Tool trajectory optimizing in ultra-precision turning of multi-mode sinusoidal perturbation surface

This paper aims at optimizing the diamond tool trajectory in ultra-precision machining of perturbation surface with single point diamond turning technology. First, the ultra-precision machining principle of multi-mode sine surface is illustrated. Second, the parallel chord bi-arc interpolating algorithm is theoretically analyzed, of which the interpolating trajectory error expression is obtained. On this basis, the parallel chord bi-arc interpolating algorithm with adaptive step length is introduced for dynamically controlling the interpolating trajectory error. And the interpolation formula is derived. Finally, the new interpolating algorithm is adopted for example analyzing with Matlab software, and is compared with two other algorithms, the linear interpolation and the parallel chord bi-arc interpolation with fixed step length. The simulation results present that the new algorithm can maximally reduce interpolating sections in conditions of trajectory error, which helps to improve the machining efficiency and extend the cutting life span.