Gear Transmission Research Articles

Traveling-wave vibration modelling for thin-walled gear with ring damper

The harmful resonances of the thin-walled gears for aviation high-speed gear transmission systems, especially the traveling-wave vibration (TWV), frequently occur under complex excitations. The ring damper is an excellent and widely used damping technology for TWV reduction. However, lacking the TWV predictive method, there are few theoretical bases for the damper optimization. In this paper, firstly, assuming that the external input energy, the gear damping energy dissipation, and the ring damper energy dissipation form an energy balance, a novel model of TWV response based on energy dissipation (TRED) is proposed for the thin-walled gear with ring damper. Secondly, to solve the complex nonlinear TRED model, using the Rayleigh damping theory, the discrete expression of TRED model is innovatively given instead of traditional equation solving methods. Considering that the TRED model is established based on the vibrational displacement, a method for the conversion of gear vibration strain and displacement is given under different TWV directions and vibration strain measurements, and the solving method is proposed for the TRED model based on the above established theories. Finally, to validate the TRED model and its solutions, the speed-up experiments are conducted, and the experimental results are compared with the TRED prediction. Results show that the experimental and theoretical results are consistent, and the maximum predictive error is 8.7 %, which validates the feasibility of the proposed theories and methods.

Applicability of Numerical Simulation to the Classification of Fluid Dynamic Loss in Aeroengine Transmission Gears

Abstract In high-speed gear systems for aeroengines, reducing the fluid dynamic loss, which accounts for the majority of power loss, can significantly improve fuel economy. However, few practical numerical examples are available regarding high-speed gas–liquid two-phase flows involving gear meshing and gear shrouds (gear enclosures, which are effective for loss reduction). Therefore, in this study, the porosity method for object boundaries including the gear meshing, the volume of fluid method, and the surface compression method for the gas–liquid interface was used as fast and numerically stable calculation methods. In addition, a gap was provided at the contact surface of the gear tooth surface to improve the calculation stability, and the oil properties were set considering the difference between the flow resistance in a two-phase flow and that in a single-phase flow (due to the separation of oil particles) to improve the calculation accuracy. To validate the numerical simulation method, a two-axis helical gearbox with a maximum peripheral speed of 100 m/s with specifications equivalent to aeroengine gears was used, and the air flow, oil flow, and fluid dynamic losses were validated. Once the practical accuracy was confirmed, the numerical simulation was used to understand the relationship between air and oil flows, torque, and the effect of the shroud. Consequently, the fluid dynamic loss could be classified phenomenologically.

Fluid Dynamic Loss Model With Wide Applicability for Aeroengine Transmission Gears

Abstract In high-speed gear systems for aeroengines, it is important to reduce the fluid dynamic loss, which accounts for the majority of power loss, to improve fuel efficiency. For reasonable loss-reduction and the standardization of low-power-loss designs, a fluid dynamic loss model with wide applicability is needed. However, there are few reports of loss models considering the gear shroud effect on the oil dynamic loss. This study developed a loss model based on fluid dynamic loss phenomena. Specifically, fluid dynamic loss models were developed for the “air side-flow loss,” “air pumping loss,” “oil-jet acceleration loss,” and “oil re-acceleration loss” in the gear meshing part, and “air vortex loss” and “oil churning loss” in the gear peripheral part, with consideration to the shrouding effect. Moreover, an experimental method and a numerical method for loss classification are proposed. The fluid dynamic loss models were validated by experiments or experimentally validated numerical simulations. To demonstrate the effectiveness of the loss model for low-power-loss design, the influence of the design parameters was investigated, and the typical parameters were optimized.

