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Abstract
This thesis presents experimentally verified smooth trajectory generation, feedrate optimization, and high performance control algorithms developed for multi-axis Cartesian machine tools.
New spline parameterization and interpolation schemes are introduced that yield smooth contouring motion with minimal feedrate fluctuation along arbitrarily shaped toolpaths. The first approach is based on optimizing the toolpath geometry to yield minimal discrepancy between the spline parameter and arc length increments, resulting in an Optimally Arc Length Parameterized (OAP) quintic spline. This spline exhibits minimal feedrate fluctuation when interpolated at constant parameter increments. The second approach is based on scheduling the spline parameter to yield the desired are displacement, hence the desired feedrate profile accurately, without having to re-parameterize the spline toolpath. The feedrate correction polynomial and iterative interpolation techniques developed for this purpose are shown to improve the feedrate consistency with reliable convergence properties, at small computational cost, making these methods viable for real-time implementation in the CNC executive.
A jerk continuous feedrate optimization technique is introduced for minimizing the cycle time, while preserving the motion smoothness and tracking accuracy for traveling along spline toolpaths. Feedrate modulation is achieved by varying the travel duration of each segment and fitting the resulting C3 continuous minimum jerk displacement profile. This results in continuous velocity, acceleration, and jerk transitions spanning the entire motion along the toolpath, allowing smoother feed motion with shorter cycle time compared to piecewise constant feedrate modulation method used in current CNC systems.
The feed drive dynamics of a three axis machining center are identified in detail in order to develop a controller with high tracking accuracy and bandwidth. (Abstract shortened by UMI.)
