Updating a Turning Center Error Model by Singular Value Decomposition

摘要

The precision of manufacturing using machine tools depends on the accuracy of therelative position of the cutting tool with respect to the workpiece. Kinetmatic modeling of machine tools is used to describe this relative position. This motion can be modeled by homogeneous coordinate transformation matrices composed of both rotational elements as well as positional offset elements of the associated coordinates. The rotation and translation components of the homogeneous transformations are considered to be functions of normal tool position and machine temperatures. In general these functions are low order polynomials in terms of position and temperatures. The coefficients are usually calculated with least square curve fitting techniques. The data for these fits are obtained by measuring actual coordinate positions and temperatures on the machine tool based upon desired programmed nominal coordinates. The process of measuring and modeling the errors of machine axis positions as functions of nominal positions and temperatures is referred to as machine tool characterization.