The present paper is devoted to a theoretical analysis of sliding friction under the influence of in-plane oscillations perpendicular to the sliding direction. Contrary to previous studies of this mode of active control of friction, we consider the influence of the stiffness of the tribological contact in detail and show that the contact stiffness plays a central role for small oscillation amplitudes. In the present paper we consider the case of a displacement-controlled system, where the contact stiffness is small compared to the stiffness of the measuring system. It is shown that in this case the macroscopic coefficient of friction is a function of two dimensionless parametersa dimensionless sliding velocity and dimensionless oscillation amplitude. In the limit of very large oscillation amplitudes, known solutions previously reported in the literature are reproduced. The region of small amplitudes is described for the first time in this paper.
This paper builds upon the results of a recent study which illustrates how the Fast Fourier Transformation (FFT) can be used to accelerate the Boundary Element Method (BEM) for arbitrary shapes. In the present work, we further deepen this understanding and focus especially on implementation details in order to calculate the boundary integrals with the FFT. Different numerical techniques are compared for an exemplary shape. Also, additions to the concept are mentioned such as the introduction of a high-resolution grid close to the boundary and a low-resolution grid farther away.
In the present paper a numerical implementation technique for the transformations of the Method of Dimensionality Reduction (MDR) is described. The MDR has become, in the past few years, a standard tool in contact mechanics for solving axially-symmetric contacts. The numerical implementation of the integral transformations of the MDR can be performed in several different ways. In this study, the focus is on a simple and robust algorithm on the uniform grid using integration by parts, a central difference scheme to obtain the derivatives, and a trapezoidal rule to perform the summation. The results are compared to the analytical solutions for the contact of a cone and the Hertzian contact. For the tested examples, the proposed method gives more accurate results with the same number of discretization points than other tested numerical techniques. The implementation method is further tested in a wear simulation of a heterogeneous cylinder composed of rings of different material having the same elastic properties but different wear coefficients. These discontinuous transitions in the material properties are handled well with the proposed method.
In this work, different numerical methods for simulating deformations and stresses in turbine blade fir-tree connections are examined. The main focus is on the Method of Dimensionality Reduction (MDR) and the Boundary Element Method (BEM). Generally, the fir-tree connections require a computationally expensive finite element setup. Their complex geometry exceeds the limitations of the faster numerical techniques which are used with great success within the framework of the half-space approximation. Ways of extending the application range of the MDR and the BEM to the particular problem of highly undulating surfaces of the fir-tree connection are shown and discussed.
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