Wear characteristics analysis of variable hyperbolic circular-arc-tooth-trace cylindrical gear transmission considering assembly error theory

Wear is the main failure form of the gear transmission interface, runs through the whole life cycle of gear service, and the distributed error of the tooth surface due to the introduced assembly error will make the actual meshing state of the tooth surface different from the ideal meshing state, thus affecting the tooth surface wear trajectory and state. Therefore, considering the coupling relationship between assembly error and tooth surface contact analysis, the variation laws of the wear amount of the gear transmission interface of the variable hyperbolic circular-arc-tooth-trace cylindrical gear were studied under the consideration of assembly error in this article. Based on the tooth surface contact analysis method and Hertz contact theory, the transient linear load, the combined radius of curvature, the length axis and short axis of the contact ellipse, and the instantaneous sliding velocity were calculated. Through revising the calculation method of adhesive wear of variable hyperbolic circular-arc-tooth-trace cylindrical gears, the correlations between the tooth surface wear amount and gear parameters of variable hyperbolic circular-arc-tooth-trace cylindrical gears under different assembly errors were analyzed. The results show that the maximum wear occurs at the root of the tooth, and the wear at the indexing circle approaches zero, whether it is standard installation or non-standard installation. The vertical axial error and horizontal axial error have little effect on the wear, while the center distance error will aggravate the wear. The proposed method comprehensively considers the influence of assembly error and gear parameters on tooth surface wear, and this method can provide a theoretical reference for the design and analysis of anti-wear, wear reduction, and life extension of variable hyperbolic circular-arc-tooth-trace cylindrical gear tooth surface.

Automatic configuration analysis method of planetary gear automatic transmission

Planetary gear trains (PGT) with the aim of achieving multiple speed ratios are widely used in automatic transmission (AT). A fast configuration analysis method is of significance for improving the efficiency of AT design, and it is essential to study the automatic configuration analysis method for AT. For this purpose, the AT configuration is represented by a matrix model, which includes the structural matrix of PGT and shifting elements (SEs) matrix. Based on the proposed matrix representation, the speed relation and torque relation matrices of AT are automatically derived to analyze the kinematics and dynamics. Five performance indexes of AT configuration, specifically transmission ratio, rotation speed of components, torque transmitted by SEs, power flow, and transmission efficiency, are automatically calculated through the analysis result. The entire analysis process can be completed in 1 s on the computer. The proposed matrix model offers a unified representation for the configuration of AT derived from different synthesis algorithms. It facilitates rapid automated configuration analysis and performance evaluation, thereby positively influencing the design of automatic transmissions. Furthermore, the matrix model can be applied to the configuration synthesis of AT.

Graphene-like 2D Ti3C2Tx MXene/dodecyltrimethoxysilane coating for corrosion protection on aluminum alloy by designing multilayer structure

Corrosion of metals leads to great economic losses and safety hazards. To address the corrosion problem of Al alloy in aggressive medium, two-dimensional (2D) graphene-like MXene composite coatings are proposed to enhance the corrosion resistance. Despite great progress, it still faces challenge to design high-performance MXene-based composite coating via a facile strategy because of the complex surface functionalization, orientation control, and the conductivity of MXene. Herein, a multilayer Ti3C2Tx MXene/dodecyltrimethoxysilane (MXene/DTMS) coating is prepared by a layer-by-layer spraying method at ambient temperature to maximize the physical barrier of MXene nanosheets. As a result, the incorporation of MXene nanosheets can avoid the structural defects of silane coating after curing process, thereby improving the coating resistance and charge transfer resistance by ~11- and ~390-fold in comparison to Al counterpart, respectively. Beyond the traditionally complex surface functionalization and orientation control, the multilayer coating with complete coverage and strong physical barrier ability exhibits the high corrosion resistance with a impedance modulus of 3.74 × 107 Ω·cm2 in 3.5 wt% NaCl solution. The designed coating shows promising applications in surface protection on Al alloy used in transmission cable, shafts, gears, and blades for offshore wind turbines.

Analysis of vibration characteristics of face gear powering-split transmission system

A nonlinear dynamic model of the face gear powering-split transmission system was established, and the nonlinear dynamic characteristics of the face gear powering-split transmission system were studied by considering various factors such as support stiffness, time-varying meshing stiffness, lateral clearance of teeth, comprehensive transmission error and bearing stiffness. The Runge–Kutta integral method is used to solve the differential dynamics of the system. The nonlinear behavior of the system is described by the phase plane diagram, time history diagram, frequency domain diagram, and Poincare section diagram. The influence of external excitation frequency on the nonlinear behavior of the system is described by the bifurcation diagram. In addition, the multi-scale method is used to analyze the superharmonic resonance of the system and determine the stability conditions of the superharmonic resonance of the system. The influence of meshing damping, time-varying meshing stiffness, and time-delay control parameters on the amplitude-frequency characteristics of the system is studied by numerical analysis of the superharmonic resonance. The results show that the system will show periodic chaotic alternating motion characteristics under external excitation. Selecting meshing damping, meshing stiffness, and time delay control parameters in a reasonable range can effectively reduce the superharmonic co-amplitude and keep the system in a stable state.

