WIAS Preprint No. 1361, (2008)

On a thermomechanical milling model



Authors

  • Chełminski, Krzysztof
  • Hömberg, Dietmar
  • Rott, Oliver

2010 Mathematics Subject Classification

  • 74F05 35Q80 35L15

Keywords

  • Thermo-elasticity, milling, process-structure interaction, work piece effects, stability, delay-differential equations

Abstract

This paper deals with a new mathematical model to characterize the interaction between machine and workpiece in a milling process. The model consists of a harmonic oscillator equation for the dynamics of the cutter and a linear thermoelastic workpiece model. The coupling through the cutting force adds delay terms and further nonlinear effects. After a short derivation of the governing equations it is shown that the complete system admits a unique weak solution. A numerical solution strategy is outlined and complemented by numerical simulations of stable and unstable cutting conditions.

Appeared in

  • Nonlinear Anal. Real World Appl., 12 (2011) pp. 615--632.

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