Modeling of variance for machine tool positioning errors

Variance in positional error of a machine tool can not be compensated and hence limits the best achievable accuracy of the machine. For micro-manufacturing, this inherent error variance of machine tool can play a very significant factor in determining the process capability for the intended operation. Incorporating vector method and variance analysis for the positional errors of machine tools is described in this study. Using an XYFZ configured machine tool as an example, this paper establishes the variance model for positioning error in the workspace. Through kinematics and variance analysis, the error variance model is completed, based on error measurements from laser vector measurement. Positioning error and variance of the machine within the workspace can then be predicted from the variance model. The error variance model is verified by comparing the model predicted variances on a circular path with measurement results from laser ballbar test. The predicted variance is shown to well coincide with experimental results.