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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper focuses on the numerical analysis of the vibroacoustic behavior of an electric window-lift gear motor for automotive vehicle which consists of a DC motor and a worm gear. A dynamic modeling of the gear motor is proposed. The excitation sources correspond to radial electromagnetic forces applied to steel stator, electromagnetic input torque fluctuation, rotor mechanical imbalance, worm gear static transmission error and mesh stiffness fluctuations and gear wheel eccentricity. Parametric equations of motion are solved using an iterative spectral method. It allows the computing of the vibroacoustic response of the system, taking account of the interaction between the mesh stiffness fluctuation and the other excitations. The simulation results are validated from comparison with experimental vibroacoustic measurements performed with a specific test bench. Spectrograms of the dynamic response show components corresponding to the harmonics of the excitation spectra, as well as lateral components arising around the mesh frequency and the input torque fluctuation frequency. This spectral enrichment is generated by the interaction between the mesh stiffness fluctuation and the other excitations. The lateral components contribute little to the overall level of the vibroacoustic response, but they may have a significant impact on the quality of noise radiated directly by the gear motor or indirectly by its supporting structure. Finally, the weights of the different excitation sources to the spatial-average mean-square velocity of the radiating surface and the equivalent global dynamic force transmitted to the supporting structure are compared. [ABSTRACT FROM AUTHOR]

The aim of this work is to present the great performance of the numerical algorithm of Particle Swarm Optimization applied to find the best teeth modifications for multimesh helical gears, which are crucial for the static transmission error (STE). Indeed, STE fluctuation is the main source of vibrations and noise radiated by the geared transmission system. The microgeometrical parameters studied for each toothed wheel are the crowning, tip reliefs and start diameters for these reliefs.Minimization of added up STE amplitudes on the idler gear of a three-gear cascade is then performed using the Particle Swarm Optimization. Finally, robustness of the solutions towards manufacturing errors and applied torque is analyzed by the Particle Swarmalgorithm to access to the deterioration capacity of the tested solution. [ABSTRACT FROM AUTHOR]