Mechanical system design incorporating non-Gaussian, nonparametric uncertainty during the conceptual stage.

Abstract

Robust products can be manufactured cost-effectively if design decisions made during the conceptual design stage account for uncertainty in specifications and variations in manufacturing processes. Capturing uncertainty is critical in order to provide the designer with the freedom to explore many possibilities. Predicting manufacturing errors is critical in order to develop a superior solution during the design stage. Using non-Gaussian, non-parametric uncertain variables, and Monte Carlo simulation, two different mechanical design problems are addressed. The first is an inverse problem of synthesizing a mechanism to meet a given set of motion requirements. The second is a forward problem of analyzing a machine tool that is assembled from individual modules to predict the total error based on component errors. The mechanism synthesis procedure using uncertainty that was developed in this dissertation seeks to offer the designer the flexibility to prescribe design specifications with uncertainty. Monte Carlo simulation of the Burmester mechanism synthesis equations using non-Gaussian, non-parametric input variables was developed. This methodology will avoid incorrect and infeasible solutions obtained previously via other synthesis techniques. Incorporating uncertainty in mechanism synthesis, as demonstrated here, provides more than just feasible solutions. The solution space described in this work is more complete since it identifies a range of solutions with different degrees of preferences. Machine tool design seeks enhanced performance in the form of increased accuracy. Using assembly tolerances, Monte Carlo simulation and a homogeneous-transformation-based error matrix, a framework for accuracy prediction throughout the entire work volume was developed. The methodology can be extended to include the temporal, wear and temperature effects. Results indicate that geometric, or form, tolerances in machine tool design are most critical and that their control provides the most benefit. The complete error matrix (full-matrix solution) developed in this work captures error due to scaling the axes in computing the work volume distortion and therefore provides a more accurate prediction of error.