Identification and compensation of main machining errors on surface form accuracy in ultra-precision diamond turning

• The machining errors are classified into five categories.
• Five error categories have different effects on different typical surface.
• The main machining errors are identified for different surface shapes.
• One plane-spherical surface was proposed to separate the main machining errors.
• The form accuracy of one freeform surface achieves a significant improvement.

Ultra-precision diamond turning is widely used in manufacturing the optical surfaces with nanometric accuracy. However, the machining errors especially geometric errors have a significant influence on the form accuracy of machined surfaces. A machining error model for a three-axis ultra-precision lathe is established based on multi-body system (MBS) theory to study the effect of geometric errors on the coordinate distortion and form accuracy. The machining errors are classified into five categories according to the coordinate distortions direction. These errors generate the coordinate distortions along the X direction, Y direction, radial direction, circumferential direction, and axial direction respectively. Five error categories have different effects on different typical surfaces, and the main machining errors on the form accuracy are identified according to the difference of the form error distribution for different surface shapes. Simulation is implemented to verify the influence of the machining errors on the form accuracy. One plane-spherical surface was proposed and machined to separate the main machining errors, which are used to be compensated in the machining experiments. The form accuracy of one freeform surface is proved to achieve a significant improvement finally.