sine bars, etc, depends on the phenomenon of wringing. The slip gauges are wrung together by hand by a combined sliding and twisting motion as shown. The gap between two wrung slip gauges is only of the order of 0.0065 microns, which is negligible. Procedure : (i) Before using, the slip gauges are cleaned (ii) One slip gauge is then oscillated slightly over the other slip gauge with a light pressure. (iii) One gauge is then raised at 90 degrees, to the other, and by using light pressure it is rotated until the blocks are in line. Principle of Interchangeability and selective assembly Interchangeability - It occurs when one part in an assembly can be substituted for a similar part which has been made to the same drawing. Interchangeability is possible only when certain standards are strictly followed. In universal interchangeability the mating parts are drawn from two different manufacturing sources. This is desirable. When all parts to be assembled are made in the same manufacturing unit, then local standards may be followed which is known as local interchangeability. Selective assembly - In selective assembly the parts are graded according to the size and only the matched grades of mating parts are assembled. The technique is most suitable where a close fit of two component assemblies is required. It results in complete protection against non-conforming assemblies and reduces machining costs since close tolerances are maintained. Different types of fits. When two parts are to be assembled, the relationship resulting from the difference between their sizes before assembly is called a fit. Clearance fit : In this type of fit, the largest permitted shaft diameter is smaller than the diameter of the smallest hole, so that
the shaft can rotate or slide through the different degrees of freedom according to the purpose of mating parts. Interference fit : It is defined as the fit established when a negative clearance exist between the sizes of the holes and the shaft. In this type of fit, the minimum permitted diameter of the shaft is larger than the maximum allowable diameter of the hole. In this case the hole members are intended to be attached permanently and used as a solid component Example : Bearing Bushes Transitional Fit : The diameter os the largest allowable hole is greater than that of the smallest shaft, but the smallest hole is smaller than the largest shaft and the hole. Example : Coupling Rings Wavelength standards and its advantages A major drawback wit the material standards, that their length changes with time. Secondly, considerable difficulty is expressed while comparing the sizes of the gauges by using material standards. Jacques Babinet suggested that wave length of a monochromatic light can be used as a natural and invariable unit of length. 7 th general Conference of Weights and Measures approved in 1927, approved the definition of standard of length relative to meter. Orange radiation of isotope Krypton-86 was chosen for the new definition of length in 1960, by the 11th General Conference of Weigths and Measures. The committee recommended Krypton-86 and that it should be used in hot cathode discharge lamp, maintained at a temperature of 63K. According to this standard metre was defined as equal to 165763.73 wavelengths of the red-orange radiation of Krypton-86 isotope. A standard can now be produced to an accuracy of about 1 part of 10^9. Advantages : (a)Not a material standard and hence it is not influeced by effects of variation of environmental conditions like temperature, pressure (b)It need not be preserved or stored under security and thus there is not fear of being destroyed. (c)It is subjected to destruction by wear and tear.
(d)It gives the unit of length which can be produced consistently at all times. (e)The standard facility can be easily available in all standard laboratories and industries (f) Can be used for making comparative measurements of very high accuracy.
CHAPTER – 2 SYSYTEM OF LIMITS, FITS, TOLERANCES AND GAUGING Definitions: Tolerance: Tolerance is defined as the magnitude of permissible variation of dimension from the specified value. They constitute an engineering legality for deviation from ideal value. Primary purpose of tolerances is to permit variation in dimensions without degradation of the performance beyond the limits established by the specification of the design. The tolerance is specified because it is impossible to have actual dimensions due to: • • •
Variations in the properties of the material being machined, introduce errors. The production machines have some inherence problems and limitations. Human effect, operator may do imperfect settings.
Tolerance may be unilateral or bilateral. Ex.: Unilateral: 25.000mm, 25.002mm (dia. of hole) 24.999mm, 24.997mm (die of shaft) OR 25.000 + 0.002 – 0.000mm (dia. of hole) 25.000 – 0.001 – 0.003mm (dia. of shaft) Bilateral 25.000 mm Basic size: The basic size is the standard size for the part and is the same for both the hole and its shaft. Ex. 50mm diameter hole and shaft. Nominal size: the normal size of a dimension of part is the size by which it is referred to as a matter of convenience (used for purposes of general identification). Often, basic and nominal sizes of a part of dimensions are used wish the same sense. Actual size: It is the measured size of part. Zero line: It is the line, which represents the base size so that the deviation from the basic size is zero. Hole above basic size. Hole of basic size.
Hole below basic size.
Fig.2.1 Limits: These are the maximum and minimum permissible size of the part. ‘Go’ Limit: It refers to upper limit of the shaft and upper limit of a hole. Corresponds to minimum material condition. ‘No Go’ Limit: It refers to the lower limit of the shaft and upper limit of the hole. Corresponds to min. material condition. Tolerance: The difference between the maximum and minimum limit of size. Grades of tolerance: It is indication of degree of accuracy of manufacture and is designated by IT followed by a number. Ex. IT01, IT0, IT1, ……… IT16
Fig.2. 2 Allowances: An intentional difference between the hole dimension and shaft dimension for any type of fit is called allowance. Deviation: Algebraic difference between a size and corresponding basic size.
fig.2.3 Upper deviation: Maximum limit of size – basic size. It is positive when maximum limit of size > basic size and vice versa. (ES for hole, es for shaft) Lower deviation: Minimum limit size – basic size positive when minimum limit of size > basic size and vice versa (EI for hole ei for shaft) Fundamental deviation: this is the deviation either the upper or the lower deviation, which the nearest one to the zero line (for both hole or a shaft). Fits: When two parts are to assemble, the relation resulting from the difference between the size before assembling is called fit. Basic size of a fit: It is that basic size which is common to the two parts of a fit. Variation of a fit: This is arithmetical sum of tolerances of the two mating parts of fit. Clearance: This is the difference between the size of the hole and shaft, before assembly, when the difference is positive (i.e. shaft smaller than the hole). Interference: This is the arithmetic difference between the sizes of the hole and the shaft before assembly, when the difference is negative. Type of fit: Depending upon the actual limits of the hole or shaft, fits may be classified into the following 3 categories.
Clearance fit Interference fit Transition fit
Fig.2. 4 Clearance fit: In this type of fit, the largest permitted shaft diameter is smaller than the diameter of the smallest hole, so that the shaft can rotate or slide through the difference degrees according to purpose of mating members Ex. Bearing and shaft. Interference fit: In this type of fit, the minimum permitted diameter of the shaft is larger than the maximum allowable diameter of the hole. In this case the shaft and the hole members are intended to be attached permanent and used as a solid component but according to the application of this combination, this type of fit can be varied. Ex. Bearing bushes, which are in interference fit in their housing Ex. The small end of the connecting rod in an engine. Transition fit: In this type of fit, the diameter of the largest allowable hole is greater than that of the smallest shaft, but the smallest hole is smaller than the largest shaft, so that small positive or negative clearance between the shaft and hole members employable. Location fits Ex. Spigot in mating holes, coupling rings and recesses are the examples of transition fit. Note: Minimum clearance: In the clearance fit it is the difference between the minimum size of the hole and the maximum size of the shaft. Maximum clearance: In a clearance or transition fit it is the difference between the maximum size of hole of the minimum size of the shaft. Minimum interference: It is the difference between maximum size of hole and the minimum size of shaft in an interference fit prior to assembly.
