Mechanical measurements and metrology

Rajendra Mane College of Engineering and Technology, AMBAV (Devrukh) -415804University of Mumbai

Mech & Automobile Engineering Sem-V (Rev) Winter 2010(10-WIN-ME/AE-V-REV-MMM)

Mechanical Measurements & Metrology

Q.P.Code: GT-6642 of 34 Prepared by: Prof. P.R.Kshirsagar

Q.No.1. a. Explain generalized measurement system elements with block diagram and function ofeach. Also indentify various elements of measurement system involving thermocouple formonitoring temperature of chemical process. 08

Ans:

Most of measurement system contains three man functional element

1) Primary sensing element

2) Variable conversion element

3) Data presentation element

Not all the elements shown in the Figure may be present in a particular case. Themeasurement process requires invariably a detector that responds to the measuredquantity by producing a measurable change in some property of the detector. The changein the property of the detector is converted to a measurable output that may be eithermechanical movement of a pointer over a scale or an electrical output that may bemeasured using an appropriate electrical circuit. This action of converting the measuredquantity to a different form of output is done by a t ransducer .

The output may be manipulated by a signal conditioner before it is recorded or storedin a computer by manipulat ion element. If the measurement process is part of acontrol application the computer can use a controller to control the measured quantity.The relationship that exists between the measured quantity and the output of thetransducer may be obtained by calibration or by comparison with a reference value. Themeasurement system requires external power for its operation.

PhysicalSystem

Sensor Transducer Manipulation

Element

Controller

Indicator

Recorder





Q.No.1. b. Define the following: 06

Ans:

i) DRIFT:

All calibrations and specifications of an instrument are only varied under controlledcondition of temperature and pressure etc.

The environmental conditions affect the output of the instrument and can be attributedthrough general term called as drift.

No drift means that with a given input, the measured value do not change with time.

Drift is a desirable quantity in industrial instrument because it can be easily compensatedfor.

It may be classified as:-

1. Zero drift2. Span drift3. Zonal drift

ZERO DRIFT:-

BourdonTube ----Primarysensing andtransducerElement

Mech LinkageDatatransmissionelement

GearingArrangement

Variablemanipulationelement

Pointer & Dial–

Datapresentationelement





The whole calibration gradually shifts due to slippage or due to wearing up of electroniccircuit then zero drift occurs.This can be prevented by zero setting.

SPAN DRIFT: -

If there is proportional change in the indication or change along the upward scale the driftis called span drift.





ZONAL DRIFT:-

It is combination of zero and span drift.

It occurs over span of instrument and many environmental factors cause zonal drift.

(ii, iii)SPAN AND RANGE:

In an analog indicating instrument the value of measured is indicated on a scale by apointer while in a recording instrument it is indicated on a chart by pen mechanism. Thechoice of proper range for instruments is important in instrumentation. The ScaleRange of an instrument is defined as the difference between the largest and smallestreading of the instrument. Supposing the highest point of calibration is Xmax units whilethe lowest is Xmin units and that the calibration is continuous between the twopoints.Then we can say that the instrument range is between Xmin and Xmax.

The instrument span is given by: Span= Xmax – Xmin

The same definitions apply in the case of digital instruments. There is another factor thatmust be considered while determining the range of instrument. This is the FrequencyRange, which is defined as frequencies over which measurements can be performedwith a specified degree of accuracy. For example a moving iron instrument may have a 0-250V range and 0-135Hz frequency range with an accuracy of 0.5 or 1% of full scalereading.

iv) Limit of size: These are the maximum and minimum possible size of the part.

1. Maximum limit: It is the maximum size permitted for the part.

2. Minimum limit: It is the minimum size permitted for the part.

v) Deviation: It is the algebraic difference between corresponding basic sizes.





1. Upper deviation: It is the algebraic difference between the maximum limit of size andcorresponding basic size where maximum limit is greater than basic size. It is positiveand when the maximum limit is greater than basic size and negative when minimum limitis less than basic size.

Upper deviation = maximum limit size – basic size.

2. Lower deviation: It is the algebraic difference between the minimum limit of size andthe corresponding basic size. When the maximum limit of size is greater than the basicsize, it is positive quantity and when the minimum limit of size is less than basic size thenit is negative quantity.

Lower deviation = minimum limit of size – basic size.

3. Actual deviation: It is algebraic difference between actual size and corresponding basicsize.

4. Mean deviation: It is the arithmetic mean between upper and lower deviation.

Vi)Tolerance: The tolerance can be defined as the magnitude of permissible variationfrom the specified value.

Tolerance has to be allowed because of limitations of machine which prevent ideal,achievement during fabrication. It is necessary to specify tolerance for the followingreasons:

1. Variation in properties of material being machined introduced error.

2. The production machines themselves have some inherent inaccuracies built in themand have the limitations to produce perfect parts.

3. It is impossible for an operator to make a perfect setting.

The tolerances compromise between accuracy required for the proper functioning and theability to economically produce this accuracy.

Tolerance can be specified by two systems:

1. Unilateral tolerance system: In this type of system the part dimension is allowed tovary on one side of the basic size i.e. either below or above it.

2. Bilateral tolerance system: It is the system in which the dimension of part is allowed tovary on both sides of basic size so limits of tolerance lie on either side of basic size.





Q.No.1. c. Explain the purpose of sine bar, its limitations and precautions to be taken while using it.06

Ans:

Sine bar is simple instrument which utilizes high degree of accuracy available for linearmeasurement in the form of slip gauges for angular measurements. The sine bar takemany forms, according the purpose of it’s use and method of application. The mostcommon type of sine bar consist of a bar rectangular section which is stepped at the ends.A roller is secured into each step by a screw which holds it in contact with bothfaces of step.

