Philippe Sainsot

Contribution of Gear Body to Tooth Deflections—A New Bidimensional Analytical Formula

The magnitude and variation of tooth pair compliance affects tooth loading and gear dynamics significantly. This paper presents an improved fillet/foundation compliance analysis based on the theory of Muskhelishvili applied to circular elastic rings. Assuming linear and constant stress variations at root circle, the above theory makes it possible to derive an analytical formula for gear body-induced tooth deflections which can be directly integrated into gear computer codes. The corresponding results are in very good agreement with those from finite element models and the formula is proved to be superior to Webers widely used equation, especially for large gears.

Meeting the Contact-Mechanics Challenge

This paper summarizes the submissions to a recently announced contact-mechanics modeling challenge. The task was to solve a typical, albeit mathematically fully defined problem on the adhesion between nominally flat surfaces. The surface topography of the rough, rigid substrate, the elastic properties of the indenter, as well as the short-range adhesion between indenter and substrate, were specified so that diverse quantities of interest, e.g., the distribution of interfacial stresses at a given load or the mean gap as a function of load, could be computed and compared to a reference solution. Many different solution strategies were pursued, ranging from traditional asperity-based models via Persson theory and brute-force computational approaches, to real-laboratory experiments and all-atom molecular dynamics simulations of a model, in which the original assignment was scaled down to the atomistic scale. While each submission contained satisfying answers for at least a subset of the posed questions, efficiency, versatility, and accuracy differed between methods, the more precise methods being, in general, computationally more complex. The aim of this paper is to provide both theorists and experimentalists with benchmarks to decide which method is the most appropriate for a particular application and to gauge the errors associated with each one.

Analytical Investigations on the Mesh Stiffness Function of Solid Spur and Helical Gears

Approximate formulae are presented which give the time-varying mesh stiffness function for ideal solid spur and helical gears. The corresponding results compare very well with those obtained by using two-dimensional (2D) finite element (FE) models and specific benchmark software codes thus validating the proposed analytical approach. More deviations are reported on average mesh stiffness which, to a large extent, are due to the modeling of gear body deflections.

Paper III (x) Deformation of a Particular Metallic Contaminant and Role on Surface Damage in High Speed Ball Bearings

An experimental study of particulate metallic contaminant deformation and of the effect on surface indentation in high speed ball bearing is presented. Particles are initially spherical and are composed of M50 high carbon steel powder. A high speed rig with a controled level of oil contamination was built. Information concerning initial and final particle dimensions and indent shape on the bearing raceway was given by microscopic investigation. An optical measurement system is also used to describe the indent topography. Investigation shows that a hard spherical metallic particle is uniformly flattened as it passes through the EHD contact.

Analytical Investigations on the Mesh Stiffness Function of Solid Narrow Faced Spur and Helical Gears

Approximate formulae are presented which give the time-varying mesh stiffness function for ideal solid narrow-faced spur and helical gears. The corresponding results compare very well with those obtained by using 2D finite element models and specific benchmark software codes thus validating the proposed analytical approach. More deviations are reported on average mesh stiffness which, to a large extent, are due to the modelling of gear body deflections.Copyright

A comparative study of multiaxial high-cycle fatigue criteria applied to rough rolling contacts

Rolling contacts are a major topic in scientific studies as they are highly exposed to fatigue damage. Indeed, the applied loads generate periodic stresses and the surface roughness generates stress concentrations close to the surface. The combination of these two phenomena facilitates fatigue damage. Many multi-axial criteria have been created to explain and predict this type of damage. Furthermore, a large number of papers compare the different fatigue criteria based on combined bending and torsion tests [1,2]. However, these studies are not representative of the stress gradients found in rough contacts, close to the surface. Hence the current work, which proposes a comparative study of several fatigue criteria with a combined experimental and numerical approach.Copyright

Three-Dimensional Voronoi and Multigrid Model for Microstructure Contact Problem

The prediction of both the tribological behaviour and mechanical analysis of the wear resistance are still of great research interest in order to improve the lifetime of material surfaces. This concerns both bulk and coated materials although coating processes have been often developed in order to protect substrates from tribological solicitations. The wear resistance of coated materials has been the subject of many studies which show that it is possible to protect and improve significantly the durability of substrates. A straightforward discretisation of the multi-scale problem of graded coatings on substrates exceed the memory and CPU capacity of current (and next generation) computers. The authors have proposed an efficient numerical model that can handle this multi-scale problem: using billion points and locally refined grids.Copyright

A 3D Multigrid Solver for the Elastic Contact Problem: Application to Graded Materials

The actual contact between solid surfaces is generally rough and time dependent. The stresses induced by the rough contact can only be correctly described using a detailed 3D model. Even finer details are required in the case of surface coatings. Consequently, the rough coated contact problem is strongly multi-scale: the characteristic dimensions of the contact, the coating and the roughness range from the millimeter to the nanometer. A straightforward discretisation of this multi-scale problem would exceed the memory and CPU capacity of current (and next generation) computers. This paper proposes an efficient numerical model that can handle this multi-scale problem: using 109 points and locally refined grids. The proposed model is based on multigrid techniques within a finite difference frame work. Localised refinement is implemented to optimize memory requirement and computing time. Validation of the solver is performed through a comparison with analytical results for simple cases. The algorithm performance is analyzed through a parametric study describing the influence of layer thickness (0.01 < t/a < 10) and mechanical properties (0.005 < Ec /Es < 10) of the coating on the contact parameters (Ph , a). A linear graded coating, used as a solution to avoid interfacial problems, is then compared to a coating with constant properties. A quantitative analysis of the evolution of the maximum tensile stress with depth is conducted in both cases.Copyright