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This work presents a high-fidelity lubricated transmission model, coupling Flexible MultiBody (FMB) dynamics with ElastoHydrodynamic Lubrication (EHL). The EHL model is discretised with a coupled finite element approach, in contrast with the more iteration-intensive finite difference approach using relaxation schemes. The finite element method yields nonlinear system matrices, requiring matrix reevaluation in each iteration. To mitigate computational overhead, tensorisation replaces integrals to compute the system matrices with tensor-vector multiplications. Furthermore, this work optimises the use of the discretised EHL model by scaling and reusing it across different contact conditions. Coupling of the contact force resulting from the EHL model with the rigid body displacement resulting from the FMB model enables the computation of steady-state equilibrium for a given torque applied to the gear pair. However, local deformations should be excluded from the FMB model to ensure proper coupling with the EHL model, which exclusively computes local deformation within the contact zone. Newly developed global line contact attachment modes allow the FMB model to exclusively calculate global tooth bending in response to a given contact force. • Elastohydrodynamic lubrication coupled with flexible multibody dynamics. • Finite element method to discretise all physical domains. • Global line contact attachment modes to exclude local deformation from gear pair. • Equivalent finite element model approximating local deformation from gear pair. • Scalable, tensorised finite element model discretising elastohydrodynamic lubrication. [ABSTRACT FROM AUTHOR]

In this paper, External Gear Machine (EGM) torque losses arising from friction at lubricating interfaces are modeled by considering mixed lubrication conditions. A novel contribution of this paper is to consider mixed elastohydrodynamic lubrication contact conditions along with the effect of gear flank surface roughness to determine the meshing losses, which are also the major contributors towards the EGM torque loss. These hydromechanical loss models are integrated in a multibody, multi-physics simulation tool Multics-HYGESim developed at the authors' research center. Experimental activity is performed on two EGM units using different surface finish for gears. Simulated hydromechanical efficiencies match the experimental trends with average deviation of 2.5%. Most importantly, the results capture effects of different gear flank roughness on the torque efficiency. An average increase of 0.9% in the efficiency value is predicted by the simulation model for the EGM with lower teeth roughness, as compared to 1.1% rise obtained via experiments. The proposed torque loss evaluation methodology shows high potential in assisting designers and manufacturers of EGMs to choose the suitable surface finishing for achieving desired hydromechanical performance. • Torque efficiency of external gear machines has been determined via simulation. • Mixed Elasto hydrodynamic lubrication model is used to evaluate meshing frictional loss. • Experimental tests show rise in torque efficiency for lower gear surface roughness. • Computational analysis of lubricating interfaces predicts leakage and friction loss. • Proposed model exhibits potential for virtual prototyping of new gear pump designs. [ABSTRACT FROM AUTHOR]

• A novel modification of spur gear flanks is proposed. • A generating process for the proposed flanks is presented. • The validation of minimizing transmission error is performed. • The effectiveness of enhancing lubrication ability is verified. • A machining process for the proposed flanks is presented. Spur gears are most extensively applied in gearing transmission because of their effortless machinability and high efficiency. However, spur gears still generate substantial noise, vibration, and wear, mainly when operating at high speeds. Therefore, this study introduces a novel modification of spur gear flanks to improve the above inherent weaknesses. Accordingly, its primary objectives encompass diminishing transmission error while augmenting lubrication efficiency. The novel modification adjusts one side of the spur gear flank like the concave side of the curvilinear gear and the other side like a convex surface using double crowning correction. In addition, both gears of the gear pair are modified to ensure the convex surface of one gear will mesh with the concave surface of the other. The modified gear pairs are then modeled and analyzed using KISSsoft software. The effectiveness of this proposed method is verified by significant improvements in the transmission and lubrication characteristics compared to longitudinal or double crowning modification. Furthermore, a complete machining process on a CNC honing machine is also utilized to demonstrate the machinability of the proposed gear flanks. [ABSTRACT FROM AUTHOR]