A sine bar is specified by the distance between the centre of the two rollers,i.e. 100mm,200mm, & 300mm. the various part of sine bar are hardened before grinding & lapping.Depending upon the accuracy of of the centre distance, sine bar are graded as, Agrade or B grade. Grade A sine bar are more nearly accurate. By placing a pile of slipgauges under one roller the bar surface can made parallel and in contact with any surfaceof the work. The slips required (h) which have a value equal to the distance between therollers (I) multiplied by sine ratio of the angle. If I (distance between roller centre ) is100mm then sine of the angle A multiplied by 100 gives h, i.e. tfe total height in mm. thesine for any angle can be obtained from trigonometrical tables.

Use of sine bar-





The use of sine bar is based on the law of geometry &trigonometry. To set a given angle,one roller of bar is placed on surface plate and combination of slip gauges inserted underthe second roller. If ‘h’ is the height of combination of the slip gauges and ‘L’ is thedistance between the roller centre, then

Sinθ = h/L or θ = sinˉ¹ (h/ L)

The sine bar is use for, 1) Measuring taper plug gauge & 2)checking lathe angle

2. S ine centre -These are used in situation where it is difficult to mount the component on the sine bar.figshows the construction of a sin center. This equipment itself consist of a sine bar, which ishinged at one roller end and mounted on the datum end.

Two blocks are mounted on the top surface of the sine bar, which carry two centers

And can be clamped at any position on the sine bar. These two centers can be adjusteddepending upon the length of the conical component. The procedure to measure is thesame as is the same as it is in case of the use of a sine bar. Figure shows the use of a sine

Centre for measuring the included angle of the taper plug gauge.

Apart from the sine centre and sine bar, sine table are also used to measure angles.

Specifically it can be used for measuring compound angles. These are used for radial aswell as linear measurement.

The sine bar is set to half the included angle of the gauge. When parallelism has

Been established using dial indicator and adjusting height of gauge block, the halfincluded angle will be

θ=sin‾1(h/L)

Hence included angle=2θ.

Q.No 2. a. What are desired and modifying and interfering inputs. Explain with example of each.

Also suggest the methods to minimize the effects of and modifying and interfering inputs.

08

Ans:

Input qty. are classified into 3 groups —

1. Desired 1/p.2. Interfering 1/p.3. Modifying 1/p





Generalised 1/p – o/p configuration of measurement system-

1. Desi red 1 /p :Inputs are defined as qty., for which the instrument or sys is specially designed tomeasure & respond.

Desired 1/p iD produce on o/p component

CD = GD iD

In accordance with 1/p –o/p relationship symbolized by mathematical operation GD ,which is defined as transfer function.

GD is mathematic operation to get on o/p from iD

Mathematically it is defined as ratio of laplace transform of o/p to 1/p.

Transfer function is effect of performance parameter over system.

Ex. of desired 1/p –

GD

GMD

GMI

GI

O/P

O/P Component due to desired &modifying I/P

O/P Component due to Interfering& modifying I/P

Desiredinput, iD

Modifyinginput, iM

Interferinginput, ii





Consider the case of measurement of differential pre. Of fluid (gas) with help of U –Tubemanometer using Hg as a manometric fluid.

Pre. Applied at two are P1 & P2.

Differential pre P= P1 –P2

Here P1, P2 are desired 1/ps. While scale read ‘ h ‘ is 0/p.

In case of P1 = P2 the diff. pre is zero & therefore ‘ h ‘ should be zero.

However, there are ex, when scale h is not zero even though p1 = p2 i. e. desired 1/p iszero. This is on amount of presence of interfering 1/p.

2. In ter fer ing 1 /p –If represents the qty., to which on instrument or measurement system becomesunintentionally sensitive.

Instruments are not desired to respond to theses 1/ps but they give on o/p due to II onaccount of their principle of working, design & other factors like environment where theyplaced.

Interfering 1/p II is operated upon by a transfer function. GI to produce on o/p.

Ex. Of interfering 1/p-

When manometer is not properly aligned with

1. Gravity vector because of angle of tilt.Therefore there is an o/p ‘h’, even thing there is no diff. pre.

Hence angle of tilt O outs as interfering 1/ps.

2. Manometer placed on accelerating vehicle, then also there is an o/p, even though p= 0, Hence acceleration acts as interfering 1/p.

3. Modi fy ing 1 /ps –Defined as 1/ps, which causes a change in 1/p -0/p relationship for either desired 1/p orinterfering 1/p or for both.

This 1/p modifies GD or GI.

The symbols GMD & GMI represent the specific manner in which IM affects GD or GIrespectively.

Ex. Of modifying 1/ps.—

Modifying 1/ps for manometer ambient temp. & gravitational force.





1. Change in ambient temp. changes length of calibrated scale thereby modifying theproportionality factor relating the 1/p with 0/p.2. Value of gravitational force is diff. at different location. Therefore use ofmanometer at different locations leads to modification of 1/p – 0/p for desired 1/ps.

Q.No. 2.b.

