Abstract
The ball-bar instrument is used to estimate a maximum number of hysteretic error sources. Machine error parameters include inter- and intra-axis errors as well as hysteresis effects. An error model containing cubic polynomial functions and modified qualitative variables, for hysteresis modeling, is proposed to identify such errors of the three nominally orthogonal linear axes machine. Such model has a total of 90 coefficients, not all of which being necessary. A numerical analysis is conducted to select a minimal but complete non-confounded set of error coefficients. Four different ball-bar test strategies to estimate the model coefficients are simulated and compared. The first one consists of circular trajectories on the primary planes XY, YZ, and XZ and the others use the XY plane, as an equator, and either four, five, or nine meridians. It is concluded that the five-meridian strategy can estimate the additional eight error coefficients: ECZ1, ECZ2, ECZ3, ECZb, EZY3, EZX3, ECX3, and ECXb. The Jacobian condition number is improved by increasing the number of meridians to 5. Further increasing the number of meridians from five to nine improves neither the number of estimable coefficients nor the conditioning, and so as it increases, the test time it was dismissed.
Highlights
The Cartesian volumetric error at the tool tip relative to the workpiece affects the quality of machined parts
Cubic polynomials enriched with hysteretic error terms capable of modeling backlashes and lateral plays are used yielding a total of 90 potential unknown error function coefficients
In order to experimentally estimate these coefficients, various 2D and 3D ball-bar test strategies are simulated and their ability to estimate a maximum number of the necessary coefficients is analyzed using the sensitivity Jacobian
Summary
The Cartesian volumetric error at the tool tip relative to the workpiece affects the quality of machined parts. Intra-axis errors of the rotary axes were estimated by running ball-bar tests on a five-axis machine tool with several circular patterns by Xiang and Yang [14] They analyzed the effect of inter-axis and setup errors on measurement results. Lee et al [16] evaluated a machine tool accuracy by means of ball-bar measurements having various bar lengths and incorporating different machine tool feed rate They ran the test for the base planes ZX, XY, and YZ and fitted a sphere to all data points using the least-square method. Zhong et al [17] proposed circular test paths considering different tool axis directions to evaluate the machine tool accuracy using spherical deviation modeling They claimed that incorporating different tangential tool axis direction let the machine tool to reflect rotary axis errors in the measurements.
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