Tolerance Charts Dr. Pulak M. Pandey http://paniit.iitd.ac.in/~pmpandey
Introduction A tolerance chart is a graphical method for presenting the manufacturing dimensions of a workpiece or assembly at all stages of its manufacturing 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 that processing 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
Purpose and Utilization of Tolerance Charts 1. It permits the process engineer to determine in advance of tooling whether or not the part can be made to part print tolerances. A surprising number of designs are actually dimensionally faulty 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 the sequence.
4. It provides assurance that sufficient stock removal will always be available for each operation in the sequence and what that amount is. If sufficient stock is not available tolerance charts will disclose the same. 5. When accuracy of the machine is known, the tolerance chart will indicate whether or not it is capable of meeting part print specifications. 6. It provides an intelligent instrument for negotiating with product design when manufacturing specifications cannot be met economically. 7. It offers a convenient and useful check on alternate methods of dimensioning the part for processing purpose. 8. It aids the process engineer in determining whether the part will arrive at its last operation with desired dimensions and tolerances.
9. It helps to determine the practicability of combined tooling. Such as form tools-or combinations of working and inspection gauging. 10. It provides a means of reducing dimensional errors which are likely to occur if complex parts are processed without the use tolerance charts. 11. It aids in determining the proper raw material sizes and in developing the necessary castings and forgings. 12. Together with the process picture sheet, the tolerance chart provides an invaluable aid in the development of complete and accurate process routings.
Definitions and Symbols A working Dimension is the distance between a locating surface and the surface being processed. Stock removal is the difference between the dimension that existed prior to machining and machining dimension. Resultant dimension is the difference between two dimensions or a dimension and an intermediate resultant. It is sometimes called as a balance dimension. An intermediate resultant occurs when additional stock removed in later operation will affect its size. Total tolerance is the total variation from the basic stock removal dimension which can result from the operation performed.
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 one another. This occurs when combination tools are used. This figure represents a resultant dimension between machined surfaces, centerlines, or a centerline and a machined surface.
Rules for adding and subtracting tolerances
Example: Cast steel drive hub
Conversion of asymmetrical tolerances into symmetrical tolerance
Example of tolerance conversion Add L 5.000 + 0.007 0.004 = = (5.000 + 0.0015) ± 5.0015 ± 0.0055 0.0055
Developing Tolerance Chart
Assumptions Rough forging dimension = 2 in Nominal finish dimension = 1.920 in Difference = 0.080 in to be removed from two surfaces 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 each surface = (0.080/2)-0.010= 0.030 in No change in dimensions due to heat treatment processes will be assumed in this example.
Operation 10
Operation 10: calculations Forging Dimension = 2.000±0.010 in Operation 10, W.D. = 1.970±0.002 in Stock removal = 0.030±0.012 in Min. of 0.018 in and max. of 0.042 in. can be removed. No final (resulting) dimension is resulted from this operation.
Operation 20
Operation 20: Calculations Three separate surfaces result from this operation. Location takes 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 B and C. Here, as in previous operation, a nominal 0.030 stock will be removed from A. The working tolerance is ±0.002 as before. Therefore, Operation 10, working dimension 1.970±0.002 Operation 20, working dimension 1.940±0.002 Stock removal 0.030±0.004
Operation 20 continued Surface C must be produced as a continuation of operation 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 later be removed from surface G by grinding, allowance must be made to insure that the final relationship between these two surfaces is maintained. Since 0.010 is allowed for stock removal in grinding, the working dimension will be 1.780±0.002. Therefore, Operation 20 (a), working dimension 1,940±0.002 Operation 20(b), working dimension 1.780±0.002 Stock removal 0.160±0.004
Operation 30
Operation 30: Calculations In the first step performed in operation 20,a nominal working dimension of 1.940 was established between surfaces B and G. To determine the nominal working dimensions for operation 30, two things must be considered. 1. The nominal dimension between surface G and surface F. 2. The nominal stock removal from surface G by grinding in the final operation. The nominal working dimension for this operation is found by subtracting these two dimensions from the nominal working dimension from operation 20. 1.940-0.200-0.010=1.730 with working tolerance as ± 0.002.
Operation 30 continued Because this operation is carried out with a form tool, two surfaces are created simultaneously. This automatically fixes the relationship between surfaces E and F. The form tool dimension which relates the two surfaces can carry the full part print tolerance. The resultant dimension between surfaces F and G can now be calculated as: Operation 20(a), working dimension 1.940±0.002 Operation 30, working dimension 1.730±0.002 Resultant (intermediate) 0.210±0.004
Operation 40
Operation 40: calculations Working dimension for this operation must take into account the allowance for grinding after hardening. Because the nominal depth of this milling cut is 0.250 and the nominal allowance for grinding is 0.010, the working dimension fro this operation is will be 0.250+0.010=0.260 with working tolerance ±0.002.
