Accurate prediction of nonlinear dynamic characteristics in gear systems remains a challenging problem. The dynamic mesh force conventionally calculated using idealized contact assumptions, a critical factor in calculation of gear nonlinear dynamics, typically results in a mesh force distribution curve that gradually increases in the double-tooth-contact (DTC) zone, plateaus in the single-tooth-contact (STC) zone, and exhibits abrupt transitions between DTC and STC. However, the actual load sharing factor (LSF) is influenced by tooth profile error, leading to significant inaccuracies in traditional mesh force calculations. These inaccuracies particularly affect the prediction of high-frequency mesh excitation components, making precise characterization of gear system nonlinearities problematic. To address these limitations, this study proposes a multi-fidelity physics-informed LSF modification algorithm for gear pairs. The proposed methodology establishes a bridge between virtual simulations and physical reality through normalized root bending stress. An optimization algorithm is employed to minimize the discrepancy between measured and simulated signals, thereby obtaining the optimal LSF. The modified LSF is subsequently integrated into an enhanced gear dynamics model, enabling accurate characterization of high-frequency nonlinear mesh excitation components. Experimental validation was conducted through comparative analysis of root bending stress and vibration acceleration measurements. The results demonstrate that the proposed method significantly improves the prediction accuracy of nonlinear dynamic characteristics in the high-frequency domain.

The planet bearings are critical components of the planetary gear set, and work under revolution-rotation coupled (RRC) conditions. With the development of higher speeds and heavier loads of transmission devices, higher failure risks of planet bearings are more likely observed in contrast to the traditional non-revolution conditions, including roller-race contact failure and cage fracture. This paper presents the findings of an investigation into the strength of planet bearings based on a comprehensive model of PGS system. Results suggest that the higher risk of roller-race contact failure can be attributed to the larger roller-race contact stresses and sliding ratios. With regard to cage fracture, the primary causes are identified as excessive impact stress and cage instability under RRC conditions. This study illuminates the increased failure risks of planet bearings under RRC conditions, and offers insights that can inform the design and application of planet bearings.

Under high-speed and heavy-load conditions, the vibrations of the CRBs (Cylindrical Roller Bearings) in the MRPGSs (Multi-Row Planetary Gear Systems) intensify due to revolution-rotation coupled motion. Thus, it is helpful to investigate the vibration characteristics of CRBs in MRPGSs under high-speed and heavy-load conditions which can provide guidance for the low-vibration configurations of CRBs in MRPGSs. In this paper, the dynamic modeling method of the MRPGS is proposed based on the Simpack platform. The MRPGS model under different operating conditions is simulated and the relationships between the CRB vibrations, the operating speed, and the load torque are revealed. The speed row CRBs exhibit more severe vibrations compared to those in the coupling row. The dynamic behaviors of the coupling row CRBs are influenced by the combined effects of input speed and load torque, while the speed row CRBs vibration intensify progressively with the increasing speed.

Considering the correlated failure characteristics of multiple subsystems in an electromechanical integrated transmission system arising from load transfer,control loops,and functional coupling,this study introduces a Copula-based approach to model the internal dependency structure while preserving the marginal reliability models of individual subsystems.By mapping subsystem lifetime data into a unified probability space via cumulative distribution functions,the proposed method achieves decoupled modeling of marginal distributions and dependency structures.The process for creating failure time samples is described,and a Gaussian Copula is chosen to build the system-level joint failure model based on an examination of the dependency characteristics of several Copula families combined with engineering failure mechanisms.The dependency structure of the generated samples is validated using the Kendall τ rank correlation coefficient,and the results show good consistency with the predefined correlation matrix.Additional investigation finds high-risk areas of joint failure and reveals a significant coupling link between the drive motor controller and the motor drive subsystem.The results demonstrate that the Copula-based framework can effectively characterize system-level correlated failures,providing quantitative support for coordinated monitoring and maintenance decision-making.

