Effects of radial immersion and cutting direction on chatter instability in end-milling

Low radial immersion end-milling involves intermittent cutting. If the tool is flexible, its motion in both the x- and y-directions affects the chip load and cutting forces, leading to chatter instability under certain conditions. Interrupted cutting complicates stability analysis by imposing sharp periodic variations in the dynamic model. Stability predictions for the 2-DOF model differ significantly from prior 1-DOF models of interrupted cutting. In this paper stability boundaries of the 2-DOF milling process are determined by three techniques and compared: (1) a frequency-domain technique developed by Altintas and Budak (1995); (2) a method based on time finite element analysis; and (3) the statistical variance of periodic 1/tooth samples in a time-marching simulation. Each method has advantages in different situations. The frequency-domain technique is fastest, and is accurate except at very low radial immersions. The temporal FEA method is significantly more efficient than time-marching simulation, and provides accurate stability predictions at small radial immersions. The variance estimate is a robust and versatile measure of stability for experimental tests as well as simulation. Experimental upmilling and down-milling tests, in a simple model with varying cutting directions, agree well with theory.