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Noise, vibration, and harshness (NVH) issues pose considerable challenges for electric vehicle powertrain engineers. Gear vibrations generate an intrusive gear whine noise, with significant impact on the sound quality of electric powertrains. Dynamic transmission error (DTE) is the most quantitative indicator for gear NVH. Backlash, time variable meshing stiffness and damping contribute to DTE. Hence, a better understanding of these excitation sources is essential. A gear tribodynamics model is developed using potential energy method to estimate time variable meshing stiffness (TVMS). A fully analytical time-efficient model is proposed for lubricated contact stiffness based on transitions in the regimes of lubrication. The model accounts for the combined effects of surface elasticity and lubricant stiffness. Film thickness and damping coefficients are transiently updated at each instant during meshing cycle. The predictions from this model are compared with measured results from the literature and predicted results from Hertz contact model. The lubricated contact model successfully shows the contribution of the lubricant stiffness to TVMS and its variations with elasticity and viscosity parameters during meshing cycle. Gear harmonic and super-harmonic resonances are accurately estimated in terms of amplitude, frequencies and stiffness softening nonlinearities. Time history responses and phase-displacement diagrams show good agreement with the gear dynamics response at the main harmonic and second super-harmonic frequencies. The proposed model has a reasonable accuracy, significantly better than those from Hertzian contact models, and is considerably time efficient in comparison to numerical EHL solvers.

This investigation comprehensively compared the elastic contact and the modified stiff impact models, aiming for the backlash-induced nonlinear vibro-impact gear rattle under lightly loaded conditions. Three meshing force models in backlash are incorporated into the elastic model independently. Unlike the previous uncoupled stiff impact model, the modified impact model employed in this paper considers the coupling between the pinion and gearwheel. Three scenarios were investigated with different components of two internal excitations, static transmission error-induced periodical backlash and the time-varying meshing stiffness. The numerical results show that the free and forced gear motion, nonlinear characteristics and rattle severity are significantly affected by static transmission error rather than time-varying meshing stiffness. Two studied hydrodynamic lubricant models show different damping effects throughout the free vibration response. The forced gear motion and rattle sensitivities show a noticeable difference below 40 rad/s 2 and turn to a slight variation above 60rad/s 2 . The high excitation level taking over the backlash determines the dynamic characteristics more deterministically than the internal excitations. Finally, the hydrodynamic lubricant model containing only the oil squeeze effect will likely match the experimental results obtained from the dedicated rattle test bench under several conditions. The experimentally detected components of the static transmission error on the gearwheel suggest that an acceptable model should be considered in the gear rattle model.

Purpose The purpose of this paper is to investigate the dynamic responses of a spur gear pair with unloaded static transmission error (STE) excitation numerically and experimentally and the influences of the system factors including mesh stiffness, error excitation and torque on the dynamic transmission error (DTE). Design/methodology/approach A simple lumped parameters dynamic model of a gear pair considering time-varying mesh stiffness, backlash and unloaded STE excitation is developed. The STE is calculated from the measured tooth profile deviation under the unloaded condition. A four-square gear test rig is designed to measure and analyze the DTE and vibration responses of the gear pair. The dynamic responses of the gear transmission are studied numerically and experimentally. Findings The predicted numerical DTE matches well with the experimental results. When the real unloaded STE excitation without any approximation is used, the dynamic response is dominated by the mesh frequency and its high order harmonic components, which may not be result caused by the assembling error. The sub-harmonic and super-harmonic resonant behaviors are excited because of the high order harmonic components of STE. It will not certainly prevent the separations of mesh teeth when the gear pair is under the condition of high speed and heavy load. Originality/value This study helps to improve the modeling method of the dynamic analysis of spur gear transmission and provide some reference for the understanding of the influence of mesh stiffness, STE excitation and system torque on the vibration behaviors.

Using the two-tooth difference swing-rod movable teeth transmission system satisfying the drive function of large optical instruments as the study object, the influence of each component error on system transmission error is analysed. Each component error is presented by the vector method, and then it is transformed into equivalent error in the direction of the meshing action line based on the equivalent meshing error principle. The instantaneous transmission ratio of the system is obtained by the instantaneous velocity center method, and the system transmission error model is established. Using numerical analysis, the influence of each component error on the system transmission error is obtained. The transmission error test platform is used to test and analyze the transmission error of the two-tooth difference swing-rod movable teeth transmission system. The research results show that the swing-rod length error and the wave generator eccentric error have a great influence on the transmission error of the system among the six types of error factors, so they should be strictly controlled during design, processing and assembly. This study provides a theoretical basis for the rational allocation of machining errors and assembling errors of the two-tooth difference swing-rod movable teeth transmission system.

Experimental measurement of transmission error and vibration of a gear pair with crown modification are developed. With the help of high-precision optical encoder, effects of gear misalignment on unloaded and lightly loaded dynamic transmission error, which are relative to gear rattle, are investigated. The gear mesh misalignment is introduced by eccentric sleeve assembled on the output shaft. Effects of modification and misalignment on the dynamic transmission error, are studied at different load and driving velocity conditions. The experimental results show that, with the increase of the crown amplitude, the peak-to-peak values of dynamic transmission error are decreasing dramatically. Impact deformation or elastic deformation is a very important part of the dynamic transmission error although they are unloaded or lightly loaded. The components in harmonics of meshing frequency will change distinctly comparing cases at low input shaft velocity without and with misalignment, but different phenomena are detected while increasing the input shaft velocity. Finally, the relation between transmission error and gear box vibration is illustrated, and spectrum kurtosis is introduced to reveal gear rattle.