The lubrication characteristics of the support bearings in the gearbox will greatly affect the operational performance of the gear transmission system. To discuss the lubrication characteristics of oil-jet lubricated cylindrical roller bearings under the wide speed range of power coupling mechanism, a fluid–structure coupling simulation model based on CFD method is established. The elastic fluid lubrication theory, two-phase flow VOF model of air-oil and slip mesh model are combined. The numerical simulation model of two-phase flow slip mesh hydrodynamics of the bearing under wide speed regulation range is established. The results show that with the increase of rotational speed, the local pressure in the contact area of the rolling element increases abruptly, which causes the lubrication environment of the bearing to decrease sharply. The local effect of pressure distribution in the bearing cavity slows down with the increase of ambient temperature. The overall lubricant content in the bearing cavity decreases significantly. This study may provide some guidance to improve the lubrication characteristics of cylindrical roller bearings in gearboxes.

This study proposes a modified quasi-static model (QSC) with the thermal deformation and elastohydrodynamic lubrication (EHL) effect for high-speed angular contact ball bearing. In doing so, the thermal deformation and central film thickness are incorporated into the QSC through thermal network method (TNM), and solved iteratively by using a quasi-Newton algorithm. The proposed method is validated. The comparison among the conventional quasi-static (QS), quasi-static model considering the hydrodynamic central film thickness (QSH) and QSC demonstrate that thermal deformation and EHL central film thickness significantly influence the contact angle, load distribution, and spin-rolling ratio at high rotational speed of bearing. Compared with the QS and QSH, more accurate predictions of contact load, centrifugal force, and ring displacement can be offered by the QSC, in which case it can provide a theoretical basis for the performance optimizing of high-speed bearing.

The paper built double internal mesh planetary gear set with FEM. With one operating condition applied, the strength of sun gear, planetary gear and ring gear with HRC profile is obtained. Transmission error (TE) and gear meshing loads are calculated from further simulation. Through gear meshing stiffness formula with TE, the gear meshing stiffness between sun gear and planetary gear, planetary gear and ring gear are calculated. This FE method for gear meshing stiffness takes account of most deformations (from bearing, gear teeth load sharing, misalignment and shaft bending etc.) during gear meshing process and all these extra deformations, which are neglected in traditional gear meshing stiffness’ formula, are transformed to TE and it is a new way to calculate gear meshing stiffness with HRC profile and proved to be easy, feasible and practical.

Roller bearing manufacturing errors have been proven to be critical factors affecting the vibrations of gear systems. Waviness is one main form of manufacturing error affecting the operational performance and life of bearings. However, most previous studies did not completely incorporate the effects of the uneven bearing waviness on the flexible gear system vibrations. To characterize the contribution of the uneven bearing waviness on the vibrations of the gear system, a gear transmission system dynamics model considering shaft flexibility was established. The evenness sinusoidal waviness model (SWM) and uneven sinusoidal waviness model considering the time-varying contact (SWMS) were compared. The influences of the time-varying gear meshing stiffness excitations and flexibilities of shafts on the vibrations of the gear system were considered. A dynamic model was established, and the vibrations of the flexible gear system with the SWM and SWMS were compared. The vibrations induced by different amplitudes and orders of bearing waviness were analyzed. Note that the waviness of the bearing has a great influence on the system vibrations. The vibrations of the flexible gear system intensified with the increase in the bearing waviness order and amplitude. The vibrations from the gear system with the SWMS were bigger than those of the SWM. This paper introduces an alternative dynamic modeling model enabling the vibration analysis of the flexible gear system with evenness and uneven bearing waviness.

This paper proposes a multi-source coordinated voltage regulation strategy based on model predictive control (MPC) to address the voltage stability issue of direct current vehicular microgrids (DC-VMG) under load disturbances. A system-level dynamic model is first established, incorporating the engine-generator set (EGS), energy storage system (Energy Storage Batteries(ESB) and Supercapacitor(SC)), and the drive motor, thereby revealing the coupling relationships among source, network, and load. On the control level, a Maximum Torque Per Ampere (MTPA) strategy is introduced to optimize the generator-side torque output, while a dual-model predictive control (D-MPC) algorithm is designed to achieve voltage regulation and frequency-domain decoupling of the energy storage system(ESS). In this scheme, the ESB handles low-frequency power demands, whereas the SC responds to high-frequency fluctuations. Simulation results show that, compared with the conventional dual-PI (D-PI) method, the proposed control strategy significantly improves DC bus voltage stability, dynamic response speed, and energy scheduling efficiency, thereby enhancing the overall robustness and energy utilization of the system. This research provides a theoretical foundation and control approach for the stable operation of DC-VMG under dynamic operating conditions.