Fig 2. 5 Maximum interference: In an interference fir or a transition fit it is the difference between the minimum size of hole and the maximum size of shaft prior assembly. Hole based system: This is one which the limits one the hole or kept constant and the variations necessary to obtain the classes of fit are arranged by varying those on the shaft (Pl. note: Hole is kept constant) Ex. Assume a hole of dimensions 1. Shaft (S1) of 28 mm – Clearance fit 2. Shaft (S2) of 28 mm – Transition fit
fig.2. 6 Shaft (S3) of 28 mm – Interference fit Shaft based system: This is one which the limits on the shaft are kept constant and the variation necessary to obtain the classes of fit are arranged by varying the limits on the holes.
fig.2.2.7 Note: (1) From manufacturing point of view it is preferable to use hole-based system. Because holes are produced with standard tooling (reamers, drills) those size not adjustable and shaft sizes are readily variable. Thus hole based system results in considerable reduction in reamers and other previsions tools as compared to a shaft – based system. (2) Basic shaft: A shaft whose upper deviations is zero. (I.e. Max. lt. of size = Basic size) (3) Basic hole: A hole whose lower deviation is zero. (I.e. Min. lt. of size = Basic size) Principles of inter-changeability: Today mass production techniques are adopted for economic production. This approach led to breaking up of a complete process into several smaller activities, which in term are specialized. As a result none of the manufacturing activity is self reliant with respect to components. Various mating components would undergo production on several machines. Hence it is absolutely essential to have a precise control over the dimensions of portions, which have to match with other part. "Any one component selected at random should assemble correctly with any other mating component, that too selected at random." When a system of this kind is ensured it is known as interchangeable system. Advantages or characteristics An operator can easily specialize since he is concerned with only a limited portion of work. (Improves quality)
Interchangeability ensures increased output with reduced production cost. Assembly time is reduced considerably. Decentralized production depending on the resources available can be achieved. (i.e. factories may be located suiting to availability of men, machine and materials). Note: Interchangeability is followed only when certain standards are strictly followed. When universal interchangeability is desired, the common standards are to be followed by all and all standards used by various manufacturing units should be traceable to single i.e. international standards. Universal or full interchangeability: This indicates that any component will match with other mating component without classifying manufactured components in sub group or without carrying out any minor alterations for mating purpose. This type of interchangeability is not a must for interchangeable production and many times not feasible also as it requires machine capable of maintaining high process capability and very high accuracy and also very close supervision on production from time to time (± 3 σ -> process capability is to be observed.) For full interchangeability only such machine, whose process capability is equal to an or less than the manufacturing tolerance allowed for that part should be selected. 2.2.18 Selective assembly: In this kind of production (assembly), the parts are manufactured to rather wide tolerances and function as though they were slowly manufactured in a precision laboratory to very close tolerance. In selective assembly the components products by machined are classified into several groups according to size. This is done both for hole and shaft and then the corresponding groups will match properly. Ex. If some parts are to assembled are manufactured to nominal tolerances of 0.01mm an automatic gauge can segregate them into ten different groups with 0.001mm limit for selective assembly. Characteristics: The parts obtained can be served with both high quality and low cost using selective assembly. The two component parts to be assembled must be kept with in the normal distribution i.e. mean value should be at desired calculated value and process capability of two machines producing shafts and holes must be identical otherwise for some components the mating components will not be available. Best and cheapest method of assembly of widely used in industries. Ex. Aircraft, automobile, ball bedding industries. This concept overcomes the drawback of scraping the ‘bad’ components after inspection, thus reducing the loss. Limit gauge: gauge are inspection tools of rigid design, without a scale, which serve to check the dimension of manufactured parts, Gauges do not indicate the
actual value of the inspected dimension on the work. They can only be used for determining as to whether the inspected parts are made with the specified limits.
Go – No go gauges: These are two gauges having basic size corresponding to the two limits of size for the component of used to check the dimensions of a component. The go gauge checks the maximum metal condition. The No-go gauge checks the minimum metal condition. Note: In case of hole the maximum metal condition is when the hole is as small as possible. In case of shafts the maximum metal condition is when the shaft is on the high limit of size. The difference between the basic sizes of the two gauges is equal to the tolerances on the component. If the size of the component is within the prescribed limits, the gauge made to the maximum metal limit will assemble with it, whereas the other will not. It for this reason the gauge made to the maximum metal limit is called the ‘Go’ gauge and that made to the minimum metal limit is called the ‘No Go’ gauge.
Note: closer attention must be paid to ‘Go’ gauges than is necessary with ‘No Go’ gauges because a component might be accepted even though the No-Go gauge assembles, under no circumstances should a component be accepted when the ‘Go’ gauge fails to assemble.
Taylor’s principle: Taylor postulated some rules for designing the form of gauges. When gauging a plain cylindrical plug gauges, the diameter of one, the Go confirming to the maximum metal limit of the hole and the diameter of the other the No-Go confirming to the minimum metal limit. If the go gauge enters while the no go fails to enter the hole is considered to be with in the specified limits.
Taylor’s principles may be stated as follows: The Go gauge should be as far as possible be the geometrical equivalent of the mating part and [(i.e. it should be able to check all the possible dimensions at a time (roundness, size, location etc)] Separate No-Go gauges should check the minimum metal condition of the dimensions of the component. No-Go gauge should check only one element of the dimension at a time. This is because a No-Go gauge designed to check more than one dimension would fail to detect any dimension out side the minimum metal limit if one of the dimensions is being checked within the minimum metal limit as illustrated below.
Fig.2.2.9 According to Taylor it is not adequate to use simple Go gauge on outer dimensions only but the shape is an important factor i.e. Go gauge should be full form gauge and it should be constructed with reference to the geometrical form of the part being checked in addition to its size. In other words go gauge should check all the dimensions of a work piece in the maximum metal condition. As regarding no go gauges, Taylor stated that it need not be of full form and each feature being dealt should be checked with a specific no go gauges. In other words no go gauge shall check only one dimension of the piece at the time for the minimum metal conditions.
Thus according to it, a hole should completely assemble with a go cylindrical plug gauge made to the length of engagement of the hole and shaft. In addition, the hole is measured or gauged to check that its maximum diameter is not larger than the no go limit. The Taylor principle interprets the limit of size for gauging holes and shafts as follows: For holes: The diameter of the largest perfect imaginary cylinder, which can be inscribed within the hole so that it just contacts the highest points of the surface. The diameter of the cylinder should not be less than the go limit of size further the maximum diameter at any position in the hole should not exceed the no go limit. For shaft: The diameter of the smallest perfect imaginary cylindrical which can be circumscribed around the shaft so that it contacts the highest points of the surface. The diameter of cylinder should not be larger than go limit of size. Further the minimum diameter At any position on the shaft should not be less than "No Go’ limit of size. Note: According the Taylor’s principle the ‘Go’ limit gauge should be a plug ring gauge with exactly ‘Go’ diameter and length equal to the engagement length of the fit to be made and this gauge must perfectly assemble with the work piece inspected. The No Go gauge should contact the work piece surface only at two diametrically opposite points and have exactly No Go diameter at these two points. The gauge should not be able to pass over in the work piece in any consecutive position in the various diametric directions on the work piece length. Variations from Taylor’s principle. In many applications Taylor’s principle cannot be blindly followed. Some of the deviations are allowed which basically do not deviate from the principles as such. For Go limit: it is not advisable to use full form and full length gauges which are bulky when the manufacturing process assures that the error of straightness will not affect the character to fit. Only segmental cylindrical bar could be used when gauge happens to be too heavy and when manufacturing process assures that the error in roundness will not have any effect on the character of fit. For shafts (heavy) full form ring gauge need not be used. The manufacturing process should take care of the error of roundness (especially lobbing) and error of straightness in such cases only gap gauges could be sufficient.
Fig.2.10 For No Go limit: only two point contact should be there according to Taylor but it is not feasible because these devices are subjected to rapid wear etc. Hence these can be safely replaced by small planes / cylindrical surfaces / spherical surfaces. For Gauging very small holes and in cases where work pieces may be deformed to an oral by a two point mechanical contact device, the No Go gauge of full form, may have to be used. Material for gauges: The material for gauges should fulfill most of the following requirements: Hardness to resist wearing. Stability to preserve size of form. Corrosion resistance. Merchantability for obtaining the required degree of accuracy Low co-efficient of linear expansion to avoid temperature effect. Ex. High carbon steel, case hardened mild steel, invar steel.
