Gear Parameters Research Articles

Effect of Geometric Parameters of High-Speed Helical Gears on Friction Flash Temperature and Scuffing Load Capacity in Electric Vehicles

High-speed reducers in electric vehicles, characterized by high rotation speeds, heavy loads, large helix angles, and high contact ratios, are prone to tooth surface scuffing due to high sliding speeds. This scuffing is caused by adhesion wear from excessive instantaneous friction flash temperatures. The prevailing approach to gear scuffing analysis relies on the standard formula method, which is a relatively rudimentary technique. This method lacks the precision required to accurately assess the intricate distribution of tooth surface flash temperature (TSFT), limiting its efficacy in targeted tooth optimization. This study introduces an enhanced semi-analytical method to calculate TSFT and analyzes its variation under different conditions: increased tooth number and reduced module, altered pressure angle, and varied helix angle. The aim is to understand how these geometric parameters affect TSFT and the scuffing load capacity of high-speed reducer gears. This study calculates load distribution and TSFT under peak operating conditions and shows that increasing the tooth number, pressure angle, and helix angle can reduce maximum TSFT by more than 30%, improving scuffing safety and load capacity. However, these improvements must consider the gear’s allowable bending safety factor and bearing service life. The research concludes that optimizing these geometric parameters can significantly enhance the scuffing load capacity of gearsets.

Analysis of tooth root three-dimensional fatigue crack initiation, propagation, and fatigue life for spur gear transmission

The gears in aviation gear systems are susceptible to fatigue fracture due to high-speed, heavy-load, and load alternation operating conditions. Therefore, a numerical calculation model with multiple mesh positions loading form has been proposed in this paper to analyze the fatigue crack initiation and propagation behavior, and to estimate the fatigue life of these gears. The fatigue life of the gear is determined by separately calculating the fatigue crack initiation life and the fatigue crack propagation life. The tooth root fatigue stress and the fatigue initiation life are calculated by the multi-axial fatigue life prediction method with the Smith-Watson-Topper criterion and the critical plane method. Afterwards, the tooth root stress–strain field is calculated in Finite element (FE) software and the stress intensity factors of the crack tip are calculated in three-dimensional (3D) crack analysis software. Then, the tooth root fatigue crack propagation trajectory and the fatigue crack propagation life are obtained separately. Finally, the influence mechanism of the loading conditions, the geometry parameters of gears, and the initial crack positions on the tooth root fatigue crack initiation life, propagation life, and fatigue crack propagation trajectory are analyzed, and a tooth fatigue test bench is built for verifying the crack propagation trajectory.

An Analysis of and Improvements in the Gear Conditions of the Automated Mechanical Transmission of a Battery Electric Vehicle Considering Energy Consumption and Power Performance

The design of the gear quantity and transmission parameters of a vehicle has large effects on its economical and power performance. This paper mainly researches the gear conditions (including the gear quantity and each gear’s transmission parameters) of two-gear and three-gear AMT (Automated Mechanical Transmission). This research uses Cruise software to build a multi-gear simulation model of a BEV (Battery Electric Vehicle) and adopts the LHS (Latin hypercube sampling) method to design an experiment plan and conduct a simulation experiment. This paper proposes a systematic method for influencing factor analyses and the optimization of transmission parameters, combining fuzzy theory, multiple regression, and particle swarm optimization. The research results show that the gear quantity allowing for optimal overall performance is three. The highest score obtained in the results of the simulation experiment for three-gear AMT is 11.15% higher than that of the two-gear AMT. The optimal design plan for the two-gear AMT is a small ig1 with a big k1, in which case the highest score of the regression model increases by 2.67% compared with that before modeling. The optimal design plan for the three-gear AMT is a big k1 with a big k2, in which case the highest score of the regression model increases by 12.78% compared with that before modeling. Then, this research uses PSO (particle swarm optimization) to further optimize the regression models and compares the difference between the highest scores in the results of the simulation experiment. The difference between the highest scores of the three-gear and two-gear AMT further increases to 21.95% after optimization. As shown in the results, the key factor influencing the performance of two-gear and three-gear AMT is gear quantity.

