It has been over a century since the interest in inventing the optimal topology for bearings arose. A significant achievement was published by Lord Rayleigh, who found the step-bearing geometry which maximise the load-carrying capacity when the classical Reynolds equation is used to model thin film flow of an iso-viscous and incompressible fluid. Since then, new optimisation methods considering some variants of governing equations for finding the best possible bearings have surfaced, one of which will be presented in this paper. Here, two different formulations for compressible flow, i.e. ideal gas and constant bulk modulus compressibility, as well as the classical Reynolds formulation will be used in combination with the method of moving asymptotes for topological optimisation. All three of these problem formulations provide us with unique geometries, which either maximise the load-carrying capacity or minimise friction, for fluids with a wide variety of compressibility.

The search for the optimal bearing geometry has been on for over a century. In a publication from 1918, Lord Rayleigh revealed the infinitely wide bearing geometry that maximises the load carrying capacity under incompressible flow, i.e. the Rayleigh step bearing. Four decades ago, Rohde, who continued on the same path, revealed the finitely wide bearing geometry that maximises the load carrying capacity, referred to as the Rayleigh-pocket bearing. Since then, the numerical results have been perfected with highly refined meshes, all converging to the same Rayleigh-pocket bearing. During recent years new methods for performing topology optimisations have been developed and one of those is the method of moving asymptotes, frequently used in the area of structural mechanics. In this work, the method of moving asymptotes is employed to find optimal bearing geometries under incompressible flow, for three different objectives. Among the results obtained are (i) show new bearing geometries that maximise the load carrying capacity, which performs better than the ones available, (ii) new bearing geometries minimising the coefficient of friction and (iii) new bearing geometries minimising the friction force for a given load carrying capacity are presented as well.

The bearing geometry has a big impact on the performance of a hydrodynamic thrust bearing. For this reason, shape optimisation of the bearing surface has been carried out for some time, with Lord Rayleigh’s early publication dated back to 1918. There are several recent results e.g. optimal bearing geometries that maximise the load carrying capacity for hydrodynamic thrust bearings. Currently, many engineers are making an effort to include sustainability in their work, which increases the need for bearings with lower friction and higher load carrying capacity. Improving these two qualities will result in lower energy consumption and increase the lifetime of applications, which are outcomes that will contribute to a sustainable future. For this reason, there is a need to find geometries that have performance characteristics of as low coefficient of friction torque as possible. In this work, the topological optimisation method of moving asymptotes is employed to optimise bearing geometries with the objective of minimising the coefficient of friction torque. The results are both optimised bearing geometries that minimise the coefficient of friction torque and bearing geometries that maximise the load carrying capacity. The bearing geometries are of comparable aspect ratios to the ones uses in recent publications. The present article also covers minimisation of friction torque on ring bearing geometries, also known as thrust washers. The results are thrust washers with periodical geometries, where the number of periodical segments has a high impact on the geometrical outcome.

In a cross-country skiing competition, the time difference between the winner and the skier coming in at second place is typically very small. Since the skier spends much of the energy on overcoming resistive forces, a relatively small reduction in these forces can have a significant impact on the results. The resistive forces come partly from the friction, at the tribological interface between the ski and the snow, and as with many tribological processes, the characterisation of its origin plays an important role in determining the frictional properties. Furthermore, in cross-country ski friction, there are several scales impacting the frictional performance, with the major contributors being the ski-camber profile and ski-base structure. Macro-scale measurements of the ski-camber profile under loading are often used to determine how adequate the ski is for use under specific conditions. The characteristic properties usually assessed are the force required to collapse the ski in order to obtain a certain camber height, the topography of the kick-wax zone, and the length (determined by simple means) of the frictional interfaces associated with the rear- and front glide zones, i.e., the apparent contact length. These measurements are, however, commonly performed by loading the ski against a much stiffer counter surface than snow and this affects the quantification of the characteristic properties. To date, some mathematical models have been proposed, but there is no reliable approach for determining the macro-scale properties of the contact between a cross-country ski and a counter surface using simulations. In the present paper, an Artificial Neural Network (ANN) has been trained to predict the ski-camber profile for various loads applied at different positions. A well-established deterministic approach has been employed to simulate the contact between the ANN-predicted ski-camber profile and a linearly elastic body with a flat upper surface, representing the snow. Our findings indicate that this method is feasible for the determination of relevant macro-scale contact characteristics of different skis with snow. Moreover, we show that the apparent contact area does not linearly depend on the load and that the material properties of the counter surface also exert a large impact when quantifying the apparent contact area and the average apparent contact pressure.