Wear Allowance: The measuring surfaces of ‘Go’ gauges, which frequently assemble with work, rubs constantly against the surfaces of the work. This result in wearing of the surfaces of the gauges of a result this loses initial dimensions. Thus due to wear ‘Go’ plug gauges size is reduced. Hence a wear allowance is added to the Go gauge in a direction opposite toe wear. Thus for a Go plug gauge the wear allowance will be added while in a ring or gap gauge the allowance is
Gauge tolerance or Gauge makers tolerance: Gauges like any other job, require a manufacturing tolerance, to compensate for imperfections in workman ship. This is known as gauge makers tolerance. There are 3 methods giving tolerances on gauges First system: (For workshop and inspection gauges) in this method, workshop and inspection gauges one made separately and their tolerance zones are different. According to this system the tolerances on the workshop gauge are arranged to fall inside the work tolerances, while the inspection any tolerances fall outside the work tolerances. In workshop gauges Go gauge should eat away 10% of work tolerance and similarly No Go gauges tolerance is 1/10th of work tolerance. In respection gauges, the gauges are kept beyond work tolerance by 10% of its value.
Disadvantages: The components may be rejected by workshop gauges by inspection gauges may accept them. The workshops of inspection gauges have to be made separately as their tolerances are different Second system: (revised gauge limits) Under this system reducing the tolerance zone of inspection gauge reduces the disadvantages of inspection gauges and the workshop gauge tolerance remains the same. In this system 110 of the range of work tolerance is covered instead of 120th as in the first system for inspection gauges.
Fig.2. 13 Third system: (Present British System) In this system following principles are followed along with Taylor’s principle. Tolerance should be as wide as is consistent with satisfactory functioning economical production and inspection. No work should be accepted which lies outside the drawing specified limits.
This system gives same tolerance limits on workshop and inspection gauges and the same gauge can be used for both purposes. The tolerance zone for the Go gauges should be placed inside the work limits and the tolerance for the No Go gauges outside the work limits. Provision for wear of Go gauges is made by the introduction of a margin between the tolerance zone for the gauge and maximum metal limit of the work.
Fig.2.15 Types of limit gauges: Limit gauges for internal diameters of holes
Full form cylindrical plug gauge: A small circumferential groove is cut near the leading end of the gauge and the remaining part of the cylinder is slightly reduced in order to act as a pilot.
Fig 2. 16 Full form spherical plug or disc gauge: Segmental cylindrical bar gauge:
Fig.2.17 Gauges for tapers: A taper is tested by using taper plug a or ring gauge. The important thing in testing a tapered job is to check the diameter at bigger end and the change of diameter per unit length.
CHAPTER - 3 Comparators Laboratory standards: comparators are used as laboratory standards from which Working or inspection gauges are set and co-related. Working gauges: they are also used as working gauges to prevent work spoilage and to maintain required tolerance at all-important stages of manufacture. Types of Comparators: The comparators differ principally in the method used for amplifying and recording the variation measured. Most commonly available comparators are of the following types: • • • • • • • •
Mechanical comparators Optical comparators Electric and electronic comparator machines Pneumatic comparators Fluid displacement comparator machines Projection comparators Multi-check comparator Automatic gauging
Application of Comparators: • • • •
Used as laboratory standards from which working or inspections gauges are set and correlated. Used, as working gauges to prevent work spoilage and to maintain required tolerance at all-important stages of manufacture. Used as final inspection gauges where selective assembly of production parts is necessary. Used as receiving inspection gauges for checking parts received from outside sources.
Advantages: • • • •
Not much skill is required on the part of operation. The calibration of instrument over full range is not required since comparison is done with a standard end length. Zero error existing in comparator also does not lead to any problem. High magnification resulting into great accuracy is possible.
Mechanical comparators use mechanical methods of amplifying the movement of the contact plunger and their manufacture requires high degree of accuracy. Usual magnification of the mechanisms ranges from about 250 to 1,000.
Mechanical Comparator: Sigma comparator is the most widely used for higher precision work. Magnification ranges from 300 to 5000. Figure shows the details of the magnifying system of the comparator. Plunger mounted on a pair of slit diaphragms obtains the frictionless linear motion. A knife-edge is mounted on it and bears upon the face of the moving member of a cross strip hinge. This hinge consists of the moving component and a fixed member, which are connected by thin flexible strips alternately at right angles to each other. A ‘Y’ arm is attached to the moving member which has an effective ‘I’. If the distance of the hinge from the knife-edge be ‘a’ then the magnification of the first stages is I/a. A phosphor – bronze strip is attached to the two extremities of the Y arm and is passed round a radius ‘r’ attached to the pointer spindle. The second stage magnification is R/r where R is the length of pointer. Then total magnification is I/a x R/r. The magnification can be altered by tightening one end slackening the other screw attaching the knife-edge to the plunger and thus adjusting the distance ‘a’. Some features of this instrument: • • • •
The shock will not be transmitted since the knife-edge moves away from the moving member of the hinge. A non-ferrous disc is mounted on the pointer spindle and it is made to move in field of a permanent magnet to obtain deadbeat reading. Parallax error is avoided by having a reflective strip on the scale. A magnet plunger on the flame and keeper bar on the top of the plunger is used to have the constant pressure over the range of the instrument.
Electrical Comparators: Electrical and electronic comparators depend on wheat stone bridge circuit for their operations. We know that for the bridge is to balance electrically the ratio of the resistance’s in each pair must be equal.
Fig 3.2 Electrical Comparator The principle of electrical comparator (electrical limit gauge) is explained with reference to the above figure. If alternating current is applied to the bridge, the inductance and capacitance of the arms must also be accounted for along with resistance. The pair of coils forms a pair of inductance. The movement of the plunger displaces an armature thus causing a variation in the inductance in the coils. The amount of unbalance caused by movement of measuring plunger is amplified and shown on a linear scale magnifications of about 30,000 are possible with this system. Zero setting arrangement is provided. The degree of magnification is adjustable and other examples of electrical comparators are electricator, electric gage and sigma electronic comparator. Advantages of Electrical Comparators: • • • • •
Remote indication is possible High magnification with smaller number of moving parts Insensitive to vibration and mechanism carrying the pointer is high The cyclic vibration reduces errors due to sliding friction on an AC supply Smaller measuring unit and several magnifications is possible with same instrument
Optical comparators: All optical comparators involve some system of magnification, generally through tilting of a mirror which provides an optical lever by reflecting a beam of light. The Cooke comparator works on this principle.
Cooke’s Optical Comparator
Fig 3.3 A plunger working in a head consists of a mechanical lever carrying two pivots at its ends. On one end a plunger actuates it and the other end actuates a mirror. A circular scale is provided. The mirror onto the scale accordingly reflects a beam of light coming through an electric bulb. Optical comparators are used in metrology labs and standard room, but not in routine production checking. The optical system offers the advantage of lightness & simplicity in its indicating unit. Pneumatic comparators: A pneumatic gauge consists of 2 important Units: • •
An air controller to regulate the pressure and the amount of airflow from the supply. The unit incorporates a manometer A gauging head designed for the work to be checked.
Air supply from the supply is fed into the instrument at pressure higher than the constant pressure required in the manometer. Air enters the tube extending downwards into a tank of liquid. Initially the tube is filled with liquid to the same level as that in the tank. Entry of air into the top of the tube exerts pressure on the liquid to completely empty it. Any excess pressure than that necessary to clear the tube will escape into the tank as air bubbles. The pressure between the valve V and the control jet G is therefore always the same, irrespective of any variation in the air supply pressure.
