Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering


Professor M.A. Elbestawi


This thesis outlines a modelling approach and compensation strategy for understanding and improving the accuracy of five-axis machining. The kinematic model of the machine was based on Homogeneous Transformation Matrices (HTM), which used small angle approximations to form shape and joint transformations. HTMs were chosen in this form because they allowed the kinematic model to include the geometric, kinematic, and thermal errors of the machine. These sources of error result in a significant loss of accuracy in the production of dies, molds, aircraft parts, and many other critical industrial components. The individual error terms in the HTM's formulation are difficult to measure on an assembled machine. Therefore, a test procedure was designed to isolate the error terms and an allocation strategy, using the kinematic model, was developed to associate the error measured in the work space to the error in each of the main components of the machine. The kinematic model of the machine was also used in calculating the compensation values to capture the interaction of the error components and all of the axis motions. The compensation strategy was implemented by adjusting each axis in the motion code with offset values based on the expected error. The motion code was modified just before being sent to the machine tool for processing. Due to the difficulties in measuring the error continuously on-line, empirical models were used to estimate the errors. The empirical models related temperature distribution and various machine conditions to the error in the machine tool's components. The empirical models took advantage of a priori information in the form of known physical relationships which described the deformation of the structures under thermal loading. A multiple linear regression model was chosen as the empirical model for implementation in the compensation strategy. It was chosen because of its simplicity, robustness, and ease of implementation. Through the recasting of the linear model's parameters, nonlinearities could also be included in the model. The regression model was found to be able to interpolate within the experimental data set. Through the inclusion of physical relationships in the development of the model, it was found to provide reasonable estimates when extrapolating. A neural network model was also considered, but was not implemented in the final compensation strategy because of the model's limitations when extrapolating beyond the training set conditions. A means of updating the error model on-line was included in the compensation strategy using measurements made from reference surfaces in the work space. This was done to account for any unmodelled variation not captured during off-line testing. Also, this includes any slowly varying changes which can occur to the machine over time due to wear and structural material instability. Realistic cutting tests using light finishing cuts, high spindle speed and axis feed were conducted. These machining conditions are typical of the mold and die industry. The cutting tests showed that a reduction of dimensional error from 0.082 mm to 0.012 mm was possible using the proposed compensation strategy.

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