An improved algorithm for cutting stability estimation considering process damping

Abstract

Process damping generated between the clearance face of the tool and wavy finish workpiece surface has a strong effect on cutting dynamics and stability, especially at low cutting speeds, resulting into higher chatter stability limit. It is particularly important for hard-to-machine materials, such as titanium, nickel super alloys, and hardened steels, which need to be machined at low cutting speed. However, process damping has been mostly ignored in chatter analysis as there is no practical model for estimation of it. In the meantime, the existing studies on the process damping encounter the challenges of computational efficiency. In this study, process damping effect is equivalent to a linear viscous damping which is described by the process damping coefficients. An energy dissipation principle is established to relate the flank-wave indentation area to the process damping coefficients. Two methods are proposed to calculate the indentation area, which is involved in the cutting stability computation and occupies the most time. In analytical integration method, the sinusoidal expression of workpiece surface undulation is fitted by piecewise polynomial to calculate the indentation area. In numerical integration method, the area is realized by summation of the divided small area unit. The time for establishing stability lobes by the above two methods is greatly reduced compared with the detailed method proposed by Ahmadi and Ismail (Int J Mach Tools Manuf 51:296–308, 2011) which took 10 min to compute one single lobe. It demonstrates that the stability lobes established in frequency domain by the proposed methods are extremely efficient. Moreover, the stability lobes maintain enough accuracy compared with stability lobes established for different amplitudes of vibration as reported by Ahmadi and Ismail (Int J Mach Tools Manuf 51:296–308, 2011), especially the finite amplitude stability, with that, the vibration stabilizes at an amplitude between fully stably and fully unstable due to process damping.