Abstract: An apparatus for machining a non-circular workpiece such as a piston wherein a tool is moved back and forth against the workpiece in accordance with profile data defining a desired final shape of the workpiece while the workpiece is rotated at a predetermined speed. The tool is moved by a composite movement of a linear motor driven in accordance with low frequency command values, and a piezoelectric actuator driven in accordance with high frequency command values. A numerical controller of the apparatus calculates the low frequency command values using a first Fourier series and the high frequency command values using a second Fourier series. Coefficients of the first and second Fourier series are determined using least square method in such a way that errors contained in the low and high frequency command values becomes within a predetermined limit.

Abstract: An apparatus for machining a non-circular workpiece, wherein the profile data of plural sections of the workpiece stored in the profile data storage means are transformed into the frequency functions of 1 to n degree which is a function of the rotary angular velocity of the workpiece. The calculation means finds the amplitudes and the phases of each degree of the frequency function of each of plural intermediate sections by means of the interpolation according to the position between selected two sections based on the frequency functions of the selected two sections so as to obtain high frequency functions and low frequency functions which are then converted to high frequency and low frequency profile data. The machining apparatus actuates a linear motor in accordance with the high frequency profile data and actuates a PZT actuator in accordance with the low frequency profile data.

Abstract: An apparatus for machining a non-circular workpiece wherein a tool is moved by a composite movement given by a linear motor and a piezoelectric actuator. The linear motor is driven by the numerical controller in accordance with the low frequency components of profile data defining a position change of the tool with respect to angular position change of the spindle, while the piezoelectric actuator is driven by the numerical controller in accordance with the high frequency components of the profile data. Further, a positioning error of the tool due to reaction force generated by the piezoelectric actuator is detected by the numerical controller to compensate the high frequency components for the detected positioning error.

Abstract: An apparatus which moves a tool back and forth in synchronism with rotation of a workpiece with respect to the workpiece to machine the workpiece into a non-circular shape. The tool is attached to a tool mount placed on a tool mount table which is connected to be moved in a direction perpendicular to the axis of a spindle by a motor. The tool is connected to be moved in a direction perpendicular to the axis of the spindle with respect to the tool mount by a high speed actuator. Profile generating movement of the tool is thus provided by a combination of movement provided by the motor and movement provided by the high speed actuator. The high speed actuator is controlled in accordance with high frequency components included in profile data while the motor is driven in accordance with low frequency components included in the profile data. As a result, the responsiveness in profile generating movement of the tool is improved, and high speed machining of a non-circular workpiece is enabled.

Abstract: A positioning controlling device for improving the machining accuracy of a work of a non-circular shape. A control axis is driven in accordance with an input function consisting of position instruction data corresponding to a machining shape of a work, and a response function of the position of the control axis is measured actually. Then, a transfer function of the servo system is determined from Fourier transformation of the input function and Fourier transformation of the response function, and a corrected input function with which a response function of the control axis ideally corresponds to the machining shape of the work is obtained from the transfer function. Even if the control axis is driven in accordance with the corrected input function, a response function obtained does not correspond to the ideal machining shape of the work.