Smooth and Time-Optimal Trajectory Generation for High Speed Machine Tools

NURBS;Interpolation;Feedrate;Optimization;Mechanical Engineering

Heng, Michele Mei-Ting

University of Waterloo

关键词: NURBS;    Interpolation;    Feedrate;    Optimization;    Mechanical Engineering;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/3770/1/Thesis_Master_UWmargins06.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

In machining complex dies, molds, aerospace and automotive parts, or biomedical components, it is crucial to minimize the cycle time, which reduces costs, while preserving the quality and tolerance integrity of the part being produced. To meet the demands for high quality finishes and low production costs in machining parts with complex geometry, computer numerical control (CNC) machine tools must be equipped with spline interpolation, feedrate modulation, and feedrate optimization capabilities. This thesis presents thedevelopment of novel trajectory generation algorithms for Non Uniform Rational B-Spline(NURBS) toolpaths that can be implemented on new low-cost CNC;;s, as well as, inconjunction with existing CNC;;s. In order to minimize feedrate fluctuations during theinterpolation of NURBS toolpaths, the concept of the feed correction polynomial is applied. Feedrate fluctuations are reduced from around 40 % for natural interpolation to 0.1 % for interpolation with feed correction. Excessive acceleration and jerk in the axes are also avoided. To generate jerk-limited feed motion profiles for long segmented toolpaths, a generalized framework for feedrate modulation, based on the S-curve function, is presented.Kinematic compatibility conditions are derived to ensure that the position, velocity, and acceleration profiles are continuous and that the jerk is limited in all axes. This framework serves as the foundation for the proposed heuristic feedrate optimization strategy in thisthesis. Using analytically derived kinematic compatibility equations and an efficientbisection search algorithm, the command feedrate for each segment is maximized. Feasiblesolutions must satisfy the optimization constraints on the velocity, control signal (i.e.actuation torque), and jerk in each axis throughout the trajectory. The maximized feedratesare used to generate near-optimal feed profiles that have shorter cycle times, approximately13-26% faster than the feed profiles obtained using the worst-case curvature approach, whichis widely used in industrial CNC interpolators. The effectiveness of the NURBS interpolation,feedrate modulation and feedrate optimization techniques has been verified in 3-axismachining experiments of a biomedical implant.