Search Results (105)

This paper presents an electromechanical coupling model integrating an equivalent magnetic network (EMN) model of a dual three-phase permanent magnet synchronous motor (DTP-PMSM) with the dynamic model of a helical planetary gear transmission system. Using this model, this study analyzes the dynamic characteristics of an electric drive system, specifically motor phase current, electromagnetic torque, and gear meshing force, under self-fault-tolerant control strategies. Simulation and experimental results demonstrate that the self-fault-tolerant control strategy enables rapid fault tolerance during open-phase faults, significantly reducing system fault recovery time. Meanwhile, compared to the open-phase faults conditions, the self-fault-tolerant control effectively suppresses most harmonic components within the system; only the second harmonic amplitude of the electromagnetic torque exhibited an increase. This harmonic disturbance propagates to the gear system through electromechanical coupling, synchronously amplifying the second harmonic amplitude in the gear system’s vibration response. This study demonstrates that self-fault-tolerant control strategies significantly enhance the dynamic response performance of the electric drive system under open-phase faults conditions. Furthermore, this study also investigates the electromechanical coupling mechanism through which harmonics generated by this strategy affect the gear system’s dynamic response, providing theoretical support for co-optimization electromechanical coupling design and fault-tolerant control in high-reliability electric drive transmission systems. Full article

To address the unclear coupling mechanism between thermal elastohydrodynamic lubrication (TEHL) and dynamic behaviors in planetary gear systems, a novel tribo-dynamic model for dual-star planetary gears considering TEHL effects is proposed. In this model, a TEHL surrogate model is first established to determine the oil film thickness and sliding friction force along the tooth meshing line. Subsequently, the dynamic model of the dual-star planetary gear transmission system is developed through coordinate transformations of the dual-star gear train. Finally, by integrating lubrication effects into both time-varying mesh stiffness and time-varying backlash, a tribo-dynamic model for the dual-star planetary gear transmission system is established. The study reveals that the lubricant film thickness is positively correlated with relative sliding velocity but negatively correlated with unit line load. Under high-speed conditions, a thickened oil film induces premature meshing contact, leading to meshing impacts. In contrast, under high-torque conditions, tooth deformation dominates meshing force fluctuations while lubrication influence diminishes. By establishing a test bench for the planetary gear transmission system, the obtained simulation conclusions are verified. This research provides theoretical and experimental support for the design of high-reliability planetary gear systems. Full article

The paper provides an analysis of the energy efficiency of the swing drive system of hydraulic excavators, which integrally includes a hydraulic motor and a planetary reducer. The indicator of the drive’s energy efficiency is determined based on the efficiency of the hydraulic motor and the planetary reducer. The efficiency of the hydraulic motor is defined as a function of the specific flow, pressure, and the number of revolutions of the hydraulic motor. The efficiency of the reducer is determined using structural analysis of planetary gearboxes and the moment method. As an example, the results of a comparative analysis of the energy efficiency of the swing drive of a tracked hydraulic excavator, weighing 16,000 kg and having a bucket volume of 0.6 m³, are presented. From the set of possible generated variant solutions of the drive, obtained through the synthesis process based on the required torque and platform rotation speed, two extreme drive variants were selected for the analysis. In the first configuration, a hydraulic motor characterized by a low specific flow is combined with a three-stage reduction gear featuring a higher overall transmission ratio, whereas the second configuration integrates a high-specific-flow hydraulic motor with a two-stage reduction gear of a lower transmission ratio. The obtained results of the comparative analysis of the drive’s energy efficiency are presented depending on the change in the required torque and the rotational speed of the platform. Full article

The transmission accuracy and meshing performance of the gearbox is determined by the internal helical gears pair. Thermal deformation of internal helical gears pair is derived from sliding friction between the contacting teeth surface, resulting in shock, vibration, and misalignments. The purpose of this paper is to compare the influence of a modified gear and an unmodified gear on the temperature field and transmission characteristics of a planetary gear system under the same working conditions. This study presents an innovative temperature field model for gear pairs utilizing Surf152 elements, integrating Hertzian contact theory, tribological principles, and finite element analysis. For the first time, we quantitatively demonstrate the enhancement of thermo-mechanical performance through topological modification in helical gears. Under light-load conditions (200 rpm), the modified gear configuration exhibits a 6.38% reduction in tooth surface temperature and a 46.5% decrease in thermal deformation compared to conventional designs. Experimental validation confirms these improvements, showing an average 62.35% reduction in transmission error. These findings establish a novel methodology for high-precision gear design while providing critical theoretical foundations for planetary gear systems, ultimately leading to significant improvements in both transmission accuracy and operational lifespan. Full article

