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Tolerance Charts
Dr. Pulak M. Pandey
http://paniit.iitd.ac.in/~pmpandey
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Introduction
A tolerance chart is a graphical method for
presenting the manufacturing dimensions of aworkpiece or assembly at all stages of itsmanufacturing dimensions of a workpiece or
assembly at all stages of its manufacturing The chart provides an intermediate control
system of checks and balances to insure thatprocessing dimensions and tolerances will
meet those specified on part prints The tolerance charts are useful in sorting
dimensional problems on individual parts, and
also useful in processing assemblies
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Purpose and Utilization of ToleranceCharts
1. It permits the process engineer to determine in
advance of tooling whether or not the part canbe made to part print tolerances. A surprisingnumber of designs are actually dimensionallyfaulty and can not be manufactured to print. If
this condition can be discovered in advance,costly scrap can be prevented.
2. It aids in developing proper manufacturing
sequence.3. It provides a means of establishing the proper
working tolerances for each operation in thesequence.
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4. It provides assurance that sufficient stockremoval will always be available for eachoperation in the sequence and what thatamount is. If sufficient stock is not availabletolerance charts will disclose the same.
5. When accuracy of the machine is known, thetolerance chart will indicate whether or not it iscapable of meeting part print specifications.
6. It provides an intelligent instrument for
negotiating with product design whenmanufacturing specifications cannot be meteconomically.
7. It offers a convenient and useful check onalternate methods of dimensioning the part forprocessing purpose.
8. It aids the process engineer in determining
whether the part will arrive at its last operationwith desired dimensions and tolerances.
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9. It helps to determine the practicability ofcombined tooling. Such as form tools-orcombinations of working and inspectiongauging.
10. It provides a means of reducing dimensionalerrors which are likely to occur if complex partsare processed without the use tolerance charts.
11. It aids in determining the proper raw materialsizes and in developing the necessary castingsand forgings.
12. Together with the process picture sheet, thetolerance chart provides an invaluable aid inthe development of complete and accurateprocess routings.
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Definitions and Symbols A working Dimensionis the distance between a
locating surface and the surface beingprocessed.
Stock removalis the difference between thedimension that existed prior to machining andmachining dimension.
Resultant dimensionis the difference betweentwo dimensions or a dimension and anintermediate resultant. It is sometimes called as abalance dimension. An intermediate resultant
occurs when additional stock removed in lateroperation will affect its size.
Total toleranceis the total variation from the
basic stock removal dimension which can resultfrom the operation performed.
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The circled dot denotes a locating
surface or centerline. The arrow
denotes the surface or centerline of the
surface to be machined.
Working dimension when tools are set
in a definite relation ship to oneanother. This occurs when combination
tools are used.
This figure represents a resultant
dimension between machined
surfaces, centerlines, or a centerline
and a machined surface.
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Rules for addingand subtracting
tolerances
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Example:
Cast steeldrive hub
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Conversion of asymmetrical tolerances into symmetrical tolerance
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Example of tolerance conversion
0055.00015.5
0055.0)0015.0000.5(000.5 007.0 004.0
=
+=+
Add L
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Developing Tolerance Chart
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Assumptions Rough forging dimension = 2 in
Nominal finish dimension = 1.920 in
Difference = 0.080 in to be removed from twosurfaces B and G
Both B and G surfaces are to be machined,hardened and ground, therefore let us assume
that 0.010 in is left for grinding for each surface.
Therefore stock to be removed from eachsurface = (0.080/2)-0.010= 0.030 in
No change in dimensions due to heat treatmentprocesses will be assumed in this example.
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Operation 10
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Operation 10: calculations
Forging Dimension = 2.0000.010 in
Operation 10, W.D. = 1.9700.002 in
Stock removal = 0.0300.012 in
Min. of 0.018 in and max. of 0.042 in.can be removed.
No final (resulting) dimension is resultedfrom this operation.
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Operation 20
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Operation 20: Calculations
Three separate surfaces result from this operation. Locationtakes place on surface G which was machined in operation 10.Surface A is faced, the center hole is core drilled and reamed,and the surface C is turned. Here, we concern with surfaces Band C. Here, as in previous operation, a nominal 0.030 stock willbe removed from A. The working tolerance is 0.002 as before.
Therefore,
Operation 10, working dimension 1.9700.002
Operation 20, working dimension 1.9400.002
Stock removal 0.0300.004
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Operation 20 continued
Surface C must be produced as a continuation ofoperation 20, using the same locating surface.Because the position of the surface C with respect to
surface G is affected by the amount which will laterbe removed from surface G by grinding, allowancemust be made to insure that the final relationshipbetween these two surfaces is maintained. Since
0.010 is allowed for stock removal in grinding, theworking dimension will be 1.7800.002. Therefore,
Operation 20 (a), working dimension 1,9400.002
Operation 20(b), working dimension 1.7800.002
Stock removal 0.1600.004
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Operation 30
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Operation 30: Calculations
In the first step performed in operation 20,a nominalworking dimension of 1.940 was established betweensurfaces B and G. To determine the nominal working
dimensions for operation 30, two things must beconsidered.
