An extended form of the reciprocal-power function for tolerance allocation

The optimization of dimensional tolerances requires that a cost-tolerance function is evaluated consistently for all the part features involved in a given functional requirement. This is difficult because the parameters of commonly used functions are set using cost data from various sources and on possibly different scales. As an alternative, the paper proposes a revised form of one of the available cost-tolerance functions (reciprocal power), which expresses its parameters in empirical relationship with a set of design specifications on the toleranced features. These include the nominal dimension, the shape, the surface area, and the material. Following a previous study based on cost data available in literature, the values and expressions of the parameters are validated and refined using a feature-based method for the estimation of machining cost. The properties of the extended function allow to develop a simplified method for tolerance allocation that avoids the task of solving the optimization problem; it is a modified version of proportional scaling where the initial solution satisfies optimal ratios between tolerances. The discussion of the results and an application example help to justify the proposed function on grounds of correctness, convenience, and reference value.