Gear whine noise has become one of the primary challenges facing noise, vibration, and harshness engineers; this is because the electrification of the powertrain has largely eliminated engine masking noise while increasing the working speed of the E-powertrain. In this study, a hybrid metal-composite gear was proposed to reduce gear whine noise, and its performance was evaluated by means of dynamic transmission error (DTE). The test results showed that the hybrid metal-composite gear produced an effectively lower DTE than that of alternatives, particularly when approaching resonance speeds. In addition, a reduction in resonance DTE was verified by acquiring and comparing the frequency response functions of a steel gear and a hybrid metal-composite gear. As DTE is the primary excitation source contributing to whine noise, the hybrid metal-composite gear is expected to be a significant candidate for the reduction in powertrain whine noise.

In manufacturing face-hobbing hypoid gears, the coupling between tooth flank errors and installation errors has a significant impact on dynamic meshing behavior, yet quantitative models for their synergistic effects remain scarce. This study elucidates the combined effects of three-dimensional (3D) installation errors and real tooth flank deviations on transmission error. First, a geometric model of the real tooth flank, incorporating midpoint pitch deviation, is established based on theoretical flank equations and coordinate transformations. Then, a finite element model integrating 3D installation errors is developed. Finally, the combined effects of installation errors and real tooth flanks on meshing performance are analyzed. Results reveal a dual role of installation errors: when compensating for midpoint pitch deviation, the peak-to-peak transmission error (PPTE) decreases by 3.78%, while the contact pattern length and area increase. Under certain conditions, despite a 26.28% increase in PPTE, the contact pattern length grows by 2.29%, accompanied by a notable reduction in maximum contact stress on the tooth flanks.

Transmission error (TE) is an important parameter in gear dynamics that has a direct impact on the vibration and noise of gears. Under quasi-static conditions, gear elastic deformation and assembly errors amplify with increasing load, potentially contributing to noise and vibration. This paper presents a novel method for measuring the quasi-static transmission error (QSTE) of spur gears under quasi-static conditions. In particular, the study investigates the relationship between quasi-static transmission error, elastic deformation transmission error, and gear tangential acceleration. Gear elastic deformation transmission error was calculated from experimental data obtained with single-point, symmetrical dual-point, and orthogonal four-point configurations of tangential acceleration sensors. The orthogonal four-point sensor configuration greatly improves measurement accuracy when compared to theoretical values derived from material mechanics calculations. A dedicated on-machine acquisition system for spur gear tangential acceleration was constructed. Tangential acceleration tests were conducted across varying loads and rotational speeds. The acquired data underwent filtering and integration processing in order to obtain gear elastic deformation and quasi-static transmission error. The feasibility of the acceleration approach for measuring both gear elastic deformation and quasi-static transmission error is confirmed by a comparative analysis of the acceleration method results with transmission errors obtained via material mechanics calculations and magnetic grating detection.

This paper proposes a function-oriented form-grinding approach to obtain excellent and stable contact performance of cylindrical gears by designing modification forms based on a predesigned controllable fourth-order transmission error (TE) function and error sensitivity evaluation. First of all, a predesigned fourth-order TE polynomial function is assigned to the gear drive. Mathematical models of modified tooth surfaces that can describe their local deviation and ease-off topography are then obtained with the predesigned fourth-order TE function. The corresponding error sensitivity analysis is applied for investigation that reflects inherent relationships between contact attributes of modified tooth surfaces and misalignments. Moreover, the form-grinding wheel’s profile equation, the coordinate transformation matrix during form-grinding, and settings of computer numerical control (CNC) form-grinding programs for this active design method can be determined. This approach is ultimately conducted on three involute cylindrical gear pairs to demonstrate its feasibility and effectiveness.

Gear transmission errors are influenced by temperature especially in the aerospace field. A model is proposed to investigate the influence of temperature on cylindrical gear transmission errors based on the thermal network (TETN). The gear temperature field distribution model is established based on the thermal network method, and gear thermal deformation can be calculated along the gear meshing line. Regarding the gear single-flank rolling process, the variation of gear transmission errors under temperature is determined. In numerical calculations in MATLAB, the variation of gear transmission errors at 100°C compared to 20°C is –4.20 μm, which decreases almost linearly while the thermal expansion coefficient of the gear material increases. The simulation of the gear transmission errors variation of temperatures using the finite element method (FEM) were carried out in Workbench software under Ansys and the average difference of the TETN model results between calculations and FEM for different temperatures was 0.24 μm. Experiments were carried out on the gear tester in temperatures ranging from 0°C to 100°C, the TETN model results in calculations were compared with the results of the tester, and the average difference was –1.15 μm. The results show that the proposed TETN can be used as an algorithm to determine the variation of gear transmission errors under the influence of temperature.