Multigrid solution of 2D and 3D stress fields in contact mechanics of anisotropic inhomogeneous materials

Abstract

Increasing demands on performance of machines lead to severer operating conditions of rolling bearings, i.e. higher loads, less lubricant, thinner lubricant films. Under these conditions, the effects of inhomogeneity and anisotropy on the fatigue life become more important. Accurate prediction of such effects requires detailed surface pressure and subsurface stress calculations. For practically relevant 3D cases with realistic grain sizes, this can only be done with very efficient numerical solution methods. In this paper, multigrid techniques are demonstrated to yield the required performance. The influence of inclusions, crystal orientation and roughness on the Von Mises stress distribution is investigated. The algorithm is suited for subsurface material analysis and optimization as well as for computational diagnostics using image analysis. (B. Zhang).Tribology International xxx (xxxx) xxx-xxx 0301-679X/

Multi-Scale Surface Texturing in Tribology—Current Knowledge and Future Perspectives

“…The first class are algorithms conceived to efficiently solve the details of the problem, including the small-scale behavior. Examples of these methods applied to solve tribological problems are the multi-grid [208][209][210][211][212][213] and adaptive mesh refinements [214][215][216][217][218] methods. In fact, these are linear scaling algorithms, which implies that their computational complexity scales linearly with the number of degrees of freedom necessary to represent the detailed micro-scale solution.…”

Further understanding of rolling contact fatigue in rolling element bearings - A review

“…Investigations by Zhang et al [136] demonstrate the combined impact of surface roughness and material anisotropy on bearing life. Surface roughness contributes to an elevated stress distribution in the subsurface which reaches its maximum at a shallower depth compared to smoother surfaces [137].…”

“…Surface roughness contributes to an elevated stress distribution in the subsurface which reaches its maximum at a shallower depth compared to smoother surfaces [137]. The surface would also consist of higher stress appearing as multiple isolated contact islands arising from asperity-asperity contact [136]. The presence of shallow inclusions and other material inhomogeneities have a more negative impact on fatigue life compared to that deeper in the microstructure [138].…”

Solid viscoelasticity in contact mechanics and elastohydrodynamic lubrication

“…For these classical applications in engineering, the understanding of the physical mechanisms governing the lubrication lm formation and the associated pressure generation has reached a very high level of predictability as a result of extensive theoretical/numerical and experimental research in the last 70 years. Nowadays even the e ect of material heterogeneity and anisotropy of bearing steels on the contact pressure, the contact stresses and the fatigue life in dry and EHL lubricated conditions can be modelled and calculated [153][154][155]. Apart from the above-mentioned elastic hard metals, soft materials such as polymers are increasingly used in modern industry due to a range of outstanding properties in terms of corrosion and chemical-resistance, low cost, less noise generation and light weight.…”

“…Numerically, the solution of an elastic half-space dry contact problem can be obtained by solving the 3D Navier-Cauchy equation such as in Ref. [153,154] or by solving the simpli ed 2D Boussinesq equation with e cient numerical methods such as the discrete convolution fast Fourier transform (DC-FFT) method [88] or the multilevel multi-integration (MLMI) method [141]. Analytical solutions and e cient numerical methods are available for idealized elastic contacts.…”