• Establish a REL-coupled ball bearing model considering EHL. • The concept of MQSH based on the model is proposed for the first time. • Propose an improved algorithm for solving nonlinear equations. • First study outer ring dynamic response considering bearing excitation and EHL. • Propose a novel coupling analysis method. The nonlinear characteristics of aero-engine spindle bearings remain unclear. To better reveal these characteristics, a ball bearing coupled with an elastic-ring squeeze film damper (ERSFD) and a squirrel cage was investigated in this work. With the elastohydrodynamic lubrication theory, a dynamic equation for a rigid-elastic-liquid-coupled ball bearing under high-speed and high-axial-load conditions was established. The Runge–Kutta method and the iterative Newton–Broyden method were applied to solve the coupling equation. The effects of the axial load and bearing speed on the bearing capacity and dynamic stiffness were analyzed. The dynamic characteristics of its bearing outer ring operating at different speeds and axial loads were studied through a numerical analysis. Finally, the theoretical model was tested and verified. The results indicated that the axial load and bearing speed significantly affect its bearing capacity and dynamic stiffness. Its vibration reduction performance of the bearing at a relatively low bearing speed and high axial load was relatively good when considering elastohydrodynamic lubrication. This work lays some references for optimal design of the spindle bearings of aero-engines. [ABSTRACT FROM AUTHOR]

• Interval processes are used to depict uncertain time-variant loads in gear drives. • A tribodynamic analysis method considering uncertain time-variant loads is given. • The proposed method is verified via both numerical and experimental tests. • Effects of uncertainty and rotating speed on tribodynamic responses are revealed. Gear drives are inherently subjected to time-variant loads, which always create an uncertainty and may degrade the vibration performance and system reliability. However, due to their complicated statistical properties, it is impractical to employ probability-based dynamic analysis methods. Additionally, most studies neglect the elastohydrodynamic lubrication behaviors between tooth surfaces under time-variant load conditions. A novel tribodynamic analysis method is proposed to evaluate system responses efficiently, in which the uncertain time-variant loads are described using interval processes. Firstly, a deterministic tribodynamic model coupling the system dynamics and elastohydrodynamic lubrication is established. To reduce the computational cost, the interval Karhunen-Loeve expansion is employed to simplify the interval processes using a small number of uncorrelated interval variables, while the Chebyshev subinterval decomposition is carried out to approximate actual responses using one-variable functions. The proposed method shares a comparable accuracy with the time-consuming Monte Carlo simulation and experiments. Parametric studies show that the uncertain time-variant loads significantly affect the uncertainty of vibration and induce a more hazardous lubricating condition. Additionally, the variation trend of uncertain tribodynamic responses is highly correlated with the rotating speed. [ABSTRACT FROM AUTHOR]

• A design method of tooth profiles based on control of relative curvature is proposed. • The mathematical model of the spur gear with constant relative curvature is built. • Evaluation of operating performance of the new gear drive is implemented. The flank shapes of gears greatly affect tooth durability, and the relative curvature and sliding of tooth profiles are the main influences. This paper advances a design method of tooth profiles based on control of relative curvature of engaged tooth profiles. The mathematical model of the spur gear with constant relative curvature is built through employing the proposed method. Equations of conjugate tooth profiles, the virtual rack cutter and undercut condition are formulated according to principle of plane engagement. Operating Performance of the new gear drive is evaluated by comparing with that of the involute gear drive. The results show that this new type of gear drive has the following advantages: With constant relative curvature of engaged tooth profiles, it enhances the contact strength of tooth surfaces and abates maldistribution of contact stress on tooth surfaces. It decreases the wear of tooth surfaces, especially the dedendum of the pinion due to the smaller sliding coefficient. It improves the lubrication of tooth surfaces owning to the higher minimum film thickness. [ABSTRACT FROM AUTHOR]

Highlights • A new approach is proposed to predict the temperature of spur gear transmissions. • It is suitable for transmissions with any gear geometry, material or lubrication. • The new approach can be applied under steady state and transient thermal conditions. • The performance of the approach is illustrated with several numerical examples. • The accuracy of the results is proved by comparing them to experimental results. Abstract This article describes a new numerical approach to determine the temperature field of polymer spur gears during their operation. The approach is based on an uncoupled procedure in which a mechanical problem is solved to determine the amount of heat that is generated by friction during the meshing of the gears, and then this heat is considered as a thermal load to perform a thermal analysis of a finite element model of the transmission. The amount of heat generated by friction is determined from the results of a numerical loaded tooth contact analysis of the transmission, which is based on the finite element method. The generality of the finite element method enables this approach to be applied to any kind of spur gear transmission, regardless of the geometry and the material of the gears and lubrication conditions. The resulting approach is applied to determine the temperature field of a spur gear transmission where polymer and metallic gears are combined, under several different operating conditions. The results obtained from this approach are compared to those obtained from experimental analyses, showing a good degree of similarity between them. [ABSTRACT FROM AUTHOR]

