In academia, research on gear units is increasingly focused on electrification, higher rotational speeds, lightweight architectures and stricter efficiency and acoustic constraints. Advanced multiphysics modelling now incorporates contact mechanics, structural flexibility, lubrication, thermal behaviour and electromechanical coupling. Significant advances have been made in the fields of dynamics, vibroacoustic, Rolling Contact Fatigue modelling and coupled power losses and thermal analyses. Furthermore, numerical tools facilitate analyses at the system-level as opposed to the component level. Within the industrial sector, transmissions are required to demonstrate an increase in power density, durability and efficiency with reduced noise, a requirement that is particularly pertinent in the context of electric transmissions. At the same time, manufacturing trends include enhanced precision, surface superfinishing, dry machining and full digitalisation with digital twins. Health monitoring is evolving towards hybrid strategies. Sustainability considerations now influence materials, lubrication strategies, eco-design, repairability and life cycle optimisation. In the field of education, transmission engineering remains fundamental. It is evolving towards systemic, multiphysical and digital approaches. Study programmes are increasingly incorporating tribology, Noise, Vibration & Harshness, thermal modelling, durability prediction, optimisation and data-based monitoring, alongside close links between research laboratories and industry. Digital skills, simulation tools and interdisciplinary training are becoming essential. Overall, far from being a mature or declining field, gear transmission engineering is undergoing a profound transformation. Its future is driven by high-speed electrified systems, integrated modelling, predictive maintenance, sustainable design and enhanced collaboration between research, industry and education.

Gears are an essential component of numerous mechanical systems across a wide range of engineering applications. However, they may be associated to high levels of radiated noise which can limit their use. Accurately predicting this noise is of paramount importance for the design, optimization and health monitoring of gear transmissions. System identification is therefore needed to reach a sufficiently high level of accuracy. However, this usually comes at the cost of high computational burden. Using traditional modeling assumptions, it is widely accepted that the radiated noise stems from the dynamic response of the gears which is itself induced by the static transmission error (STE) and time-varying mesh stiffness. These physical quantities are governed by the local contact conditions between the gear teeth. An accurate computation of these physical quantities is therefore crucial. However, this is a difficult problem as gear contact resolution is intrinsically nonlinear and multiscale. Even considering simplifying assumptions, the computation of this physical quantities entails a significant computational effort when coupled to optimization procedures. In this work, we introduce an efficient neural network-based surrogate model for predicting static gear contact conditions in near real time in order to facilitate the identification and optimization of mechanical systems equipped with geared systems.

This paper proposes an original method to determine the gear tooth root stresses from a 3D finite element (FE) flexible multibody approach and a full-FE contact-based formulation. The contact problem is dealt with an augmented Lagrangian formulation whereas the analysis is performed by a preconditioned gradient solver (PCG). Tooth flank modifications are directly introduced within the 3D model. This one is thus able to take into account straightforwardly tooth bending and Hertzian-like deformations as well as the micro-geometry effect. Simulations are performed for several mesh periods, without making any assumptions about load distribution, tooth and gear blank flexibilities, and possible premature or delayed contacts between tooth pairs in quasi-static conditions. A precise distribution of tooth root stresses associated with instantaneous contacts conditions is then computed. For this study, a single stage spur gear with micro-geometry modifications corresponding to an arc-shaped profile crowning is modeled. Several output torques are considered. The obtained results are compared to those obtained using a 2D FE ISO-based model, where external forces are applied along the theoretical line of action.

The goal of this study is to perform a multi-objective optimization of a gear unit in order to improve its performance in terms of mechanical power losses, gear dynamics and equivalent sound power radiated by the housing. All these key performance indicators are closely related to the gear macro- and micro-geometry parameters. Decision variables chosen are the helix and pressure angles as macro-geometry parameters, and the amount and dimensionless roll length of tip relief as micro-geometry parameters corresponding to gear profile modifications. The multi-objective optimization is carried out under geometric and load capacity constraints using the evolutionary NSGA-II algorithm. Various results, observed in the form of 3D Pareto front confirm that improvements in energy efficiency and vibroacoustic performance are antagonistic. Nevertheless, a significant decrease of mechanical power losses is possible without degrading the vibroacoustic performance much. Otherwise, the correlation between the gear dynamic response and the equivalent radiated sound power (ERP) is partial. The minimization of the equivalent sound power radiated by the housing is not equivalent to the minimization of the gear transmission error fluctuation. These results underline the interest of modelling the whole gear unit to optimize its efficiency and NVH behaviour.