An Advanced DEM-FEM Method for Herringbone Gear in Shot Peening

Introduction: The complex geometry of herringbone gear can lead to uneven surface strengthening, which affects the overall effect of treatment. Methods: A discrete element model (DEM) of shot peening for herringbone gears was developed, incorporating accurate gear surface parameters to study impact characteristics along the tooth profile. A finite element model (FEM) was created for small local units of the gear surface to calculate the residual stress and roughness. Results: There are a large number of low-velocity shots at the root of the gear, and the closer to the top of the gear, the higher the impact velocity of the shots, but the number of impacts also decreases. The surface roughness Sa near the root of the tooth is the smallest, the Sa at the pitch circle is the largest, and the Sa at the top of the tooth is intermediate. However, the residual stress levels at different positions of the tooth surface are not significantly different. Conclusion: The difference in tooth surface roughness of herringbone gear is the synergistic effect of shot impact velocity and shot frequency, but this synergistic effect has no significant effect on the stress after shot peening.

Multi-objective optimization of helical gear transmission geometric parameters using MOPSO

Abstract Helical gears are widely used in mechanical devices, but insufficient tooth strength can easily lead to premature failure, which is an urgent problem to be solved. To overcome this challenge, this paper introduces a multi-objective particle swarm optimization algorithm, which comprehensively considers the comprehensive effects of modification coefficient, number of teeth, and modulus on the performance of helical gears. By constructing a mathematical model with the geometric parameters of helical gears as the core design variables, aiming to minimize the difference between the maximum bending stress of helical gear roots and the contact stress on the tooth surface, we have achieved optimization of gear performance. Using MATLAB for algorithm programming, the established model was efficiently optimized and solved. After optimization, the bending strength difference and tooth surface bearing capacity of the gear pair have been significantly improved, ensuring the stability and reliability of the operation of the high-pressure sleeve disassembly transmission device.

Analysis and optimization of time-varying meshing parameters of spiral bevel gear with consideration of load sensitivity

Analysis and optimization of time-varying meshing parameters of spiral bevel gear with consideration of load sensitivity

A novel forward performance-driven design method for gear parameters

Gear is one of the most crucial components of the transmission system, and the performance of gear directly affects the efficiency and reliability of the transmission system. Conventional methods for designing gear parameters involve several time-consuming and complex steps, which may not guarantee optimal performance. Therefore, we propose a new method for designing gear parameters that aims to improve efficiency and accuracy. First, the tooth surface equations of spur and helical involute gears suitable for symmetric and asymmetric teeth are deduced based on the gear-forming machining principle. Second, the performance evaluation models for load capacity, dynamic performance, efficiency, and power density of the gears are established based on the precise gear surface. The design objectives are standardized and evaluated comprehensively using a linear weighting method. Finally, a forward performance-driven design method of gear parameters is established. The proposed method is applied to a helical gear pair design case, and the results show that 90.7% of the individuals in the Pareto optimal front are asymmetric gears, with 9.3% being symmetric gears. This suggests that asymmetric gears have more opportunities to be optimal than symmetric gears. The highest-ranked gear designed using the proposed method is superior to the gear designed using conventional methods.

Comprehensive Analysis and Development of Electric-Drive-Wheel with Idler Gear

This paper provides a comprehensive analysis of the electric-drive-wheel (EDW) with idler gear. From the perspective of automotive engineering, the EDW is an integrated execution unit that combines the function of powertrain and suspension. As a result, the research on EDW involves the intersection of multiple disciplines. The evolution of idler gear configuration requires some geometric constraints. Under this premise, the longitudinal and vertical dynamic characteristics of the system were studied, respectively. There are several factors that influence the system performance, such as the gear parameters, the position of the electric motor, and the suspension K&C value. The principles of each parameter on the output indicators were studied, with an optimized plan and simulation comparison to check the correctness of theory. In the end, the prototype was equipped with a test bench, covering a wide range of working operations to examine the expected performance of EDW design. The step response test of the EDW result showed a balanced performance in transmission smoothness and responsiveness agility.

