Optimal D-Shaped Toolpath Design for Minimizing X-Axis Servo Following Error in Turning the Off-Axis Optical Surfaces

In the slow tool servo (STS) turning technology for optical lenses, the D-shaped toolpath can improve the quality of the optical surfaces of off-axis aspheric and cylindrical microlens arrays. However, the traditional D-shaped toolpath has the problem of excessive servo following error in the X-axis. To address this issue, the projection of the D-shaped toolpath in the XZ plane is divided into a cutting zone and a transition zone. In the transition zone, an equation system based on continuity constraints (surface height, feed-rate, acceleration) is established. By solving this system of equations, a toolpath can be obtained along which the feed-rate of the X-axis varies smoothly. An example shows that the acceleration of the X-axis of the lathe is reduced by 84% compared to the traditional D-shaped toolpath. In the XZC interpolation mode, the spindle velocity of the C-axis changes smoothly. An off-axis spherical surface and an integral mirror have been machined using the optimized D-shaped toolpath. The X-axis servo following error of the lathe during processing is within 7 nm, and the surface shape accuracy reaches 0.361λ at 632.8 nm. This method enables high-precision processing of off-axis curved surfaces and cylindrical arrays.