Unified and Efficient Analysis of Machining Chatter and Surface Location Error

TL;DR

This paper introduces a novel modeling framework combining semi-discretization and lifting techniques to efficiently analyze machining chatter stability and surface location error, improving surface quality predictions.

Contribution

It presents an innovative approach that models machining dynamics as an angle-varying delay differential equation and enables efficient computation of stability and surface errors.

Findings

The proposed method improves computational efficiency over existing techniques.

It accurately predicts chatter stability and surface location errors.

Simulation results validate the effectiveness of the framework.

Abstract

Although machining chatter can be suppressed by the choice of stable cutting parameters through means of stability lobe diagram (SLD), surface roughness still remains due to the forced vibration, which limits surface quality, especially in the surface finish. Better cutting parameters can be achieved considering surface location error (SLE) together with SLD. This paper proposes an innovative modeling framework of the machining dynamic system that enables efficient computation of the chatter stability and SLE. The framework mainly embodies two techniques, namely semi-discretization method (SDM) and lifting method. The machining dynamics system is mathematically expressed as an angle-varying delay differential equation (DDE). The SDM approximates the angle-varying and delayed terms to ordinary terms using zero-phase interpolations and governs the discrete angle-varying dynamics system. Then, the system is merged over the tooth passing angle using the lifted approach to establish an explicit dynamic system in the compact state-space form. Based on the compact state-space model, the chatter stability and SLE prediction are easily and efficiently conducted. Simulation results show the improved efficiency of the proposed method over other well-known methods.