Dimensional Tolerance Allocation of Stochastic Dynamic Mechanical Systems Through Performance and Sensitivity Analysis

Abstract

Uncertainties due to random dimensional tolerances within stochastic dynamic mechanical systems lead to mechanical errors and thus, performance degradation. Since design standards do not exist for these systems, analysis and design tools are needed to properly allocate tolerances. This paper presents probabilistic models and methods to allocate tolerances on the link lengths and radial clearances such that the system meets a probabilistic and time dependent performance criterion. The method includes a general procedure for sensitivity analysis, using the effective link length model and nominal equations of motion. Since the sensitivity analysis requires only the nominal equations of motion and statistical information as input, it is straight forward to implement. An optimal design problem is formulated to allocate random tolerances. Examples are presented to illustrate the approach and its generality. This paper provides a solution to the tolerance allocation problem for stochastic dynamically driven mechanical systems.