On a thermomechanical milling model
- Chełminski, Krzysztof
- Hömberg, Dietmar
- 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.
- Nonlinear Anal. Real World Appl., 12 (2011) pp. 615--632.