The air will now pass through the control jet at the full controlled pressure and will reach the measuring jet S. If this jet S cannot pass the full volume of the air from the control jet, then a pressure will tend to develop between them. The back pressure is instantly released through the opening into the manometer tube where it will change the height of the liquid, which indicates the amount of back pressure built up. The back pressure is the result of restriction at the measuring jet due to the effect of variations in the dimension of the work being checked so that the variations in the height of the liquid of the manometer are a measure of the dimension variations. Pneumatic Comparator
Fig 220.127.116.11 The pneumatic method is easily adaptable for the examination of bores, since the machining element can be housed inside the plug used for accommodating the component. This method is very simple and minimum wear of working parts takes place, but it requires a supply of air to provide the motive force.
Angular measurements and Interferometer Bevel protractors as per Indian standard practice. The bevel protractors are of two types. They are 1. Mechanical bevel protractor, and 2. Optical bevel protractor.
Mechanical Bevel Protractor The mechanical bevel protractors are further classified into four types; A, B, C and D. in types A and B, the Vernier is graduated to read to 5 minutes of arc whereas in case of type C, the scale is graduated to read in degrees and the bevel protractor is without Vernier or fine adjustment device or acute angle attachment. The difference between types A and B is that type A is provided with fine adjustment device or acute angle attachment whereas type B is not. The scales of all types are graduated either as full circle marked 0-90-0-90 with one Vernier or as a semicircle marked 0-90-0 with two Verniers 1800 apart. Type D is graduated in degrees and is not provided with either Vernier or fine adjustment device or acute angle attachment.
Fig 4.1 Optical bevel protractor: In case of an optical bevel protractor, it is possible to approximately 2 minutes of arc. The provision is made for scale, which is graduated in divisions of 10 minutes of arc. against a fixed index line or Vernier by means of an optical which is integral with the instrument.
take reading upto an internal circular Readings are taken magnifying system,
Fig 4.2 Clinometers : A Clinometer is a special case of application of spirit level. Here the spirit level is mounted on a rotary member carried in a housing. One face of the housing forms the base of the instrument. On the housing, there is a circular scale. The circular scale can measure the angle of base. The Clinometer is mainly used to determine the included angle of two adjacent faces of work piece. Thus for this purpose, the instrument base is placed on one face & the rotary body adjusted till zero reading of the bubble is obtained. The angle of rotation is then noted on the circular scale against the index. A second reading is then taken in a similar manner on the second face of the work piece. The included angle between the faces is the difference between the two readings. Clinometers are also used for checking angular faces, and relief angles on large cutting tools & milling cutter inserts. These can also be used for setting inclinable table on jig boring machines & angular work on grinding machines etc.. The most commonly used Clinometer is of the Hilger & Watts type. Precision Microptic Clinometer : These are also used for measuring angular displacements of small parts & setting out angles. The special features of Precision Microptic Clinometer are direct reading over the range 00-3600, optical reading system; totally enclosed glass circles & easy to read scales ; main scale & micrometer scale visible simultaneously in the eyepiece external scale for rapid coarse setting, slow motion screw for fine setting, eye piece rotatable to most convenient viewing position, & hardened ground steel base. Precision Microptic Clinometer utilizes bubble unit with a prismatic coincidence reader, which presents both ends of the bubble as adjacent images in a split field of view. As the vial is leveled, the two half images move into coincidence, making it very easy to see when the bubble is exactly centered, without reference to any graduation. To determine the inclination of the Clinometer, the bubble unit is levelled & scale is read. On looking through the reader eyepiece, the apertures can be seen. The upper aperture contains two pairs of double lines & two single lines; to set the micrometer the knob is turned until the single lines are brought exactly central
between the double lines. The scales can be read, the required angle being the sum of the readings of the main scale & the micrometer scale. The double lines are imaged from one side of circle & the single ones from a point diametrically opposite; by using the double lines as an index for the single line, any residual centering error of the circle is cancelled out. An integral low voltage lamp illuminates the scales. The bubble unit is day light illuminated, but is also provided with a lamp for alternative illumination. The reference for inclination is the bubble vial. In order to measure the inclination of a surface, the vial to which the circle is attached is turned until it is approximately level; then the slow motion screw is used for a final adjustment to center the bubble. To measure the angle between two surfaces the Clinometer is placed on each surface in turn & the difference in angle can be calculated. The Clinometer can be used as a precision setting tool to set a tool head or table at a specific angle also.
Fig 4.3 Optical Instruments for Angular Measurement: Autocollimator: This is an optical instrument used for the measurement of small angular differences. For small angular measurements, autocollimator provides a very sensitive & accurate approach. It is essentially an infinite telescope & a collimator combined into one instrument. 18.104.22.168 Principle of auto collimator: Auto collimator is an optical instrument of small angular differences. For small angular measurement, auto collimator provides a very sensitive and accurate approach. Auto collimator is actually a infinity telescope and a collimator combined into one instrument. The instrument is designed to measure small angular defection and may be used in conjuncture with a plane mirror or other reflecting device. If a scale is provided on the graticule the tilt of the reflecting
surface, so that a direct two to one reading is obtained. The light rays thus reflected are linearly displaced from the target by a amount of 20f.
Fig4.4 Figure shows the diagrammatic representative principle of a autocollimator. The gratitude GH is focused in the principal focal plane of the objective lens is illuminated from a suitable light rays parallel to the optic axis. If a reflecting mirror AA is situated at right angle to the optical axis, then the light rays will be reflected back on their original paths and the returned image of the object will coincide with the object at G. If the mirror is deflected about ‘O’ through an angle θ to the position BB’ and therefore to be at right angles to the optical axis, the graticule, an image of the object, giving a displacement x from G. the distance x is a measure of angle 2θ and which is twice the angle deflection of the mirror. If X distance traveled by the image from the initial position of the object.
F focal length of the lens. θ the angle of tilt of the reflecting mirror and considered to be small. Then, 2θ = x/f where x = 2fθ . The points to be noted are: 1. The position of the final image does not depend upon the objective lens. 2. If the reflector is completely moved back i.e. if θ become gauge, the reflected rays will completely miss the lens and no image will be formed. 3. For high sensitivities i.e. for large value of X for smaller angular deviation a long focal length is required. Autocollimator Applications : i. ii. iii. iv. v.
The measurement of straightness & flatness Precise angular indexing in conjunction with polygons Comparative measurement using master angles Assessment of square ness & parallelism of components Measurement of small linear dimensions
Angle Dekkor: This is also a type of an autocollimator. It contains a small illuminated scale in the focal plane of the objective lens. This scale in normal position is outside the view of the microscope eye piece as shown in the fig: The illuminated scale is projected as a parallel beam by the collimating lens which after a striking the reflector below the instrument is re-focused by the lens in the field of view of the eye piece. In the field of view of the microscope there is another datum scale fixed across the center of screen & the reflected image of the illuminated scale is received at right angle to this fixed scale & the two scales, in this position intersect each other. Thus the reading on the illuminated scale measures angular deviation from one axis at 900 to the optical axis & the reading on the fixed datum scale measures the deviation about an axis mutually perpendicular to the other two. In other words, changes in angular position of the reflector in two planes are indicated by changes in the point of intersection of the two scales. Readings from scale are read direct to 1’ without the use of a micrometer. The whole of the optical system is enclosed in a tube, which is mounted on an adjustable bracket. There is a lapped flat & reflective base on which all these things are placed. It is mostly used as a Comparator. The instrument measures by comparing the readings obtained from a standard, a sine bar or combination of angular gauges with that from the work under test. Though this is not a precise instrument in comparison to autocollimator, it has wide field of application for general angular measurement, as angular variations are read direct without the operation of a micrometer.
