Growing interest in sustainable bio-lubricants as alternatives to conventional mineral oils has increased the demand for renewable feedstocks that do not compete with agricultural land use. In this study, waste cooking oil (WCO) was chemically modified through transesterification/partial hydrogenation (H-FAME), partial hydrogenation (H-WCO_l and H-WCO), estolide formation (E-WCO), and epoxidation (EOs) followed by ethanol ringopening (POs) to produce potential bio-lubricants. The thermal, physicochemical, and rheological properties of the resulting products were evaluated and compared with a commercial mineral lubricant (ISO VG 46), representative of oils used in industrial hydraulic systems. Tribological tests were performed as a preliminary comparative screening to determine friction and wear behaviour under selected pin-on-disc conditions. The WCO-derived products exhibited a broad range of properties depending on the applied chemical modification. Most samples showed thermal stability in air equal to or greater than ISO VG 46. Rheological analysis over 25-100 degrees C revealed Newtonian behaviour for H-FAME and POs, while E-WCO and EOs exhibited shearthinning behaviour, indicating fluid-like and grease-like structures, respectively. Kinematic viscosity at 40 degrees C ranged from 3.61 to 286 cSt, with polyols (POs) displaying viscosity indices between 111 and 133, exceeding that of ISO VG 46 (107). Friction coefficients were similar across all samples, although WCO, H-WCO_l, and H-WCO showed slightly lower values. Wear testing demonstrated comparable or reduced wear for E-WCO and almost fully epoxidized oil (EO_100) relative to ISO VG 46. These results highlight the potential of WCO-derived products as sustainable bio-lubricant candidates with tuneable properties, while further tribological testing under varied load, speed, and temperature conditions will be required to assess their application-specific performance.

Tilting pad journal bearings are critical components in high-speed turbomachinery. The use of sensors within the bearing is crucial to ensure operational safety and to validate computational models. The objective of this study is to improve the experimental investigation of the performance of a tilting pad journal bearing by enhancing the selection and placement of conventional and non-conventional sensors based on the results of a thermohydrodynamic model. The multi-sensor system measures film pressure and pad temperature at multiple locations, as well as pad tilt and film thickness. Redundant measurements are also performed to evaluate the performance of new induction coils capable of detecting magnetic flux variations due to vibrations. This work contributes to the discussion of bearing instrumentation by proposing a synergic sensor system comprising a suitable number of appropriately located conventional sensors together with non-conventional, non-invasive sensors. The experimental results obtained with the refined conventional sensor system agree with the predicted results, with differences that can be attributed to manufacturing and assembly tolerances of the bearing and simplified assumptions in the model. The results of the non-conventional sensor device, although promising, need further investigation.

Hertz's classical theory of contact requires the surfaces to be non-conformal. Despite of this, Hertzian formulas are often used also for conformal contacts as for instance for the evaluation of pivot stiffness in tilting pad journal bearings. In this paper, finite element simulations of conformal contacts between spherical elastic bodies are performed for different materials and geometry, in particular by varying the clearance. A first result is the introduction of a novel normalization which allows to calculate stiffness as a clearance-invariant function. Then, a novel model for stiffness is introduced. The model reduces back to Hertz's theory in the non-conformal limit. The model requires fitting of three empirical parameters which depend on the boundary conditions and on the material properties. Analytical expressions for the parameters are provided for a subset of contact problems with a simple geometry and given material properties. More general formulas for the parameters will be developed in a future work.

Journal bearings are typically lined with thin coatings that enhance tribological properties with respect to the underlying structural material. Traditionally, white metal coatings have been used, but they are currently being replaced to improve environmental sustainability, mechanical and thermal properties, wear resistance, and to reduce friction. This paper reviews recent progress in advanced materials for bearing coatings. After reviewing different materials and their deposition technologies, testing methods for evaluating materials performance are analysed. The results from comparative tests are presented. Furthermore, a unified comparison of tribological properties across different experiments is shown. Then, numerical modelling techniques are discussed. Based on the findings, conclusive recommendations for future bearing coating development are provided.

In this paper, an innovative method for the determination of the dynamic coefficients of tilting pad journal bearings (TPJBs) is described, and some of its characteristics are analyzed. The calculation is based on a parabolic modeling of the dependence of the dynamic coefficients on the excitation frequency, on the estimation of the forces acting on the bearing as a function of the estimated displacements using a linear model and, finally, on the search for the best estimate of the parabola coefficients by minimizing the sum of the squares of the normalized residuals of displacements and forces on the bearings. The normalization is performed by dividing the deviations (between the measured values and those calculated by the model) by an estimate of the standard deviation of the force and displacement measurements. The results for a flooded tilting pad journal bearing, TPJB, are presented and compared with those obtained using traditional methods. The synchronous coefficients are also calculated and compared with those determined by linear interpolation. A preliminary statistical analysis of the sensitivity of the results to the variation in the standard deviation of the forces and displacements is presented. An extension of the model is proposed so that the coefficients of the optimal parabolas can be estimated as a function of the shaft rotation frequency.

