Forward and inverse kinematics for vertical 5-axis turning center with angular head of non-intersectional axes, with compensation for table moving caused by base thermal dilatation

Abstract

The paper presents the solution for forward and inverse kinematics of the vertical 5-axis turning centers with 2 linear and 3 rotational axes (Cy, X, Z, Bt and Ct) which for the 5-axis milling achieves the motion accomplished by 3 linear and 2 rotational axes (X, Y, Z, Bt and Cy). It has been done in such a way to provide for machine motion programming as if machining were performed on a 5-axis gantry milling machine. This has essentially facilitated machine programming, because tool positions and orientations required for programming are determined disregarding the workpiece swiveling during machining and current positions and orientations taken by the tool during machining relative to the workpiece. Turning center has a 2-rotary-axis head with axes Ct and Bt which do not intersect. This type of angular head has increased the possibilities of machining and allowed for performing certain types of machining without machine’s taking the singular positions, but it has made the machine control algorithm more complex. A high number of rotating of the table, required for turning, causes heating of the table bearing support and base thermal dilatation. If milling or drilling is done immediately after turning, the table and X axis motion control should be corrected to eliminate the error in machining appeared due to dilatation, as has been done in this paper.