CHAPTER - 5 Screw Thread and Gear Measurement Terminology:
Fig 5. 1 Screw thread: a screw thread is the helical ridge produced by forming a continuous helical groove of uniform section on the external or internal surface of a cylinder or a cone. A screw thread formed on a cylinder is known as straight or parallel screw thread, while the one formed on a cone is known as tapered threads. External thread: a thread formed on outside of a work piece is known as external thread. Example: on bolts or studs etc. Internal thread: a thread formed on inside of a work piece is known as internal thread. Example: on a nut or female screw gauge. Multiple-start screw thread: forming two produces this or more helical grooves equally spaced and similarly formed in an axial section on a cylinder. This gives ‘quick traverse’ without sacrificing core length. Axis of a thread: this is imaginary line running longitudinally through the center of the screw. Hand (right or left hand thread): Suppose a screw is held such that the observer is looking along the axis, if a point moves along the thread in clockwise direction and thus moves away from the observer, the thread is right hand: and if it moves towards the observer the thread is left hand. Form of thread: this is the shape of the contour of one complete thread as seen in axial section. Crest of thread: this is defined as the prominent part of thread, whether it is external or internal.
Root of thread: this is defined as bottom of the groove between the two flanks of the thread, whether it is external or internal. Flanks of thread: these are straight edges, which connect the crest with the root. Angle of thread (included angle): this is the angle between the flanks and slope of the thread measured in an axial plane. Flank angle: the flank angles are angles between individual flanks and the perpendicular to the axis of the thread which passes through the vertex of the fundamental angle. The flank angle of a symmetrical thread is commonly termed as the half angle of thread. Pitch: the pitch of the thread is the distance, measured parallel to the axis of the thread, between corresponding points on the adjacent forms in the same axial plane and on the same side of the axis. The basic pitch is equal to the lead divided by the number of the thread starts. On drawings of thread sections, the pitch is shown as the distance from the center of one thread crest to the center of next, and this representation is correct for single start as well as multi-start threads. Lead: lead is the axial distance moved by the threaded part when it is given one complete revolution about it’s axis with respect to fixed mating thread. the uniformity of pitch measurement does not necessarily assure uniformity of lead. variations in either or pitch cause the functional or virtual diameter of thread to differ from the pitch diameter. Thread per inch: this is the reciprocal of pitch in inches. Lead angle: on straight threads, lead angle is the angle made by the helix of the thread at the pitch line with plane perpendicular to the axis. The angle is measured in actual plane. Helix angle: on a straight thread, the helix angle is the angle made by the helix of the thread at the pitch line with the axis. the angle is measured in an axial plane. Depth of thread: this is the distance from the crest or tip of the thread to the root of the thread-measured perpendicular to the longitudinal axis. This could also be defined as the distance measured radially between the major and minor cylinders. Axially thickness: this is the distance between the opposite faces of the same thread measured on the pitch cylinder in the direction parallel to the axis of the thread. Truncation: a thread is sometimes truncated at the crest or at the root or at both crest and root. Truncation at crest is the radial distance from the crest to nearest apex of the fundamental triangle. Similarly the truncation at the root is the radial distance from the root to the nearest apex.
Addendum: for an external thread, this is defined as the radial distance between the major and pitch cylinders. For an internal thread this is the radial distance between the minor and pitch cylinders. Dedendum: this is radial distance between the pitch and minor cylinder for an external thread and for internal thread, this is radial distance between the major and pitch cylinders. Major diameter: in case of a straight thread, this is the diameter of the major cylinder (imaginary cylinder, coaxial with the cylinder, which just touches the roots of an internal thread). It is often referred to as root diameter or cone diameter of external threads. Effective diameter or pitch diameter: in case of straight thread, this is the diameter of the pitch cylinder (the imaginary cylinder which is coaxial with the axis of the screw and intersects the flank of the threads in such a way as to make the width of the threads and width of the spaces between the threads equal.). If the pitch cylinder were imagined as generated by the straight line parallel to the axis of the screw that straight line is referred to as pitch line. Along the pitch line the widths of the threads and the widths of the spaces are equal on a perfect thread. This is the most important dimension as it decides the quality of the fit between screw and nut. Functional (virtual) diameter: for an external or internal thread, this is the pitch diameter of the enveloping thread of perfect pitch, lead and flank angles having full depth of engagement but clear at crest and root. This is defined over a specified length of thread. This may be greater than the effective diameter by an amount due to errors in pitch and angle of thread. The virtual diameter being the modified effective diameter by pitch and angle errors is the most important single dimension of a screw thread gauge. In case of a taper screw thread, the cone angle of taper, for measurement of effective diameter and whether the pitch is measured along the axis or along the pitch code generator also needs to be specified. Errors in threads: In case of plain shafts and holes, there is only one dimension, which has to be considered, and errors on this dimension if exceed the permissible tolerance, will justify the rejection of the part. While in case of screw threads there are at least five important elements, which require consideration, and error in any one of these can cause rejection of the thread. In routine production all of these elements (major dia, minor dia, effective dia, pitch and angle of thread form) must be checked and method of gauging must be able to cover all these elements. Errors on the major and minor diameters will cause interference with the mating thread. Due to errors in these elements, the root section and wall thickness will be less, also the flank contact will be reduced and ultimately the component will be weak in strength. Errors on the effective diameter will also result in weakening of the assembly due to interference between the flanks. Similarly pitch and angle errors are also not desirable as they cause progressive tightening and interference on assembly. These two errors have a special significance as they can be precisely related to effective diameter. Pitch errors in screw threads:
A point cutting tool generates Generally screw threads. In this case, for pitch to be correct, the ratio of linear velocity of tool and angular velocity of work must be correct. This ratio must be maintained constant; otherwise pitch errors will occur. If there is any error in the pitch the total length of thread engaged would be either too great or too small, the total pitch in overall length of the thread being called the cumulative pitch error. Various pitch errors are: Progressive pitch error Periodic pitch error Drunken error Irregular errors Drunken error: this is the one having erratic pitch, in which the advance of the helix is irregular in one complete revolution of the thread. Thread drunkenness is a particular case of a periodic pitch error recurring at intervals of one pitch. In such a thread, the pitch measured parallel to the pitch measured parallel to the thread axis will always be correct, the error being that the thread is not cut to the true helix. If the screw thread be regarded as an inclined plane wound around the cylinder and if the thread be unwound from the cylinder, (that is development of the thread be taken) then the drunkenness can be visualized. The helix will be a curve in the case of drunken thread and not a straight line as shown in the figure.
Fig 5.2. It is very difficult to determine such errors and moreover they do not have any great effect on the working unless the thread is of very large size. Progressive pitch error: this error occurs when the tool work velocity ratio is incorrect, though it may be constant. It can also be caused due to pitch errors in the lead screw of the lathe or other generating machine. The other possibility is by using an incorrect gear or an approximate gear train between the work and lead screw. E.g. while metric threads are cut with an inch pitch lead screw and a translatory gear are not available. A graph between the cumulative pitch error and the length of thread is generally a straight line in case of progressive error.
