Modelling and indirect measurement of machine tool equivalent joint compliances

Abstract

Machine tools require high geometric accuracy and stiffness. Both of these characteristics affect the radius of a radially loaded circular test. By using various loads, the machine's volumetric compliance can be studied as a function of position, orientation, and load. Further processing of the data using a kinematic and compliance model of the machine allows the equivalent joint compliances to be estimated. This model also allows to produce the characteristic patterns of loaded telescopic double ball bar readings associated with each compliance term. The compliance model contains numerous superfluous and confounded terms that are pruned from the model. The analytical model is then used to produce a numerical identification Jacobian that is further applied to estimate the compliances from test data gathered at various force levels. By using all force data at once global compliance values are estimated whereas using only adjacent force level data allows observing the change in compliance with force. The new nomenclature is introduced where each compliance term has three subscripts. The first subscript is the direction of the displacement, the second subscript is the applied force direction, and the third subscript is the relevant joint or axis. The dominant compliances are the X-axis on-axis compliance C XXX (confounded with the lateral compliance of the Y-axis C XXY ) and C YYY (confounded with C YYX ). It is observed that as the load increases from 76 to 706 N (by increments of 126 N), the dominant compliances increase by around 5%. Type A uncertainties of the calculated compliances are estimated from repeated measurements and are found to be relatively small. Some non-dominant compliances, such as the torsional compliance of the Y-axis C CCY account for deflection of less than 0.5% of that for the main compliances and has a negative value which is mechanically unexpected. It is explained in detail in the results and discussion section.