Calculation of the deformation values of the ammortizer in the compound angle gear transmission

The article presents the method of calculating the axial deformations of the rubber bush used in the bevel gear with the recommended composition and the formulas for determining the axial deformations. Based on the analysis of the connection graphs, the recommended values of its parameters were determined. The article presents the results of an analysis of the design features and disadvantages of cylindrical gears. An effective design scheme for a helical cylindrical gear transmission with elastic elements has been developed, allowing it to absorb peak values of oscillations of torques and axial force components arising from the meshing of wheel teeth, as well as cycling noise indicators.

The bending-torsional vibration characteristics of gear transmission under the effect of tooth surface roughness

The bending-torsional vibration characteristics of gear transmission under the effect of tooth surface roughness

Development of a Hardware-in-the-Loop Platform for the Validation of a Small-Scale Wind System Control Strategy

The use of renewable energies contributes to the goal of mitigating climate change by 2030. One of the fastest-growing renewable energy sources in recent years is wind power. Large wind generation systems have drawbacks that can be minimized using small wind systems and DC microgrids (DC-µGs). A wind system requires a control system to function correctly in different regions of its operating range. However, real-time analysis of a physical wind system may not be feasible. An alternative to counteract this disadvantage is using real-time hardware in the loop (HIL) simulation. This article describes the implementation of an HIL platform in an NI myRIO 1900 to evaluate the performance of control algorithms in a small wind system (SWS) that serves as a distributed generator for a DC-µG. In the case of an SWS, its implementation implies nonlinear behaviors and, therefore, nonlinear equations, and this paper shows a way to do it by distributing the computational work, using a high-level description language, and achieving good accuracy and latency with a student-oriented development kit. The platform reproduces, with an integration time of 10 µs, the response of the SWS composed of a 3.5 kW turbine with a fixed blade pitch angle and no gear transmission, a permanent magnet synchronous generator (PMSG), and a three-phase full-bridge AC/DC electronic power converter. The platform accuracy was validated by comparing its results against a software simulation. The compared variables were the PMSG currents in dq directions, the turbine’s angular speed, and the DC bus’s voltage. These comparisons showed mean absolute errors of 0.04 A, 1.9 A, 0.7 rad/s, and 9.5 V, respectively. The platform proved useful for validating the control algorithm, exhibiting the expected results in comparison with a lab-scale prototype using the same well-known control strategy. Using a well-known control strategy provides a solid reference to validate the platform.

Research on speed regulation method of high power magnetic gear

Magnetic gears have attracted the attention of many scholars due to their advantages of low noise, maintenance free, high torque density and inherent overload protection. In this paper, three speed regulation methods of high power magnetic gear transmission system are summarized and proposed, and the finite element analysis of the three speed regulation methods is carried out by COMSOL Multiphysics simulation software. The results show that when the sizes of the three magnetic gears are similar, the output torque and load power of the speed regulation method of the magnetic gear using the magnetic field modulated type is the largest. On the contrary, the axial magnetic gear with air gap length regulation method has the lowest output torque and load capacity. Compared with the other two methods, the coupling length regulation method has the minimum eddy current loss and the simple speed regulation structure, which is the most suitable for high power magnetic gear.

Tooth interior fatigue fracture in automotive differential gears

Tooth Interior Fatigue Fracture (TIFF) is an emerging gear failure mode with significant implications for gear lifetime and reliability, particularly in modern mechanical transmissions subjected to higher loads, smaller sizes, and increased Noise, Vibration, and Harshness (NVH) requirements. This paper investigates fatigue cracks initiated within the interior of pinion and/or side gear teeth in transmission differentials, representing a new area of recent failure detection. Conventional modeling has suggested that TIFF cracks originate in the case/core area of gear teeth, primarily seen in idler transmission gears. However, this study challenges this notion by presenting evidence that cracks often form closer to the middle of the tooth at various heights. These findings indicate the need for a deeper understanding of TIFF, as the existing theoretical descriptions may not fully explain the observed behaviors. By focusing on this novel area of failure, the paper highlights the importance of addressing TIFF to improve the reliability and durability of gears in modern mechanical transmissions.