While measuring the speed of steam turbine with stroboscope stationary images wereobserved for 3 consecutive stroboscope settings of 3000, 4000, 5250 flashes per minute.Calculate the rotational speed of turbine. 07

Ans:

Given: Highest flashing frequency Nh=5250

Lowest flashing frequency Nl=3000

No of floating frequency N=03

Speed of turbine Nr= Nh*Nl*(N-1) / (Nh-Nl)

=5250*3000*(3-1) / (5250-3000)

Nr= 14000 rpm

Q.No. 2.c. Write a note on wringing of slip gauges. 05

Ans:

When two clean and very accurately flat surfaces are slide together under pressure theyadhere

Firmly this phenomena is called wringing

Generally a minute amount of grease or moisture must be present between the surfaces

For them to wring satisfactorily This effect is caused by molecular attraction betweensurfaces and he liquid film

Use of this phenomena is made when several slip gauge are to be in combinationbecause the

Stack then can be handled as unit without need of clamping

The wring two pieces together they are first cleaned because if any dust presentbetween te surfaces they won’t wring together. After cleaning they are placed together atright angles





In the form of cross and then rotated through 90 degree

Q.No. 3.a.

A resistor has a normal value of 10 Ώ ± 0.1 %. A voltage V is applied across the resistor ofresistance R and the power consumed is calculated in 2 ways:

1. P = V2/R 2. P = VI

Where I is the current passing through the circuit.Calculate the uncertainity and power consumed ineach case when the measured value V & I are V= 100V±1%., I= 10Amp ± 1%. Comment on result.

10

Ans:

1) P = V2 / R

And,

=

= - 100 V/Ώ

Hence uncertainty in power measurement,

Wp = (Wv)² + (WR)²

= (Wv)² + (WR)²

Hence percentage uncertainty in measurement of power is calculated by putting

P = V2 / R

Wp / P x 100 =

= ± 2.004 %





II) P = VI

dP/dV = I

And dP/dI = V

Percentage uncertainty in power measurement

WP/P X 100 = 1 / P X 100

= 1/p X 100

=

= X 100

= ± 1.414 %

The second method of power determination gives a much lower uncertainty than the firstone even though basic uncertainties in each quantity are the same.

Q.No. 3. b. Define fit and classifiy it depending upon actual limits of hole and shaft. 06

Ans:It is defined as relationship existing between two parts shaft and hole, which are to beassembled with respect to the difference in their sizes before the relationship is called fit.It is also the degree of tightness or looseness between two mating parts.

Depending on the mutual position of tolerance zone of the coupled parts the tree types offits can be distinguished.





A) Clearence fit: (a-h) shaft): When the differences between the size of hole and shaftbefore assembly are positive then the fit is called clearance fit. In this fit the largestpermissible shaft diameter is the smallest permissible diameter of hole.

1. Minimum clearance: In case of clearance fit, it is the difference between minimum sizeof hole and maximum size of shaft.

2. Maximum clearance: In case of clearance fit, it is the difference between maximumsize of the hole and minimum size of the shaft.

B) Interference fit: (p-z shaft)

When the difference between the size of the hole and shaft before assembly is negativethen the fit is called interference fit.

The tolerance zone of hole is entirely below the tolerance zone of the shaft.

1. Minimum interference: It is the difference between maximum size of hole andminimum size of shaft before assembly.

2. Maximum interference: It is the arithmetic difference between the minimum size ofhole and maximum size of shaft before assembly.

C) Transition fit:

It is a fit which may provide either clearance or interference. The tolerance zones of holeand shaft overlap in this type of fit. This type of fit lies between clearance andinterference fit.

1. Push fit: Considering examples like changing gears, slipping, bushing etc whose subcomponents are disassembled during operation of machine. It requires small clearancewhere push fit is suitably employed.

Q.No. 3.c. Explain stroboscopic method of angular velocity measurement. 04

Ans:

In the Motors pages of this site, there is an explanation of how to perform tests on yourmotors to obtain the motor characteristic graph. This graph is useful for makingcalculations and predictions of how you robot will perform. One part of this testing is tomeasure the speed of the motor. This can be performed using either a tachograph, whichdirectly measures the speed, or a stroboscope, which compares the speed with a knowfrequency.





Tachographs are slightly more complicated to make than a stroboscope, since you need toattach a device to the motor that can affect an external device which then counts thenumber of disturbances in a given time frame. Here I present the design of a stroboscope,and describe how it can be used to measure the rotational speed of a motor, or wheel.

The types of stroboscope used to measure care engine speeds are not suitable for ourpurposes. This is because they do not have an independent and measurable oscillator tocontrol the frequency of the flashing. Instead they use the ignition timing of the engine tocontrol the flash. They are actually designed for measuring the phase angle of an object(i.e. the timing of the spark relative to the position of the camshaft) rather than thefrequency of the object.

How to measure rotat ional speed us ing a s t roboscopeAn oscillator is made to produce a pulse wave of a known frequency. This is then used todrive a bright LED, which can cope with the fast rate of flashing (note that anincandescent bulb is no use since when it is driven at a high frequency, the filamentremains hot when the power goes off, and you end up with a light that is not flashing atall, but is permanently on).

A mark is made on the object that is rotating that you wish to measure, and the object isspun up to speed. The oscillator is set to a low frequency to start with, and the LED isshone at the object where the mark is. At first, the mark will appear at random pointsaround the object

When it is stationary, the LED is flashing at the same frequency as the object is rotating.Since the frequency is known, the rotational speed is also known, and can be stated inRPM using the formula:

RPM = 60 x f- stroke

Q.No. 4.a.

