Method and apparatus for controlling a machine tool

An apparatus for controlling a machine tool in which a main spindle on which a tool is mounted and a table that holds a workpiece are moved relative to each other by two or more machine tool translation axes and at least one machine tool rotation axis to machine the workpiece with the tool, at least two of the machine tool translation axes not perpendicular to each other, the apparatus comprising:

• an error calculation unit that [1] obtains a position of the tool in presence of a geometric error by performing a homogeneous coordinate transformation from a tool coordinate system to a workpiece coordinate system with the geometric error being taken into consideration, and [2] obtains an ideal position of the tool by performing the homogeneous coordinate transformation from the tool coordinate system to the workpiece coordinate system with the geometric error not being taken into consideration, and [3] calculates an error in a position of the tool with respect to the workpiece due to the geometric error from the position of the tool in presence of the geometric error and the ideal position of the tool;
• a conversion unit that converts the error in the position of the tool with respect to the workpiece into an imaginary Cartesian coordinate system that comprises two or more Cartesian coordinate system axes that are perpendicular to each other, and converts a workpiece coordinate system correction value for correcting the error in the position of the tool with respect to the workpiece into an imaginary Cartesian coordinate system correction value in the imaginary Cartesian coordinate system by performing a homogeneous coordinate transformation from the workpiece coordinate system to the imaginary Cartesian coordinate system;
• a correction value calculation unit that calculates a command value coordinate system correction value in a command value coordinate system by performing a homogeneous coordinate transformation of the imaginary Cartesian coordinate system correction value converted into the imaginary Cartesian coordinate system by the conversion unit from the imaginary Cartesian coordinate system into the command value coordinate system;
• an update unit that calculates an updated command value by updating a command value for controlling the machine tool by adding the command value coordinate system correction value calculated by the correction value calculation unit to the command value,
• the main spindle and the table configured to move relative to one another in response to the updated command value.