Computer numerical controlled (CNC) machines have become an integral part of the manufacturing industry, allowing companies to increase the accuracy and productivity of their manufacturing lines. The next step to improving and accelerating the development process of a part is to involve virtual prototyping during the design phases. Virtual manufacturing has become an invaluable tool to process planners and engineers in recent years to model the manufacturing environment in a virtual setting to determine the final geometry and tolerances of new parts and processes. For a virtual twin of a CNC machine to be built, the dynamics of the drive and CNC controller must be identified. Traditionally, these identification techniques require several intrusive tests to be run on the machine tool, causing valuable time lost on production machines. In this thesis, three new techniques of developing virtual models of machine tools are discussed.

The first model presented is a quasi-static model which is suitable for trajectory tracking error prediction. This technique is used to determine the contributions of the commanded velocity, acceleration, and jerk to the tracking errors of each axis of the machine tool. After determining these contributions, process planners can modify the axis feedrates in a virtual environment during trajectory optimization to find the best parameters for the shortest cycle time. This method was validated using a laser drilling machine tool from Pratt and Whitney Canada (P&WC) and was able to predict the root mean square (RMS) of the tracking error within 2.62 to 11.91 µm. A simple graphical user interface (GUI) was developed so that process planners and engineers can import data collected from the FANUC and Siemens CNC controllers to identify quasi-static models.

The second model presented is a single input – single output (SISO) rigid body rapid identification model. In previous literature, a rapid identification method was proposed where a short G-code was run on machine tools, the input and output signals were collected from the controller and the dynamics were reverse engineered from the gathered data. However there were some shortfalls with this older method, the new proposed rapid identification model addresses these by improving parameter convergence and using commanded signal derivatives for identification. Tests were conducted on a five-axis machine tool located at the University of Waterloo (UW) to verify and compare the new rapid identification model to the previous model. It was determined that the model is able to predict the RMS of the tracking errors with 50-76% improvement and maximum contour error discrepancy with 22-35% improvement. Another GUI was developed for the SISO rigid body rapid identification model that allows users to import data collected from different machine tools and identify a model.

The third model that is discussed in this thesis is a multi input – multi output (MIMO) model. This model builds upon the SISO rigid body model and is able to capture vibratory and elastic dynamics. Relations between inputs, such as reference and disturbance signals, can be related to a variety of measurable outputs. The model is used to predict the relationship between the inputs of commanded position and disturbance to the outputs of tracking error and velocity of the x- and y- axes of a P&WC five axis milling machine tool. Three different models were identified using this algorithm, two 1-axis 3rd order decoupled models and two 2-axis 6th order coupled model are compared in this thesis. The two 6 th order models have different search spaces, the first has a search space defined from the 3rd order decoupled identified parameters while the second has a more general search space. Overall, the 6th order model with a larger search space was able to predict the RMS and maximum tracking error more closely, with a maximum improvement of 19% for both metrics. However it should be noted that 6th order model with a smaller search space was still able to predict the RMS and maximum tracking error similarly to the 6th order model with the larger search space. The smaller search space configuration can save on computational time which can be advantageous in real world applications.

In order to verify that the MIMO rapid identification technique would be able to identify a vibration mode, an experimental setup was designed and machined. A flexure mount with known vibration modes was designed, built and tested to validate Solidworks frequency simulation results. It was concluded that the simulation results were able to estimate the frequencies of the flexure with 95-98% accuracy and with a maximum absolute difference of 2.87 Hz.

The flexure was mounted onto the five-axis machine tool at UW to introduce vibratory dynamics. Since there is a flexible mode being introduced at the tool-workpiece interface, the motor encoders would not be able to capture these dynamics, therefore a two-dimensional grid encoder (KGM) and two 3-axis accelerometers (one located on the tool head and the other on the workpiece table) were also placed on the machine tool to record the true tool-workpiece response. The data collected from the accelerometers were corrected for possible roll, pitch and yaw misalignments before synchronizing the accelerometer and KGM data to the motor encoder data. This data was then used to build MIMO rapid identification models with the commanded position (recorded from the motor encoders) and normalized Coulomb disturbance as the inputs to the system and the true tool-workpiece position or acceleration and machine tool feed drive velocity as the outputs to the model. The model estimated from the position measurements from the KGM yielded better results 19-1496% improvement in RMS tracking error prediction over the acceleration based models. The contouring error estimated using the KGM position model also has an improvement of 233- 370% over the acceleration models. Using the transfer functions estimated from the accelerometer data, there was a 16-33% improvement in the RMS tracking error prediction and an 11-51% improvement in the maximum tracking error prediction over the KGM acceleration based model. The RMS contour prediction error also improved 4-5% and the maximum contour error prediction improved by 1-6% between the two models.

Further development into the MIMO LTI algorithm is currently being done in the laboratory, including research into more complex friction models. It is also recommended to machine an actual part on the fiveaxis machine tool and to measure the contouring error of the part on the coordinate measuring machine to verify the predictions presented in this thesis.