Calculate the dimensions of plug and ring gauge to control the prod of 50 mm shaft andhole of H7d8 as per the IS specifications the following assumptions are to made 50 mmlies in diameter step of 30 and 50 mm and upper deviation for shaft d is -16D.44 & lowerdeviation for hole H is zero. Tolerance unit in micron

i= 0.45

And IT6 = 10i. And above IT6 grade the tolerance magnitude is multiplied by 10 at each5th step. 10





Ans:For calculation of tolerance value of diameter is taken as mean of range in which it lies,D =

= 38.73 mmValue of tolerance unit,i = 0.45

= 0.45= 1.523 micron= 0.001523 mm

Now hole is type H & grade 7,IT 7 = IT6 X 100.2

= 10i X 100.2

= 15.85 iFor H hole fundamental deviation = 0 & value of tolerance = 15.85 x 0.001523 = 0.02413mmHence for hole H7, disposition of work tolerance will be 0.02413 mm

For shaft d8Tolerace = IT8 = 100.2 X IT 7

= 1.585 X 15.85 i = 25.122 i= 25.122 x 0.001523 = 0.0383 mm

Fundamental deviation d SHAFT = - 16 D0.44 = - 16 x 38.730.44

= - 80 micron = - 0.08 mmUpper deviation = - 0.08 mmWork tolerance = - 0.0383 mmLower deviation = - 0.08 – 0.0383

= - 0.1183 mmVarious tolerances and deviations have been determined.

Considering for gauges,i) Plug gauges:According to new system go gauges are given 1/10th of work tolerance in tolerance zoneand NO GO gauges outside it.Since work is less than 0.09 mmEffect of wear in GO gauge is not consideredWork tolerance = 0.02413 mmGauge tolerance = 0.002413 mmLimits for GO gauges are 50.000 and 50.0024 mm and NO GO gauge dimensions are 50+ 0.02413 = 50.02413 and50.02413 + 0.0024 = 50.02653 mmii) Ring gauge:Dimensions for GO gauges are 50 – 0.08 = 49.92 mm and49.92 – 0.00383 = 49.91617 mmDimensions for NO GO gauge50 – 0.1183 = 49.8817 mmAnd 49.8817 – 0.00383 = 49.87787 mm





Q.No. 4.b. Define gauge factor for strain gauge. Also derive expression for it. 10

Ans:

Let us consider a strain gauge made up of circular wire. The wire has dimensions:

Length = L, Area = A, Diameter = D before being strained.





The material of the wire has a resistivity ρ

Resistance of unstrained gauge R = ρL/ A

Thus when wire is strained therer are changes in its dimensions.

Let ΔL = Change in length, ΔA = Change in area, ΔR = Change in resistance, ΔD =Change in diameter

Differenciate w r t stress s

dR/ dS = ρ / A (dL/dS) - ρL / A2 (dA/dS) + L /A (dρ / dS) ------------1)

Dividing eq 1) by R = ρL/ A

1 / R dR/dS = 1/L dL/ dS – 1/A dA / dS + 1/ρ dρ/dS -------------------2)

It is evident from eq 2) that the per unit change in resistance is due to,

1. Per unit change in length2. Per unit change in area3. Per unit change in resistivityArea = A = π /4 D2

dA/ dS = 2π/4 x D (dD/dS) OR

1/A dA/ dS = (dD/dS)

= 2/D dD/dS

Eq 2) can be written as

1/R dR/dS = 1/ L dL/dS - 2/D dD/dS + 1/ρ dρ/dS

Now Poisson’s ratio, µ = Lateral strain / Longitudinal strain

= - (dD/D)/ (dL/L)

dD/D = - µ x dL/L

Hence 1/R dR/dS = 1/L dL/dS + 2µ/L dL dS + 1/ρ dρ/dS

For small variations, the above relationship can be written as,

ΔR/R = ΔL/L + 2µ ΔL/L + Δρ/ρ

The gauge factor is defined as ratio of per change in resistance to per change in length

GF = (ΔR/R) / (ΔL/L)





Hence, ΔR/R = GF * ΔL/L = GF * e

The GF can be written as 1 + 2 µ + (Δρ/ρ) / e

= Resistance change due to change in length + Resistance changedue to change in Area + Resistance change due to piezoresistive effect

So, GF = 1 + 2µ + (Δρ/ρ) / (ΔL/L)

Q.No. 5.a. Explain the following: 12

Ans:Dynamic pressure sensors are designed to measure pressure changes in liquids and gassessuch as in shock tube studies, in-cylinder pressure measurements,

field blast tests, pressure pump perturbations, and in other pneumatic and hydraulicprocesses. Their high rigidity and small size give them excellent high frequency responsewith accompanying rapid rise time capability. Acceleration compensation makes themvirtually unresponsive to mechanical motion, i.e., shock and vibration.

Figures 1a and 1b are representative cross sections of Dytran Model Series 2300V LIVM(Low Impedance Voltage Mode) acceleration compensated pressure transducers. Thisseries is characterized by very high frequency response and fast rise time. Theseinstruments contain integral impedance converting IC amplifiers which reduce the outputimpedance by many orders of magnitude allowing the driving of long cables withnegligible attenuation.

Series 2300V utilizes thin synthetic quartz crystals stacked together to produce ananalogous voltage signal when stressed in compression by pressure acting on the





diaphragm. This pressure, by virtue of diaphragm area, is converted to compressive forcewhich strains the crystals linearly with applied pressure producing an analog voltagesignal. Figure 1: Low Impedance Voltage Mode (LIVM) pressure sensor. As with allLIVM instruments, the voltage generated by the crystals is fed to the gate terminal of theFET input stage of an impedance converting IC amplifier which drops the impedancelevel 10 orders of magnitude. This allows these instruments to drive long cables with littleeffect on frequency response.

