Mechanics and multi-regenerative stability of variable pitch and variable helix milling tools considering runout

Variable pitch and variable helix (VPVH) milling tools are usually utilized to mitigate regenerative chatter vibrations by destroying the vibration phases between adjacent teeth. But this chatter suppression mechanism may considerably be disturbed by the inevitable tool runout, which could also change the phases, even to a larger extent. Thus the cutting performance of VPVH tools in terms of mechanics and dynamics should be re-evaluated by taking runout into consideration. This paper firstly sets up the mechanistic model for VPVH tools and then presents a combined nonlinear optimization procedure to identify the cutting coefficients and runout parameters. Secondly, the dynamic system of VPVH tools considering runout is modeled by a periodic-coefficient delay differential equation with multiple underdetermined delays. Afterwards, the generalized Runge-Kutta (GRK) method is extended to tackle the runout-induced multi-regenerative effects and thus to analyze the milling process stability. The accuracy and efficiency of the GRK method is validated using published numerical examples. A series of cutting experiments with a commercially available VPVH tool are performed to verify the presented mechanistic and dynamic models. It confirms that runout cannot be neglected when evaluating the cutting performance of VPVH tools. Finally, the joint influences of runout and pitch/helix angles on cutting forces and chatter stability of VPVH tools are discussed in detail based on the proposed approach.