IPE - 302 Sessional Sheet

8/6/2019 IPE - 302 Sessional Sheet

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Bangladesh University of Engineering and TechnologyDepartment of Industrial and Production Engineering

IPE 302

Report should contain

1. Exp. number and name of the experiment

2. Objectives

3. Figure and deduction of equation used

4. Equipments used

5. Data and sample calculation

6. Results and graphs (if necessary)

7. Discussions.

8. Answer to the given questions.

Note for the Students

1. The student should read the supplied sheet thoroughly and try to understand

conceptually

2. Reports must be competent with the required contents

3. The student should be familiar with the measuring instruments beyond theseexperiments.

4. The student should deduce the formula to be used.

5. The procedure for each experiment mentioned in the sheet is just a guideline. For

details, books are referred.

References

1. Grumman, E.V: Metrology in Alignment of M/c. tools.

2. Sharp K.W.B: Practical Engineering Metrology

3. ASTME & Handbook of Industrial Metrology

4. Kenedy, C.W: Inspection and Gaging.


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IPE 302

Expt. No. 1i) Check the normality by X 2 (Chi-square) test.ii) Measurement of angle of Template by,

a)

Bevel protractor b) Angle gauge.

Expt. No. 2i) Measurement of Splinesii) Determination of radius of Convex are.iii) Determination of radius of Concave areiv) Measurement of Screw thread by wire

Expt. No. 3

i) Design and Implementation of a Lot- By- Lot Acceptance Sampling Planii) Calibration of Slip Gauges using Supermicrometer iii) Measurement of propeller by using Pitchometer.

Expt. No. 4i) Measurement of angles by

a) 3 rollers and b) 2 rollers.

ii) Measurement of gear teeth by gear teeth Vernier Calipersiii) Measurement of Bore by,

a) Two balls. b) Pin gauge.

Expt. No. 2 Measurement of Tapers:

i) By rollers, Slip gauges and Micrometer.ii) Ring gauge measurement by unequal Balls.iii) Taper Plug measurement by Sine Bar and Dial Gauges

General Information

Factors affection the accuracy of measurement

1. Least count of subdivisions

2. Line matching

3. Parallax in reading

4. Elastic deformation of the instrument and work-piece

5. Temperature effect


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Measurement Instruments:

A. Linear

i) Direct-reading: Machinist scale, combination set, Rule-depth gauge, Vernier calipers, Vernier height gauge, Micrometer.

ii) Indirect-reading: There are various methods.

B. Angle: Bevel protractor, m attachment on the combination set, Universal bevel, Sine bar,Angle gauge clock.

C. Taper : Taper plug gauge, Ring gauge.

Gauge: A comparison type measuring instrument. Common gauges are: Plug gauges, plain pluggauges, Taper Plug gauges, Thread plug gauges, Spline gauges, Ring gauges, Ring threadgauges, Snap gauges, Slip gauges, Form gauges, Radius gauges, Pin Hole gauge, telescopicgauges, Screw thread pitch gauges, dial indicators.

Experiment No. 1

1(i) Check the normality by 2(chi-square) test

1. Measure the diameter of 150 rollers.

2. Calculate mean ( ) and standard deviation ( )3. Make ten equal intervals (between the lowest and highest measurement)

4. Count the number of rollers in each interval

5. Draw the histogram (frequency distribution)

6. Apply 2 test to check the conformity with normal distribution (assume 0.05)A goodness of fit test between observed and expected frequencies is based on the quantity

( )ei

eioi X

ical

==

r

1

2

2 = is the value of a random variable whose sampling distribution isapproximately very close to chi-square distribution

oi = observed frequencyei = Expected frequency

Expected frequency (e i): Expected frequency for each interval is obtained from a normal curve

having the same mean and standard deviation as our sample.

For ith interval,ei

= (Area under the interval from normal curve) Total no. of sample.

No. of degrees of freedom= No of interval or cell No of quantities needed from the sample to calculate

the expected frequency.