Highlights • An elastic dynamic model for a valve train is developed based on EHL and FE theory. • A numerical computation method for the coupled dynamics equations is proposed. • A combined contact model for a cam-tappet with oil film stiffness is established. • The predicted stress of the pushrod is verified by a rig experiment. • Oil film stiffness significantly influences the DTE of a valve train. Abstract An elastic dynamics model for a valve train including combined stiffness of oil film and dry contact between a cam and a tappet, is proposed. Multi-directional elastic deformations of the valve train are solved by discretizing slender components into Rayleigh beam and bar elements. The oil film stiffness is determined by non-Newtonian elastohydrodynamic lubrication in the line contact, whereas the dry contact stiffness is achieved by using finite element contact analysis. A numerical solution for the dynamic model is developed and verified by conducting a dynamic stress experiment. The influences of rotation speed on the oil film stiffness and contact force between the cam and the tappet are discussed, and the combined effects of rotation speed and oil film stiffness on a dynamic transmission error of the valve train are analyzed. Results show that the oil film stiffness decreases when the cam rotation speed increases within a certain range, whereas the sharp increased contact force may enlarge the oil film stiffness when the speed exceeds a critical value. The oil film stiffness variation slight influences the contact force, but such variation significantly affects the dynamic transmission error. [ABSTRACT FROM AUTHOR]

Highlights • Based on Kirchhoff assumption, the finite element method is employed to investigate the deformation of elastic ring. Dynamical characteristic of the ERSFD-rotor system is analyzed by fluid-structure interaction approach. • Sixteen oil film coefficients of the ERSFD are analyzed by Perturbation method. • Influences of the ERSFD parameters, number of elastic ring boss, ring thickness and oil film thickness respectively, on the dynamical characteristics of ERSFD-rotor are discussed. • Resonant responses of both the SFD-rotor system and the ERSFD-rotor system are simulated, which reveals that the jump phenomenon appearing in the SFD-rotor system is suppressed by ERSFD. • The study reveals that three effects of elastic ring make better dynamical performance of ERSFD than SFD and rigid ring squeeze film damper. Abstract In this paper, a calculation procedure is proposed to investigate the dynamic characteristics and response of an elastic ring squeeze film damper supported rotor system (ERSFD-rotor). First, the oil film pressure and force of ERSFD are analyzed by solving the Reynolds equations. Next, deformation of elastic ring is calculated by using the finite element method (FEM) based on Kirchhoff assumption. Then the dynamical equations of rotor system are numerically simulated with cooperation of the former two steps. Using the procedure, both the response of rotor and the oil film coefficients of the ERSFD can be determined simultaneously. Calculations show that the nonlinearity of oil coefficients of ERSFD are smaller than that of classic squeeze film damper (SFD). Thus, the ERSFD behaves better than the SFD in preventing bi-stable vibration of rotor by suppressing nonlinear effects of the oil film. Influences of the ERSFD parameters, namely the oil film thickness, ring thickness and number of elastic ring bosses, on the dynamical characteristics and response of the rotor are also discussed. The study reveals that the elastic ring enable better dynamical performance of the ERSFD than the SFD in three aspects. [ABSTRACT FROM AUTHOR]

In this proposal, the effect of the friction coefficient on the efficiency of spur gears with tip reliefs was analysed. For this purpose, the efficiency values using an average friction coefficient along the mesh cycle were compared with those obtained implementing an enhanced friction coefficient formulation, which is based on elastohydrodynamic lubrication fundamentals. In this manner, it can be established the differences between both formulations in the efficiency and friction coefficient values, as well as the advantages of using this enhanced friction coefficient with respect to formulations implemented in traditional approaches of efficiency calculation. In addition to studying the impact of the friction coefficient choice on efficiency, the profile modifications influence on the friction coefficient and efficiency was also assessed. In this regard, three tip relief case studies were set out; pinion tip reliefs, driven wheel tip reliefs and profile modifications in both gears. From the results, it was inferred that the choice of friction coefficient formulation clearly influences the efficiency in gear transmissions with tip reliefs, obtaining discrepancies between both formulations with regard to which tip relief case study provides the lowest efficiency values. [ABSTRACT FROM AUTHOR]