Referring to figure 1a and 1b, series 2300V contains an integral accelerometer builtinto the crystal stack. This accelerometer, consisting of one quartz crystal and a seismicmass, produces a signal of opposite polarity (to that produced by pressure on thediaphragm) when acted upon by vibration or shock. This signal cancels the signalproduced by vibration or shock acting upon the diaphragm and end piece, negating theeffects of mechanical motion on the output signal.

APPLICATIONS

Used in difficult application such as ballistics ,blasts explosions , ).,fuel injection highintensity sound

(2) BRIDGEMAN GAUGE:

- Pressure upto about 70,000 MPa can be easily measured with strain gauge cells or

Bourdon tubes.

- Bourdon tube gives little output displacement resulting in poor sensitivity.

- For measurement or pressure above 70,000 MPa, electrical gauge based upon the

principle of change of resistance with change of pressure are made.

- Resistance of fine wires changes with pressure.

- Pressure transducer based upon theses principle is called Bridgman gauge.

- Although pressure sensitivity of gold chrome is lower, it has much smaller temp

error. Kerosene experience transient (sudden) temp change when sudden

pressure change occurred due to adiabatic compression (Const. heat).

- It employs fine wire of manganin or gold chrome.

- Wire is wound in the form of coil enclosed in pressure container filled with

kerosene oil.

- One end of coil is ground and other is brought through suitable insulator.

- Bellows transmits the pressure under measurement to coil.





- Change in resistance with change in pressure is measured with Wheatstone

bridge.

- Gold chrome is refered to manganin in many applications as it gives change in

resistance which is 1/4th of that of manganin for some change in pressure.

Advantages:

1. Available with full scale upto pressure of 15 MPa with accuracy of 0.1 – 0.5 %2. Good dynamic response.Disadvantages:

1. Overall frequency response is limited.

(3) Pyrometers:

OPTICAL PYROMETER:

The radiation from a heated body at high temperatures falls within the visible regionof the electromagnetic spectrum. Within the visible region a given wavelength has a fixedcolour and the energy of radiation is interpreted as intensity or brightness. In an opticalpyrometer the wavelength of radiation is restricted by means of colour filter and thebrightness is measured by comparison with a standard lamp.

Disappearing Filament Optical Pyrometer:

An image of the radiating source is produced by a lens and made to coincide withthe filament of electric lamp. The current through the lamp filament is made variable sothat lamp intensity can be adjusted. The current through the filament is adjusted until thefilament and the image are of equal brightness. However, if the temperature of thefilament is higher than that required for the equality of brightness it becomes too bright.On the other hand, if the temperature is lower, it becomes dark. Since the intensity oflight of any wavelength depends upon the temperature of the radiating body and thetemperature of filaments depends upon the current flowing through lamp. However thefilament current depends upon resistance of filament, therefore, modern pyrometers arecalibrated in terms of resistance of filament circuit. The range of temperature which canbe measured by instruments of this type is governed by the maximum allowabletemperature of the lamp which is of the order of 1400°c. The range can be extended byusing an absorption type screen near objective lens.





The optical pyrometer is widely used, for accurate measurement of temperature offurnaces, molten metal’s and other heated materials.

Q.No. 5.b.

Explain in brief various possible errors on gears. Also explain with neat sketch the use ofParkinson gear tester. 08

Ans:-Adjacent pitch errors

- Cumulative pitch error

- Profile error

- Single flank error

-Total composite error

-Cyclic error

-periodic error

- Axial run out

- Undulation

- Tooth alignment error





PARKNSON GEAR TESTER

The principle of the device is to mount std gear on fixed vertical spindle and thegear to be tested on another similar spindle mounted on sliding carriage maintaining gearsin mesh by

Spring pressure movement of the sliding carriage as the gear are rotated are indicated by adial in indicator and these variations are a measure of any irregularities in the gear testalternatively a recorder can be fitted in the form of waxed circular charts and record madeof the gear.

The gears are mounted on two mandrels so that they are free to rotate withoutnmeasurable clearance The left spindle can be move along the table and clamped in anydesirable position The right mandrel slide is free to move running on steel balls againstspring pressure.

The two mandrels can be adjusted so that their axial distance is equal to designedgear distance. There are two screws for limiting the movement of sliding carriage .A scaleis attached to one carriage and vernier to other this enables centre distance to be measuredwithin 0.025 mm

Q.No. 6.a. Explain the following form of thread gauge. 09

Ans:1-Types of l imi t gauges: -

1. According to type

a) Standard gauges b) Limit gauges

2. According to purpose

a) Workshop gauges b) Inspection gauges

c) Reference /Master Gauges

3. According to the form surface

a) Plug gauges b) Snap or Ring gauges

4. According to the design

a) Single & Double limit gauges

b) Fixed & Adjustable gauges

c) Solid & Hollow gauges

Plug Gauges:-





Plug & pin gauges are use for GO/NOGO assessment of hole & slot dimensions orlocations compared to specified tolerances. GO end of the plug gauge is made to size oflower limit of the hole & NOGO end of the upper limit of the hole. If ‘GO’ end goes intothe hole but NOGO ends does not go, then part dimension lies within the limits.

The plain plug gauges are normally of double ended type upto 63mm & single ended typeabove 63mm. The plain plug gauges are marked with following on their handles

1. Nominal size

2. Class of tolerance

3. ‘GO’ on go side

4. ‘NOGO’ on nogo side

5. Actual value of tolerance

6. Manufactures name & trade mark

The ‘NOGO’ side is always painted with red band.

