Optimal setup for five-axis machining

This paper presents a new optimization model designed to minimize kinematics error introduced by the initial setup of a five-axis milling machine. An initial setup consists of the position and orientation of the workpiece with respect to the mounting table and, optionally, the machine's initial configuration. Given a set of cutter contact points and tool orientations, a least-squares optimization procedure finds the optimal setup parameters. Since the set of optimization parameters depends on the machine's characteristics, three basic types of five-axis kinematics are introduced. The classification into types depends on the sequence of positions of the machine's rotary axes in its kinematics chain. For each type, sets of invariant and dependent variables are identified, a corresponding system of nonlinear equations is constructed, and then the system is solved numerically. The method is not only efficient, but also provides tangible accuracy increases in tests on practical machining problems.