Operation 50 The prints requires a finished hardness depth of 0.015±0.010. Actually, this depth can be controlled within ±0.005. Because 0.010 is to be removed from each ground surface, the working case depth is set as 0.025±0.005. Since nothing has been removed from the workpiece in carburizing and hardening, no stock removal is recorded. As indicated previously, there is no change in workpiece dimension and hence no change in the resultant occurs.
Operation 60
Operation 60: Calculations The working tolerance on grinding can be achieved as ±0.0005. Because 0.010 has been allowed for grinding, the working dimension that must be held in this operation is 1.930±0.0005. Thus stock removal Operation 20, working dimension 1.940±0.002 Operation 60, working dimension 1.930±0.0005 Stock removal 0.010±0.0025
Operation 60 continued With the completion of operation 60, the dimensions from surface G to, G to C, and F to E are now finalized. Since the dimension from F to E was established earlier by the form tool and is not affected by this operation, it can be recorded as a resultant as shown in figure. Operation 30 was the last to be performed on surface F before operation 60. The resultant from G to F can now be recorded. Operation 60, working dimension 1.930±0.0005 Operation 30, working dimension 1.730±0.002 Resultant 0.200±0.0025 The resultant dimension between surfaces C and G now becomes final and can be checked. Its previous dimension was attained in operation 20(b). Operation 20(b), working dimension 1.780±0.002 Operation 60, Stock removal 0.010±0.0025 Resultant 1.770±0.0045
Operation 60 continued The case hardened depth of G must be checked to make certain the grinding operation did not cause it to fall below the depth specified. The case hardened depth is determined by the difference between the initial case depth working dimension and the stock removal in grinding Operation 50, working dimension 0.025±0.005 Operation 60, Stock removal 0.010±0.0025 Resultant 0.015±0.0075
Operation 70
Operation 70: Calculations Aside from balancing final tolerances, operation 70 completes the machining operations on the workpiece, unless it is found that additional operations must be performed to correct tolerance stacking. Stock removal may be calculated as Operation 60, working dimension 1.930±0.0005 Operation 70, working dimension 1.920±0.0005 Stock removal 0.010±0.001 Other resulting dimension of B and D Operation 40, Working dimension 0.260±0.002 Operation 70, working dimension 0.010±0.001 Resultant 0.250±0.003 Dimension of B (case hardened depth) Operation 50, Working dimension 0.025±0.005 Operation 70, working dimension 0.010±0.001 Resultant 0.015±0.006
Complete tolerance Chart (unbalance)
Balancing of Tolerance Chart If the developed tolerance chart is accepted at this stage, tight and costly processing increases cost of the product. The first step in balancing the tolerance chart is to examine the final resultant dimensions and compare them with those specified the part print. The resultant whose tolerance compare closest with the part print tolerance will be the logical place to start. As can be seen in the developed chart, the resultant dimension between surfaces C and G is 1.770±0.0045, which compares with the print dimension of 1.770±0.005. This comparison is closer than the others, balancing will start from here.
Balancing operation 60 Operation 60 can now be recalculated as: Operation 20(a), working dimension 1.940±0.002 Operation 60, working dimension 1.930±0.001 Stock removal 0.010±0.003 Operation 20(b), working dimension 1.780±0.002 Operation 60, stock removal 0.010±0.003 Resultant 1.770±0.005 The preceding resultant is now identical with the part print specifications.
An intermediate resultant between surfaces F and G was established as a result of operation 30. The final resultant was obtained in Operation 60. Because the relationship between surfaces E and F was determined by form tool, an increase can be made in the working tolerance of operation 30 without affecting other surfaces. The working dimensions of operation 30 can be changed to 1.730±0.004. The correct resultant between surfaces F and G will now be: Operation 60, working dimensions 1.930±0.001 Operation 30, working dimensions 1.730±0.004 Resultant 0.200±0.005 The dimension 0.100±0.002 remains unchanged because it was established from the form tool.
Balancing Operation 70 Operation 70 now can be recalculated as follows: Operation 60, Working dimension 1.930±0.001 Operation 70, working dimension 1.920±0.002 Stock removal 0.010±0.003 Operation 40, working dimension 0.260±0.002 Operation 70, stock removal 0.010±0.003 Resultant 0.250±0.005 Operation 50, working dimension 0.250±0.007 Operation 70, Stock removal 0.010±0.003 Resultant 0.015±0.010
Completed Tolerance Chart