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Test for good fit of the Normal distribution:1. Normally distributed2. H Non-normally distributed3. Level of significance a (given)4. 2cri (critical), degrees of freedom (from table)5. 2

cal cal (From data)

6. Conclusion: Accept or reject1(ii) : Measurement of angle of template by

a) Bevel protractor b) Angle gaugea) Bevel protractor consists of a round body with a fixed blade on which a graduated

turret rotates. The turret is slotted to accommodate a non-graduated blade.Through locking mechanism any desired angle up to 360 can be measured.

b) Angle gauges consist of pieces of hardened and stabilized steel. There are thirteen pieces in the set one being square plate and with these few places it is possible toset up any angle to the nearest 3 sec.

The set consists of three serves of values of the angle, namely:

1, 2, 9, 27 and 41 degrees1, 3, 9 and 27 minutes0.1, 0.3 and 0.5 minutes

Exp. No. 2

2(i) Measurement of Splines

To measure the angle between splines, it is first necessary to measure the root diameter of the shaft and the width of each spline.

Fig : 2.1


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Referring to the figure,

d D

d SSin

d Dd W

d Dd W

Sin

+

+=+

+=

++=

++=

d)1/2(D

d)1/2(S

)()(

)(1/2)(1/2

2(ii) Determination of radius of a Convex Arc with the help of fixed roller instrument

Referring to figure the distance a from the arc to the line joining the roller centers is measured by means of the micrometer. From this dimension together with the center distance of the rollersand their diameter, the radius is calculated.

The instrument is first placed o a true straightedge and a reading of the micrometer taken withthe spindle end in contact with the straightedge. It is then placed on the arc and a reading takenon this. The difference between the two readings is the height of the arc above the tangent to therollers (dimension h).

Fig : 2.2

2)(

8h

)2

()2

(

a)(R )2C

()2

(

)2d

(

2

22

222

hd C R

hd

RC

d R

ha

=

++=

++=+

=

Assignment:

Find the possible error in the radius,


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diameter will be obtained only if the wires make contact at the pitch line. Wires of this sizes arereferred to as best size wires. The diameter of the wires used should be such that they contactthe flanks at a distance from the pitch line not exceeding one-twentieth of the length of thestraight flank.The effective diameter E is given by:

E = T + P

T is measured as shown in the Fig. 2.4

Fig. 2.4Here, T = D-2dP is a constant whose value depends on the diameter of the wires

1)-2/(cos2/cot2 ecd f P =

where f =1/TPI

Experiment No. 3 (i): Design and Implementation of a Lot- By- Lot Acceptance SamplingPlan

Sampling is a quality assurance tool. It is based on the idea that a random selection of a samplefrom a homogenous lot represents the quality of the lot. It is obvious that sampling involvesrisks but apart from the necessity of acceptance sampling as in the case of destructive testing,advantages of sampling are significant. It is also to be remembered that the purpose of sampling is to guide the course of action, not to estimate lot quality. Further, acceptancesampling is not an attempt to control the quality but to assure the quality.

A typical application of acceptance sampling is as follows: a company receives a shipment of product from a vendor. This product is often a component or raw material used in thecompanys manufacturing process. A sample is taken from the lot, and some qualitycharacteristics of the units in the sample is inspected. On the basis of the information in thissample, a decision is made regarding lot disposition.

Most generally applied sampling scheme is single sampling plan, where other sampling planslike double sapling plans, multiple sampling plan and sequential sampling plans are other advanced varieties. A single sampling plan is a lot sentencing procedure in which one sample


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of n units is selected at random from the lot and the disposition of the lot is determined basedon the information contained in that sample.

The real problem in most acceptance sampling is to design a satisfactory acceptance samplingsystem or more commonly, to select such a system from a number of possible systems alreadydeveloped. To judge the suitability of any proposed acceptance sampling system in a particular

case, it is desirable to have an understanding of the strategy and tactics built into the variousavailable types of systems.

Based on manufacturers product quality, data-type e.g. variables and attributes, can alsoclassify sampling plan. Variables, of course, are quality characteristics that are measured on anumerical scale. Attributes are quality characteristics that are expressed on a go, no-go basis.Present day industrial practice of acceptance sampling is by attributes and will doubtlesscontinue to be so. But, the growth of knowledge of statistical quality control techniques has ledto a considerable increase in the industrial use of acceptance sampling by variables. It seemslikely that this tendency will continue.

