Tolerance allocation of a system is formulated as a cost minimization problem, subject to a system reliability requirement. A reciprocal cost-tolerance model is used. The system reliability is calculated by the Monte Carlo simulation. Optimum tolerance combination is studied by the Taguchi Method. Assembly, binding, noise, backlash and transmission errors are considered as failure functions.
Regarding the tolerance allocation, a two step optimization is suggested. In the first step, the minimization of (cost/reliability) is applied with no reliability limit, and then the maximization of (reliability increment/cost increment) applied enforcing the constraint.
A planetary gear system and a spur gear train are taken as examples. The optimum tolerances are obtained in 20 and 15 iterations respectively. The method used is shown effective and practically applicable to the design of complex systems.