Periodic pitch error: this repeats itself at regular intervals along the thread. In this case, successive portions of the thread are either shorter or longer than the mean. This type of error occurs when the tool work velocity ratio is not constant. This type of error also results when the thread is cut from a leads crew, which lacks square ness in the abutment causing the leads crew to move back and forth in each revolution. Thus the errors due to these cases are cyclic in nature and so the pitch increases to a maximum value, decreases to the mean and then to the minimum value and so on. The graph between the cumulative pitch error and length of threads for this error will, therefore, be of sinusoidal form. Irregular errors: these arise from the disturbances in the machining setup, variations in the cutting properties of material etc. thus they have no specific causes and correspondingly no specific characteristics also. These errors could be summarized as follows: Erratic pitch: this is irregular error in pitch and varies irregularly in magnitude over different lengths of thread. Progressive error: when the pitch of a screw is uniform, but is shorter or longer than its nominal value, it is said to have progressive error. Periodic error: if the errors vary in magnitude and recur at regular intervals, when measured from thread to thread along the screw are referred to as periodic errors. Screw threads measurements: There are a large number of different standard forms of screw threads in common use. A few important measuring types of screw thread elements are discussed here. Here the nomenclature of the screw threads is not discussed here. Full diameter: for measuring the full diameter of a screw, an ordinary micrometer with anvils of a diameter sufficient to span two threads may be used. To eliminate the effect of errors in the micrometer screw and the measuring faces, it is advisable first to check the instrument on a cylindrical standard of about the same diameter as the screw. For such purposes a plug gauge is useful. Core diameter: the diameter over the root of a thread may be checked by means of a special micrometer adapted with shaped anvils, or an ordinary micrometer may be used in conjunction with a pair of vee pieces. The second method is more universal in application, and a diagram showing the arrangement is given in the figure. It is important that while making the test the micrometer is positioned at right angles to the axis of the screw being measured. The vee pieces used for this test are of hardened steel with an angle of about 45 0 finished with a radius less than that of the root of the thread. The back faces should be finished flat, perpendicular with the axis of the vee and parallel with the edge of the radius. Effective diameter: the only reliable means of inspecting the effective diameter of a screw is to use some method, which enables a reading to taken from the straight, sloping flanks of the threads. This is accomplished in a simple manner by using small cylindrical test wires, which rest in the thread angle and make contact with the sloping sides. If means
are available (e.g. a floating micrometer) for maintaining the micrometer at the right angles to the screw axis, two opposite wires may be used; or else three wires are required to align the micrometer, and this method is the rule when using an ordinary micrometer. The wires should be hardened and polished and their surfaces should be round, straight, parallel, and uniform to a high degree of accuracy.
Three-wire method: checking the effective diameter when a screw is measured over wires is given below for general case. One side of the screw is shown in the figure, where w= distance over the wires and D E the effective diameter. The wire is designated with radius r and diameter d.From this general formula we may apply the special adaptation for common threads.
Pitch: An error in the pitch requires a compensating reduction in effective diameter of approximately twice the amount; pitch errors are to be reduced to absolute minimum. A pitch-measuring device consists of a bed with centers at each end to support the screw, with alternative means for holding nuts and sleeves when internal threads are to be tested. Sliding along the bed and moved by an accurate micrometer is head which carries a feeler piece or stylus shaped to fit in the vee of the thread provided with an indicator which shows when it is bedded home centrally in the vee (i.e. in its lowest position). When making a test, the head is moved along causing the stylus to seat itself successively in each of the threads over the length being examined. Observation and analysis of the micrometer reading obtained then enables the pitch of the thread to be determined. A diagrammatic sketch of the stylus is shown in the figure.
Fig 5.5 With a good projection measuring the image and dividing by the magnification may determine the pitch of the portion of the thread. Greater accuracy is obtained if, the measurement is made perpendicular to the thread flanks (instead of measuring parallel to the screw axis), and the result divided by the cosine of half of the thread angle. Thus in figure length AB is measured when pitch AC=AB/cosa .
Measurement of gear teeth elements: A few types of measuring gear teeth elements are discussed here. The nomenclature of a toothed is a prerequisite for the following section. The tooth Venire:
Fig 5.6 A gear tooth Vernier, figure is provided with two mutually perpendicular scales 1 and 5; the first is used in adjusting for a chordal height and the second, to measure the chordal tooth thickness. Before measurement, the adjustable tongue 3 is set by means of Vernier 2 to the height at which the chordal thickness is to be measured and locked in position. The measuring jaws are moved apart, and after testing the instrument with the tongue on the tip circle of gear being measured, the jaws are drawn closer together and brought into contact with the tooth flanks. The values of the measured chordal thickness are directly read from Vernier 4. Measurement at the constant- chord tooth thickness is preferable (the constant chord is the chord between the points of contact of the basic rack profile with the tooth flanks at a normal section). The nominal values of the constant chord height and tooth thickness are selected from the corresponding tables compiled or are calculated by the corresponding formulae. For standard spur gears with a normal pressure angle of 20 0< the constant-chord height h equal to h=0.7476m. And the constant chord tooth thickness is S=1.387m. Where m is module, mm. Base pitch:
The base pitch is the circular pitch of the teeth measures on the base circle. The tooth span micrometer is used to check the mean value and variation in the base tangent length. It varies from the standard micrometers only with respect to the measuring anvils. Here disk type measuring anvils are used. The disk anvil frame may be partly cut away. These micrometers are often used to determine an unknown gear module. To this end the base tangent length is measured first over n teeth then over n-1 teeth. The difference in measurement gives the base pitch t0 which is used for module by the formula m=t0/p cosf where f is the pressure angle.
Gear Measurements The most commonly used forms of gear teeth are involute & cycloid. The involute tooth is derived from the trace of the point on a straight line, which rolls without slipping around a circle, which is the base circle, or it could be defined as a locus of a point on a piece of string which is unwounded from a stationary cylinder. The cycloid tooth is derived from the curve, which is the locus of a point on a circle rolling on the pitch circle of the gear. Here the addendum tooth is the trace of the point on a circle rolling outside of the pitch circle and this is an epicycloidal curve whereas the dedendum portion of the tooth is the trace of the point on a circle rolling on the inside of the pitch circle of the gear and is hypocycloidal gear. The various types of commonly used gears are: Spur gear: it is a cycloid gear whose tooth traces is straight line. Helical gear: it is a cylindrical gear whose tooth traces is straight helices. Spiral gear: a gear whose tooth traces is curved line. Straight bevel gear: a gear whose tooth traces is a straight-line generator of a cone. It is conical in form in operating and intersecting axes usually at angles. Worm gear pair: the worm and mating worm wheel have their axes non-parallel and non-intersecting. Gear Terminologies
PITCH CIRCLE When two gears are meshed and running there are two circles which appear to roll one on another. These two rolling circles are called pitch circles. Diameter of the gear is represented by diameter of the pitch circles and is denoted by "d". ADDENDUM CIRCLE It is a circle, which passes through the tip of the tooth. DEDENDUM CIRCLE It is a circle, which passes through the root of the tooth. TOOTH THICKNESS It is the thickness of the tooth measured along the pitch circle. SPACE WIDTH It is the distance between two adjacent teeth measured along the pitch circle. CIRCULAR PITCH (P or Pc) It is the distance from a point on one tooth to a similar point on the adjacent tooth measured along the pitch circle. It is also the ratio of the circumference of the pitch circle to the number of teeth. Pc = π d/t Where t number of teeth FACE WIDTH It is the length of the tooth measured parallel to the axis of the gear. ADDENDUM It is the radial height of the tooth between the pitch circle and addendum circle. DEDENDUM It is the radial height of the tooth between the pitch circle and dedendum circle. FACE It is the working area of the tooth between addendum circle and pitch circle. FLANK
It is the working area of the tooth between pitch circle and dedendum circle. MODULE (m) It is the diameter measured per tooth of the gear. It is always represented in mm only m= d/t But Pc = π d/t Pc = π m DIAMETRAL PITCH (Pd) It is a reciprocal of module of the number of teeth per mm of diameter. PITCH POINT It is the point of contact or tangency of two pitch circles. LINE OF CONTACT It is the line along which the points of contact between two pairs of teeth proceed. PRESSURE ANGLE It is the angle between the line of contact and the common tangent at the pitch point. CLEARANCE It is the difference between the dedendum and addendum. BACKLASH It is the difference between the space width and tooth thickness. LENGTH OF PATH OF CONTACT It is the distance measured along the line of contact from the point of engagement to the point of disengagement. GEAR RATIO (G) It is the ratio of the gear diameter to the pinion diameter or the ratio of the pinion speed to the gear speed or ratio of number of teeth on gear to that on pinion. G = D/d = n/N = T/t Measurement of individual elements Measurement of tooth thickness
The permissible error or the tolerance on thickness of tooth is the variation of actual thickness of tooth from its theoretical value the tooth thickness is generally measured at pitch circle and is therefore, the pitch line thickness of the tooth. It may be mentioned that the tooth thickness is defined as the length of an arc, which is difficult to measure directly. In most of the cases, it is sufficient to measure the chordal thickness that is the cord joining the intersection of the tooth profile with the pitch circle. Also the difference between chordal tooth thickness and circular tooth thickness is very small for gear of small pitch. The thickness measurement is the most important measurement because most of the gears manufactured may not undergo checking of all other parameters, but thickness measurement is a must for all gears. There are various methods of measuring the gear tooth thickness: Measurement of tooth thickness by Gear tooth vernier caliper. Constant chord method. Base tangent method. Measurement by dimension over pins The tooth thickness can be very conveniently measured by a gear tooth vernier. Since the tooth thickness varies from the tip of the base circle of the tooth, the instrument must be capable of measuring the tooth thickness at a specified position on the tooth. Further this is possible only when there is some arrangement to fix that position where the measurement is to be taken. The tooth thickness is generally measured at pitch circle & is, therefore, referred to as pitch line thickness of tooth. The gear tooth in the vernier has two vernier scales & they are set for the width ‘w’ of the tooth & the depth ‘d’ from the top, at which w occurs.