Optimizing Failure Diagnosis in Helical Gear Transmissions with Stochastic Gradient Descent Logistic Regression using Vibration Signal Analysis for Timely Detection

Optimizing Failure Diagnosis in Helical Gear Transmissions with Stochastic Gradient Descent Logistic Regression using Vibration Signal Analysis for Timely Detection

Dynamic modeling of spur gear transmission system with evolutive coupling fault of fatigue crack and wear

Parallel shaft spur gear system is widely used in various machineries because of its simple structure, high transmission efficiency and strong adaptability. The health status of spur gear greatly affects the safety and reliability of equipment in service, so it is quite necessary to reveal the evolution law of gear fault and clarify the fault dynamic response. Fatigue crack is a typical gear fault, and it is often accompanied by wear which is generally unavoidable in the life cycle of gear transmission system. The two typical gear faults reduce the meshing stiffness of the gear pair, whereupon a calculation approach of time-varying meshing stiffness for the coupling fault of fatigue crack and wear is proposed. First, the prediction models of fatigue crack and wear are respectively investigated, then a coupling fault evolution model is built by combining them. Using this model, a new approach for calculating the time-varying meshing stiffness is put forward. Via embedding the obtained meshing stiffness into the eight-degree-of-freedom dynamics model of spur gear transmission system as the fault excitation, an evolutive coupling fault dynamics model is constructed. Finally, the effectiveness and accuracy of the proposed evolutive fault dynamics model is verified by the experiment on a faulty single-stage gearbox. The proposed model has important guiding significance for the fault diagnosis and prognosis of spur gearbox.

Investigation of Effect of the Tooth Profile Modification on the Engagement Characteristics of the Gear Pair

As a vital component in the electric vehicle, the higher requirements for the gear precision are urgently needed in the service environment with high speed and heavy load. The tooth profile modification can greatly improve the accuracy and strength of the gear transmissions. Therefore, accurately obtaining the optimum modification parameters of the gear system under the action of specific loads is the premise of the research of gear vibration and noise reduction. The time-varying mesh stiffness calculation model is established in this paper considering the coupling effect of the tooth profile errors and structural coupling effect. The minimum variations of the loaded static transmission error are selected as the objective function to obtain the optimum modification parameters of gear pair. In addition, the effect of torque, modification amount and modification length on the engagement characteristics of the gear pair are studied. The research can provide some references for the design and optimization for the gear transmission system in the electric vehicle.

Dynamic performance analysis of a gear transmission system due to cavitation in gerotor pump

In this work, a dynamic model considering time-varying mesh stiffness and backlash was proposed and a test rig was built to investigate the vibration behavior of the idle gear set in a gerotor pump. The effects of input shaft speed, torque fluctuation, and gear tooth backlash on the dynamic performance of gerotor pump were analyzed according to the numerical and experimental results. Results demonstrate that when the torque fluctuation is neglected, the dynamic transmission error of drive gear is dominated by the first three mesh harmonic components; however, the RMS values of vibration acceleration have high frequency characteristics. When the torque fluctuation is considered, the dynamic responses of gerotor pump are modulated by the torque fluctuation. The effect of tooth backlash on the dynamic performance of gerotor pump is limited and mostly depended on the torque fluctuation condition. The gerotor pump noise is dominated by the low frequency component around the mesh frequency. The vibration energy can be divided into two parts in the frequency domain. In the low frequency band, the vibration energy is caused by the mechanical vibration. However, in the high frequency band, the cavitation phenomena may cause the concentration of the vibration energy and resonant of pump structure.

