A dynamic thermoviscoelastic contact problem with friction and wear

Andrews, Kevin T.; Shillor, Meir; Wright, Steve; Klarbring, Anders

doi:10.1016/s0020-7225(97)87426-5

Cited by 73 publications

(46 citation statements)

References 9 publications

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“…Beginning with [20][21][22], a new direction of the development of the model of the sliding contact of two elastic bodies arose, taking into account friction, wear and heat generation, built on the principle of virtual energy and the basic laws of thermodynamics. The solution of problems on the basis of this model is carried out by the finite element method [22].…”

Section: № 1 / 2017mentioning

confidence: 99%

Mathematical modelling of thermoelastic behavior of a coating taking into account frictional heating and wear

Zelentsov¹,

Mitrin²,

Lubyagin³

et al. 2017

CMIT

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This work describes application of the integral transform method to solution of a quasi-static contact problem of the coating wear-out. Frictional heating and wear of the coating occurs during the sliding of a rigid body over its surface. The problem is considered in the framework of the coupled thermoelasticity theory. The solution of the problem is constructed in the form of contour quadratures of the inverse Laplace transformation. After the calculation of the quadratures the solution of the problem is constructed in the form of series over the poles of the integrands. Investigation of the poles of integrands is performed in dependence on four dimensionless parameters of the problem. The solutions obtained are studied in detail with respect to the dimensionless and dimensional parameters of the problem. Numerical examples of the obtained solutions for contact stresses, displacements, temperature and wear of the coating are presented.Keywords: coating, friction, wear, frictional heating, thermoelasticity, Laplace transform, contour integral Introduction. The study of thermoelasticity problems, taking into account the interaction of deformation and temperature fields, began with [1][2][3]. This line of research was called the coupled thermoelasticity. Generalization and solution of particular problems of the new direction of research was continued in [3][4][5]. In subsequent years, both analytical, starting with [4,5], and numerical methods [6] were developed to solve problems of coupled thermoelasticity. In the latter paper the authors were one of the first who developed a scheme of application of the finite element method and gave its implementation for solving the coupled problems of thermoelasticity. Analysis shows that in the overwhelming majority of studies in the solution of coupled thermoelasticity problems the finite element models of a fairly general purpose were developed, for example [7][8][9][10][11].The analytical methods for solving this class of problems did not become as widespread as the numerical ones. The results obtained with their help were summarized in [12]. Beginning with papers [13][14][15][16][17][18], scientists consider uncoupled problems of thermoelasticity about the sliding contact of a rigid body with an elastic coating, taking into account friction, heating of the coating from friction, and abrasive wear. Because of the large number of parameters of the problem, the onedimensional and quasi-static problems were considered. In [15][16][17][18], for their solution the integral Laplace transform with a solution in the form of functional series along the poles of the integrands of the contour quadratures of the inverse Laplace transform were used. The solution method allows

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Section: № 1 / 2017mentioning

confidence: 99%

Mathematical modelling of thermoelastic behavior of a coating taking into account frictional heating and wear

Zelentsov¹,

Mitrin²,

Lubyagin³

et al. 2017

CMIT

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“…Concrete examples of contact models which lead to aforementioned subdifferential boundary conditions will be provided in Sect. 4.…”

Section: Physical Setting Of the Problemmentioning

confidence: 99%

“…This is the case when the superpotential j 4 = j 4 (x, t, ζ, ρ, θ) is independent of (ζ, ρ) and nonconvex in θ . Then the friction law (41) takes the form −σ τ (t) ∈ ∂j 4 x, t, u τ (t) on C × (0, T ).…”

Section: Nonmonotone Friction Independent Of Slip and Slip Ratementioning

confidence: 99%

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Hyperbolic Hemivariational Inequalities for Dynamic Viscoelastic Contact Problems

Kulig

2012

J Elast

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“…This task is rendered difficult because of the complex and coupled physical mechanisms involved such as dislocation, thermal gradients, large displacements [1] and mass removal depending on the investigated type of material. In the framework of turbomachines, where large relative displacements between contacting components together with high abradable wear rates are observed, most of the existing theoretical statements with strongly limiting assumptions do not seem relevant and easy to implement [21], even though some of them seem promising [23,4].…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of Abradable Coating Wear Through Plastic Constitutive Law: Application to Aircraft Engines

Legrand

Pierre

2009

Volume 1: 22nd Biennial Conference on Mechanical Vibration and Noise, Parts a and B

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In the field of turbomachines, better engine performances are achieved by reducing possible parasitic leakage flows through the closure of the clearance distance between blade tips and surrounding casings. Together with new technologies involving higher casing conicity for improved compression rates, direct contact is now considered as part of aircraft engines normal life. In order to avoid possibly catastrophic scenarios due to high contact efforts between the rotating and static components, implementation of abradable coatings has been widely recognized as a robust solution offering several advantages: reducing potential damage to the incurring blade as well as adjusting operating clearances, in-situ, to accept physical contact events. Nevertheless, the process of wear undergone by abradable coatings is not well understood and its consequences are still under investigation. In the present work, its macroscopic behavior is numerically approximated through a piecewise linear plastic constitutive law which allows for real time access to the current abradable layer profile. First results prove convergence in time and space of the proposed approach and show that the frequency content of the blade response is clearly affected by the presence of abradable coatings. It seems that opening the clearance between the blade tip and the casing during wear leads to large amplitudes of motion far from the usual linear conditions provided by the well-known Campbell diagrams.

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A dynamic thermoviscoelastic contact problem with friction and wear

Cited by 73 publications

References 9 publications

Mathematical modelling of thermoelastic behavior of a coating taking into account frictional heating and wear

Mathematical modelling of thermoelastic behavior of a coating taking into account frictional heating and wear

Hyperbolic Hemivariational Inequalities for Dynamic Viscoelastic Contact Problems

Numerical Investigation of Abradable Coating Wear Through Plastic Constitutive Law: Application to Aircraft Engines

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