In geared system, the main source of excitation is generated by the mesh process itself. Depending on the dynamic conditions involved, the system may present a variety of problems, ranging from acoustic nuisance to system failure. Predicting and controlling the mesh process at an early design stage is a key point to avoid such issues. The problem is complex, mainly due to its multi-scale nature. Indeed, the vibroacoustic behavior of geared systems (on the scale of a meter) depend on the local micro-geometry of the teeth (of the scale of a micron), associated with the transmission error. Moreover, the problem is parametric in nature, due to the periodic fluctuation of the mesh stiffness. These parametric internal excitations generate dynamic mesh forces which are transmitted to the housing through wheel bodies, shafts and bearings. In the case of planetary gear sets, the numerical prediction presents a complementary challenge as, in many application, the carrier rotation modulates the housing vibration response, at its rotational frequency. This paper present an original simulation process to deal with modulation effects in planetary gear systems.

The present work investigates the influence of uncertain tooth profile modifications on the nonlinear dynamic response of a spur gear pair induced by a backlash nonlinearity. To this end, an original approach based on bifurcation tracking is developed. The equations of motion are solved in the frequency domain with the harmonic balance method (HBM) coupled to an arc-length continuation algorithm and a bordering technique. The evolution of the bifurcation points with respect to the uncertain parameter is computed in a deterministic way. The study focuses on minimizing the amplitude-jump instabilities induced by the backlash nonlinearity around the primary resonance peak. The proposed methodology allows for a fast and reliable estimation of the tooth profile modification that minimizes the amplitude-jump instability by defining two criteria using the results of the bifurcation tracking algorithm. Probability density functions (PDF) of various indicators of the severity of vibro-impacts can be computed with Monte-Carlo (MC) simulation with minimal computational burden. Results show that the tooth profile modification that minimizes the amplitude-jump instabilities differs from the optimum obtained with static computations.

This work is concerned with the analysis of vibro-impact responses observed in large-scale nonlinear geared systems. Emphasis is laid on the interactions between the high-frequency internal excitation generated by the meshing process, i.e. the static transmission error and time-varying mesh stiffness, and low-frequency external excitations. To this end, a three-dimensional finite element model of a pump equipped with a reverse spur gear pair (gear ratio 1:1 ) is built. The model takes into account the flexibility of the kinematic chain, the bearings and the housing and the gear backlash nonlinearity. A reduced-order model is solved with the Harmonic Balance Method coupled to an arc-length continuation algorithm which allows one to compute the periodic solutions of the system. The onset and disappearance of vibro-impact responses is studied through the computation of grazing bifurcations. Results show that the coupling between the external excitation and the time-varying mesh stiffness term greatly modifies the characteristics of the responses in terms of number and periodicity of impacts and contact loss duration.

This study aims to implement multi-objective optimization of a gear unit in order to minimize the power loss and the vibrational excitation generated by the meshing, via a multi-scale approach that extends from gear contact to the complete transmission. All these indicators are closely linked to the macro and micro-geometry definition of the gear pair. The optimization is carried out using a genetic algorithm, namely the Non-Dominated Sorting Genetic Algorithm II (NSGA-II). The design variables chosen for the problem are the pressure angle and the helix angle, as macro-geometry characteristics of the gear, and/or the length and the amount of tooth profile modifications, as micro-geometry characteristics of the gear. Constraints are imposed in order to not exceed a maximum bending stress at the tooth root of the gear and to not fall below a minimum total contact ratio. From the results obtained, it is found that the multi-objective optimization with both micro and macro-geometry parameters simultaneously gives different results than those obtained with macro-geometry first and then micro-geometry parameters. In order to study the importance, or not, to take into account the complete gear unit, a comparison is made between the local power loss generated by gear tooth friction and the total power loss in the single stage gear unit in terms of design variables values.

