Selection of parameters in cost-tolerance functions: review and approach

The paper deals with the cost-tolerance functions used in minimum-cost tolerance allocation on mechanical assemblies. The consistency of the cost-tolerance functions associated with different dimensions of a tolerance chain is a necessary condition for a correct optimization of tolerance values. This requires a careful selection of function parameters, in order to take into account all the variables influencing the cost, and thus to compare the costs of the different dimensions in a common scale. The cost-tolerance functions proposed in the literature are reviewed, revealing that the parameters are often selected without explicit reference to empirical data or objective rules. The development of procedures for parameter selection has been addressed in several studies, which are also reviewed along with the needed cost data published in textbooks and reports. Finally, an original approach is proposed to build cost-tolerance functions for combined processes, for which fewer results or methods are available. The parameters of a reciprocal power function, chosen for the favorable balance between accuracy and ease of use, are expressed through an empirical relationship with some design variables; these include the nominal dimensions and the type and size of the part features involved in the allocation problem. An application example shows that the proposed procedure results in optimal tolerance values consistent with common design criteria.