Comparison of Combinatorial Rules for Machine Error Budgets

Abstract An error budget is an analysis tool for the prediction and control of the total error of a machine system for which accuracy is an important measurement of performance. The error budget concept is commonly applied in designing precision machine tools and precision measuring machines and requires application of a combinatorial rule to assess total error which is contributed to by a number of individual error components. No single generally agreed upon combinatorial rule exists for predicting maximum told error that may result from many error components, and precision machine designers often apply empirical formula rules that have evolved from practical experience. Combinatorial rules based on the central limit theorem (CLT) in probability theory and uncertainty interval concept are described in this paper and compared to two empirical formula rules using two precision machine error source examples reported in the literature. It is shown using Monte Carlo simulations that the CLT combinatorial rules and the empirical formulas adequately predict maximum total errors. However, the CLT rules provides a more rigorous methodology than an empirical formula for predicting total error. Moreover, a confidence level associated with the estimated total errors can be specified for error budgeting in precision machine design.