Self-Identification and Compensation of Squareness Error in CNC Turning Center by Servo-Signal-Based Tool–Workpiece Contact Detection with Dynamic-Model Fitting

Geometric errors of machine tools are conventionally identified with dedicated instruments or reference artifacts in a measurement stage separate from machining, which is cost/time-consuming. This paper presents a method to identify and compensate for the squareness error between the C- and X-axes of a CNC turning center using only the servo signals without any additional sensor. Tool–workpiece contact is detected from the spindle torque command after subtracting that of a reference revolution. The contact instant is determined by fitting a dynamic model: the response of the spindle system to the contact force is modeled as a critically damped second-order system excited by a ramp input. The squareness error is identified by contacting a pre-faced surface, which becomes conical owing to the error, along the Z-axis at multiple X-positions on the side of the C-axis center line opposite to the facing tool position. The pre-faced surface shows that the detected Z deviation varies with X with a slope equal to twice the squareness error. The accuracy of the contact detection was −0.67 μm on average with a standard deviation of 1.00 μm. The identified squareness error of 0.0060° was close to the surface inclination of 0.0067° measured by a contour measuring instrument, and facing with the compensated tool path reduced the inclination of the machined surface to 0.0007°.