Improved dynamic cutting force model in ball end milling - Part 1: Theoretical modelling and experimental callibration

An accurate cutting force model of ball-end milling
is essential for precision prediction and compensation of tool
deflection that dominantly determines the dimensional accuracy
of the machined surface. This paper presents an improved theoretical
dynamic cutting force model for ball-end milling. The
three-dimensional instantaneous cutting forces acting on a single
flute of a helical ball-end mill are integrated from the differential
cutting force components on sliced elements of the flute
along the cutter-axis direction. The size effect of undeformed
chip thickness and the influence of the effective rake angle are
considered in the formulation of the differential cutting forces
based on the theory of oblique cutting. A set of half immersion
slot milling tests is performed with a one-tooth solid carbide
helical ball-end mill for the calibration of the cutting force coefficients.
The recorded dynamic cutting forces are averaged to fit
the theoretical model and yield the cutting force coefficients. The
measured and simulated dynamic cutting forces are compared
using the experimental calibrated cutting force coefficients, and
there is a reasonable agreement. A further experimental verification
of the dynamic cutting force model will be presented in
a follow-up paper.