Research on Nonlinear Vibration Characteristics of Internal Beveloid Gear Transmission System

The internal beveloid gear has good scientific research value and a broad application field. However, there is a lack of research on the nonlinear vibration characteristics of internal beveloid gears. The present study establishes a nonlinear vibration model that takes into account axial vibration, gear torsional vibration, and radial support vibration. The effects of various excitation parameters on the vibration characteristics of the gear transmission system are analyzed and computed using the Runge–Kutta method. After analyzing the dynamic model of the gear pair using numerical methods, the harmonic balance method is employed to obtain the theoretical analytical solution for a single−stage gear. The obtained results are compared with the velocity and acceleration time−domain response curves obtained from the numerical method, and they show excellent agreement.

Dynamic modeling and analysis of planetary gear system for tooth fault diagnosis

This study concentrates on the dynamic modeling and analysis of a planetary gear system with tooth broken faults. Firstly, a systematic calculation method of time-varying mesh stiffness (TVMS) for the planetary gear system is developed. Analytical models are established for both external-external and external-internal gear pairs under both healthy and tooth broken conditions. Then, a translational-torsional nonlinear dynamic model is established for a planetary gear system and coupled with the TVMS calculation method, to achieve dynamic simulations with tooth broken faults on the sun, planet and ring gears. The influences of tooth broken faults at different gears and at different damage degrees on the vibration responses are revealed. In addition, 15 condition indicators are chosen to assess their sensitivity to the tooth broken faults in a wide range of operational speed rather than a specific operational speed, in order to provide comprehensive information for evaluating the vibration characteristics and health conditions. Finally, experimental vibration signals from a gear transmission test rig are applied to verify the proposed dynamic model. The modeling method and analysis results here could provide some suggestions for the vibration analysis and fault diagnosis of planetary gear systems, and further provide data basis for the development of fault diagnosis methods.

Features of Wear of Gears of Agricultural Machinery

Abstract The paper presents data on the resource and wear of the gears of agricultural tractor transmissions, on the basis of which the research problem and the novelty of the proposed methodology are formulated, based on the development and application of the stress state model of the gear, taking into account surface hardening. The methodology and calculation scheme for determining the power parameters of gearing are described in detail. In this case, the dependences and results of previous studies in the field of increasing the durability and reducing the wear of gears of transmission elements of vehicles of various functional purposes were used. To achieve this goal, the mathematical models of the stress state of gears are constructed without the presence of an external diffusion hardening coating and with a coating. Based on the simulation of the process of interaction of rubbing pairs of gears, the distribution of stresses in the contact zone over the surface layer of non-hardened and cemented to a depth of 1 mm gears, as well as the dependence of deflection on the thickness of the cemented layer and the deformation of the cemented layer during operation was established. Considering the research results given in literature, as well as those obtained on the basis of our own research, it should be noted that the analysis of gear stress state is an important direction in the study of the durability of gear units, the entire gearbox, and other gears of tractor transmissions and automotive technology at the present time. At the same time, the actual task is to establish the ratios of the allowable wear of gears and the limiting value of displacement of the centre distance, taking into account changes in the stress state scheme when using various types of coatings.

Dynamic response of the axle-box bearing of a high-speed train excited by wheel flat

Axle-box bearings are directly affected by wheel–rail impacts as fixedly connected to wheelset. As an inevitable wheel-failure, wheel flat can cause severe wheel-rail impact, which may deteriorate the performance of axle-box bearings, even threatening train running safety. To investigate the dynamic response of axle-box bearings excited by wheel flat, two rigid-flexible coupled vehicle dynamics models of motor and trailer cars are developed. The axle-box bearing, flexible axle-box and wheelset are thoroughly established in trailer car model. The gear transmission system and flexible gearbox are further integrated into motor car model relative to trailer model. The accuracies of models are verified by the field-test results. The dynamic responses of axle-box bearings excited by wheel flat are analyzed. Results indicate that the vibration and dynamic forces acting on axle-box bearing augment with the increasing of flat length. The vibrations intensify gradually from wheelset, inner ring, and outer ring to axle-box, particularly increasing significantly with long flat lengths. Moreover, the dynamic forces within axle-box bearing first increase before decreasing with the growing operating speed. Being structurally difference, wheel flat exerts more significant effects on the axial and radial forces within the bearings of motor car than those of trailer car.