Influence and suppression of periodic contour error of tool path and velocity deviations on surface error

When using multi-axis machines with a pneumatic tool to polish large-aperture optical surfaces, the paths generated by the computer numerical control system deviate from the desired ones. This causes periodic contour errors and surface ripples. In addition, because of the different machine layouts, the tool end velocity also can change. We introduce a multi-axis machine and analyze the surface error and power spectral density (PSD) of three commonly used paths (raster, spiral, and random path) in terms of the contour error using different position interpolation methods. A cubic polynomial is introduced to smooth the axis motion, and a velocity compensation method is considered to diminish the velocity deviation from the machine layout. The results show that the circular interpolation method exhibits a balanced performance in terms of both the contour error and the PSD for various paths. In addition, the optimization can be performed before G-code generation without affecting the characteristics of the original optimization system.