Plain Ring gauges:-

For checking shafts, ring gauges are used.

They are made of suitable wear resistance steel7 gauging surface are hardened, stabilized,ground & lapped.

These are GO & NOGO gauges, designated by ‘GO’ & ‘NOGO’





Snap gauges:-

The snap gauges are also used to check the shafts. They may be rib type & and plate typesnap gauges.

The gauges are set to GO & NOGO tolerance. A snap gauges ‘GO’ contact dimensionsare based on maximum tolerance of the round bar, thickness or port feature being gaugedby snap gauges.

In adjustable snap gauges GO & NOGO sizes in the anvils can be set to check therequired dimensions by using slip gauge.

Taper Gauge and Feeler Guge:

- Non dimensional gauges but rather mins of checking in terms of degree.- Their use a matter of fitting rather than measuring.

Feeler Guge:

- It consists of number of thin blades of sheet steel.- Used for cheking clearance and for gauging in narrow places.- E.g. to measure the width of gap between two parallel flat faces of piston andcylinder.- Working depends upon sense of feel.- Blade should neither be forceed between surfaces, nor should it slide freely.- Thickness range 0.03 to 1 mm available.

Workshop gauges:-

It is used by machine operator to check the dimension of the parts, as they are beingproduced. These are designed so as to keep the size of the part near the centre line of thelimit tolerance.





Inspection gauges:-

These are used by inspector in the final acceptance of the manufactured parts whenfinished. These are made of slightly larger tolerances from the workshop gauges so as toaccept work slightly nearer the tolerance limit than the workshop gauge.

Q.No. 6.b. Write notes on thermodynamic temperature scale and IPTS. 05

Ans:Thermodynamic temperature scale proposed by Lord Kelvin in 1848 provides thetheoretical basis for a temperature scale independent of any material property and basedon Carnot cycle. Here perfectly reversible heat engine transfer heat from a reservoir ofinfinite capacity at temperature T₂ to another such reservoir at T₁. If heat taken fromreservoir 2 is Q₂ that supplied to reservoir 1 Q₁,

For Carnot cycle, Q₂/Q₁=T₂/T; this may taken as a definition of temperature ratio.

If, also, a number is selected to desire the temperature of a fixed point, then temperaturescale is completely defined. At present, fixed point is called triple point of water becausethis is the most reproducible state known. The number assigned to this point is 273.16 Κsince this makes the temperature interval from the ice point [273.15 Κ] to the steam pointequal to 100 Κ.

While the Kelvin absolute thermodynamic scale is ideal in the sense that it isindependent of any material properties, it is not physically realizable since it depends onan ideal Carnot cycle. Fortunately, it can be shown that a temperature scale defined by aconstant-volume or constant-pressure gas thermometer using an ideal gas is to identical tothe thermodynamic scale. A constant-volume gas thermometer keeps fixed mass of gasconstant volume and measures the pressure changes caused by temperature.

In ternat ional Pract ica l temperature Scale ( IPTS) :

International practical temperature scale (IPTS):

The International Practical Temperature Scale is set up to confirm asclosely as possible with the thermodynamic scale. At the triple point of water, the twoscales are in exact agreement, by definition. Five other fixed points are used. These arethe boiling point of liquid oxygen(-182.962°c) and water(100°c) and the freezing pointsof Zinc(419.58°c).silver(961.93°c), and gold(1064.43°c).Various secondary points alsoestablished, with the lowest being the triple point of Hydrogen(-359.34°c), which also isthe lowest value defined on the scale (the gold point 1064.43°c is the highest definedfixed point). In addition to the fixed point, IPTS also specifies certain instruments,equations and procedures to be utilized to interpolate between the fixed points.

Above the gold point, IPTS is defined and uses a narrow-band radiationpyrometer and plank equation to establish temperature. The formula is,





Where, gold-point temperature, 1064.43°C

= Effective wavelength of pyrometer, cm

In principle, this method can be applied arbitrarily to high temperatures, but in practicefew results above 4000°C are known. The highest reproducibility of the IPTS occurs atthe triple point of water, which can be realized with a precision of a few ten-thousands ofa degree, giving an accuracy of about 1 ppm.

Dif ferent Temperature Scales:

Scale Ice-point

Steam-point

Absolutezerotemperature

Celsius 0°C 100°C -273.15°C

Fahrenheit 32°F 212°F -459.67°F

Kelvin 273.15 K 373.15 K -0 K

Rankine 491.670°R 671.67°R 0°R

Scale convers ion:

(i) =(ii) K =(iii)°R =

Q.No. 6.c. What are the different types of errors encountered in measurement system 06

Ans:TYPES OF ERRORS:

Errors may be defined as difference between the measured value and the exact value ofthe quantity. There are different types of errors.

Types of Error

Errors: They arise from different sources are usually classified as under;

1. Gross error

2. Systematic error

3. Random error





1. Gross er ror :

This class of error mainly covers human mistakes in reading instruments in recordingin calculating measurement results. The responsibility of mistake normally lies withexperimenter. The experimenter may grossly misread the scale. For example may due toan oversight read the temperature as 31.5oC while the actual reading may be 21.5oC. Inanother case he may transpose reading while recording – for example he may read 28.5 oCand record it as 25.8 oC. but as long as human beings are involved, some gross error willdefinitely be committed. Although complete elimination of gross error is probablyimpossible, one should try to anticipate and correct them. Some gross errors are easilydetected while the other may be very difficult to detect.

