A comparative study of the methods for calculation of surface elastic deformation

Abstract

A fundamental issue of lubrication analysis is the calculation of surface deformation, which includes two major steps: determination of influence coefficients and multiplication and summation. There are various interpolation schemes, such as the bilinear interpolation, the piecewise constant function or Green's function, available for determining the influence coefficients, while the summation operation may be performed by using one of the following methods: direct summation (DS), multilevel multi-integration (MLMI) or the discrete convolution and fast Fourier transform (DC-FFT) method. To limit the periodical errors, the proper way to implement the DC-FFT method is described in detail. The computation efficiency and numerical accuracy are compared by applying the different methods to typical contact problems. The results show that the three methods can achieve comparable numerical accuracy, but the DC-FFT method shows much higher computation efficiency than the others, especially when a great number of grid points are involved. It is concluded that the DC-FFT method has great potential in applications to the numerical analysis of, for example, surface deformations and temperature rises.

Complete boundary element formulation for normal and tangential contact problems

“…The basic idea is to interpret Eq. (8) as a two-dimensional convolution and doing the same in the .ourier space by means of element-wise multiplication [16] [ ] A comparison of both techniques can be found in [17]. In practice we have found the fast convolution to be by far more favorable.…”

A Quantitative Solution for the Full Shear-Thinning EHL Point Contact Problem Including Traction

“…Later the DC-FFT method [25,26] was incorporated to accelerate the time-consuming computation for elastic deformation. Recently, differential schemes and mesh density were investigated for further refinement of the model using finite difference method (FDM) especially in the thin film regime [27].…”

Micro Textures in Concentrated-Conformal-Contact Lubrication: Effect of Distribution Patterns

“…It has been proven to be effective and robust, capable of solving three-dimensional mixed EHL problems under severe operating conditions [18,24]. In order to accelerate the surface deformation calculation, which is a dominant part of the total solution process, a discrete convolution-fast Fourier transform (DC-FFT) method developed by Liu et al [25] was incorporated into the EHL model mentioned above, and the computation using the resultant model was proven to be fast [26].…”