Time-varying mesh stiffness (TVMS) of the internal mesh transmission is a significant source of excitation that causes vibration and noise in planetary gear systems, and is also an important parameter in dynamics analysis. Currently, the calculation of mesh stiffness for internal gear pairs primarily relies on finite element simulation, and there still lacks a mesh stiffness analytical model that accounts for tooth surface nonlinear contact. Therefore, this paper proposes an analytical model for nonlinear contact mesh stiffness that comprehensively accounts for tooth surface modification and the flexibility of the ring gear. Firstly, a mesh stiffness calculation model for a sliced tooth pair was established using the potential energy method, which accounted for the influence of gear ring flexibility. Secondly, the tooth deviation ease-off diagram was derived from the modified tooth surface equations, which provided data support for the nonlinear contact analysis. On this basis, slicing element pairs that met the contact conditions were identified by combining elastic deformation with mesh clearance. The comprehensive mesh stiffness in nonlinear contact was calculated by integrating the deformation coordination equation with the principle of minimum potential energy. Finally, using a group of internal helical gear pairs as an example, the validity of the proposed method was verified through finite element simulation. The effects of load, modification amount, and face width on the TVMS and load transmission error (LTE) of an internal helical gear pair were investigated by the analytical model. The results show that the analytical model can provide a reference for the optimal design of internal gear transmission. Full article

A high-gear-ratio anti-backlash 3K planetary gearbox with a preloaded flexure-based carrier is a suitable reducer for robot joints owning to its compact design and high transmission accuracy. However, to design such a 3K planetary gearbox with high bidirectional efficiencies for backdrivable robot joints, it is critical to develop an accurate transmission efficiency model to predict the effects of the preloaded flexure-based carrier on the efficiency of the 3K planetary gearbox. To determine the meshing forces of gear pairs in the 3K planetary gearbox, a quasi-static model is formulated according to tangential displacements of planet gears resulting from the preloaded flexure-based carrier. Considering the reverse meshing forces in the anti-backlash 3K planetary gearbox, a modified efficiency model is developed and the bidirectional transmission efficiencies are analyzed. Simulation results show that both forward and backward transmission efficiencies of the anti-backlash 3K planetary gearbox decrease as the preload increases, while they all increase with the increasing load torque. It is also revealed that the preload primarily affects the meshing efficiency of the sun–planet gear pair. Four different carrier prototypes are fabricated for experiments. The average errors between the predicted and measured results for forward and backward transmission efficiencies are 2.30% and 4.01%, respectively. Full article

The dynamic characteristics of high-precision planetary reducers in terms of vibration response and dynamic transmission error have a significant impact on positioning accuracy and service life. However, the dynamics of high-precision two-stage helical planetary reducers have not been studied extensively enough and must be studied in depth. In this paper, the dynamic characteristics of the high-precision two-stage helical planetary reducer are investigated in combination with simulation tests, and the microscopic modification of the gears is optimized by the helix modification with drums, with the objective of reducing the vibration response and dynamic transmission error. Considering the time-varying meshing stiffness of gears and transmission errors, a translation–torsion coupled dynamics model of a two-stage helical planetary gear drive is established based on the Lagrange equations by using the centralized parameter method for analyzing the dynamic characteristics of the reducer. The differential equations of the system were derived by analyzing the relative displacement relationship between the components. On this basis, a finite element model of a certain type of high-precision reducer was established, and factors such as rotate speed and load were investigated through simulation and experimental comparison to quantify or characterize their effects on the dynamic behavior and transmission accuracy. Based on the combined modification method of helix modification with drum shape, the optimized design of this type of reducer is carried out, and the dynamic characteristics of the reducer before and after modification are compared and analyzed. The results show that the adopted modification optimization method is effective in reducing the vibration amplitude and transmission error amplitude of the reducer. The peak-to-peak value of transmission error of the reducer is reduced by 19.87%; the peak value of vibration acceleration is reduced by 14.29%; and the RMS value is reduced by 21.05% under the input speed of 500 r/min and the load of 50 N·m. The research results can provide a theoretical basis for the study of dynamic characteristics, fault diagnosis, optimization of meshing parameters, and structural optimization of planetary reducers. Full article