Wear of mechanical components is a problem due to the related material and energy consumption. Its reduction is important for sustainability particularly according with the Goal 12 “Responsible Consumption and Production”. In order to design components with lower wear experimental tests are usually performed. The most common configuration used is the pin-on-disc one where a spherical pin is put in contact with the plane surface of a disc. While in certain real contacts the contact pressure does not vary much, the wear of the surface specimens during running of a pin-on-disc test, commonly performed at constant normal load using a spherical pin, produces variations. The aim of this work is to investigate how significant and rapid the reduction of pressure throughout the test can be. An estimation of the pressure variation is made based on the results of two tests in different extreme conditions: wear occurring on the spherical pin only and wear on the flat surface of the disc only. The analysis shows that the pressure reduction in the first case is faster than the second one.

Rotational speed and defect monitoring are of crucial relevance for all the rotating machinery. Traditional sensors require to be mounted on or near the rotating bodies, exposing them to significant thermal and mechanical stress. In this work, a method has been developed to measure the angular velocity and to detect the presence of potential bearing defects from the analysis of the magnetic field generated by the residual magnetization of moving parts. To test such an approach, a dedicated experimental setup using a bare induction coil and a magnetoresistive device as separate sensing elements has been developed. This contactless technique provides reliable results and can achieve performance similar to or better than that of accelerometers, which are commonly used for this purpose. The presence of defects has been further assessed using white light interferometry. Finally, the results are discussed and compared with alternative techniques.

Geared automotive and aerospace transmissions are one of the most critical systems regarding wear. Limiting wear is of paramount importance to improve sustainability by reducing replacements that lead to increased waste and energy consumption for re-manufacturing. Simulation of gears including the wear effect can be very useful for the design of new more efficient and compact gears. Thermal effects may play a decisive role in the wear phenomena and should be included in the models used for simulations. In this study, some tests are conducted on a pin-on-disk apparatus under varying temperatures to assess its influence on steel-to-steel wear rate. A modified Archard law is used for wear estimation which includes the experimentally derived parameters accounting for thermal effects. This model is then coupled with a loaded tooth contact analysis (LTCA) tool to obtain accurate predictions of the contact pattern, as well as the instantaneous load shared by the mating teeth pairs during the meshing cycle. This coupled simulation framework is then employed to carry out simulations of wear evolution during the lifespan of a gear pair. A comparison between wear simulations using a constant wear coefficient and one incorporating temperature dependency is presented. The wear law as function of temperature is scaled to account for boundary lubrication condition. Results put in evidence a limited impact of the local temperature on wear with this preliminary approach. The differences however increase with the number of working cycles.

This study expands the research described in Part 1 with additional tests and an in-depth analysis of the results. The contact between bearing steel balls and the flat surface of bronze-coated disks is investigated with velocity set at 0.1 m/s, normal load of 10 N and sliding distances of 1 km and 500 m. Wear volume, constant and depth are deeply analyzed by using the experimental data and measurements and by comparing them with analytical estimations. Results confirm the influence of the initial surface condition and of the radius of the track found in Part 1. In particular, the presence of an oxide layer has a great impact on bronze-coated parts providing unpredictable run-in phases that are nearly eliminated when it is removed through surface grinding. The track radius employed for the experiments seems to have negligible impact on the wear constant.

Some tests have been performed with a pin-on-disk experimental apparatus to define the methodology to be used in a successive experimental campaign for investigating friction and wear performances of new materials, coatings, and surface textures. The pin-on-disk drive of a multi-function tribometer is used with a bearing steel ball pressed against the bronze coating of a disk. The test conditions have been selected based on a preliminary analysis of the most used standard for pin-on-disk tests. A velocity of 0.1 m/s, a normal load of 10 N and a sliding distance of 1 km has been chosen. Wear depth and friction coefficient are continuously monitored and recorded during tests. After tests wear volume estimation is performed with two different approaches: the gravimetric and the volumetric ones. Further information on wear evolution is provided by the 3D reconstruction of the worn track obtained in additional tests involving interruptions and restarts by using the optical interferometry system of the multi-function tribometer. The preliminary results evidence the influence of the initial surface condition and of the radius of the track. The presence of an oxide layer on the coating produces a delay in the start of significant wear and some friction fluctuations. As expected, reduced wear depth and a marginally grater wear volume is obtained with the larger track radius.