Gross error may be of any amount and therefore their mathematical analysis isimpossible. However, they can be avoided by adopting two means and these are,

1. Great care should be taken in reading and recording the data.

2. Two, three or even more reading should be taken for the quantity under measurement.This reading should be taken preferably by different experimenters and the reading shouldbe taken at different reading points to avoid rereading with the same error. This has theadvantage that if two sets of reading show large difference, gross error may be suspectedin the results.

2. Systemat ic er rors:

Systematic Errors are divided into three categories:

1. Instrumental Errors2. Environmental Errors3. Observational Errors

1. Instrumental errors:-

Due to inherent shortcoming in the instruments:

These errors are inherent in instruments because of their mechanical structure. They maybe due to construction, calibration of instruments. Misuse of Instruments: The errors caused in measurements are due to the fault of the operator than that ofthe instruments. Loading effects:

One of the most common error committed by beginners, is the improper use of aninstruments for measurement.

2. Environmental errors:-





These errors are due to condition external to the measuring device including theconditions in the area surrounding the instrument. These may be due to temperature, pressure, humidity, dust, vibrations or externalmagnetic or electrostatic fields.

3. Observational errors:-

There are many sources of observational errors. As anexample, the pointer of voltmeter resets slightly above the surface of the scale. Thus anerror on account of PARALLAX will be incurred unless the line of vision of the observeris exactly above the pointer. As in the fig

1. Since the parallax error arises on account of pointer and the scale not being in the sameplane, we can eliminate this error by having pointer and the scale in same plane.

2. Different observers should take the readings especially when sound and lightmeasurements are involved, to eliminate such errors.

3. Modern electrical instrument with digital display completely eliminate such errors

3 . Random Errors: -

It has been consistently found that experimental results show variation from onereading to another; even after all systematic errors have been accounted for.

These errors are due to multitude of small factors which change or fluctuate from onemeasurement to another. The happenings or disturbances about which we are unaware arelumped together and are called ‘Random’ or ‘Residual’. Hence errors

Caused by these happenings are called Random or Residual errors.





For example, in LVDT after successive measurement of displacement, We may get someoutput voltage at null position, called as residual voltage.

To eliminate random error:

1. Great care of systematic error should be taken.2. The random errors should be nullified time to time.

Q.No. 7.a. Write note on following: 20

Ans:i ) Thermal conduct i v i ty gauge for vacuum measurement .

a) Thermocouple:The most common electrical method of temperature measurement uses the thermocouple.If the two materials are connected to an external circuit in such a way that a current isdrawn, the emf may be altered slightly owing to phenomenon called the Peltier effect.'Jean Peltier' (1834) discoverd this effect.

A

B

HEATLIBERATED

HEATABSORBED

PELTIER EFFECT

If a temperature gradient exists along either or both of the materials, the junction emf mayundergo an additional slight alteration. This is called the Thomson effect. Sir WilliamThomson (Lord Kelvin) (1851) discoverd this effect.

There are, then, three emfs present in a thermoelectric circuit : the Seebeck emf, causedby the junction of dissimilar metals; the Peltier emf, caused by a current flow in thecircuit; and the Thomson emf, which results from a temperature gradient on the materials.The Seebeck emf is of prime concern since it is dependent on junction temperature. If theemf generated at the junction of two dissimilar metals is carefully measured as a functionof temperature, then such a junction may be utilized for the measurement of temperature.The main problem arises when one attempts to measure the potential. When the twodissimilar materials are connected to a measuring device, there will be another thermalemf generated at the junction of the materials and the connecting wires to the voltage-measuring instrument. This emf will be dependent on the temperature of the connecton,and provision must be made to take account of this additional potential.





It may be observed that all thermocouple circuits must involve at least two junctions. Ingeneral, one of the junctions senses the desired or unknown temperature. This junction iscalled the hot or measuring junction. The second junction is usually maintained at aknown fixed temperature and this junction is called the cold or reference junction. If thetemperature of the reference or cold junction is known, the temperature of the hot or themeasuring junction can be calculated using the thermo-electric properties of the materials.

b) R .T .D. :- In RTD temp measurements are conveniently made by change of resistance of suitablemetals of known characters.

- Range of this thermometer is 200 – 6500C.

- With increase in temp the electrical resistance of most of the metals increases in almostdirect proportion to temp rise.

- Therefore if electric resistance of wire of known calibrated material is measured thetemp of wire can be determined.

- The resistance element should be of suitable metal having high temp coefficient,reproducibility, stability.

Materials:

- Nickel, iron alloy, tungsten, Al, Cu, lead, silver, gold, platinum etc.

c) Thermistors:

Thermistors are generally composed of semi –conductor material. It having negativetemperature co –efficient of resistance, in contrast to positive co –efficient displayed bymost metals. Thermistors are widely used in application which involve measurements inthe range of -60°c to 15°c.The resistance of thermistors ranges from 0.5Ώ to0.75Ώ.Thermistors is a highly sensitive device in terms of linearity the thermistorsexhibits a highly non-linear characteristic of resistance versus temperature. Themathematical expression for the relationship between the resistance of a thermistor andabsolute temperature of thermistors is:

Rt₁=Rt₂ exp [β (⅟T1–⅟T2)]

Where, Rt₁=resistance of thermistor at absolute temperature T₁;K,

Rt₂= resistance of thermistor at absolute temperature T₂;K,

And β=constant depending upon the material of thermistor, typically 3500 to 4500K

The thermistor is a semiconductor device and therefore is subject to deterioration at hightemperatures: for this region they are limited to temperature measurements below about300°c.





i i ) Nozz le f lapper t ransducer :

It is basic component of pneumatic and hydraulic measurement and control apparatus.Fluid at restricted pressure is supplied to fixed flow restriction and variable flow





restriction connected in series. The variable flow restriction is varied by moving theflapper to change the distance Xi. This causes a change in output pressure Po which, forlimited range of motion is nearly proportional to Xi and extremely sensitive to it.