The rotary vector planetary gear reducer is a critical joint reducer widely employed in various robotic systems. Due to numerous components and complex motion, the machining and assembly of its components significantly impact its motion accuracy. This paper utilizes transmission error (TE) traceability analysis and Fourier analysis to identify and characterize the TE components in rotary vector planetary reducers. By analyzing the motion characteristics of individual components, this study identifies the frequency characteristics of each component. Fourier frequency domain discretization, based on experimental TE measurements, verifies these characteristics, identifying the main factors affecting TE and providing theoretical support for enhancing transmission accuracy. Full article

In this paper, a variable gear ratio for active steering systems with a double planetary gear configuration is presented to optimize the steering performance of commercial vehicles. First, a variable transmission ratio system with a dual-row planetary gear mechanism is developed in ADAMS/Car, where the steering mechanism’s transmission ratio can be adjusted according to different driving conditions, thereby improving the vehicle’s stability and sensitivity. Second, a new type of dual-inverter permanent magnet synchronous motor (DPMSM) has been designed to solve the power limitation problem in the electric drive steering of commercial vehicles. Finally, the step steering and lane change driving scenarios are chosen for co-simulation using ADAMS/Car and MATLAB to evaluate the proposed method’s effectiveness. The co-simulation results show that the proposed variable transmission ratio and control strategy can effectively improve the steering sensitivity and stability of commercial vehicles. Full article

The recent advancements in wearable exoskeletons have highlighted their effectiveness in assisting humans for both rehabilitation and augmentation purposes. These devices interact with the user; therefore, their actuators and power transmission mechanisms are crucial for enhancing physical human–robot interaction (pHRI). The advanced progression of 3D printing technology as a valuable method for creating lightweight and efficient gearboxes enables the exploration of multiple reducer designs. However, to the authors’ knowledge, only sporadic implementations with relatively low reduction ratios have been reported, and the respective experimental validations usually vary, preventing a comprehensive evaluation of different design and implementation choices. In this paper, we design, develop, and examine experimentally multiple 3D-printed gearboxes conceived for wearable assistive devices. Two relevant transmission ratios (1:30 and 1:80) and multiple designs, which include single- and double-stage compact cam cycloidal drives, compound planetary gearboxes, and cycloidal and planetary architectures, are compared to assess the worth of 3D-printed reducers in human–robot interaction applications. The resulting prototypes were examined by evaluating their weight, cost, backdrivability, friction, regularity of the reduction ratio, gear play, and stiffness. The results show that the developed gearboxes represent valuable alternatives for actuating wearable exoskeletons in multiple applications. Full article

The article aims to describe the design and operation of a fundamentally new self-regulating planetary transmission, which, without a control system, changes the gear ratio under the influence of a variable external load. A self-regulating transmission can be created based on a kinematic chain with two degrees of freedom, having only one input. According to the laws of mechanics, such a chain has no definability of motion, since the number of inputs must be equal to the number of degrees of freedom. The equilibrium of a two-movable chain with one input can obtained by creating an additional constraint that substitutes a reaction in the instantaneous center of the intermediate link velocities by the friction moment in the hinge of the intermediate link. The friction moment creates a force constraint, which is taken into account in the equilibrium condition. The obtained equilibrium conditions ensure the definiteness of motion and the ability of self-regulation in the form of an inversely proportional dependence of the speed of the output link on the variable external load. The described method makes it possible to create a fundamentally new class of self-regulating mechanisms in all branches of technology. The interaction of kinematic and force parameters and the construction of parameter graphs was performed using the SolidWorks 2021 program with certain additions. The experimental studies performed confirm the reliability of the theoretical developments. Full article