In this work, a statistical method to determine the dynamic coefficients of Tilting Pad Journal Bearings (TPJBs) is described. The method is based on a priori modelling of the dependency of the dynamic coefficients on the excitation frequency, on the estimation of the forces acting on bearing as a function of the estimated displacements (using a linear model) and, finally, on a search of the optimum functions by minimization of the squares of the normalized residuals of displacements and forces on bearings. Normalization is done by dividing the residuals by estimating the standard deviation of the forces and displacements. The results for a flooded Rocker Back TPJB are presented.

Computational software based on Reynolds equation is widely used in the design of tilting pad journal bearings, its accuracy generally satisfactory for ordinary operating conditions. Computational models can be particularly useful to quickly quantify the sensitivity of certain bearing parameters to manufacturing tolerances, errors in assembly, and uncertain operating conditions. In this paper, predictions obtained from a thermoelastohydrodynamic model are compared against experimental data procured from static load tests. The flooded configuration test bearing is a four-pad, load-on-pad, with centered pivots and 0.3 pad preload. The shaft angular speed reached 12 krpm (surface speed 64 m/s) with a maximum unit load of 2.0 MPa. The supply oil flow rate varied from 50

Tribology is related to all studies on friction, wear, and lubrication. One of the main aims of these studies is a reduction in friction and wear. Tribology is extremely vast, being also multidisciplinary and interdisciplinary. Therefore, it is very difficult to organize the several tribology subjects in an unique way and different classifications have been proposed by different authors. In this work, several subjects treated by tribology are reviewed and organized in six branches: Fundamental Tribology, Tribology of Materials and Lubricants, Micro and Nanotribology, Industrial Tribology, Biotribology, and New Frontiers of Tribology. The main subjects treated by the six branches are briefly reviewed in this paper in order to highlight the vastness of tribology and its important contribution to sustainability. Particularly, friction and wear reductions are strictly related to greater efficiency and material saving, which means less energy losses and material wastes, less pollution and therefore a more sustainable life according to the sustainable development goals. The connections among the latter and the several different tribological subjects are discussed.

Tribological aspects must be taken into account for a sustainable design of new components and materials developed to obtain weight reduction and greater efficiency. Reducing friction and wear produces energy and material savings, both connected with several Sustainable Development Goals. To limit the time consuming expensive experimental tests on new materials and components, simulations can be performed for which reliable values of the friction coefficient are necessary. In this work, some basic aspects of the lubrication regimes are firstly reviewed with the related friction coefficient trends represented with the Stribeck and Lambda curves, also evidencing the reasons of the similarity between the two curves. Formulas and diagrams are then reported for the friction coefficient of full lubricated conformal pairs. For thrust bearings the friction coefficient f can be expressed as a function of the parameter m and is related to the Kingsbury number K. For tilting pads f is proportional to K the power of 0.5. For plain journal bearings f is a function of the dimensionless eccentricity ε and is related to the the Sommerfeld number S to powers ranging roughly from 0.5 to 0.8 depending on the ratio between the axial length and the diameter for S smaller than 0.1, and tending to 1 for higher values of S. The reported formulas and diagrams can be used for design purpose.

The theoretical contact point of the pivot in rocker back (RB) tilting pad journal bearings (TPJB) is normally considered fixed in common software programs for the study of the bearing rotordynamic behavior. In a previous paper the authors proposed an equivalent pivot rotational stiffness to be implemented in commercial software to simulate the effect of the variation of the circumferential coordinate of the theoretical contact point due to the pad rolling motion in RB TPJB. This work is devoted to a preliminary comparison of the predicted performance and the experimental one for a 280 mm diameter RB TPJB in different operating conditions in order to validate the proposed approach. The inclusion of a pivot rotational stiffness among the data for simulation affects especially the cross-coupled dynamic coefficients. The latter, predicted as negligible without the new implementation, were closer, in order of magnitude, to the experimental results.

The rolling motion of the pads with rocker back (RB) and ball and socket pivots is normally neglected in common software programs for the study of the rotor dynamic behavior of tilting pad journal bearings (TPJB). In other words, the theoretical contact point of the pivot is considered fixed. The aim of this work is to provide a novel way to implement in commercial software the effect of the variation of the circumferential coordinate of the theoretical contact point due to the pad rolling motion in RB TPJB. This is done by introducing an equivalent pivot rotational stiffness evaluated with an analytically derived formula, validated through finite element analysis. Such a stiffness is a function of the pad load and the radii of the contact pair, increasing with the load, the radii, and the degree of conformity of the contact. The static and dynamic characteristics of a five pad RB TPJB are then evaluated with a commercial software with and without the rotational stiffness contribution for two different pivot geometries. Non-negligible differences were found, particularly regarding the cross-coupled dynamic coefficients that show the higher sensitivity to the rotational stiffness. The inclusion of a pivot rotational stiffness among the data of commercial software for simulation of RB TPJB could contribute to fill the gap between numerical and experimental results.