Thus pressure measuring device connected to Po can be calibrated to it. Ideally suddenchange in Xi would cause an instantaneous change in Po. Its application is also in non-contact displacement measurement.

Case 1 - A f lapper approaches to nozz l e

Resistance to flow of air supply increases.

Back pressure of nozzle increases.

Case 2 - A nozz le is complete ly c losed by f lapper

Back pressure is equal to air supply.

Case 3 - A f lapper move away f rom nozz l e

Resistance to flow of air is minimum. Total air escapes to atmosphere.

i i i ) Tachogenerators:

By the late 1950s and early 1960s, electric tachometers became the standard in theindustry. The main reason they did so was one of cost, since an electric tachometer caneasily cost less than 1/4th that of a mechanical equivalent, and there are no machinedparts necessary for operation - only a length of wire. Incidentally, electric tachometers aremore accurate, making them far more useful. An electric (or electronic) tachometer issimply a voltmeter. Instead of reading direct voltage from a wire, however, thetachometer reads from the ignition's circuitry.

Since the voltage comes in pulse form from the ignition, the electric tach's needle onlymoves upward momentarily, following each pulse of current. The greater the number ofpulses in a fixed period of time, the further the needle moves, because it is ultimatelymeasuring average voltage.

Properly calibrated, electric tachometers are extremely accurate. If their internal circuitryis designed to limit voltage spikes and extraneous interference, such tachometers are veryreliable and will last the life of the car. The only possible downside of electrictachometers is that, since they are connected to the ignition system, a major short circuitin the tachometer can disable the ignition. This happened to one of the Falcon Sprintsduring the 1963 Monte Carlo Rally. The driver had to pull out of that portion of the racebecause he wasn't smart enough to disconnect the tachometer wire. Similar thingshappened frequently in races during the 1960s until the instruments were designed toprevent ignition shorts.





A C Tachogenerators:

In order to overcome some of the difficulties mentioned above, A.C tachometergenerators are used. The tachometer generator has rotating magnet which may be either apermanent magnet or an electromagnet. The coil is wound on the stator and therefore theproblems associated with commutator (as in D.C tachometers) are absent.

D C Tachogenerators:D.C.tachometer generators consist of a small armature which is coupled to the machinewhose speed is to be measured. This armature revolves in the field of a permanentmagnet. The emf generated is proportional to the product of flux and speed. Since the fluxof the permanent magnet is constant. The voltage generated is proportional to the speed.The polarity of output voltage indicates the direction of rotation; this emf is measuredwith help of a moving coil voltmeter having scale and calibrated directly in terms ofspeed.

Fig shows a d.c. tachometer generator. A series resistance is used in the circuit for thepurpose of limiting the current from the generator in the event of a short circuit on theoutput side.

iv ) Autocol l imator :

The spirit level or auto collimator use, reference line which are straight. In level it is thetrue horizontal line and in auto collimator, it is its optical axis. The principle of themethod of measurement is shown in fig. ‘a’. ABCDE is the surface to be tested forstraightness. It is divided into four parts as shown. The level or the auto collimator

reflector block, is wrong with lapped feet at the required pitch. The level or block ispositioned on AB, BC, CD, and DE and reading are noted. These readings are convertedinto height differences between the points. These are shown in column 2 of Table 8. Incolumn 3 the values in column 2 are added cumulatively giving consideration to propersign. This gives height of each point from the true horizontal passing through, the first

C D

B

FE

A





point A. If the line joining the end points is regarded as the reference line, then theheights of the points on this line are shown in column 4. The errors at various points fromthis line joining the end points are calculated in column 5. The line joining the endpoints are not always, the reference line but in any case heights of points on the decidedreference line can always be found to obtain the errors in straightness.

v) St ra in gauge based accelerometer :

- The seismic mass is mounted on cantilever beam.

- A strain gauge is mounted on each side of the cantilever beam in order to sense thestrain in beam resulting from vibrational displacement of mass.

- Damping is provided by completely filling the housing with viscous fluid (of highviscosity).

- O/p of strain gauges is connected to an appropriate wheatstone bridge circuit whose o/pindicates the relative displacement or mass w.r.t. housing frame.

- Low natural frequency can be obtained with this system. This is on account of largelength of cantilever beam are used in order to accommodate the strain gauge.

vi ) Tool maker ’s Microscope:

- It has provision for fitting of various stds, against which magnified image of profileunder test can be compared.

- This stds are in the form of graticules – glass discs on which thread angles or referencelines are engraved.

- Mechanical linkage used is tilting mirror projecting light spot.

- Graticule (a) is used to check rack-tooth angle form.

- Spatial device allows rapid setting of line shown as P parallel to direction of worktabletravel, when circular scale is set at 00.

- Fig (a) shows the image of the rack tooth with axis of a rack parallel to worktablemovement.

- At this position circular scale reads zero.

- Fig (b) shows technique adopted to determine rack tooth angle.

- Work is rotated in order to bring surface of tooth shown as RT, parallel with line S.

- In this way very accurate determination of accuracy of small rack teeth may be made.

Mechanical measurements and metrology

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