A new approach to identify geometric errors directly from the surface topography of workpiece in ultra-precision machining

Geometric errors are caused due to the inaccuracy of machine components’ manufacturing and assembling, and significantly impact the dimensional precision of workpieces. Many researches have researched the methods of inversely identifying geometric errors of multi-axis milling machines from the workpiece profile, but those methods are inapplicable to identify geometric errors of ultra-precision lathe. This paper presents a new approach to research the inverse identification of geometric errors from the surface topography of workpiece for an ultra-precision lathe. First, a volumetric error model is built to analyze tool position errors caused by geometric errors. Next, a matrix decomposition method is put forward to simplify the calculation of tool position errors and describe the propagation process of geometric errors during the manufacturing process. This method decomposes final tool position errors into a sum of three components, and each has a definite geometric meaning. Then, an equivalent machining model is constructed to identify crucial geometric errors from the surface topography of workpiece. Geometric errors in this model can be worked out precisely through topography data sampled along a radial path on workpiece surface. Finally, some simulation experiments are implemented to verify the precision of matrix decomposition method and one plane surface is machined to validate the effectiveness of equivalent machining model.