FIG- 5.8 Considering one gear tooth, the theoretical values of w & d can be found out which may be verified by the instrument. In the fig it may be noted that w is a
chord ADB, but tooth thickness specified as an arc distance AEB. Also the distance d adjusted on instrument is slightly greater than the addendum CE, w is therefore called chordal thickness & d is called the chordal addendum. From the fig, w=AB=2AD, Now angle AOD = θ = 3600/4N Where N is the number of teeth, w=2AD=2*AO*sinθ = 2R sin (360/4N) (R=PITCH CIRCLE RADIUS) Module, m= P.C.D/number of teeth = 2R/N R=N*m/2 w=(N*m)*sin(360/4N) Also from fig, d= OC-OD OC = OE+ addendum = R+m = (N*m/2)+m OD = R * cosθ = N*m/2 cos(90/N) d = (N*m/2)+m-(N*m/2) cos(90/N) Any error in the outside diameter of the gear must be allowed for when measuring tooth thickness. In case of helical gears the above expressions must have to be modified to take into account the change in curvature along the pitch line. These formulae apply when backlash is ignored. Gear tooth Caliper
It is used to measure the thickness of gear teeth at the pitch line or chordal thickness of teeth & the distance from the top of a tooth to the chord. An adjustable tongue, each of which is adjusted independently by adjusting the screw on graduated bars, measures the thickness of the tooth at pitch line & the addendum. The effect of zero errors should be taken into consideration. This method is simple & inexpensive. However it needs different setting for a variation in number of teeth for a given pitch & accuracy is limited by the least count of instrument. Since the wear during use is concentrated on the two jaws, caliper has to be calibrated at regular intervals to maintain the accuracy of measurement. Gear tooth Vernier Most of the times a gear Vernier is used to measure the tooth thickness. As the tooth thickness varies from top to the bottom, any instrument for measuring on a single tooth must.
Fig 5.10 A gear tooth Vernier, figure is provided with two mutually perpendicular scales 1 and 5; the first is used in adjusting for a chordal height and the second, to measure the chordal tooth thickness. Before measurement, the adjustable tongue 3 is set by means of Vernier 2 to the height at which the chordal thickness is to be measured and locked in position. The measuring jaws are moved apart, and after testing the instrument with the tongue on the tip circle of gear being measured, the jaws are drawn closer together and brought into contact with the tooth flanks. The values of the measured chordal thickness are directly read from Vernier 4. Measurement at the constant- chord tooth thickness is preferable (the constant chord is the chord between the points of contact of the basic rack profile with the
tooth flanks at a normal section). The nominal values of the constant chord height and tooth thickness are selected from the corresponding tables compiled or are calculated by the corresponding formulae. For standard spur gears with a normal pressure angle of 20 0< the constant-chord height h equal to h=0.7476m. And the constant chord tooth thickness is S=1.387m. Where m is module, mm. Base pitch The base pitch is the circular pitch of the teeth measures on the base circle. The tooth span micrometer is used to check the mean value and variation in the base tangent length. It varies from the standard micrometers only with respect to the measuring anvils. Here disk type measuring anvils are used. The disk anvil frame may be partly cut away. These micrometers are often used to determine an unknown gear module. To this end the base tangent length is measured first over n teeth then over n-1 teeth. The difference in measurement gives the base pitch t0 which is used for module by the formula m=t0/π cosφ where φ is the pressure angle.
GENERAL MEASUREMENT SYSTEM 1. Introduction 2. General Measurement System 3. Types of Input Quantities 4. Error Classification 5. Calibration 6. Experimental Test Plan 7. Measurements
1. Introduction Measurements are important for quality assurance and process control, and to obtain process information. Three aspects will be covered in the Experimental Engineering class: • Sensors-- fundamentals of sensors for mechanical and thermal quantities. • Systems-- response and configuration. • Experimental methods-- planning, acquisition, and analysis. Quantities of interest include displacement, strain, temperature, pressure, force, torque, moment,velocity, acceleration, volumetric flow rate, mass flow rate, frequency, time, heat flux, etc. 1.1 Definitions commonly used in Sensors and Instrument • Readability-- scales in analog instrument. • Least Count-- smallest difference between two indications. • Static Sensitivity-- displacement versus input, e.g., scale in oscilloscope (cm/mV), etc. • Hysteresis-- measured quantity which depends on the history to reach that particular condition; generally it is a result of friction, elastic deformation, magnetic, or thermal effects. • Accuracy-- deviation of a reading from a known input. • Precision-- related to reproducibility of measurement.
• Error-- deviation from a known input, a measure of accuracy. • Uncertainty-- data scatter, a measure of precision. 1.2. Calibration Calibration involves a comparison of a particular instrument with respect to a known Quantity provided from (1) a primary standard, (2) a secondary standard with a higher accuracy than the instrument to be calibrated, or (3) a known input source. 1.3. Standards The National Institute of Standards and Technology (NIST) has the primary responsibility to maintain standards for such quantities as length, time, temperature, and electrical quantities for the US. Mass. International Bureau of Weights and Measurements (Sevres, France) maintains several primary standards, e.g., the kilogram is defined by the mass of a particular platinum iridium bar maintained at very specific conditions at the Bureau. Time. One second has been defined as the time elapsed during 9,192,631,770 periods of the radiation emitted between two excitation levels of the fundamental state of cesiumThe Bureau International del' Hueure (BIH) in Paris, France maintains the primary standard for clock time. The standard for cyclical frequency is based on the time standard, 1 Hz = 1 cycle/second, or 1 Hz = 2π radian/second. Length. One meter is defined as the length traveled by light in 3.335641 x 10-9 second (based on the speed of light in a vacuum). Temperature. The absolute practical scale is defined by the basic SI unit of a Kelvin, K. The absolute temperature scale, Kelvin, is based on the polynomial interpolation between th eequilibrium phase change points of a number of pure substances from the triple point of th eequilibrium hydrogen (13.81 K) to the freezing point of gold (1337.58 K). Above 1337.58 the 4 scale is based on Planck's law of radiant emissions. The details of the temperature standard are governed by the International Temperature Scale-1990.