1. The nominal dimension between surface G andsurface F.
2. The nominal stock removal from surface G bygrinding in the final operation.
The nominal working dimension for this operation is foundby subtracting these two dimensions from the nominalworking dimension from operation 20.
1.940-0.200-0.010=1.730 with workingtolerance as 0.002.
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Operation 30 continued
Because this operation is carried out with a
form tool, two surfaces are createdsimultaneously. This automatically fixes therelationship between surfaces E and F. Theform tool dimension which relates the twosurfaces can carry the full part print tolerance.The resultant dimension between surfaces Fand G can now be calculated as:
Operation 20(a), working dimension 1.9400.002
Operation 30, working dimension 1.7300.002
Resultant (intermediate) 0.2100.004
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Operation 40
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Operation 40: calculations
Working dimension for this operationmust take into account the allowance for
grinding after hardening. Because thenominal depth of this milling cut is 0.250and the nominal allowance for grindingis 0.010, the working dimension fro thisoperation is will be 0.250+0.010=0.260
with working tolerance 0.002.
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Operation 50
The prints requires a finished hardnessdepth of 0.0150.010. Actually, thisdepth can be controlled within 0.005.Because 0.010 is to be removed fromeach ground surface, the working casedepth is set as 0.0250.005. Since
nothing has been removed from theworkpiece in carburizing and hardening,no stock removal is recorded. As
indicated previously, there is no changein workpiece dimension and hence nochange in the resultant occurs.
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Operation 60
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Operation 60: Calculations
The working tolerance on grinding can be
achieved as 0.0005. Because 0.010 hasbeen allowed for grinding, the workingdimension that must be held in this
operation is 1.9300.0005. Thus stockremoval
Operation 20, working dimension 1.9400.002
Operation 60, working dimension 1.9300.0005Stock removal 0.0100.0025
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Operation 60 continued
With the completion of operation 60, the dimensions fromsurface G to , G to C, and F to E are now finalized. Sincethe dimension from F to E was established earlier by theform tool and is not affected by this operation, it can be
recorded as a resultant as shown in figure. Operation 30was the last to be performed on surface F beforeoperation 60. The resultant from G to F can now berecorded.
Operation 60, working dimension 1.9300.0005
Operation 30, working dimension 1.7300.002
Resultant 0.2000.0025
The resultant dimension between surfaces C and G now
becomes final and can be checked. Its previousdimension was attained in operation 20(b). Operation 20(b), working dimension 1.7800.002
Operation 60, Stock removal 0.0100.0025
Resultant 1.7700.0045
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Operation 60 continued
The case hardened depth of G must bechecked to make certain the grinding
operation did not cause it to fall below thedepth specified. The case hardeneddepth is determined by the difference
between the initial case depth workingdimension and the stock removal ingrinding
Operation 50, working dimension 0.0250.005
Operation 60, Stock removal 0.0100.0025
Resultant 0.0150.0075
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Operation 70
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Operation 70: Calculations
Aside from balancing final tolerances, operation 70completes the machining operations on the workpiece,unless it is found that additional operations must beperformed to correct tolerance stacking. Stock removal
may be calculated as Operation 60, working dimension 1.9300.0005 Operation 70, working dimension 1.9200.0005
Stock removal 0.0100.001
Other resulting dimension of B and D Operation 40, Working dimension 0.2600.002
Operation 70, working dimension 0.0100.001
Resultant 0.2500.003
Dimension of B (case hardened depth) Operation 50, Working dimension 0.0250.005
Operation 70, working dimension 0.0100.001
Resultant 0.0150.006
C l t t l Ch t ( b l )
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Complete tolerance Chart (unbalance)
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Balancing operation 60
Operation 60 can now be recalculated
as: Operation 20(a), working dimension 1.9400.002
Operation 60, working dimension 1.9300.001
Stock removal 0.0100.003
Operation 20(b), working dimension 1.7800.002
Operation 60, stock removal 0.0100.003
Resultant 1.7700.005
The preceding resultant is now identical with the part printspecifications.
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An intermediate resultant between surfaces Fand G was established as a result ofoperation 30. The final resultant was obtainedin Operation 60. Because the relationshipbetween surfaces E and F was determined by
form tool, an increase can be made in theworking tolerance of operation 30 withoutaffecting other surfaces. The workingdimensions of operation 30 can be changed
to 1.7300.004. The correct resultantbetween surfaces F and G will now be: Operation 60, working dimensions 1.9300.001
Operation 30, working dimensions 1.7300.004Resultant 0.2000.005
The dimension 0.1000.002 remains unchangedbecause it was established from the form tool.
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Balancing Operation 70 Operation 70 now can be recalculated as
follows: Operation 60, Working dimension 1.9300.001
Operation 70, working dimension 1.9200.002
Stock removal 0.0100.003
Operation 40, working dimension 0.2600.002
Operation 70, stock removal 0.0100.003
Resultant 0.2500.005
Operation 50, working dimension 0.2500.007
Operation 70, Stock removal 0.0100.003
Resultant 0.0150.010
Completed Tolerance Chart
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Completed Tolerance Chart