Acceptance sampling by variables is often preferable, though costly, to acceptance sampling byattributes, particularly for those quality characteristics that are source of troubles. The greatadvantage of the use acceptance sampling by variables is that more information is obtainedabout the quality characteristics in question. In this experiment, an acceptance sampling planfor variables will be designed and implemented.Nomenclatures and Equations: = Producers risks = Consumer risk P 1 = Lot fraction defective for which probability (Acceptance) 1- P 2 = Lot fraction defective for which probability (Acceptance) LSL = Lower Specification Limit USL = Upper Specification Limit n = Sample Size k = Critical Value

X = Sample meanP LSL = Fraction defective estimates corresponding to LSLP USL = Fraction defective estimates corresponding to USLM = Allowable fraction defective

1

2)(

= n

X X S

ZLSL=s LSL X

ZUSL=s

X USL


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Procedure:The nomograph shown in figure 3.1 is used to find the required sample size n and the criticalvalue k to meet a set of given conditions P 1 ,P 2, 1- , for both the known and unknowncases. The greater uncertainty in the case where the standard deviation is unknown requires alarger sample size than does known case but the same value of k is used.

After determining n and k from the nomograph, the diameters of the balls supplied ismeasured and X & s is calculated. From given LSL and USL values Z LSL and Z USL iscalculated. From figure 3.2 the value of M is determined. P LSL and P USL can be determinedfrom figure 3.3.

If P LSL + P US L M , the will be accepted, otherwise it will be rejected.

Figure 3.1 : Nomograph for Designing Variables Sampling Plan


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Figure 3.2 Chart for determining maximum allowable fraction defective M

Figure 3.3 Chart for determining P from Z


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Again, let the vertical distance traveled by the screw fitted on any point of pitch circle be for angle of rotation.

Then the pitch,

h

P 360=

Experiment No. 4

4(i): 3 rollers and 2 rollers

The standard units of angular measurement is the degree, m Radian for mathematicalinvestigation. The selection of an angle measuring instrument depends upon the component andthe accuracy of measurement required.

Part I

(a) In this method 3 rollers of equal diameter are used referring to Fig..4.1 the distance H ismeasured by a depth micrometer or a straight edge and slip gauges and hers,

AC = H

D H

AB AC

Cos ==2

whereD is the diameter of the roller.

This arrangement is used for angles between 180 and about 60. But for angles below 90 it may be preferable to measure the gap between the two outer rollers as shown in Fig (b) in this case.

D DS

22sin

+=

Fig. 4.1(a) Angle measurement by equal discs


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Fig. 4.1(b) Angle measurement by equal discs

Fig. 4.1(c) Angle measurement by equal discs

(b) For angles less than 60 only two rollers are used as shown in fig. (C). Thedistance S being measured by slip gauges with this arrangement, BC = S and

DS

AB BC

Sin ==

Questions:

(a) What is the Indirect measuring instrument used in the experiment?

(b) Which angle measuring instrument used in the laboratory is comparatively moreaccurate?

(c) Sing /2 = (S + D)/2D. Assuming S to be 5 0.01 mm, find error

4(ii) Measurement of gear teeth by Gear Teeth Venire Caliper

1. Calculate the chordal thickness (w) of the teeth.


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2. Calculate the chordal addendum (H) of the teeth3. Measure the height (h) with width (w)4. Measure the width (w) with height (h)5. Find the percentage errors.

Here the chordal thickness (w) is,

T90

SinPT

T90 == DSinW

Where,P = Diametrical pitch

..2

DOT

P+=

Pitch Circle radius,P

T Nm R22 ==

ChordalP1

)T90

Cos1()( += R H addendum

Experiment No. 4 (iii)

a) Two ball method:

This method can be applied to obtain the diameter of a recessed hole. Higher accuracycannot be attained with this method. Referring to fig.4. 2.

