UBC Theses and Dissertations

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UBC Theses and Dissertations

Feedrate optimization with contouring error and drive constraints in five-axis machining Nesbit, Erina Okuda


Five-axis Computer Numerical Controlled (CNC) machine tools are used to machine parts with complex, curved surfaces. When the reference toolpath contains frequencies beyond the bandwidth of the servo drive, the actual axis position lags the reference position commands which leads to axis tracking error. The tracking errors of three translational and two rotational drives are projected along the path using a kinematic model of the machine to form contouring errors i.e. the geometric deviation of the actual tool movement from the commanded toolpath. Parts with contouring errors larger than the design tolerance are often scrapped. Although contouring errors can be decreased by reducing the machining feedrate, this causes the cycle time to increase resulting in less productivity. This thesis proposes a feedrate optimization method which minimizes the process cycle time without violating contouring error limits as well as velocity, acceleration and jerk limits of the machine drives. First, discrete 5-axis tool positions are fitted to two quintic b-splines to represent the desired tooltip position and tool orientation trajectory. An initial, uniform feedrate spline is also generated in quintic b-spline form. Derived from the toolpath splines, discrete tool positions at uniform path displacement intervals are decomposed into axis commands based on the machine kinematics, and velocity, acceleration and jerk are calculated. The axis commands are also passed through the equivalent transfer function of each drive to predict their tracking errors, which are projected onto the toolpath to find contouring error. The optimization algorithm takes in the calculated axis tracking errors, contouring error, and cycle time for the given toolpath and feedrate profile. Within the optimizer, a gradient descent algorithm iteratively modifies the feedrate spline control points where the new feedrate profile is used to re-evaluate the cycle time, contouring error, and drive signals until a local minimum has been found. The final output of the algorithm is an optimized feedrate spline which ensures a minimum cycle time for the process, while maintaining drive and contouring error limits. The proposed algorithms are experimentally validated on a 5-axis machine tool controlled by an in-house developed open CNC system.

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