Gear tooth surface wear is a common failure mode. It occurs over relatively long periods of service nonetheless, it degrades operating efficiency and leads to other major failures such as excessive tooth removal and catastrophic breakage. To develop accurate wear detection and diagnosis approaches at the early phase of the wear, this paper examines the gear dynamic responses from both experimental and numerical studies with increasing extents of wear on tooth contact surfaces. An experimental test facility comprising of a back-to-back two-stage helical gearbox arrangement was used in a run-to-failure test, in which variable sinusoidal and step increment loads along with variable speeds were applied and gear wear was allowed to progress naturally. A comprehensive dynamic model was also developed to study the influence of surface wear on gear dynamic response, with the inclusion of time-varying stiffness and tooth friction based on elasto-hydrodynamic lubrication (EHL) principles. The model consists of an 18 degree of freedom (DOF) vibration system, which includes the effects of the supporting bearings, driving motor and loading system. It also couples the transverse and torsional motions resulting from time-varying friction forces, time varying mesh stiffness and the excitation of different wear severities. Vibration signatures due to tooth wear severity and frictional excitations were acquired for the parameter determination and the validation of the model with the experimental results. The experimental test and numerical model results show clearly correlated behaviour, over different gear sizes and geometries. The spectral peaks at the meshing frequency components along with their sidebands were used to examine the response patterns due to wear. The paper concludes that the mesh vibration amplitudes of the second and third harmonics as well as the sideband components increase considerably with the extent of wear and hence these can be used as effective features for fault detection and diagnosis. [ABSTRACT FROM AUTHOR]

In this paper, the effects of non-uniform loading on the performances and abrasion evolution of cylindrical roller bearings are explored and analyzed both theoretically and experimentally. The elasto-hydrodynamic lubrication phase of roller bearings is modeled and the lubricant film thickness is calculated. A comprehensive calculation method is subsequently proposed to analyze non-uniform contact loading distribution due to the combined radial and moment loads. Furthermore, increased metallic contact due to the breakdown of the lubricant film during the abrasive wear phase is investigated, and the contact deformation and stress distributions are analyzed accordingly. A test rig is designed and built to experimentally investigate these influences under different loading conditions. The experimental results demonstrate that the wear and deformations of the bearing raceway surfaces can be significantly promoted by the non-uniform loading due to the sliding motions between asperities of the bearing contact surfaces. Polishing wear of the bearing surfaces, such as surface induced cracks and material delamination, is expected when the bearing is further exposed to long-term non-uniform loading. Numerical simulation results are also obtained and analyzed to investigate the effects of material flexibility on the bearing responses, which show that the material flexibility can reduce bearing responses. [ABSTRACT FROM AUTHOR]

Elastohydrodynamic (EHD) lubrication happens in any situation when elastic deformation occurs due to high hydrodynamic pressure in lubricated contacts. It affects the dynamic behavior of the system and might imply in tribology problems. For many years, the emphasis has been focused on the prediction of EHD pressure and film thickness; mostly central to the contact area and minimum oil film. An approach for boundary layer representation of EHD lubricated contact studies as a function of EHD stiffness parameters is proposed here. The model avoids excessive computational costs and it is promising for applicability in dynamic problem with one or multiples EHD contacts with considerable accuracy. The proposed contact force simulation is applied to a cam-follower mechanism. Since the radius of curvature, the load and the entrainment velocity varies over the cam's rotation cycle, the lubrication study in these kinematics pairs has been limited. In this work, an EHD stiffness map is evaluated to characterize the EHD contact over several different rotation speeds. [ABSTRACT FROM AUTHOR]

The estimation of the losses due to friction of meshing tooth flanks is an important point in the design of gear drives. In addition to other design factors, the efficiency of a gear stage is an important criterion for selecting the type of gear and the number of gear stages in order to achieve a desired gear ratio. This manuscript deals with various approaches with which the friction losses that result from the meshing flanks of a face-gear stage can be estimated. In addition, the influence of the directions of sliding and rolling speed is investigated, which is particularly important for gear stages with axle offset, since the two velocities are not collinear. The calculation method is validated for low speeds by means of experiments on a transmission test bench. • Meshing efficiency prediction for face-gear drives. • Determination of the coefficient of friction using a physics-based model. • Coefficient of friction for non-collinear sliding and rolling velocities. • Experimental validation for a face-gear stage with axle offset at low speeds. [ABSTRACT FROM AUTHOR]

