Complex Trajectory Planning for Lapping of Diamond Cutting Tool

The practice shows that complex lapping motion trajectory can decrease the adverse effects caused by the lapping direction which has a great influence on the lapping of the natural single crystalline diamond cutting tool. For example, addition of a reciprocating motion can get better lapping performance and surface roughness. On some kinds of natural diamond cutting tool lapping machines a further improvement is made by designing an additional planetary spindle to provide planetary motion to the main shaft, which offers a more complex motion trajectory. With an increase in degrees of freedom of the lapping machine, it becomes difficult for technicians to master a good suit of motion process parameters. This paper proposes a set of methods to plan the lapping trajectory with respect to the machine that can perform complex lapping motion. Firstly, the proposed method designed a statistical parameter which is the variance of the direction angle distribution for the lapping velocity and its calculation method to evaluate the complexity of the trajectory. And then the multi-body kinematics model was established by using Simulink tool box in Matlab software for the purpose of model kinematics simulation and outputting data for calculation of the statistical parameter above. Finally, the genetic algorithm was used to find the best motion parameters of every shaft under certain restrictions. The advantage of the set of lapping trajectory planning method presented in this paper is that it combines the powerful multi-body simulation and signal processing ability of Simulink tool box and the characteristics of the genetic algorithm in almost no limitation on awaiting optimization function and suitable for complicated problems. So the method provides not only a way for planning complex diamond lapping trajectory but also a general approach to solve the problem on machine motion process parameters optimization.