Mechanistic modelling of the milling process attempts to relate the inprocess chip parameters to the forces encountered in the cut. Knowledge of these forces grants process planners the unique ability to properly set cutting conditions to maximize the metal removal rate, and overall efficiency of the operation. While 3-axis mechanistic models have existed for some time, efficient 5-axis models have not been developed, due to the difficulties of simply computing the instantaneous chip thickness and edge contact length in a fully 3-dimensional environment. This thesis describes a solution to these concerns, with the development of a volumetric mechanistic model based on a local and adaptive depth buffer of a rendering engine.

A rendering engine allows for any portion of a scene composed of graphics primitives to be viewed from any orientation. The depth buffer stores the distance of each visible object in the scene from the viewing location. In the case of a milling simulation, the scene is composed of the graphical representations of the stock and tool geometry. When this scene is viewed along the current tool position axis as a plan view, the difference in depth values of the tool and the current state of the workpiece allow for a computation of the instantaneous volume of material removed. The tool edge contact length is determined by projecting depth buffer elements onto the tool shape. With these two quantities, and with experimentally determined cutting constants that account for tool geometry and workpiece material properties, the forces and torque acting on tlie tool can be predicted. Because the depth buffer is consistently oriented to the current tool axis, it is called an adaptive depth buffer. Moreover, because the rendered scene is limited to a viewing about the tool (to increase rendering efficiency and resolution), the model is called a local method.

However, the problem of computing in-process chip parameters is compounded by the dependence of the relative tool-workpiece velocity on the individual geometry of the milling machine, specifically the variable radial distance from the rotational axes. To this end, the inverse kinematics of a tilt-rotary 5-axis machine configuration were developed as well as the methodology necessary to compute the instantaneous velocity information from the cutter location data or program G-code. The machine kinematic effects were then integrated with the graphical method to realize a fully functional 5-axis mechanistic model.

The model was applied and compared to 3- and 5-axis machining experiments, and were found to agree closely for the tangential and radial cutting components as well as the cutting torque. Factors such as tool runout and edge forces were accounted for. The effect of tool balance and gyroscopic effects of 5-axis machining were also explored.

Force measurements in 5-axis machining are difficult due to the orientation changes between the stock and workpiece, and this thesis fully explores this challenge. The effect of a rotating cutting force dynamometer (ROD) measurement system was investigated and the equations necessary for determining milling force constants using this system were derived.

To complete this work, feed scheduling was investigated in full 5-axis machining. Experimental results show a near constant force on the tool while reducing the machining time by 50%.