To enhance the stability of the electrical system in electric vehicles, this paper adopts a small-signal analysis method based on impedance modeling to analyze and model the DC microgrid system consisting of power electronics-based sources, networks, loads, and energy storage devices in electric vehicles. Utilizing the Middlebrook impedance-ratio stability criterion, combined with system simplification, linearization of nonlinear systems, and transformation of three-phase AC systems, small-signal output impedance models of the DC bus and input impedance models of the inverter and motor are established. Furthermore, a simulation model of the DC propulsion system is developed to investigate the impacts of the support capacitor, equivalent resistance, and equivalent inductance of the DC bus on system stability. Simulation results demonstrate that the impedance matching between the source and load sides effectively reveals the stability patterns and underlying mechanisms under various operating conditions and parameter variations, providing theoretical guidance and a solid foundation for optimizing the DC bus system parameters.

A new entropy named refined composite multi-scale reverse bubble entropy (RCMRBE) is proposed in this paper for bearing performance degradation (BPD) assessment. Firstly, Teager energy operator (TEO) was employed for enhancement of the fault information in vibration signals. Secondly, RCMRBE values were extracted from enhanced vibration signals concerning different bearing status, and the RCMRBE values at the first or second scale were selected as the bearing performance degradation indicators (PDIs) based on the correlations with time. Finally, a group of the life-cycle bearing tests were employed for verification. The results show that the proposed approach could clearly demonstrate the degradation process of bearing performance with time, which illustrates the effectiveness of the proposed method.

This paper focuses on the overall finite element modeling of an electromechanical transmission (EMT) coupling mechanism, which mainly establishes FE model of coupling mechanism between two planetary gear sets including sun gear, planet gear, ring gear and carrier, Ring gear and carrier are coupled with the other of the opposite gearset. The needle and cylindrical bearings are modeled in detail for each planetary gear set. With accurate assembling of planetary gear sets, elements such as sun gear, ring gear, planet gear and carrier are modeled with gearing mesh and other bearing contacts. The load of high-speed and heavy-duty operating conditions is applied to the integrated model. The structure strength for the sun gear, planet gear, ring gear and carrier was obtained with stiffness matrix bearing model before. This time the bearings in the planetary gear sets are modeled with detailed contact model including needle rollers, cylindrical rollers and their races. With different loading conditions applied, the contact analysis of two kinds of bearings in the coupling planetary gear sets are made. Through this comparative analysis of maximum contact stresses of bearing rollers, the needle roller bearing performs better than that of cylindrical one. Therefore it provides a better selection for the design of coupling transmission system.

The P2 configuration plug-in hybrid electric vehicle (P2-PHEV) equipped with a multi-speed transmission has a high potential for recovering more regenerative energy, as the shifting strategy can be employed to adjust the working zone of the electric motor (EM). However, the existing shifting strategy designed for normal driving conditions cannot achieve optimal regenerative energy recovery. In this study, a shifting strategy used in the regenerative braking process is proposed. First, to make the EM provide more regenerative force during braking, a braking force distribution algorithm is devised while simultaneously considering braking stability and safety. Second, to realize maximum regenerative braking energy recovery, an optimal shifting strategy is designed for regenerative braking. Third, the classical braking process is analyzed and six thresholds are abstracted and optimized to establish a rule for restraining frequent gearshifts raised in the proposed optimal shifting strategy. Finally, the proposed strategy is verified under three standard cycles, results show that the proposed shifting strategy can recover considerable regenerative energy without frequent gearshifts.

