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In this study, the accuracy of a machine tool was evaluated by modeling the spherical deviation based on double ball-bar measurements under unloaded conditions. Circular measurement paths on the XY -, YZ -, and ZX- planes were planned, and three linear axis drives were commanded to follow the paths describing a nominal sphere. The spherical deviation, defined as the maximum radial range of deviations around a least-squares sphere, is affected by the accuracies of the three linear axes together. Therefore, the spherical deviation represents the accuracy of machine tools by quantifying the effect of the accuracies of three linear axes, whereas the circular deviation only quantifies the accuracies of two linear axes among the three linear axes. In this experimental study, spherical deviations of vertical/horizontal machine tools were measured and analyzed under various nominal lengths of a double ball-bar for various feed rates. The measurement uncertainty of the measured spherical deviation was investigated to determine the confidence interval.

In this study, position-independent geometric errors, including offset errors and squareness errors of rotary axes of a five-axis machine tool are measured using a double ball-bar and are verified through compensation. In addition, standard uncertainties of measurement results are calculated to establish their confidence intervals. This requires two measurement paths for each rotary axis, which are involving control of single rotary axis during measurement. So, the measurement paths simplify the measurement process, and reduce measurement cost including less operator effort and measurement time. Set-up errors, which are inevitable during the installation of the balls, are modeled as constants. Their effects on the measurement results are investigated to improve the accuracy of the measurement result. A novel fixture consisting of flexure hinges and two pairs of bolts is used to minimize set-up error by adjusting the ball's position located at the tool nose. Simulation is performed to check the validation of measurement and to analyze the standard uncertainties of the measurement results. Finally, the position-independent geometric errors of the five-axis machine tool (involving a rotary axis and a trunnion axis) are measured using proposed method.

Fabrication of free-form surfaces that are frequently demanded for the construction of optical imaging systems is described. To obtain a tool motion with large amplitude and high bandwidth, a novel long-stroke fast tool servo is proposed and installed on the Z-axis of a diamond turning machine as an additional synchronized axis. In addition, a special on-machine measurement device is used to measure the optical parameters of the machined surface and to compensate for the residual form of errors that are commonly produced in the diamond turning process. Actual machining test results show that the proposed procedures are capable of generating the copper free-form mirrors of 50 mm diameter to a form accuracy of 0.15 μm in peak-to-valley value error.