Generalized actual inverse kinematic model for compensating geometric errors in five-axis machine tools

摘要

Geometric errors of five-axis machine tools, i.e. position independent and position dependent geometric errors (PIGEs and PDGEs), should be compensated in order to improve the machining precision of workpieces. To achieve this purpose, this paper proposes a generalized actual inverse kinematic model (IKM), which provides explicit solution for the compensated motion commands and can be directly applied to five-axis machine tools with arbitrary configurations, especially for those with non-orthogonal rotary axes. The typical characteristic of this model lies in three aspects. First, it is the first effort to compensate both PIGEs and PDGEs in a generalized way. Second, it provides an explicit solution for changing the motion commands of the machine tool's axes so that the geometric errors can be compensated. Third, as the configuration of machine tool changes, the model can be directly used without additional theoretical derivations, which is usually required by existing methods. Rotation-constrained equation is newly formulated and its solution is derived in detail to obtain the compensated motion commands of rotary axes. By introducing the incremental motion commands of translational axes, the solution to the actual IKM does not explicitly include the geometric error items and the model's formulations are greatly simplified. Simulation results verify the effectiveness, feasibility and universality of the proposed method. Experimental results confirm that the machined workpiece has a remarkable precision improvement by using the proposed compensation method.