Approximation of CNC part program within a given tolerance band

Abstract

Freeform surfaces are widely used in various fields of engineering design such as automotive, aerospace and mold and die industries. With the geometric model designed by freeform surfaces in the CAD system, the tool path will be next constructed and sampled by the CAM system according to the predefined chordal deviation. The sequentially sampled short linear blocks are stored in the file called the part program, which is later interpreted by the CNC system to control the machine tool and mill the workpiece.In order to deliver the desired motion smoothly and rapidly, the short linear blocks in the part program will be approximated with smooth spline curves within a specified tolerance band. With spline curves, which consist of longer polynomial pieces, the attainable feed rate of the machine tool can be greatly enhanced. In addition, with minimization of curvature variation, velocity and acceleration jumps in the relevant machine axes and undesired mechanical oscillation of the machine can be reduced significantly. This allows higher traversing speeds and reduces the vibration of the machine, thus improves the surface quality.