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UBC Theses and Dissertations

Five-axis trajectory generation methods Sencer, Burak

Abstract

Five-axis machining has been widely adopted manufacturing parts with sculptured surfaces in the aerospace, die and mold and other industries. Five-axis machine tools have a kinematic structure compromising three Cartesian axes couples with two rotary joints enabling the tool to reach any given position and the orientation on the workpiece surface. Five-axis motion allows the orientation of the tool along the toolpaths with varying curvatures and sculptured surfaces. However, optimal trajectory generation methods are required in achieving a smooth coordinated motion of the tool tip and tool axis orientation, which is essential in reducing the fluctuations in the feed, accelerate and jerk of the drives. In this thesis, a toolpath generation algorithm has been developed for smooth trajectories based on compressing the C⁰ continuous Numerical Control (NC) motion commands into continuous b-spline format. With the aid of the b-spline toolpath representation, the discontinuities and unwanted acceleration harmonic in the multi-axis motion are reduces. The tool position and orientation vectors are interpolated continuously enabling a smooth and synchronized motion of the drives. In order to achieve higher smoothness in the change of feed direction, the spline toolpath is optimized by solving the linear quadratic minimization problem during the least squares fit. The resultant angular motion of the tool is further smoothed by minimizing the integral square of third derivative of the orientation spline using a non-linear optimization technique. The Feed Correction Polynomial algorithm is implemented in the real time interpolation of the generated b-spline toolpath yielding a consistent feedrate profile during contouring operations. It is shown that feed correction method exhibits reduced feedrate fluctuations when compared to the widely used Taylor Series approximations. A jerk continuous feedrate profile in terms of C³ quintic spline is adapted for five-axis trajectory generation. The feedrate profile is generated utilizing the minimum jerk criteria for the smoothness of the motion and tracking accuracy. The feed profile is then optimized to achieve minimum cycle time while adhering to the machine tool's velocity, acceleration and jerk limitations. The developed trajectory generation algorithms have been simulated using the kinematics of a widely used five-axis machine tool promising potential applications in rough machining.

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