Mechanics and Dynamics of Ball End Milling

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Abstract
Mechanics and dynamics of cutting with helical ball end mills are presented. The helical ball end mill attached to the spindle is modelled by orthogonal structural modes in the feed and normal directions at the tool tip. For a given cutter geometry, the cutting coefficients are transformed from an orthogonal cutting data base using an oblique cutting model. The three dimensional swept surface by the cutter is digitized using the true trochoidal kinematics of ball end milling process in time domain. The dynamically regenerated chip thickness, which consists of rigid body motion of the tooth and structural displacements, 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, surface finish and chatter stability lobes, and is verified experimentally under both static and dynamic cutting conditions.

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