WIAS Preprint No. 1361, (2008)

On a thermomechanical milling model


  • Chełminski, Krzysztof
  • Hömberg, Dietmar
    ORCID: 0000-0001-9460-5729
  • Rott, Oliver

2010 Mathematics Subject Classification

  • 74F05 35Q80 35L15


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




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.

Download Documents