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UBC Theses and Dissertations

Mechanics and dynamics of ballend milling Lee, Peter Pak Wing


Ball end milling has been used extensively in current manufacturing industry in producing parts with sculptured surfaces. Due to its complex cutter geometry, ball end milling mechanics and dynamics have not been studied until recently. In this research, the mechanics and dynamics of cutting with a special helical ball end cutter are modeled. A unified mathematical model, which considers the true rigid body kinematics of milling, static deformations and forced and self excited vibrations, is presented. The ball end mill attached to the spindle is modeled by two orthogonal structural modes in the feed and normal directions at the tool tip. For a given cutter geometry, the process dependent cutting coefficients are obtained by applying oblique tool geometry to the fundamental properties such as shear yield stress, shear angle and average friction angle measured from orthogonal cutting tests. The three dimensional surface finish generated by the helical flutes is digitized using the true kinematics of ball end milling process. The dynamically regenerated chip thickness, which consists of rigid body motion of the cutter and structural vibrations, is evaluated at discrete time intervals by comparing the present and previous tooth marks left on the finish surface. The process is simulated in time domain, by considering the instantaneous regenerative chip load, local cutting force coefficients, structural transfer functions and the geometry of ball end milling process. The proposed model predicts cutting forces, finished surface and chatter-free condition charts, and is verified experimentally under both static and dynamic cutting conditions. The model allows process planners to select cutting conditions to minimize dimensional surface errors, shank failure and chatter vibrations for end milling operations.

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