Jože Flašker

Numerical procedure for predicting the rolling contact fatigue crack initiation

Abstract A computational numerical model for contact fatigue damage analysis of mechanical elements is presented in this paper. The computational approach is based on continuum mechanics, where a homogenous and elastic material model is assumed in the framework of the finite element method analysis. Cyclic contact loading conditions are simulated with moving Hertzian contact pressure. The time-depending loading cycles are defined for each observed material point on and under the contact area. Furthermore, the influence of friction upon rolling–sliding contact loading cycles is analysed in detail, using Coulomb’s friction law. The model for prediction of the number of loading cycles, required for initial fatigue damages to appear, is based on Coffin–Manson relations between deformations and loading cycles, and includes characteristic material fatigue parameters. As a general example, the model is used to analyse a fundamental contact problem of a cylinder and flat surface, which is usually a substitutional model for analysing real mechanical problems. However, the results concerning the identification of critical material points and the number of loading cycles, required for initial fatigue damages to appear at those points, are the main purpose of the presented study.

Surface Fatigue of Gear Teeth Flanks

Mechanical behaviour of various machine elements, such as gears, brakes, clutches, rolling bearings, wheels, rails, and screw and riveted joints, are influenced by interaction between contact elements and surfaces. Surfaces in rolling and/or sliding contact are exposed to material contact fatigue. Contact fatigue can be defined as a kind of damage caused by changes in the material microstructure which results in crack initiation followed by crack propagation, under the influence of time-dependent rolling and/or sliding contact loads. The contact fatigue process can in general be divided into two main parts: initiation of micro-cracks due to local accumulation of dislocations, high stressesat local points, plastic deformation around inhomogeneous inclusions or other imperfections in or under the contact surface; crack propagation, which causes permanent damage to a mechanical element.

Numerical calculation of bending fatigue life of thin-rim spur gears

Abstract Mechanical elements subjected to cyclic loading have to be designed against fatigue. The aim of this paper is to examine the bending fatigue life of thin-rim spur gears of truck gearboxes. The gear service life is divided into the initiation phase of the damage accumulation and the crack growth, respectively. The analysis of thin-rim gear fatigue life has been performed using the finite element method and the boundary element method. The continuum mechanics based approach is used for the prediction of the fatigue process initiation phase, where the basic fatigue parameters of the materials are taken into account. The remaining life of gear with an initial crack is evaluated using the linear-elastic fracture mechanics.

Numerical simulation of surface pitting due to contact loading

A two-dimensional computational model for simulation of surface pitting of mechanical elements subjected to contact loading conditions is presented. In the model it is assumed the initial crack of length 0.015 mm is initiated at the contacting surfaces due to previously thermal or mechanical treatment of the material. The discretised model with the initial crack is then subjected to normal contact pressure, which takes into account the EHD-lubrication conditions, and tangential loading due to friction between contacting surfaces. The model accounts also for the influence of fluid trapped in the crack on crack propagation. The virtual crack extension (VCE) method in the framework of finite element analysis is then used for two-dimensional simulation of fatigue crack propagation under contact loading from the initial crack up to the formation of the surface pit. The pit shapes and relationships between the stress intensity factor and crack length are determined for various combinations of contacting surface curvatures and loadings. The comparison of computational and available experimental results shows that the proposed model reliably simulates the surface fatigue crack growth under contact loading and can be used for computational predictions of surface pitting for various contacting mechanical elements.

Simulation of surface pitting due to contact loading

A computational model for simulation of surface pitting of mechanical elements subjected to rolling and sliding contact conditions is presented. The two-dimensional computational model is restricted to modelling of high-precision mechanical components with fine surface finishing and good lubrication, where the cracks leading to pitting are initiated in the area of largest contact stresses at certain depth under the contacting surface. Hertz contact conditions with addition of friction forces are assumed and the position and magnitude of the maximum equivalent stress is determined by the finite element method. When the maximum equivalent stress exceeds the local material strength, it is assumed that the initial crack develops along the slip line in a single-crystal grain. The Virtual Crack Extension method in the framework of finite element analysis is then used for two-dimensional simulation of the fatigue crack propagation under contact loading from the initial crack up to the formation of the surface pit. The pit shapes and relationships between the stress intensity factor and crack length are determined for various combinations of contacting surface curvatures and loadings. The model is applied to simulation of surface pitting of two meshing gear teeth. Numerically predicted pit shapes in the face of gear teeth show a good agreement with the experimental observations.

