Cutting forces in fast-/slow tool servo diamond turning of micro-structured surfaces

Although fast-/slow tool servo (F-/STS) diamond turning is widely employed to generate micro-structured surfaces, very limited attention has been focused on the cutting force which directly reflects the material removal behavior in F-/STS. In this study, theoretical analysis on the cutting force is conducted through both finite element and mechanistic analytical models to present a systematic investigation. Based on direct observation from the FE model that the shear angle varies with respect to the auxiliary servo motion, an analytical model is proposed to simultaneously predict the average and variation of the shear angle considering features of the oscillated servo motion. A comprehensive force model is developed for orthogonal cutting with a round-edged cutter, and the depth-of-cut (DoC) dependent shearing and ploughing effects are considered. With the shearing based material removal, dynamic shear strain, shear strain rate, and stress distribution inside the shear band are modeled together with the dynamic equivalent rake angle to derive the material removal force through the slip-line field theory, and the complex interaction between the chip and cutter in the rake face is also investigated to obtain the corresponding frictional force. With the DoC being smaller than the critical chip thickness, the ploughing force is modeled to be proportionate to the interference volume between the cutter and workpiece with full consideration of the dynamic equivalent clearance angle. Finally, the overall cutting force in F-/STS is estimated using the cutter edge discretization method with further experimental demonstration through the slow tool servo diamond turning of a typical micro-structured surface.