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Extended bisection method for parameter identification of the transient heat conduction equation for thermo-elastic deformations during drilling

  • Janine GlänzelEmail author
  • Arnd Meyer
  • Roman Unger
  • Michael Bräunig
  • Volker Wittstock
  • Steffen Ihlenfeldt
ORIGINAL ARTICLE

Abstract

A new interdisciplinary approach is discribed to identifying unknown parameters using an extended version of the known interval bisection method. This developed method is based on the use of finite elements for calibrating the simulation calculation. The resulting thermo-elastic deformations which occur in drilling processes with impaired cooling lubrication are to be used as correction values for tool positioning in the NC control. Based on the strong impact on workpiece temperature of machining, a simulation approach is presented for calculating the temperature fields and their thermo-elastic consequences. In addition, methods are presented to correct these effects. This paper particularly deals with the temperature fields of drilling operations. Special attention is paid to the technique employed for iterative numerical determination of the unknown heat flux η w and heat transfer coefficient \(\bar {\gamma }\) values. Finally, the data obtained from experiments are compared with those achieved by numerical simulation in order to verify the efficiency of simulation and determination of parameters.

Keywords

Adaptive FE simulation Thermo-elasticity Parameter approximation Temperature simulation in nc-drilled workpieces 

Symbol

Description

c

Specific heat capacity

fT(x,t)

Volume force

\(g_{T_{D}}\)

Boundary temperature for Γ D

gD

Explicit displacement for Γ D

gN

Force density for Γ N

n

Surface normal

t

Time

T(x,y)

Temperature field

Ta

Ambient temperature

Tref

Reference of temperature

u(x,t)

Deformation field

α

Coefficient of thermal expansion

γ

Heat transfer coefficient

\(\bar {\gamma }_{l}\), \(\bar {\gamma }_{r}\)

Interval limits for heat transfer

Γ

Boundary of Ω

ΓD

Periphery Γ of Dirichlet b. c.

ΓN

Periphery Γ of Neumann b. c.

ΓR

Periphery Γ of Robin b. c.

𝜖

Green’s strain tensor

ηw

Heat flux

\(\eta _{\omega _{l}}\), \(\eta _{\omega _{r}}\)

Interval limits for heat flux

κ

Thermal conductivity

μ, λ

Lamé constant

ρ

Density

σ

Cauchy’s stress tensor

ψ

Scalar test function H 1(Ω)

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Copyright information

© Springer-Verlag London 2016

Authors and Affiliations

  • Janine Glänzel
    • 1
    Email author
  • Arnd Meyer
    • 2
  • Roman Unger
    • 2
  • Michael Bräunig
    • 2
  • Volker Wittstock
    • 2
  • Steffen Ihlenfeldt
    • 1
    • 3
  1. 1.Fraunhofer Institute for Machine Tools and Forming Technology IWUChemnitzGermany
  2. 2.Technische Universität ChemnitzChemnitzGermany
  3. 3.Technische Universität DresdenDresdenGermany

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