Experimental results of the fatigue crack growth in a gear tooth root

A spur gear pair from the first stage of an industrial vehicle gear box has been subjected to experimental testing. The effects of different load distributions along the gear tooth width on the fatigue crack growth in the gear tooth root are measured on an appropriate testing device. The recorded experimental results are represented using the methods of statistical analysis. Analysing the results proves that different load distributions along the tooth width have a significant influence on the crack growth and thus on the service-life of the gear. Since the experiments provide a three-dimensional experimental analysis of fatigue crack propagation in the tooth root, the results of such analysis can be used for calibrating the numerical simulation of similar problems.

Expert system for designing and manufacturing of a gear box

Abstract This paper presents the expert system STATEXS for dimensioning optimization and manufacture of gears and gearing. To determine the optimum dimensions of gearing, we used genetic algorithms which are well suited for such problems, particularly because of their robustness and ability to detect global extremes. After completion of calculations and optimization of gears or gear pairs, one of the most difficult operations follows, i.e. the manufacture of the product with theoretically determined and optimized properties. To this end, at our Faculty we have also started to develop an expert system for the field of manufacture of various products of demanding shapes.

Stress intensity factor for cracked gear tooth

Abstract The weight function method based on the crack opening displacement is used to derive the stress intensity and shape factor for a cracked gear tooth. An isolated force is applied at points of engagement with the mating gear. The analysis applies to narrow gears such that the two-dimensional stress state prevails. Analytical and experimental results are compared for an edge crack located at the root of the gear.

The influence of different parameters on surface pitting of contacting mechanical elements

The paper describes a general computational model for simulation of surface pitting of mechanical elements subjected to contact loading conditions. In the model it is assumed that the initial crack of length 0.015 mm is initiated at the contacting surfaces due to previously running in process or thermal and/or mechanical treatment of the material. The discretised model with the initial crack is then subjected to normal contact pressure, which takes into account the elastohydrodynamic lubrication conditions, and tangential loading due to friction between contacting surfaces. The model accounts also for the influence of fluid trapped in the crack and residual stresses due to heat treatment of the material on crack propagation. The virtual crack extension method in the framework of finite element analysis is then used for two-dimensional simulation of fatigue crack propagation from the initial crack up to the formation of the surface pit. The pit shapes and relationships between the stress intensity factor and crack length are determined for various combinations of contacting surface curvatures and loadings. The comparison of computational and available experimental results shows that the proposed model reliably simulates the surface fatigue crack growth under contact loading and can be used for computational predictions of surface pitting for various contacting mechanical elements.

Review of mathematical and experimental models for determination of service life of gears

Abstract For designing machines and devices the dimensioning with respect to service life is increasingly taken into account. This applies also for gearing which are still today one of very important components of almost all machines. We have developed a stochastic model for determination of service life of gears. In our model we propose a new parameter by which we describe the fracture mechanics conditions in the tooth root where the defects, causing destruction, occur statistically most frequently as shown. We named that factor the tooth stress intensity factor Z. The value of the factor Z is related to dislocation, propagation of the plastic zone, deformation and orientation of grain in case of short cracks and stress intensity factor K in case of long cracks. For determination of the service life for the area of short cracks we used Bilby, Cottrell and Swinden model which is based on the theory of continuously distributed dislocations and we complemented it with random generation of structure of material before cracks. For the long crack we have developed a stochastic model for determination of service life of gears. For confirm mathematical models we developed different non-standard test pieces and on this pieces we used combination of mixed experimental methods. The aim of these combinations was to obtain as complete information about the individual influences as possible and to determine the interaction between different fracture mechanic magnitudes. In this way we confirmed the mathematical models as a whole and also determined some physical interpretations in models. With this we were able to ensure that the presented model is not purely a mathematical model.