Variability Analysis of Precision Mechanical Devices

An analytical method has been developed for estimating variability in the performance of a precision mechanical device that arises from variability of its internal parameters. This parameter variability is due both to initial in-tolerance variations and to subsequent environmental and time-dependent effects.

A mathematical model of the device is formulated to define the relationships between individual parameters and various performance characteristics. This model is then manipulated on either an analog or a digital computer to permit calculation of partial derivatives of performance characteristics with respect to internal parameters. These partials are used in evaluating the Propagation of Variance formula, a mathematical statement that relates performance variance (an index of variability) to parameter variances (which must be known) and to the partial derivatives. This analytical approach is called the Moment method because it makes use of the mean and variance, the first two moments of the parameter value frequency distributions. The output of this type of analysis is extremely useful to the designer, for it tells him directly which parameters are most critical in determining the performance of the device, and it guides him in making necessary design modifications to reduce variability in performance.

The Moment method is illustrated by application to the variability analysis of a two-stage electrohydraulic servo valve.