Modelling, Simulation, and Optimization of Thermal Deformations from Milling Processes

  • Alfred Schmidt
  • Carsten Niebuhr
  • Daniel Niederwestberg
  • Jost Vehmeyer
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


During a machining process, the produced heat results in thermomechanical deformation of the workpiece and thus an incorrect material removal by the cutting tool, which may exceed given tolerances.

We present a numerical model including a finite element simulation for thermomechanics, a dexel model for material removal, and a process model for forces and heating produced by the machining tool.

For minimization of the final shape deviation, this forward model defines the constraints for an optimal control problem. Main control variables are the process parameters and the path of the machining tool. These are varied according to a compensation and optimization approach.



We thank Dietmar Hömberg for organizing MS37 “Maths for the digital factory” where we could report about the subject.

The presented results have been obtained within the research project “Thermomechanical Deformation of Complex Workpieces in Drilling and Milling Processes” (DE 447/90-3, MA 1657/21-3) within the DFG Priority Program 1480 “Modeling, Simulation and Compensation of Thermal Effects for Complex Machining Processes”. The authors would like to thank the DFG for its financial and organizational support of the project.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Alfred Schmidt
    • 1
  • Carsten Niebuhr
    • 1
  • Daniel Niederwestberg
    • 2
  • Jost Vehmeyer
    • 1
  1. 1.Center for Industrial Mathematics and MAPEX Center for Materials and ProcessesUniversity of BremenBremenGermany
  2. 2.Institute of Production Engineering and Machine ToolsLeibniz Universität HannoverHannoverGermany

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