Weight reduction is a recurring concern in the design of modern mechanical systems. This search may lead engineers to resort to using gears with holes in order to meet their requirements. This paper presents a methodology to carry out nonlinear dynamic analyses of a gear transmission with holes in the gear blanks subjected to a multiharmonic internal excitation. This work investigates the influence of these holes on the vibration levels, occurrence of contact loss and possible bifurcations. The numerical model features two flexible shafts coupled by a spur gear pair with holes. The gear model consists in two lumped masses and inertias and includes the gear backlash as well as the internal excitation sources that are the time-varying stiffness and the static transmission error (STE). The resulting mechanical system is solved in the frequency domain by the Harmonic Balance Method (HBM) coupled with an arc-length continuation algorithm and its stability is evaluated with Hill's method. Results show that adding holes not only impacts the STE but also the mesh stiffness. The interactions of these two quantities has a substantial influence on the bifurcation structure along the main solution branch and leads to a decrease of the span of vibro-impact regions. As the applied static torque is increased, it is found that using holed gear blanks can effectively prevent contact loss and lead to a linear response.

This paper provides an insight into the efficiency and accuracy of a multibody approach to model gear transmission error. The multibody model is based on an augmented Lagrangian contact formulation considering a surface-to-surface contact detection. The case of spur and helical gears transmitting power between parallel shafts is considered. The static transmission error is computed without any assumptions about the contact lines positions and orientations. Tooth and wheel body flexibility and tooth profile deviations are taken into account. The main objective of this study is to evaluate the efficiency and possibilities of the proposed methodology. To this end, the static transmission error is benchmarked against the results obtained from a classical approach which is based on the computation of the equation describing the static equilibrium of the gear pair for a set of successive positions of the driving wheel.

The prediction of noise and vibrations generated by geared systems remains a challenging field of study. The analysis of such systems is computationally demanding mainly due to the large size of the finite element model used to describe the system and the nonlinear behaviour arising from the contact between the gear teeth. As a consequence, very few models have been proposed to handle lightweight gears which are widespread in current industrial designs. Lightweight gears lead to a strong modification of the gear compliance, and therefore the contact force distribution. The static transmission error and the mesh stiffness fluctuations are thus influenced by these changes. In this paper, a 2D decomposition method is proposed to compute the static transmission error of gears with holes in the gear blanks without heavy computational effort. The original methodology relies on the substructuring of the holed gear blank from the gear teeth. It is applied on several spur gear systems with holed gear blanks and compared with a fully flexible multibody method. The validity of the approach is assessed in terms of static transmission error and mesh stiffness fluctuations. Moreover a parametric study is carried out using the 2D decomposition method in order to analyse the influence of holes regarding their position and number.

We herein propose an algorithm for tracking smooth bifurcations of nonlinear systems with interdependent parameters. The approach is based on a complex formulation of the well-known harmonic balance method (HBM). Hill’s method is used to assess the stability of the computed forced response curves, and a minimally extended system is built to allow for the parametric continuation of the detected bifurcation points. The feasibility of coupling HBM-based minimally extended systems and arc-length continuation algorithms is established and demonstrated. The method offers an efficient way of determining the stability regions of the system. The methodology is applied on a spur gear pair model including the backlash nonlinearity and subjected to transmission error and mesh stiffness fluctuation whose harmonic contents depend on several parameters that do not appear explicitly in the equations of motion.

This paper presents an experimental study of gear rattle noise induced by vibroimpacts between gear teeth. A specific experimental set-up is designed to analyse the nonlinear dynamic behaviour of a spur gear submitted to input velocity fluctuation. The drag torque, the mean drive gear rotational speed, the velocity fluctuation amplitude and frequency are controlled during experiment. The dynamic transmission error is measured thanks to high resolution optical encoders. The originality of the experimental set-up consists in using a high-speed camera in order to visualize the contact zone and to identify the occurrence of successive impacts between gear teeth. The rattle threshold is identified as a function of velocity fluctuation amplitude and frequency for various operating drag torques and mean rotational speeds. Experiments show very good agreement with the theoretical master curve. Once impacts occur, stationary nonlinear gear dynamic response and rattle noise radiated by the mechanical system are investigated. Most of the time, an almost periodic response is observed with 2 impacts per period. One impact between the active flanks alternates with one impact between the reverse flanks. A contact phase between gear teeth is observed after each impact instead of an instantaneous rebound. The number of successive tooth pairs crossing the meshing zone without any contact between gear teeth varies according to the ratio of the excitation frequency to the rotation frequency. Analytical and numerical works performed using a gear rattle model show good agreement with experiments. Finally, sound pressure emitted from the gear pair is measured. The acoustic power imputable to gear rattle is found to be proportional to the total kinetic energy transferred per second to the system by the successive impacts.