OPTIMAL BUDGETING OF QUASI-STATIC MACHINE-TOOL ERRORS

Quasistatic errors are responsible for a major component of the errors of a numerically controlled machine tool. Such errors are comprised o f geometric/kinematic errors, self-induced mechanical strains and ther mal strains developed during the operation of the machine. The ability to model the effect of such errors on the volumetric accuracy of a ma chine tool, opens up the prospect of being able to track and compensat e 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 err or budgeting scheme. Next, the following allocation problem is address ed: 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. Spec ify standard deviations for the distributions so that some function (e .g., the total cost) is minimized. The error model and the error alloc ation approach are applied to optimal error budgeting. The approach de veloped is implemented in software and an example of budgeting the geo metric errors for a two axis machine is also given. The budgeting proc edure developed in this paper can be extended further to subassemblies and components within a machine-tool.