Influences of rotary axes on nonlinear error for five-axis machine tool with different configurations: Theoretical model, deduction and simulation

In five-axis machining, the ideal straight line trajectory between adjacent cutter location points becomes a space curve in actual machining, which inevitably produces nonlinear errors due to the coupled motion of translational and rotational axes. The two rotary axes of five-axis machine tool are the essential causes of the nonlinear error, but the quantitative role of the mechanism and influences have not been clearly studied. This paper proposes a theoretical model of the influences of the rotary axes on nonlinear error for an orthogonal five-axis machine tool. Two essential variables are identified: the distance from the cutter location point to the pivot point of rotary axes, and the relationship between cutter axis vector and rotary axes angle. The two essential variables are decoupled into several key elements in five-axis machining, including rotary axes configuration in the kinematic topology, tool length, clamping position and attitude of a workpiece. The theoretical models of three typical configurations of orthogonal five-axis machine tool, namely, spindle-tilting type, table-tilting type and table/spindle-tilting type are established. The influence laws of the above key elements on nonlinear error have been theoretically summarized into 9 deductions and proved in the blade machining simulation. Three blade workpieces with identical surface geometries but significant dimensional differences are specified, and the machining performance comparisons of the three configurations in terms of nonlinear error are demonstrated. Finally, the advantages and disadvantages of the three configurations and their applicability to machining workpieces with varying dimensions are summarized. The proposed model and deductions can be used to adapt the surface machining performance of five-axis machine tools accurately and can be further applied to optimize the design of the machine's kinematic topology.