Optimal Budgeting of Quasistatic Machine Tool Errors

Abstract

Quasistatic errors are responsible for a major component of the errors of a numerically controlled machine tool. Such errors are comprised of geometric/kinematic errors, self-induced mechanical strains and thermal strains developed during the operation of the machine. The ability to model the effect of such errors on the volumetric accuracy of a machine tool, opens up the prospect of being able to track and compensate their effects during the operation of the machine. Further, the same model can be used for (cost) optimal allocation of manufacturing and assembly tolerances and specification of operating conditions to get a desired performance. This paper first discusses a model developed for quasistatic static errors and its use as the basis for an optimal error budgeting scheme. Next, the following allocation problem is addressed: Given: (i) a parameter vector whose elements are drawn from normal distributions with unspecified standard deviations and zero means (ii) a set of constraining half spaces defined over parameter space. Specify standard deviations for the distributions so that some function (e.g., the total cost) is minimized. The error model and the error allocation approach are applied to optimal error budgeting. The approach developed is implemented in software and an example of budgeting the geometric errors for a two axis machine is also given. The budgeting procedure developed in this paper can be extended further to subassemblies and components within a machine-tool.