The multi-degree-of-freedom characteristics of the planetary gear electronic continuously variable transmission (ECVT) configuration in series-parallel hybrid tractors impose more complex requirements for energy management strategies under variable load conditions. For a high-power hybrid tractor, this paper takes the hybrid tractor output-split (OS)-ECVT configuration as the research object and describes the principles of stepless transmission and power-splitting within the configuration. In order to improve the fuel economy of high-power hybrid tractors and the running status of power components, an energy management strategy focused on ploughing conditions based on the Bellman minimum dynamic programming (DP) algorithm is proposed in this paper. Second, equivalent fuel consumption is selected as the performance index for energy-saving control, and the solving principle of the energy management strategy based on the dynamic programming algorithm is established to facilitate the resolution process of the energy management strategy. Finally, the energy-saving control simulation is completed under ploughing conditions. The results show that compared with the energy management strategy based on the optimal operating line (OOL), the energy management strategy based on DP fully utilizes the benefits of low-cost electric energy and enables the hybrid power system to have a wider range of stepless transmission performance. In addition, the hybrid power system has the advantages of enhanced decoupling of speed and torque, higher efficiency, and more economical secondary energy conversion. As a result, the whole machine has enhanced power-split performance, greatly improving the running conditions of the power components. The equivalent fuel consumption values of the energy management strategies based on DP and OOL are about 3.1238 L and 4.2713 L, respectively. The equivalent fuel consumption based on DP is reduced by about 26.87%, which effectively improves the fuel efficiency of hybrid tractors. Full article

Planetary gear transmission mechanisms (PGTMs) are widely used in mechanical transmission systems due to their compact structure and high transmission efficiency. To implement the reliability design and optimization of a PGTM, a novel multi-objective dynamic reliability optimization approach is proposed. First, a multi-objective reliability optimization model is established. Furthermore, considering the strength degradation of gears during service, a dynamic reliability analysis is conducted based on the theory of nonlinear fatigue damage accumulation. In addition, to improve computing efficiency, a random forest surrogate model based on the particle swarm optimization algorithm is proposed. Finally, an adaptive multi-objective evolutionary algorithm based on decomposition (AMOEA/D) is designed to optimize the mechanism, along with an adaptive neighborhood updating strategy and a hybrid crossover operator. The feasibility and superiority of the proposed approach are verified through an NGW planetary gear reducer. The results show that the proposed surrogate model can reduce the calculation cost and has high accuracy. The AMOEA/D algorithm can improve transmission efficiency, reduce gear volume and ensure reliability at the same time. It can provide guidance for actual gear production. Full article

Electromechanical energy conversion systems (EECSs) are widely used in vehicles to combine the double-row planetary gear system (DRPGS) with high transmission efficiency and high-performance motors. The integrated structure of the ring gear and motor rotor have put forward higher demands for the vibration performance of the DRPGS. This paper establishes a multibody dynamic model of the DRPGS for an EECS. Based on the kinetic relationship between the gear pairs and bearing components, the dynamic equations of the DRPGS are derived. The DRPGS model is simulated under different operating conditions. The results are compared to reveal the relationships between the system vibration and the operating speed and load torque. The typical conditions are selected to study the effectiveness of the structural parameters in reducing the DRPGS vibrations. The structural parameters, including the bearing clearance, the ball numbers, the gear tooth modification amount, and length, are comprehensively discussed. Several suggestions for the low-vibration design of the DRPGS for the EECS are provided. Full article

This paper presents a coaxial counter-rotating planetary transmission system. The transmission system under study is a two-stage planetary gear train (PGT) comprising a fixed-axes PGT and a differential PGT. A dynamic model of the transmission system is established, considering both the excitations caused by the time-varying mesh stiffness (TMS) and the transmission errors, respectively. The Runge–Kutta algorithm is used to calculate and analyze the dynamic characteristics of the system. This includes studying dynamic meshing forces, planet gear displacements, and load-sharing coefficients (LSCs) under both internal and external excitations, as well as different input torques. The results indicate that when considering external excitations, the variations in the meshing force curves become more pronounced. The radial displacements of the planet gears in the differential PGT are greater than that in the fixed-axes PGT. With increasing input torque, the average displacements of the planet gears in all directions tend to increase. The differential PGT, transmitting a higher power, demonstrates a better load-sharing performance compared to the fixed-axes PGT. Full article