Determination of Geometry-Based Errors for Interpolated Tool Paths in Five-Axis Surface Machining

Abstract

Five-axis computer numerical control (CNC) machining is characterized with a multitude of errors. Among them an important component comes from the computer-aided manufacturing software known as the geometry-based errors. A new and accurate method to determine these errors is presented in this paper as opposed to the conventional chordal deviation method. The present method allows establishing the exact linearly interpolated tool positions between two cutter contact points on a given tool path, based on the inverse kinematics analysis of the machine tool. A generic procedure has been developed to ensure wide applicability of the proposed method. Analytical derivation of the geometry-based errors provides insights regarding the origin of these errors and their affecting parameters. Due to the highly non-linear characteristics of the problem, analytical solutions can only be obtained for simple surface geometry. Numerical computation is able to determine the errors for general surface shapes but it would be difficult to uncover further insightful information from the calculated error values. Besides the local surface geometry, the configuration of the kinematic chain of the CNC machine has been found to be the primary factor controlling the resulting value and type of the geometry-based errors. Implementations with a typical complex free-form surface demonstrated that the conventional chordal deviation method was not reliable and could significantly underestimate the geometry-based errors.