Wave attenuation effects on the chatter instability of end-milling

The non-linear force law is incorporated into 2-DOF modelling of chatter in end-milling. Modified full-discretization map is generated for the resulting coupled delay differential equation. The generated map is validated using simulation results of MATLAB dde23. A new theory called “Theory of wave attenuation” is presented. The theory says that the curved surface behind a cutting edge has a flattening effect on some waves generated by the cutting edge. This flattening effect is termed “Wave attenuation effect” since it tends to counteract regenerative effect. Wave attenuation effect is posited as explanation for rise of chatter stability with rise in feed, fall in number of teeth and fall in hardness of workpiece material.