The electromechanical transmission system has emerged as the dominant type of transmission in the heavy vehicle field. In this research, a finite element model is established for the gear box of the electromechanical transmission system. It can be revealed the inherent characteristics of the electromechanical transmission system by analyzing the 10 modal frequencies and vibration modes under three different constraints, which can provide robust support for its integrated and high-speed development.

The motors are critical components of the electromechanical transmission in vehicles, and its operating status directly affects the maneuverability of vehicles. To quickly and accurately identify the operating status of motors, this paper proposes a new entropy - Composite Multi-scale Weighted Reverse Slope Entropy (CMWRSlE) for motor fault diagnosis, which is a more interpretable entropy due to its deep exploration of signals. Firstly, the composite multi-scale weighted reverse slope entropy values are extracted from the vibration signals of the motor in different states; Secondly, the extracted features are dimensionally reduced by the manifold learning algorithm – Neighbourhood Preserving Embedding (NPE) and classified by the hierarchical prototype-based approach (HPA) to achieve the fault diagnosis of the motor. Finally, the method proposed in this paper is validated through two sets of experimental data: motor rotor faults and motor bearing faults. The results show that the accuracy of the proposed method in motor fault diagnosis reaches 100 %, which indicates the effectiveness of the proposed method.

The meshing efficiency is a very important parameter for the gear system, which can greatly affect the system transmission performance. However, the unreasonable design parameters can reduce the meshing efficiency, especially for the meshing efficiency caused the gear elastic deformation. To overcome this problem, a meshing efficiency calculation method of a spur gear system with the gear elastic deformation is presented in this paper. The effects of the tooth number, transmission ratio, addendum coefficient, pressure angle, friction coefficient, center distance, tooth elastic deformation on the meshing efficiency are discussed. It seems that the meshing efficiency of the gear system can be affected by the operational conditions and gear geometric parameters. This works can provide some guidance for the improvement method of the power loss of the oil stirring of the spur gear systems.

The shift quality of an automatic transmission directly affects the human-perceived comfort and the durability of the automatic transmission. In general, the inconsistency caused by manufacturing errors, life-cycle changes, or other changes in hydraulic characteristics are the main reason affecting the shift quality, which should be compensated by adaptive control in the shifting process. In this paper, we first provide an in-depth analysis of the relationship between proportional solenoid current, clutch pressure, speed and torque in the shifting process control. Then we propose two efficient adaptive control strategies for the torque phase and inertia phase, respectively. Both algorithms are tested and verified on a riot utility vehicle. The experimental results indicate that the adaptive control strategies proposed in this paper can effectively compensate the engine flare and the clutch tie-up of the torque phase, and keep the inertia phase within a proper time range.

The power loss is a very important parameter for the planetary gear train. It can significantly influence the transmission performance of the planetary gear train. Thus, the power loss analysis can be helpful for improving the transmission performance of the planetary gear train. To overcome this problem, this paper presents a numerical analysis method to analyze the churning power loss of a planetary gear train. A computational fluid dynamics (CFD) model for a planetary gear train with four planet gears are proposed. The transient oil distribution and pressure distribution in the flow field of the planetary gear train are discussed. It seems that this works can provide some guidance for the improvement method of the churning power loss of the planetary gear train.

Planetary gear systems are widely used in wind power, ships, aircraft, and construction machinery, etc. In the planetary gear system, when the eccentricity error exists in the planetary gear, the vibrations of the whole system should be affected. However, the influence of the eccentricity error was rarely considered in the previous dynamic models. To solve this problem, a planetary gear system with six planetary gears is established. The influence of the eccentricity error on the vibrations of the planetary gear system is analyzed. Different eccentricity error cases in the planetary gears are considered in the model, as well as the bearings with the radial clearance. The model with the eccentricity error is compared with the normal model. The statistics of dynamic responses of the ring gear and its variations are analyzed. Not that the vibrations of the planetary gear transmission system increase with the eccentricity error of planetary gear. This study can provide a new method for simulating and detecting the eccentricity errors in the planetary gear systems.