Minimizing NVH and friction-induced power losses is becoming paramount in the design of geared transmissions. The aim of this paper is to present an automatic methodology to explore Pareto-optimal designs of bevel gears when minimization of noise and frictional losses is essential. In the first part, a semi-empirical model to estimate frictional power losses under elasto-hydrodynamic lubrication is described. The model has been validated against experimental data available in the literature in previous works by the authors. The efficiency calculation is coupled with a state-of-the-art loaded tooth contact analysis (LTCA) tool to obtain accurate predictions of the instantaneous load shared by the mating tooth pairs during the meshing cycle. In the second part, an automatic framework based on multi-objective optimization (MOO) is presented where the tooth micro-geometry is systematically designed. The design variables are represented by few coefficients of a polynomial basis that embodies the tooth flank ease-off topography. To ensure manufacturability, the polynomial modifications are projected onto the feasible set of the machine-tool envelopes. This step is achieved through a state-of-the-art identification algorithm that the authors have developed in previous work. Frictional losses are estimated with the aforementioned model, whereas the NVH level is measured by the loaded transmission error (LTE), directly available from the simulation tool. The maximum contact pressures are limited by the material properties, thus proper nonlinear constraints are prescribed. Application to a test case involving the design of a spiral bevel gearset reveals that the methodology presented allows the designer to obtain Pareto-optimal solutions in a systematic and automatic manner.

AbstractMinimizing NVH and friction-induced power losses is becoming paramount in the design of geared transmissions. The aim of this paper is to present an automatic methodology to explore Pareto-optimal designs of bevel gears when minimization of noise and frictional losses is essential. In the first part, a semi-empirical model to estimate frictional power losses under elasto-hydrodynamic lubrication is described. The model has been validated against experimental data available in the literature in previous works by the authors. The efficiency calculation is coupled with a state-of-the-art loaded tooth contact analysis (LTCA) tool to obtain accurate predictions of the instantaneous load shared by the mating tooth pairs during the meshing cycle. In the second part, an automatic framework based on multi-objective optimization (MOO) is presented where the tooth micro-geometry is systematically designed. The design variables are represented by few coefficients of a polynomial basis that embodies the tooth flank ease-off topography. To ensure manufacturability, the polynomial modifications are projected onto the feasible set of the machine-tool envelopes. This step is achieved through a state-of-the-art identification algorithm that the authors have developed in previous work. Frictional losses are estimated with the aforementioned model, whereas the NVH level is measured by the loaded transmission error (LTE), directly available from the simulation tool. The maximum contact pressures are limited by the material properties, thus proper nonlinear constraints are prescribed. Application to a test case involving the design of a spiral bevel gearset reveals that the methodology presented allows the designer to obtain Pareto-optimal solutions in a systematic and automatic manner.

Hertzian formulas are commonly used for the evaluation of deformation and pressure distribution of non-conformal and slightly conformal mechanical pairs to estimate component stiffness and durability. For the sake of simplicity, their use is extended even to those cases in which Hertz’s hypotheses do not hold. This paper summarizes Hertz’s theory and compares the results obtained with theoretical and finite element analysis of the point contact of non-conformal and conformal pairs made of spheres, caps, and spherical seats. This study was motivated by the non-Hertzian behavior of a tilting pad bearing ball-and-socket pivot conforming contact observed by the authors in previous experiments. In particular, the displacement and force relation were investigated by varying the geometrical parameters, the materials, the boundary conditions, and the friction coefficient. In the case of non-conformal contact, the parameter variations had negligible effect in agreement with Hertz’s theory while for conformal contact, the cap and seat height and width and the relative clearance were the most influential parameters on the non-Hertzian behavior. These novel results indicate that in conformal pairs, such as for tilting pad bearing ball-and-socket pivots, whenever Hertz’s hypotheses are not satisfied and the assessment of contact stiffness is crucial, Hertzian formulas should not be applied as done in common practice, instead more accurate numerical or experimental evaluation should be made.

This paper proposes a model for the estimation of the coefficient of friction and the friction-induced power losses in lubricated hypoid gears. A specific hypoid gear set is designed to replicate the one used in an experimental investigation of the efficiency of hypoid gears, available from the literature. Despite the simplicity of our lubrication model, a good agreement with the experimental data is achieved. Additional results obtained through a commercial software that implements the ISO/TR 15144-1 standard are also shown for further comparison.