• A novel traction drive with large speed ratio and cam loading is proposed. • The performance evaluation model is developed under the new loading principle. • The model is established based on non-smooth surface under non-ideal contact. • Performances are investigated in terms of traction capability, and efficiency. • The spin loss is negligible, resulting in higher transmission efficiency. The development of high-speed motors has stimulated the demand for high-speed reducers. Aiming at the lack of high-speed reducer and the NVH problem of high-speed gear transmission, an asymmetric loading multi-roller planetary traction drive (AL-MPTD) scheme is proposed to fill the gap of traction drive with large speed ratio, zero spin and self-adaptively loading. By comprehensively considering the effects of axis tilt, elastic deformation, rough surface contact and elastohydrodynamic lubrication (EHL), this paper establishes a more refined theoretical analysis model and provides the analysis method under the condition of the non-smooth surface and non-ideal contact. This paper also studies the transmission performance of AL-MPTD from the aspects of traction ability, transmission efficiency and so on. The results obtained by theoretical calculations show that AL-MPTD can be considered to achieve zero-spin transmission in the entire operation range. In addition, the loading mechanism achieves a good self-adaptively loading effect, effectively reducing the sliding of the AL-MPTD and improving its efficiency, with the peak of the global sliding coefficient being only 0.402% and the maximum transmission efficiency of 98.5%. [ABSTRACT FROM AUTHOR]

Abstract: The Pericyclic Mechanical Transmission (PMT) system is a high reduction ratio, high tooth contact ratio, and nutating/rotating gear mechanism which incorporates meshing conjugate face-gear pairs. The PMT kinematics, gear tooth load capacity, bearing load capacity, and mesh efficiency are investigated in this paper. The gear train kinematics and the reduction ratio formulas are identified initially. The tooth load capacities of the meshing conjugate face-gear pairs are calculated analytically as a function of gear tooth loads and dimensions. The dynamics of the nutating gear and the overturning moments produced by nutation are formulated. The effect of gear mesh loads and overturning moment on the bearing load capacity is investigated based on the Hertzian contact stress of the most heavily loaded rolling element. PMT mesh efficiency is first estimated based on Elastohydrodynamic Lubrication (EHL) theory. Then, an analytical formula is developed to approximate the mesh efficiency without lengthy EHL computations. Finally, 760HP level helicopter transmission design spaces are investigated at different reduction ratios. The PMT system shows substantial gear weight improvement without sacrificing efficiency. [Copyright &y& Elsevier]

• A model couples piston skirt-liner system and floating pin assembly is developed. • Tribo-dynamic interaction mechanisms between the two friction pairs are revealed. • Effects of design parameters including piston pin clearance and offset are probed. • Friction torque on pin visibly affects piston tribo-dynamic behavior near the FTDC. • Piston is more sensitive to pin offset than pin assembly in tribo-dynamic behavior. Piston Skirt-Liner (PSL) system and Piston Pin Bearing (PPB), two key friction pairs in piston-assembly, interact with each other via impact and friction when transmitting the combustion load to crank train. Literature reporting such an interaction behavior in terms of tribology and dynamics is still rare, due to the complexity in a systematic modeling way. This paper proposed an efficient numerical model that fully couples these two friction pairs to investigate tribo-dynamic interactions between them. The model is built by coupling Reynolds-based mixed lubrication models for the friction pairs with Lagrange multibody motion equations for the piston-connecting rod-crank mechanism. Coupling effects between the piston skirt-liner system and the pin assembly are explored by comparing the cases contain the two friction pairs and one of them. Based on the above analyses, some design parameters including pin assembly clearance and pin offset, are further studied to disclose their influences on the tribo-dynamic performance of these two friction pairs. This work has a guiding significance for the systematic design of piston-assembly aiming to improve the dynamic property, economical efficiency and environmental-friendliness of engines. [ABSTRACT FROM AUTHOR]

