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Modern CNC machine tools provide lookup tables to enhance the machine tool's precision but the generation of table entries can be a demanding task. In this paper, the coefficients of the 25 cubic polynomial functions used to generate the LUTs entries for a five-axis machine tool are obtained by solving a linear system incorporating a Vandermonde expansion of the nominal control jacobian. The necessary volumetric errors within the working volume are predicted from machine's geometric errors estimated by the indirect error identification method based on the on-machine touch probing measurement of a reconfigurable uncalibrated master ball artefact (RUMBA). The proposed scheme is applied to a small Mitsubishi M730 CNC machine. Two different error models are used for modeling the erroneous machine tool, one estimating mainly inter-axis errors and the other including numerous intra-axis errors. The table-based compensation is validated through additional on-machine measurements. Experimental tests demonstrate a significant reduction in volumetric errors and in the effective machine error parameters. The LUTs reduce most of the dominant machine error parameters. It is concluded that although being effective in correcting some geometric errors, the generated LUTs cannot compensate some axis misalignments such as EB(OX)A and EB(OX)Z. The Root Mean Square of the translational volumetric errors are improved from 87.3, 75.4 and 71.5 µm down to 24.8, 18.8 and 22.1 µm in the X, Y and Z directions, respectively.

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.

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