Tool Orientation Optimization Considering Second Order Kinematical Performance of the Multi-Axis Machine

This paper presents a new tool orientation optimization approach for multi-axis machining considering up to second order kinematical performance of the multi-axis machine. Different from the traditional optimization approach, tool orientations are optimized with the goal of improving the kinematical performance of the machining process, not only increasing the material removal from purely geometrical aspect. The procedure is to first determine a few key orientations on the part surface along the tool path according to the curvature variation. Key orientations are initially optimized to be able to achieve high material removal by comparing the tool swept curve and the actual part surface. Intermediate orientations between key orientations are interpolated smoothly using rigid body interpolation techniques on SO(3). The time-optimal trajectory planning problem with velocity and acceleration constraints of the multi-axis machine is then solved to adjust the initially determined tool orientations to better exploit the multi-axis machine’s motion capacity. Simulation and experiment validate the feasibility and effectiveness of the proposed approach.

[1]  Hsi-Yung Feng,et al.  Determination of Geometry-Based Errors for Interpolated Tool Paths in Five-Axis Surface Machining , 2005 .

[2]  Yuan-Shin Lee,et al.  Non-isoparametric tool path planning by machining strip evaluation for 5-axis sculptured surface machining , 1998, Comput. Aided Des..

[3]  Stanislav S. Makhanov.  Optimization and correction of the tool path of the five-axis milling machine: Part 2: Rotations and setup , 2007, Math. Comput. Simul..

[4]  Klaus Weinert,et al.  Swept volume generation for the simulation of machining processes , 2004 .

[5]  Youlun Xiong,et al.  Fundamentals of robotic grasping and fixturing , 2007 .

[6]  Stanislav S. Makhanov,et al.  Grid generation as applied to optimize cutting operations of the five-axis milling machine , 2003 .

[7]  Allan D. Spence,et al.  A constant feed and reduced angular acceleration interpolation algorithm for multi-axis machining , 2001, Comput. Aided Des..

[8]  Abbas Vafaeesefat,et al.  Penetration–elimination method for five-axis CNC machining of sculptured surfaces , 2007 .

[9]  Chuang-Jang Chiou,et al.  A machining potential field approach to tool path generation for multi-axis sculptured surface machining , 2002, Comput. Aided Des..

[10]  Paul J. Gray,et al.  Rolling ball method for 5-axis surface machining , 2003, Comput. Aided Des..

[11]  Jingyan Dong,et al.  Feed-rate optimization with jerk constraints for generating minimum-time trajectories , 2007 .

[12]  Han Ding,et al.  A GPU-based algorithm for generating collision-free and orientation-smooth five-axis finishing tool paths of a ball-end cutter , 2010 .

[13]  Han Ding,et al.  Analytical Expression of the Swept Surface of a Rotary Cutter Using the Envelope Theory of Sphere Congruence , 2009 .

[14]  Frank Chongwoo Park,et al.  Smooth invariant interpolation of rotations , 1997, TOGS.

[15]  Taejung Kim,et al.  On actuator reversal motions of machine tools , 2004 .

[16]  Sanjeev Bedi,et al.  Tool path planning for five-axis machining using the principal axis method , 1997 .

[17]  Taejung Kim,et al.  Optimal sweeping paths on a 2-manifold: a new class of optimization problems defined by path structures , 2003, IEEE Trans. Robotics Autom..

[18]  Stanislav S. Makhanov,et al.  Optimization of rotations of a five-axis milling machine near stationary points , 2004, Comput. Aided Des..

[19]  W. T. Lei,et al.  Robust real-time NURBS path interpolators , 2009 .

[20]  Der-Min Tsay,et al.  Removing tool marks of blade surfaces by smoothing five-axis point milling cutter paths , 2009 .

[21]  Erik L.J. Bohez,et al.  Optimal setup for five-axis machining , 2006 .

[22]  Xiong Caihua.  An approach to error elimination for multi-axis CNC machining and robot manipulation* , 2007 .

[23]  Tao Ye,et al.  Geometric parameter optimization in multi-axis machining , 2008, Comput. Aided Des..

[24]  Elizabeth A. Croft,et al.  Feed optimization for five-axis CNC machine tools with drive constraints , 2008 .

[25]  Radha Sarma,et al.  On local gouging in five-axis sculptured surface machining using flat-end tools , 2000, Comput. Aided Des..

[26]  Pierre Bourdet,et al.  A new format for 5-axis tool path computation, using Bspline curves , 2004, Comput. Aided Des..

[27]  Yusuf Altintas,et al.  High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation , 2001 .

[28]  Stanislav S. Makhanov.  Optimization and correction of the tool path of the five-axis milling machine: Part 1. Spatial optimization , 2007, Math. Comput. Simul..

[29]  Rida T. Farouki,et al.  Contour machining of free-form surfaces with real-time PH curve CNC interpolators , 1999, Comput. Aided Geom. Des..

[30]  Matthieu Rauch,et al.  Improving trochoidal tool paths generation and implementation using process constraints modelling , 2009 .

[31]  Jingyan Dong,et al.  A Generalized Time-Optimal Bidirectional Scan Algorithm for Constrained Feed-Rate Optimization , 2006 .

[32]  Jan Swevers,et al.  Time-Optimal Path Tracking for Robots: A Convex Optimization Approach , 2009, IEEE Transactions on Automatic Control.

[33]  M. Diehl,et al.  Time-energy optimal path tracking for robots: a numerically efficient optimization approach , 2008, 2008 10th IEEE International Workshop on Advanced Motion Control.

[34]  Chih-Ching Lo,et al.  Efficient cutter-path planning for five-axis surface machining with a flat-end cutter , 1999, Comput. Aided Des..