Abstract
Tolerance transfer techniques are used extensively for allocation of tolerances for each machining operation in the process sequence, and hence are used to coordinate the process planning and the design activities in the evolution of a new product. This paper deals with an extended approach to allocate process tolerances based on a tree topology called technologically and topologically related surfaces (TTRS) and its subsequent extension to cost optimization. The benefit of this approach is that equations are generated explicitly with regard to tolerance transfer. These have been exploited by implementing the cost function in the generated explicit equations and subsequent optimization. The TTRS approach has been extended which scores over the limitations of some of the already existing techniques in that, it is optimal with respect to two factors namely, cost of producing the required tolerances, as also the process capability of the machines involved in producing the part. This technique has been proved practically feasible as it has been implemented in an industry. To enable a better view of the advantages of the approach, a comparative study with the existing techniques has been carried out in addition to a simulation using the Monte Carlo method.
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Abbreviations
- TTRS:
-
Technologically and topologically related surfaces
- Cost function:
-
\(C = A + B/T^{k} \)
- A:
-
Fixed cost include setup cost, tooling, material cost etc.
- B:
-
Cost of producing a single component dimension to a specified tolerance and includes the charge rate of the machine
- T:
-
Specified tolerance in mm
- k:
-
Sensitivity of the process cost to changes in tolerance specifications
- C:
-
Total cost of producing a single component dimension to a specified tolerance
- MGDE:
-
Minimum geometrical datum elements
- TTRS 1, TTRS 2, .... etc.:
-
Design specification TTRS
- S1, S2, S3,.... etc.:
-
Finished surfaces
- S1′, S2′, ..... , S1″,S2″,.... etc.:
-
Surfaces formed in intermediate machining operations and the final operations are yet to be performed
- TTRS1′, TTRS2′.... etc.:
-
Process plan related TTRS
- IS:
-
Indian standards
- TB.P :
-
Blue print tolerance
- Ti :
-
Tolerance of the ‘ith’ dimension
- Ai :
-
Fixed cost for the ‘ith’ dimension
- Bi :
-
Value of B for the ‘ith’ dimension
- n:
-
Number of dimensions
- λ:
-
Lagrangian multiplier
- B/P:
-
Blueprint
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Kumaravel, P., Anand, S., Ullas, U. et al. Cost optimization of process tolerance allocation-a tree based approach. Int J Adv Manuf Technol 34, 703–713 (2007). https://doi.org/10.1007/s00170-006-0641-0
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DOI: https://doi.org/10.1007/s00170-006-0641-0