Concept for the integration of geometric and servo dynamic errors for predicting volumetric errors in five-axis high-speed machine tools: an application on a XYC three-axis motion trajectory using programmed end point constraint measurements

A modelling approach for volumetric error prediction taking into account geometric and servo dynamic errors in a five-axis high-speed machine tool is proposed in this paper. Polynomial functions are used to represent and then predict the geometric errors. A simple second-order transfer function model is used to model and predict the servo dynamic error. The servo dynamic errors are added to the axis position geometric errors and propagated to the tool and workpiece using matrix transformations. The validity of the error integration concept is tested for a XYC three-axis motion trajectory. Two experimental setups are used. The first experimental test used the KGM grid encoder instrument to estimate the parameters of the servo dynamic error models of the X- and Y-axes. The second experimental test used a programmed end point constraint procedure with measurement of the 3D volumetric positioning errors between a point on the tool holder and another fixed to the machine table. The tests involve maintaining the nominal coincidence of these two points whilst exercising the three axes. These last tests are used to estimate the geometric error parameters and also to validate the prediction performance of the integrated geometric and dynamic model. The result shows the effectiveness of the error integration concept.