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Identification of the Heat Losses at the Jaws of a Tensile Testing Machine

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Abstract

In the present paper, an application of infrared thermography to inverse heat conduction problems is presented. The study involves the identification of conductive losses at the jaws of a tensile testing machine, which must be assessed in situ, because of variable fastening conditions of the specimen, inducing variable thermal resistances at the jaws. For this purpose, a photo-thermal technique has been developed to identify all the heat exchanges of the sample. An optical excitation, based on a halogen lamp projector, illuminates the specimen in situ on the tensile machine, while the radiative flux excitation is measured using a photodiode. The conductive fluxes are identified, transient and steady, then the equivalent exchange coefficients at the jaws. For this purpose, a direct numerical model by finite differences and an inverse procedure allow to estimate these exchange coefficients. The resolution of the inverse problem is based on the optimization by the conjugate gradient method, of a least square criterion between the temperatures measured by infrared thermography and the temperatures calculated from the direct model.

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Abbreviations

d :

descent direction

e :

thickness (m)

h a :

heat transfer coefficient (W. m − 2 K − 1)

L :

length (m)

m :

fin coefficient (m −1)

P :

perimeter (m)

q(x):

heat flux (W. m − 2)

S :

error functional

S C :

transverse section (m 2)

t :

time coordinate (s)

t f :

final time (s)

x, y :

spatial coordinates (m)

Y i (t):

transient measured temperature, obtained by infrared thermography (°C)

α :

thermal diffusivity (m 2 ⋅ s − 1)

β :

conjugate coefficient

θ(x, t):

temperature (°C)

θ a :

room temperature (°C)

δθ(x, t):

sensitivity of temperature to the x and t parameters

λ :

thermal conductivity (W ⋅ m − 1 ⋅ K − 1)

ξ(θ, Φ1, Φ2, ψ):

Lagrange functional

Φ1, Φ2 :

heat fluxes at the ends of the sample

ψ(x, t):

Lagrange multiplier

N :

iteration index

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Acknowledgments

This work has been realised with the support of the French National Agency for Research.

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Authors and Affiliations

  1. Université de Reims, GRESPI, Campus du Moulin de la Housse, BP 1039, 51 687, Reims Cedex 2, France

    T. Bouache, H. Pron & D. Caron

Authors
  1. T. Bouache
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  2. H. Pron
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  3. D. Caron
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Correspondence to H. Pron.

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Bouache, T., Pron, H. & Caron, D. Identification of the Heat Losses at the Jaws of a Tensile Testing Machine. Exp Mech 56, 287–295 (2016). https://doi.org/10.1007/s11340-015-0096-z

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  • DOI: https://doi.org/10.1007/s11340-015-0096-z

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