2dd

CD

)2

ddH(H)

2dd

(C

21

21212

2212

++=

++=

Fig. 4.2: Measurement of Diameter of Hole by Two Balls


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2)d(d 21 ++= C D

(b) Pin gauge method:

Internal diameter is measure by a pin with spherical ends, the length of which isslightly less than the diameter to be measured. The pin is placed in the bore with itsends in contact with the bore surface, keeping one end in contact with the boresurface, the other end is brought across to make contact at the other side of a diameter.The distance between the two points of contact is measured and from this dimensionand the length of the pin gauge, the diameter of the bore is determined.Referring to the Fig. 4.3

AE.EB = DE.EC = W 2 AE 2 = AC 2 EC 2

Fig. 4.3: Measurement of bore by pin gauge

22

2

22

222

WL

L

WL

WWL

=

+=

+= EB AE D

It may be simplified (applying binomial theorem) as,

)2LW(L)

LWL(1)W(LL 2

2

2

1

2

2

2

1

222 +===

D

Question:

i) What is the two ball method more advantageous?ii) What is the difference between a measuring tool and a gaugeiii) How do the error in measurement can be eliminated?


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iv) What is the contact surfaces of two slip gauges?v) How do we find a venire constant?vi) What happens when the diameter of both the balls are equal for 2 ball method?

Experiment No. 5 Measurement of Tapers

5(i) Measurement of a Taper Plug gauge by Rollers, Step Gauge and SlideCalipers

In this method, measurements are made over two equal rollers standing on slip gaugesat each side of the taper plug. Two measurements are needed, one near each and of the

plug. From these, together with the difference in heights of the stacks of slip gauges.The angle of the taper is easily calculated. The diameters at the ends of the plug arederived from additional measurements of the axial distances from the ends to the

planes through the roller centers.

The half angle of the taper is given by

)h2(hMM

/2tan12

12

=

Fig. 5.1 Measurement of Taper Plug Gauge by Means of Rollers

The diameters in the planes through the roller centers are obtained from

D1 = M 1 d(1 + sec /2)

D2 = M 2 d(1 + sec /2)

The diameter at any other position is then easily found. Thus at the ends

Ds = D 1-2 (h 1 H 1) tan /2DL= D 2 + 2(H 2 h 2) tan /2

Equipments used:1. Rollers of equal diameters


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2. Slide calipers3. Depth gauge4. Slip gauge

In order to obtain satisfactory results a number of practical details require attention.The plug gauge should be set up on its small end, so that the force exerted by the

micrometer used for the micrometer used for the diametrical measurements tends towedge he rollers against the cone and the slip gauges. If set up on its large end, asmay sometimes be unavoidable, care must be taken to prevent the rollers riding up thetaper. The force applied by the slide calipers must be kept small by using theinstrument with a light touch, to avoid errors caused by elastic indentation. The roller and gauge make contract at a point and the stress here may be very high. An error of 0.0025 mm can quite easily occur.

Generally, it will be possible to stand the gauge directly on the surface pate, therebydispensing with the slip gauges on which it is shown supported in the figure. Thisreduces the number of dimension to be observed and results in slightly increasedaccuracy. With a small gauge, especially one which is long in relation to its diameter,some difficulty may be experienced in keeping it on its base. In this case, a smallvertical force may be applied to the bop of the gauge by means of a spring-loaded

plunger with a rounded and which is supported from a vertical column with a heavy base resting on the surface plate.

The rollers should preferably be of about the same diameter as the slide calipersanvils, which can then be rested on the slip gauges to ensure that the measurement ismade at right angles to the gauge axis. This is particularly important on gauges of small diameter.

The uniformity of taper is checked by taking a third diametrical measurement aboutmid way along the gauge and comparing this with the value as this position calculatedfrom the two other readings. An additional test is done for the straightness of thecontact against an illuminated background.

To test for any out-of-roundness of the cross section, three sets of readings should betaken along different diameters at each axial position. If these readings do not vary bymore than the variation in the readings of any one diameter, the out-of-roundness isnot measurable with the equipment and skill employed.