• A complete multi-DOF dynamic model for defective cases is established. • The effects of outer raceway defect on bearing dynamic behaviors are revealed. • The traction in ball-raceway contact changes rapidly around defect exit event. • The defect greatly affects load characteristics and angular misalignments. • Reciprocating collisions between ball and pocket will result from surface defect. Angular contact ball bearing plays a significant role in guaranteeing the service performance of the mechanical equipment. However, the occurrence of localized defect dramatically affects the tribo-dynamic performance of the bearing, which can further result in serious accidents. Considering the influence of cage and oil lubrication, this paper proposes a complete multi-degree-of-freedom (DOF) dynamic model for defective angular contact ball bearing by analyzing the full multi-body interactions. The defect is modeled in the geometrical constraint relationships to replace the excitation functions proposed in previous studies. Based on the analysis of high-speed conditions, the effects of outer raceway defects with different sizes and position angles on the dynamic behaviors of the bearing are revealed. It is found that the defect significantly influences the load characteristics and the angular misalignments, and the traction in the ball-raceway contact shows an abrupt change around the defect exit event. The results also show that the reciprocating collisions between the ball and the cage pocket occur in the defective case which are affected by the defect scale and the bearing speed. [ABSTRACT FROM AUTHOR]

• The paper presents a methodology for modeling hydro-mechanical losses in external gear machines. • Friction at the gears' tooth tips, lateral surfaces, shafts and meshing interfaces is considered. • The gear meshing friction is found to be the major contributor to the torque losses. • The simulated hydro-mechanical efficiency trends match the experimental data. During the operation of external gear machines (EGMs), the friction between the internal components results in the loss of hydro-mechanical (or torque) performance of these units. However, current EGM simulation models either do not consider these losses or have significant limitations in their approach. This paper presents a novel methodology for modeling the hydro-mechanical losses in EGMs. The sources of torque losses considered are the friction at the gears' tooth tips, lateral surfaces, shafts, and meshing interfaces. The friction models are developed for each of these sources considering the effects of micromotion of the gears and bushings. Further, the effects of elastohydrodynamic lubrication (EHL) are considered in the modeling of meshing friction. The friction models are integrated in a lumped parameter simulation tool, and the operation of a commercial gear pump is simulated. From the simulation results, the meshing friction is determined to be the dominant source of torque losses. Further, the hydro-mechanical efficiencies predicted by the model are found to match those observed in the experiments indicating the validity of the model developed in this work. [ABSTRACT FROM AUTHOR]

• Spur gear bulk temperature modeling. • Non-Newtonian thermal mixed EHL modeling of gear contacts. • Coupling of bulk and flash temperature formulation to find max. temperature. • Demonstration of roughness and speed influences on scuffing torque. This study proposes a scuffing model for spur gear contacts. A heat transfer formulation is devised to evaluate gear bulk temperature, with frictional heat flux yielded from thermal mixed elastohydrodynamic lubrication (EHL) analysis. In return, the bulk temperature is fed back into the EHL modeling to determine tribological behavior within contact zone, including flash temperature. After bulk temperature stabilizes, the bulk and flash components are added to arrive the total surface temperature, whose maximum is compared to a scuffing limit for failure determination. Utilizing the model, a set of simulations is performed to demonstrate the influences of surface roughness and rotational speed on scuffing load. [ABSTRACT FROM AUTHOR]

• Ball CVT performance evaluation model is established based on EHL traction theory. • Performances were investigated in terms of traction capability, and effectiveness. • Most design and performance factors are expressed as dimensionless values. • Conformal ball CVT has better traction capability than Non-conformal CVT. In this study, we established a performance analysis model of two types of ball continuously variable transmissions (CVT), conformal type and non-conformal type, by modifying the rheological model based on the elastohydrodynamic contact behavior for the existing toroidal traction drive to suit the working mechanism of ball CVTs. The main purpose of this study is, based on our analysis model, to identify the tendency of performance change according to design factors of ball CVTs and to compare the performance between two ball CVTs. Performance was analyzed in terms of torque capability, torque density and efficiency; factors affecting performance were selected through analysis of individual shapes and operating conditions. In this process, all design and performance factors were expressed as dimensionless quantities. It was confirmed that the conformal ball CVT has superior traction capability compared to the non-conformal ball CVT. In addition, by solving an example problem for ball CVT design and describing the process of designing optimal ball CVTs, it was proved that this study is applicable to real on-site problems. [ABSTRACT FROM AUTHOR]

