Engineering Metrology - IIT Kanpur

1 Engineering MetrologyProf. J. RamkumarDepartment of Mechanical EngineeringIIT KanpurOctober 24, 2017 OutlineIntroduction and Types of InstrumentsEngineering ToleranceCommon Metrology InstrumentsCommon Metrology Instrumentscoordinate measuring machine (CMM)Introduction to MetrologyIMetrology is the science of measurementIDimensional Metrology is that branch of Metrology whichdeals with measurement of dimensions of a part or workpiece(lengths, angles, etc.)IDimensional measurements at the required level of accuracyare the essential link between the designer s intent and adelivered width, depth, angles and other dimensions all must beproduced and measured accurately for the machine tool tofunction as : Metrology is a vast area.

2 In this lecture, the mainfocus on Dimensional MetrologyDimensional Metrology NeedsILinear measurementsIAngular measurementsIGeometric form measurements(Roundness, Straightness,Cylindricity, Flatness etc.)IGeometric relationships(Parallel, perpendicular,Concentric,runout etc.)IControlled surface textureTypes of Measurement and Instruments UsedLinear Measurement DevicesIVernier Caliper:It is a visual aid that allows the user tomeasure more precisely than could be done unaided whenreading a uniformly divided straight or circular count:The least count of a measuring instrument isthe smallest change in the measured quantity that can beresolved on the instrument s scaleLinear Measurement DevicesLeast count of Vernier.

3 It is the difference between the value ofone Main scale division and the value of one Vernier scale the smallest main scale reading, that is the distance betweentwo consecutive graduations (also called its pitch) be S and thedistance between two consecutive Vernier scale graduations be Vsuch that the length of (n-1) main scale divisions is equal to nVernier scale ,the length of (n-1) main scale divisions = the length of n vernierscale divisionor, (n-1)S=nVor, nS-S=nVor,S/n=S Vor (Pitch)/(Number of Vernier scale divisions) = (Length of onemain scale division Length of one Vernier scale division)So,S/nand (S V) are both equal to the least count of Measurement DevicesExample-1:Ten divisions on the vernier scale coincide with 9smallest divisions on the main scale (mm), Main scale Reading cm and vernier scale coincides with 7 division of the main ) Calculate the Least Count( ) of the vernier ) Calculate the observed = Value of one main scale division - Value of onevernier scale = 1 mm 9/10mm= Reading = Main scale reading + Vernier scale readingObserved Reading = cm + 7 x Reading = cm + 7 x cmObserved Reading = cmLinear Measurement DevicesIAnalog and Digital Micrometers:(a) A vernier (analog) micrometer(Similar to Vernier caliper).

4 (b) A digital micrometer with a range of 0 to 1 in. (0 to 25mm) and a resolution of 50 in. ( m). It is generallyeasier to read dimensions on this instrument compared to theanalog micrometerAngle Measuring InstrumentsIUniversal Bevel Protractor1) It is an angular measuring instrument capable of measuringangles to within 5 min2) The name universal refers to the capacity of the instrumentto be adaptable to a great variety of work configurations andangular Measuring InstrumentsISine Bar1) A sine bar is made up of a hardened steel beam having aflat upper ) The bar is mounted on two cylindrical rollers and the axesof the two rollers are parallel to each )

5 The accuracy attainable with this instrument is quite Measuring InstrumentsUse of Sine Bar for Angle Measurementsin =hL(1)For error in angle measurement, differentiating h with respect to ,we haved dh=sec L(2)Therefore, the error in angle measurementd , due to an error dhin height h is proportional to sec .Measuring RoundnessMeasuring Profilescoordinate measuring machine (CMM)IIt is a device for measuring the physical geometricalcharacteristics of an are defined by a probe attached to the thirdmoving axis of this may be mechanical, optical, laser, or white light,among is the consistency of a single appraiser tomeasure the same part multiple times with the samemeasurement is related to the standard deviation of the measured ErrorIMeasurement Error is the statistical summing of the errorgenerated by Repeatibility (the variation within an appraiser)and Reproducibility (the variation between appraisers)

6 Error= 2repeatability+ 2reproducibility(3)where repeatabilityand reproducibilityare the standarddeviations of the measured values in repeatability formula for standard deviation is = N i=1(xi x)2N 1(4)wherexiis the measured value and xis the mean value and Nis the number of observations in the sampleExample of Standard DeviationIHere, if we calculate the standard deviation of your marksthenxiis the individual s marks and xis the mean of classmarks and N is the number of normal distribution includes your real marks(Mid-sem+Quiz+Lab exercise+lab Reports+Drawing)Introduction to Engineering ToleranceIDefinition:The allowable deviation from a is the total amount a dimension may vary and is thedifference between the upper (maximum) and lower(minimum) of Tolerance.

7 Dimensional and GeometricalIAllowance for a specific variation in the size of part is calledDimensional for a specific variation in the geometry of part iscalled Geometrical are used to control the amount of variationinherent in all manufactured of the great advantages of using tolerances is that itallows for interchangeable parts, thus permitting thereplacement of individual in relation to CostICost generally increases with smaller tolerance-Small tolerances cause an exponential increase in cost-Therefore your duty as an engineer have to consider :Doyou need or is good enough?IParts with small tolerances often require special methods with small tolerances often require greater inspectionand call for the rejection of parts Greater QualityInspection Greater not specify a smaller tolerance than is necessary!

8 Dimensional Tolerance representationDimensional Tolerance representationImportant Terms in TolerancingIShaft:A term used by convention to designate all externalfeatures of a part, including those which are not :A term used by convention to designate all internalfeatures of a part, including those which are not Terms in TolerancingIBasic Size:the nominal diameter of the shaft (or bolt) andthe hole. This is, in general, the same for both Size:the measured size of the finished part Line:It is a straight line corresponding to the basicsize. The deviations are measured from this line. The positiveand negative deviations are shown above and below the zeroline of Size:The term limits of size referred to the twoextreme permissible sizes for a dimension of a part(hole orshaft), between which the actual size should Limit of Size:The greater of the two limits ofsize of a part(Hole or shaft).

9 Important Terms in TolerancingIMinimum Limit of Size:The smaller of the two limits ofsize of a part(Hole or shaft).IAllowance:It is the difference between the basic dimensionsof the mating the shaft size is less than the hole size, then theallowance is positive and when the shaft size is greater thanthe hole size, then the allowance is :It is the difference between the upper limit andlower limit of a Terms in TolerancingITolerance Zone:It is the zone between the maximum andminimum limit Deviation:It is the algebraic difference between themaximum size and the basic upper deviation of a hole is represented by a symbol ES(Ecart Superior) and of a shaft, it is represented by Deviation.

10 It is the algebraic difference between theminimum size and the basic lower deviation of a hole is represented by a symbol EI(Ecart Inferior) and of a shaft, it is represented by ExampleFit TypesIClearance fitoccurs when two toleranced mating parts willalways leave a space or clearance when fitoccurs when two toleranced mating parts willalways interfere when fitoccurs when two toleranced mating parts willsometimes be an interference fit and sometimes be a clearancefit when of FitsClearance FitIIn clearance fit, an air space or clearance exists between theshaft and holeISuch fits give loose clearance fit has positive allowance, there is minimumpositive clearance between high limit of the shaft and lowlimit of the rotation or sliding between the mating of Clearance FitILoose Fit:It is used between those mating parts where noprecision is required.