Abstract

This thesis investigates an ultra-precision multi-axis CNC machining problem encountered in machining sculptured surfaces. Conventional multi-axis CNC machining uses straight line segments to connect consecutive data points, and uses linear interpolation technique to generate the command signals for positions between machining data points. However, due to the multi-axis simultaneous and coupled translational and rotational movements, the actual machining motion trajectory is a non-linear curve. The non-linear curve segments deviate from the linearly interpolated straight line segments, resulting in non-linearity errors, which in turn cause obstacles to ensuring high precision machining. The problem in multi-axis CNC machining is that non-linearity errors result in total machining error which is beyond the range of the machining tolerance. The problem arises from the fact that the linear interpolation technique generates commands for positions along a straight line segment, while rotational movements superimposed onto translational movements cause the cutting point moving along a curved machining motion trajectory. The machining motion trajectory depends on both multi-axis CNC machine tool configuration and the machining rotational movements. The machining rotational movements are kinematically related to cutter orientation variations. Thus, The factors causing the multi-axis CNC machining error problem are the spatially varying cutter orientations and the utilization of linear interpolation method. A novel off-line tool path generation methodology for is developed and reported in this thesis in order to solve the non-linearity error problem in ultra-precision multi-axis CNC machining. The new off-line tool path generation method reduces non-linearity errors by modifying cutter orientation changes based on machine kinematics and machining motion trajectory. A software routine for implementing the new tool path generation methodology is developed. A simulation of the process for machining a sculptured surface by applying the novel methodology illustrates that it increases machining precision considerably. A novel interpolator design technique for solving the non-linearity error problem in ultra-precision multi-axis CNC machining is also presented. A 3D circular interpolation principle is developed which is capable of tracking spherical curves with low position errors and uniform feedrates. On the basis of this (3D circular) interpolator, a combined 3D linear and circular (L&C) interpolator is proposed for five-axis CNC machining. The proposed 3D L&C interpolator is able to drive the pivot of rotational movements along a predesigned 3D curve and conduct the cutting point along a linear spatial path, so that the elimination of non-linearity errors in five-axis CNC machining is achieved. A software interpolation routine of the 3D L&C interpolator is developed, and a computer simulation illustrating the machining of a sculptured surface validates the novel technique