• Multi-objective optimization of weight and power loss in planetary gearbox. • Elastohydrodynamic lubrication and scuffing constraint included in the optimization • Significant reduction in weight and power loss was obtained. • Six different ISO grades of oils were compared and ISO VG 460 found to be best. • Without scuffing constraint, earlier failure of gear due to scuffing was observed. A novel multi-objective optimization of planetary gearbox is presented using a discrete version of Non-Dominated Sorting Genetic Algorithm (NSGA-II). Minimization of weight and total power loss of planetary gearbox are two objective functions. Number of teeth in the sun, planet and ring gears, module, face width, input shaft and planet pin diameter are design variables. Regular mechanical, bearing selection and scuffing are various design constraints considered. Investigations were done for three different gear profiles on an industrial planetary gearbox. The results were compared with an industrial gearbox provided in the AGMA standard, which showed not only significant reduction of weight and power loss, but were also found safer in scuffing. Pareto fronts of different ISO grade oils were compared for all gear profiles, and ISO VG 460 was found to be the best oil. Further analysis without a scuffing constraint showed moderate to high levels of scuffing risk for lower-grade ISO oils and lower level risk for higher-grade ISO oils. Ultimately, this study helps to reduce weight, enhance the efficiency and prevent early failures in planetary gearbox. [ABSTRACT FROM AUTHOR]

• Bridge dynamics and tribology for line contact. • Show high sensitivity of acceleration to pit excitation. • Show evident difference between tribo-dynamic and quasi-static simulation. This study proposes a dynamic model of a lubricated roller contact, focusing on the excitation of surface pit/defect. The fluctuation of contact force caused by periodic surface topography variation is used to determine the dynamic displacements and velocities of contact bodies. These responses, in turn, affect the thickness and flow of lubrication film, impacting contact pressure, and consequently contact force that is required in the dynamic analysis. It is shown, as the pit size grows, the acceleration increment escalates, therefore, can be used as an effective indicator for pitting failure occurrence. Additionally, a comparison of contact pressure between dynamic simulation and its quasi-static counterpart points to the importance of dynamic responses in tribological behavior description. [ABSTRACT FROM AUTHOR]

• Calculation of lubricant forces under non-stationary conditions. • Double-side tooth contacts were considered to calculate the lubricant forces. • Wedge and squeeze terms in lubricant hydrodynamic forces were analysed. • The lubricant role in gear transmissions subjected to low-torque levels was studied. Multi-stage-constant-mesh gearboxes contain two different kinds of gear pairs, called active and inactive stages. The latter are engaged but not transferring energy to the output shaft, whilst the former transmits power from the input to the output shaft. Due to the interaction between these stages, undesirable impacts are provoked, which could result in the failure of elements connected to the gearbox. This phenomenon is called gear rattle. The lubricant is the only element between teeth in contact, and therefore, its role is the key to understand the system behaviour and to palliate the potential consequences of this non-stationary phenomenon. In this regard, it was proven in previous gear rattle analysis performed by the authors that two lubricant effects must be considered to correctly model this phenomenon; the effect of the fluid entraining in the conjunction and the lubricant squeeze produced when profiles are approaching. In light of these factors, in this work, low-loaded gear transmissions dynamic behavior were analysed, making special emphasis on the fluid viscosity influence on the dynamic behavior and on hydrodynamic forces under non-stationary conditions. [ABSTRACT FROM AUTHOR]

In this paper a multi-objective optimization method of hypoid gears correlating to the operating characteristics is presented. Optimal design of hypoid gears demands that multiple objectives be simultaneously achieved. Four objectives considered in this study are the minimization of the maximum tooth contact pressure, transmission error and the average temperature in the gear mesh, and the maximization of the mechanical efficiency of the gear pair. The goals of the optimization are achieved by the optimal modification of meshing teeth surfaces. In practice, these modifications are introduced by applying the appropriate machine tool setting for the manufacture of the pinion and the gear, and/or by using a tool with an optimized profile. The proposed optimization procedure relies heavily on the loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors, and on the mixed elastohydrodynamic analysis of lubrication to determine temperature and efficiency. A fast elitist nondominated sorting genetic algorithm (NSGA-II) is applied to solve the model. The effectiveness of the method is demonstrated by using hypoid gear examples. The obtained results have shown that by the optimization considerable improvements in the operating characteristics of the gear pair are achieved. [ABSTRACT FROM AUTHOR]