Rapid stability analysis of serrated end mills using graphical-frequency domain methods

• Published in: International journal of machine tools & manufacture Vol. 171; p. 103805
• Main Authors: Bari, Pritam, Kilic, Zekai Murat, Law, Mohit, Wahi, Pankaj
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.12.2021; Elsevier BV
• Subjects: Angles (geometry); Approximation; Chatter stability; Differential equations; Discretization; End milling; Exact solutions; Frequency domain; Graphical; Graphical methods; Machining; Methods; Numerical integration; Numerical methods; Serrated end mills; Simulation; Stability analysis; Stability criteria; Stability lobes; Time domain analysis; Varying time delays; Frequency domain; Varying time delays; Serrated end mills; Graphical; Chatter stability
• ISSN: 0890-6955; 1879-2170
• DOI: 10.1016/j.ijmachtools.2021.103805

Serrated tools result in an irregular distribution of chip thickness and varying time delays along their flutes that disturb the regenerative chatter mechanism and maximize productivity in rough machining operations. The chatter stability simulation with such tools is complex due to the delay differential equations with multiple and distributed delays. Although the time domain numerical integration methods and the semi-discretization method are accurate, they are computationally expensive and hence inhibit the optimal design of serrated cutters. Despite the advantages that serrated tools offer, there has been little attention paid to rapidly predict stability lobes diagram for these tools to help instruct their optimal designs. To address this need, new graphical-frequency methods are presented to solve for stability of serrated tools with arbitrary geometry. The graphical method averages the number of teeth in cut to make the system time-invariant and results in a closed-form analytical solution. It reduces the simulation time by up to ∼99% compared to the semi-discretization method. Generalized solutions to the classical zero-order approximation and the multi-frequency methods are also presented by using the Nyquist stability criterion. The use of the zero-order approximation method and the multi-frequency method reduces simulation times by up to ∼97% and ∼79% respectively compared to the semi-discretization method. These are significant improvements over reports in the previous literature. Stability predictions are validated experimentally and benchmarked with high-fidelity time domain methods. The presented methods are general and can be applied to any end mill with non-uniform pitch and helix angles as well. [Display omitted] •New graphical-frequency-based methods are proposed to aid stability predictions.•Methods are benchmarked and shown to offer up to 99.8% computational savings.•Methods are generalized and can be extended to end mills with arbitrary geometry.•Experimental validation was done with two non-standard profiled serrated cutters.•Multi-frequency solution takes as much time as the semi-discretization method.