In cross-country skiing races, the difference between the fastest and the second fastest time can be minuscule. As in all endurance sports, cross-country skiing requires the use of energy to overcome resistive forces, in this case primarily aerodynamic drag and friction between the skis and snow. Even a slight reduction in either of these can determine the outcome of a race. The geometry of the ski exerts a profound influence on the friction between the skis and snow. As a result of the flexible modern cross-country skis, the camber profile and gliding properties to be influenced by the skiers’ position. Here, based on the location of the normal force corresponding to the plantar pressure, we characterize the ski camber while performing three variations of the downhill tucking position. We found that when gliding on a classic ski, the risk of contact between the kick wax and snow can be reduced by tucking in a leaning backwards position (i.e. by moving the skier’s center of mass backwards). With the tucking position, the percentage of the skier’s body weight that is distributed onto the friction interface at the rear of the skis varies between 63.5% in Gear 7 (leaning forward) on a skating ski and 93.0% in Gear 7 (leaning backwards) on a classic ski.

Predicting the contact mechanical response for various types of surfaces is and has long been a subject, where many researchers have made valuable contributions. This is because the surface topography has a tremendous impact on the tribological performance of many applications. The contact mechanics problem can be solved in many ways, with less accurate but fast asperity-based models on one end to highly accurate but not as fast rigorous numerical methods on the other. A mathematical model as fast as an asperity-based, yet as accurate as a rigorous numerical method is, of course, preferred. Artificial neural network (ANN)–based models are fast and can be trained to interpret how in- and output of processes are correlated. Herein, 1,536 surface topographies are generated with different properties, corresponding to three height probability density and two power spectrum functions, for which, the areal roughness parameters are calculated. A numerical contact mechanics approach was employed to obtain the response for each of the 1,536 surface topographies, and this was done using four different values of the hardness per surface and for a range of loads. From the results, 14 in situ areal roughness parameters and six contact mechanical parameters were calculated. The load, the hardness, and the areal roughness parameters for the original surfaces were assembled as input to a training set, and the in situ areal roughness parameters and the contact mechanical parameters were used as output. A suitable architecture for the ANN was developed and the training set was used to optimize its parameters. The prediction accuracy of the ANN was validated on a test set containing specimens not seen during training. The result is a quickly executing ANN, that given a surface topography represented by areal roughness parameters, can predict the contact mechanical response with reasonable accuracy. The most important contact mechanical parameters, that is, the real area of contact, the average interfacial separation, and the contact stiffness can in fact be predicted with high accuracy. As the model is only trained on six different combinations of height probability density and power spectrum functions, one can say that an output should only be trusted if the input surface can be represented with one of these.

Research in tribology are often connected to tribosystems operating in specific environments, where climate chambers are needed for tribotesting to resemble the environmental conditions in the real application. Although the effect of humidity on the tribological performance of many materials and lubricants is evident, many studies are conducted without sufficient systems to accurately monitor and control the humidity level throughout testing. In this paper, a humidity controlling system was developed to enable continuous monitoring and precise control of the humidity at trace moisture levels. The climate controller was validated in a tri-pin-on-disc tribometer with excellent performance and can be fitted to most climate chambers. To further improve the control of operating conditions during tribotesting, a thermodynamic simulation of the contact temperature was developed. The developed climate controller is a simple and cost-effective method to accurately monitor and control the humidity in a climate chamber at trace moisture levels. The portable design of the humidity controller enables use with most climate chambers and enclosed tribometers. To have better control over the temperature in the sliding interface during testing, a thermodynamic simulation method was used to estimate contact temperature between sliding bodies from near-contact temperature measurements and the measured friction forces.

At the highest level of endurance sports, the differences in finishing times are small, so equipment is constantly being constantly improved to enhance the athletes' performance. For instance, one dominant resistive force in connection with cross-country skiing is the friction between the skis and snow and since the 1930s, research designed to understand and reduce this friction has been ongoing. The mechanisms involved in ski-snow friction include compaction, micro-ploughing, adhesion, viscosity, and water-bridging. Of these, adhesive and viscous friction have been most studied, while much less is presently known about compaction, micro-ploughing, and water-bridging. At the macro-scale, the ski-camber profile plays a key role in determining whether, with respect to friction, a particular cross-country ski is suitable for use under a given set of conditions. Through its influence on where ski-snow contact occurs, this ski-camber profile has a profound impact on adhesive and viscous friction, micro-ploughing, the formation of water bridges, and the rate of compaction. Different contact zones with different apparent areas of contact and pressure have been found to be most suitable for different conditions. In addition, the micro-scale texture of the ski base is also an important determinant of ski-snow friction. Topographical measurements of this texture can be achieved with white-light interferometer and recent characterisation has focused on the mechanical properties of contact. In numerous tribological studies the interactions between features at different scales are modelled. In most tribological systems, features on several scales influence friction and ski-snow contact is certainly no exception. Accordingly, the current investigation was designed to evaluate the multi-scale properties of different combinations of two skis with two different base textures. The real area of contact and the average interfacial separation and total average reciprocal interfacial separation between the ski and snow were taken into consideration. We found that different macro- and micro-scale properties of the ski favour different mechanisms of friction. Both the profile of the ski camber and texture of the base play decisive roles in determining viscous friction. At the same time, the texture of the ski base exerts a greater impact on the average real contact pressure, real contact area and minimal average interfacial separation between the ski and snow than does the ski-camber profile.