In general, a tight tolerance is required to ensure high system reliability, but this also means high manufacturing cost. Therefore, depending on the system requirement, a proper trade-off should be considered and corresponding optimal allocation of tolerances becomes very important. A planetary gear system is taken as a realistic practical problem of tolerance optimization. The main purpose is to allocate optimal tolerances to critical dimensions with the objective of minimizing manufacturing cost while keeping the system reliability above a prescribed level.
Various geometric relations and constraints are obtained and the problem is formulated as a reliability based optimization. In calculating the system reliability, the Monte Carlo simulation is preferred to analytical methods because of the complexity of the system and constraint functions. The effect of sample size is first studied. A numerical optimization that is similar to the coordinate line search is used due to the convenience of programming, although computationally inefficient. The numerical solution obtained is compared with the data from existing product drawings and judged to be very reasonable with a significient saving.
