PSI - Issue 57

Yuri Kadin et al. / Procedia Structural Integrity 57 (2024) 236–249 Kadin et. al / Structural Integrity Procedia 00 (2023) 000 – 000

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ii) The semi-analytical solution of the contact problem is based on the half space assumption, meaning that the features at the contact zone edge (chamfer, edge defect, etc.) have no influence on the pressure distribution. The pressure formed at the contact between an inner ring and a roller is governed by the crowned geometry of a ceramic roller and a steel ring (inner ring is considered here). The Green functions method is used here to predict the stress and deformation state due to a concentrated force acting on an elastic half-space (see Hamrock et. al (2004)). By integrating the Green functions over the 2D contact zone domain, the surface deformation (resulted by the contact pressure) is evaluated, which is fulfilled by the numerical solution of integral equation. Various numerical algorithms can be used for the solution of this equation; in the current work the conjugate gradient method (see e.g. Jin et. al (2013)) is used.

Pressure, [MPa]

Fig. 7: Comparison of the current semi-analytical method for the contact pressure evaluation with the slicing technique (implemented in SKF software). The continuous curves correspond to the current solution and the symbols to the solution by the slicing method; the contact pressure distribution without misalignment (a) and with misalignment of 0.4 minutes (b). The validity of the current semi-analytical approach was verified against the so-called slicing method (see Reusner (1977), De Mul (1986)), which is implemented in SKF software. The comparison is presented in Figs. 7, for a fully aligned (Fig. 7a) and a slightly misaligned (Fig. 7b) contacts. It is clearly indicated that both methods provide almost the same solutions, meaning that the currently implemented one, can be safely used for the contact pressure analysis. More detailed description of the current contact analysis can be found in Kadin et. al (2022). 4. Imperfection modelling The variety of crack morphologies observed in the optical inspection requires definition of an “idealized” crack geometry, representing “the most characteristic” morphology. The FE modelling is implemented with the commercial software ABAQUS, incorporating the programming environment Python, which is used for the evaluation of SIF distributions at the post-processing stage. As is typical for rolling contact, a crack is subjected to compression meaning that the frictional interaction between the crack faces is developed. In general, this friction plays beneficial role, inhibiting the shearing modes of crack propagation ( K II and K III ), however is plausibly causing the material alteration on the crack faces, which in steel components is known as white etching (see Kadin and Sherif (2017)). Consistently with the previous studies (see e.g. Zolotarevskiy et. al (2020), Nazir et. al (2018)) it is assumed that the crack faces friction can be modelled with the Coulomb law. In the current FE simulations the crack faces friction coefficient is fixed to 0.7, which was found to be adequate value for the RCF modelling in Si3N4 (Zolotarevskiy et. al (2020)). Note, that this parameter can hardly be measured, so the assumption is based on experience and some indirect experimental measurements (Pyrzanowski, (2006), Ivanytskyi et. al (2016)). Recall, that due to the friction, the J y -coordinate (along the roller length), [mm]