The possible error in the angle of taper may be calculated in the following manner.

Let M 2 M 1 = M

and h2 h 1 = h

Then, since

.2hM

.2

2.Cos.2h1

.2

2.Cos

..

2hM

)h2(hMM

2

tan

222

12

12

=

+=

==

hh

M M


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Now,22 h)

2M

(

h2

+=Cos

]h.2h

MM.

2h1

[h)

2M

(

2h2

22

2

+=

]..[h)

2M

(

122

h M M h +

=

Usually, the error is very small, being that in the slip gauges used. If this error isneglected, the expression reduces to

M .h)

2M

(

h22 +

=

from which it is clear that, for any given value of h, the error the angle increases asthe value of M decreases. This means that the error in the measured value of the angleof a slow taper is larger than that of a quick taper. It is, however, only slightly larger,

but, when expressed as a percentage of the angle, given it larger figure. As examples,suppose that, m in measuring two this gauges, the dimension h is 100 mm in bothcases and the values of h are 75 mm for one gauge and 6 mm for the other, with a

possible error on 0.005 mm. The angle of the taper is approximately 41 degree for thefirst gauge and 2.5 degree for the second.

5(ii) Ring Gauge Measurement by Unequal Balls

Many internal tapers are either too long or too small in diameter to permit of using themethod described in the preceding experiment. In these cases, two balls are used of such sizes that one will rest in the cone near the large and one near the small end.Their distances from a datum surface, such as one end of the gauge, are measured by amicrometer depth gauge.

Referring to Fig. 5.2 the semi-angle of the taper is given by

)(21

)(21

2sin

2121

21

d d hh

d d

BC CD

+

==


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or 1)()(2

2cos

21

21 +=

d d

hhec

The diameter in the places of the ball centres are

2

secd 11 = D 2

secd 22 = D

Fig. 5.2: Internal Taper Measurement by Unequal Balls.

Then the diameters at the ends of the taper are

2tan)

21

(2 111

hd D D L +=

2tan)2(

2sec 111

hd d +=

and 2tan)22(2sec 222

d h H d D S = Equipments used:

1. Two unequal balls2. Micrometer depth gauge3. Slide calipers

The uniformity of the taper can be checked by taking a measurement to a third ballseated midway along the taper.


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The errors which may occur in the results obtained from these measurements arecalculated from the following expressions.

Let the distance between ball centres = c and the difference between ball radii = r

Thencr =

2sin

The error in the angle is

( )cr r cr cc

ccr

r c

cc

r r

..2

..1

)2/sec(2

..

22

2

+

5(iii) Taper Plug Measurement by Sine Bar and Dial Gauge

The arrangement for this method is shown Fig. 5.iii.1 The sine bar is set up on asurface place to the nominal angle of the taper plug which is then placed in positionon the bar, being prevented from sliding down by the stop plate at the end. Care must

be taken to ensure that the axis of the plug gauge is aligned with the sine movement.

The dial gauge, supported in a stand on the surface place, is then passed over the pluggauge near each end and at one or two positions between the ends. If there is anyvariation in the readings two alternatives are available for finding the true angle of thecone. Either the variation over a measured distance along the surface of the pluggauge can be used to obtain the difference between the true angle and the angle set upor the height of the slip gauge pile can be adjusted until no variation occurs in thereadings of the dial gauge. If only the angle of the gauge is to be found. The former method is quicker, but adjustment of the slip gauge pile is preferable if the diameter of the small end is also to be determined by the method about to be described.

Fig. 5.3(a): Measurement of Taper Plug Gauge by Sine Bar and Dial Gauge


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DF = BG sec /2= (h + d) sec /2

DE = 2.d/2 tan /2Ds = (h + d) sec /2 + d tan /2

The diameter at the large end of the plug gauge can then be found from the equationDL = D s + 2H. tan /2

Where, H is the axial length of the gauge. Too much reliance should not be placedupon the accuracy of the diameter obtained in this way. It is considerably less than theaccuracy of the small end diameter, because of the effect of errors in the angle.

IPE - 302 Sessional Sheet

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