Electric Dimensions; volt (V), ampere (A), and ohm ( Ω ) . One ampere absolute is defined by 1.00165 times the current in a water-based solution of AuN2 that deposits Au at an electrode at a rate of 1.118 x 10-5 kg/s. One ohm absolute is defined by 0.9995 times the resistance to current flow of a column of mercury that is 1.063 m in length and has a mass of 0.0144521 kg at 273.15 K. The practical potential standard makes use of a standard cell consisting of a saturated solution of cadmium sulfate. The potential difference of two conductors connected across such a solution is set at 1.0183 V at 293 K. Laboratory calibration is made with the aid of secondary standards, e.g. standard cells for Voltage sources and standard resistors, etc. 1.4. Dimensions and Units Fundamental dimensions are: length, mass, time, temperature, and force. Basic SI units are: m, kg, s, A, K, cd (candela, luminous intensity), and supplemental units are rad (radian, plane angle) and sr (steradian, solid angle). There are many derived SI units, for example, N, J, W, C (Coulomb = A • s), V (W/A), Ω(V/A), Hz, W/m2, N/m2 (Pa), Hz (1/s), etc. Conversion factors between the SI and US engineering units are fixed, e.g. 1 in. = 0.02540005 m, 1 lbm =0.45359237 kg., (oC) = (K) - 273.15, (oF) = (K) -459.67, etc. 2. General Measurement System Most measurement systems can be divided into three parts: Stage I -- A detector-transducer or sensor stage, Stage II -- An intermediate stage (signal conditioning), and Stage III-- A terminating or read-out stage ( sometimes with feedback signal for control). The dynamic response of a generalized measurement system can be analyzed by a mechanical
System. A schematic of the generalized measurement system is shown below. INDICATOR RECORDER PROCESSOR CONTROLLER TRANSDUCER SIGNAL SENSOR CONDITIONER CALIBRATION CONTROL STAGETO PROCESS
STAGE I STAGE II STAGE III 3. Types of Input Quantities • Time relationship Static-- not a function of time. Dynamic-- steady-state, periodic, a periodic, or transient (single pulse, continuing, or random). • Analog or digital Analog-- temperature, pressure, stress, strain, and fluid flow quantities usually are analog (continuous in time). Digital-- quantities change in a stepwise manner between two distinct magnitudes, e.g., TTL signals. The time relationship is important in selecting an instrument adequate for the required time response, and proper but different signal conditioners are usually needed depending on the inputsignal is digital or analog. 4. Error Classification Three types of error can be identified: systematic, random and illegitimate errors. Systematic errors are not susceptible to statistical analysis, and generally result from calibration Errors, certain type of consistently recurring human error, errors of technique, uncorrected loading errors, and limits of system resolution. Random or accidental errors are distinguished by lack of consistency. They involve errors stemming from environmental variations, certain type of human
errors, errors resulting from variations in definition, and errors derived from insufficient definition of the measuring system. Illegitimate errors are those should not exist-- blunders or mistakes, computational errors, and chaotic errors. Error analysis is necessary for measurements. 5 . Calibration (Output versus Known Input) Static Calibrations Static ⇔ independent of time Only the magnitude of the known input is important in static calibrations. D ynamic Calibrations Time dependent variables are measured in dynamic calibrations. C a libration Curve Usually plotted in terms of output versus input of known values or standards. 6.Experimental Test Plan A well thought-out experimental test plan includes (1) An identification of pertinent process variables and parameters. (2) A measurement pattern. (3) A selection of a measurement technique and required equipment. (4) A data analysis plan. • Random tests-- a random order set to the applied independent variables. • Replication-- an independent duplication of a set of measurements under similar Controlled conditions. • Concomitant Methods-- two or more estimates for the result, each based on adifferent method. 7. Measurement Overview The overall planning of experiments should include (1) Objective (2) Plan -- to achieve the objectives (3) Methodology (4) Uncertainty Analysis (5) Costs (6) Calibration (7) Data Acquisition (8) Data Analysis
UNCERTAINTY ANALYSIS I. Statistical Analysis I.1 Introduction I.2 Statistical Properties of a Single Point Measurement I.3 Test of Data Outliers I.4 Chi-squared Test I.5 Number of Measurements Required I.6 Student's t distribution I.7 Least Squares Fit II. Uncertainty Analysis II.1 Introduction II.2 Measurement Errors II.3 Error Sources II.4 Bias and Precision Errors II.5 Uncertainty Analysis : Error Propagation II.6 Design-Stage Uncertainty Analysis II.7 Multiple - Measurement Uncertainty Analysis II.8 ASME/ANSI 1986 Procedure for Estimation of Overall Uncertainty Statistical Analysis I.1 Introduction Variations are usually observed in engineering measurements repeatedly taken under seemingly identical conditions. Source of the variation can be identified as follows: M easurement System Resolution and Repeatability M easurement Procedure and Technique Repeatability M easured Variable Temporal variation and spatial variation Statistical analysis provides estimates of (1) Single representative value that best characterizes the data set, (2) Some representative value that provides the variation of the data, 1. Introduction
Transducers - electromechanical devices that convert a change in a mechanical quantity such as displacement or force into a change in electrical quantity. Many sensors are used in transducer design, e.g., potentiometer, differential transformers, strain gages, capacitor sensors, piezoelectric elements, piezoresistive crystals, thermistors, etc. 2 . Metrology The science of weights and measures, referring to the measurements of lengths, angles, and weights, including the establishment of a flat plane reference surface. 2.1 Linear Measurement Line Standard are defined by the two marks on a dimensionally stable material. End Standard the length of end standards is the distance between the flat parallel end faces. Gauge Block length standards for machining purposes. Federal Accuracy Grade; combination of gauge blocks yields a range of length from 0.100to 12.000 in., in 0.001 in. increments. Vernier Caliper Micrometer Tape Measure measuring tape up to 100 ft, uncertainty as low as 0.05%; hand measuring tools are commonly used for length measurements. 3. Displacement Sensor Potentiometer, Differential Transformer, Strain Gage, Capacitance, Eddy Current 3.1 Potentiometer Displacement can be measured from the above equation. Different potentiometers are available to measure linear as well as angular displacement. Potententiometers are generally used to measure large displacements, e.g., > 10 mm of linear motion and > 15 degrees of angular motion. Some special potentiometers are designed with a resolution of 0.001 mm. Differential Transformer LVDT (Linear Variable Differential Transformer) is a popular transducer which is based on a variable-inductance principle for displacement measurements. The position of the magnetic core controls the mutual inductance between the center of the primary coil and the two outer of secondary coils. The imbalance in mutual inductance
between the center location, and an output voltage develops. Frequency applied to the primary coil can range from 50 to 25000 Hz. If the LVDT is used to measure dynamic displacements, the carrier frequency should be 10 times greater than the highest frequency component in the dynamic signal. In general, highest sensitivities are attained at frequencies of 1 to 5 kHz. The input voltages range from 5 to 15 V. Sensitivities usually vary from 0.02 to 0.2 V/mm of displacement per volt of excitation applied to the primary coil. The actual sensitivity depends on the design of each LVDT. The stroke varies in a range of +150 mm (low sensitivity). There are two other commonly used differential transformers: DCDT--Direct Current Differential Transformer and RVDT-- Rotary Variable Differential Transformer (range of linear operation is ± 40 degrees). Consult Figs. 12.9 and 12.11 of Textbook for typical schematic diagrams of LVDT and Fig. 12.12 for that of RVDT. LVDT and RVDT are known for long lifetime of usage and no over travel damage. 3.2 Resistance-type stain gage Lord Kelvin observed the strain sensitivity of metals (copper and iron) in 1856. The effect can be explained in the following analysis. R =ρL A (uniform metal conduction) Where R = resistance, ρ = specific resistance, L = length of the conductor, A = cross sectional area of the conductor dR R =dρρ+dL L –dA/A Consider a rod under a uniaxial tensile stress state: Lεa =dL L , εt = - νεa = -ν dL L where εa = axial strain, εt = transverse strain, ν = Poisson ratio df = do ( l - ν dL/L ).