Abstract
A new method for optimal concurrent process tolerance is proposed. Information related to process planning is used during the structure design stage of a product. The functional tolerances of the assembly of a product are considered process tolerances. A nonlinear optimal concurrent process tolerance model has been established to minimize the total manufacturing cost with different weight factors for the operations of the product. The constraints include concurrent process tolerance chains, the standard coefficient of process tolerance, and the economical maximum tolerance of the machine tools. In order to obtain optimal process tolerances, a new approach based on grey difference degree is presented in this paper. This approach takes the sequence consisting of the optimal value of every objective as the standard sequence, and that consisting of the actual values as the objective sequence. Thus, grey difference degree is calculated and used as the objective of the function. Finally, a practical example is introduced to demonstrate the effectiveness of the proposed method.
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Abbreviations
- Y 0 :
-
standard sequence
- Y 0(k):
-
k-th component of the standard sequence
- Y i :
-
objective sequence
- Y i (k):
-
k-th component of the objective sequences
- ξ (k):
-
the grey correlation coefficient of Y i relative toY 0 at point k
- y i :
-
the i-th required tolerance specification of assembly structure
- TX :
-
design tolerance vector of assembly structure
- r u :
-
the total number of relative process steps for u-th part
- T uv :
-
v-th relative process tolerance vector of u-th part
- λ uv :
-
selection coefficient of process sequence
- w uv :
-
the weight coefficient of the process tolerance T uv
- C uv :
-
manufacturing cost of the process tolerance T uv
- C uv * :
-
the ideal value of C uv
- z uv :
-
the standard normal transform coefficient relative to process tolerance T uv
- σuv :
-
the standard deviation of T uv
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Acknowledgements
This research work is funded by Doctoral Program Foundation of the Ministry of Education (No.20010487024).
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Chen, Y., Huang, M., Yao, J. et al. Optimal concurrent tolerance based on the grey optimal approach. Int J Adv Manuf Technol 22, 112–117 (2003). https://doi.org/10.1007/s00170-002-1448-2
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DOI: https://doi.org/10.1007/s00170-002-1448-2