Polymer gear failure prediction: A regression-Based approach using FEA and photoelasticity technique

The research aims to develop a model to predict the maximum contact stress depth, which will be correlated with polymer gear failures such as wear and rapid thermal deformation. A thorough 3D Finite Element Analysis (FEA) was performed for different gear parameters (varying module, number of teeth, and face width) in different combinations (Polymer – Polymer, Steel – Polymer, and Polymer – Steel). The simulation results showed that the contact stress depth increases with respect to the module and number of teeth; meanwhile, very negligible variations were found along the face width. Also, the findings indicate that the contact stress depth varied in the following descending combinations of gear pair: Polymer – Polymer, Steel – Polymer, and Polymer – Steel. The 3D FEA contact stress patterns were validated experimentally by utilizing the in-house developed photoelasticity test rig. The data obtained from the simulation results were used to develop regression models (Linear regression and Random Forest regressor) for estimating the maximum contact stress depth. A feature importance study was done using the mean reduction of the Gini index or impurities in random forest. It was found that torque applied and contact width of the gear pair were significantly influenced by the contact stress depth. Finally, an equation was developed correlating torque and contact width to predict the depth occurrence of maximum contact stress through which the failure mode of the polymer gear could be predicted.

Research on High-Precision Measurement Method for Small-Size Gears with Small-Modulus.

Small-modulus gears, which are essential for motion transmission in precision instruments, present a measurement challenge due to their minuscule gear gaps. A high-precision measurement method under the influence of positioning errors is proposed, enabling precise evaluation of the machining quality of small-modulus gears. Firstly, a compound measurement platform for small-modulus gears is developed. Using a 3D model of the measurement system, the mathematical relationships governing motion transmission between various components are analyzed. Secondly, the formation mechanism of gear positioning error is revealed and its important influence on measurement accuracy is discussed. An optimization method for spatial coordinate transformation matrices under positioning errors of gears is proposed. Thirdly, the study focuses on small-sized gears with a modulus of 0.1 mm and a six-level accuracy. Based on the aforementioned measurement system, the tooth profile measurement points are collected in the actual workpiece coordinate system. Then, gear error parameters are extracted based on the established models for tooth profile deviation and pitch deviation. Finally, the accuracy and effectiveness of the proposed measurement method are verified by comparing the measurement results of the P26 gear measuring center.

Support vector machine-based optimisation of traction gear modifications for multiple-condition electric multiple unit

The traction gear train is subjected to various internal excitations under different traction conditions, such as stiffness excitation, error excitation, meshing shock excitation, and tooth side clearance. The optimal modification scheme is different for each state, and the optimal modification plan based on a single working condition may not be applicable to every working condition. In this paper, we investigate the vibration response characteristics of electric multiple unit gearing under multiple conditions and propose a multi-condition modification scheme. Under different traction conditions, the mapping between gear modification parameters and vibration acceleration in gear transmissions is investigated using support vector machines. Genetic algorithms are used to solve the gear-modifying parameters to minimise the maximum vibration acceleration. A weight assignment principle is proposed to calculate the electric multiple unit traction gear transmission under different conditions, with the operating time and the amount of vibration in each condition as the measurement index. The results of the simulation show that the vibration acceleration under continuous conditions is reduced by 3.55 m/s2, a decrease of 69.88%; the vibration acceleration under high-speed conditions is reduced by 3.301 m/s2, a reduction of 58.74%, and the results show that the overall index of the electric multiple unit traction gear transmission system under different conditions has been improved after the optimisation of the multi-conditions modification, the gear transmission system's vibration is significantly reduced.

Analysis of the dynamic contact behaviour of high-speed train transmission gear excited by wheel defects

Studies on wheel flatness and polygonal wear have demonstrated that wheel defects cause severe impact forces at the wheel–rail interfaces. This study investigated the dynamic contact mechanical behaviour of high–speed train transmission gears when subjected to wheel defects. First, a train-track coupling dynamics model was established, considering the localized contact characteristics of transmission gears. This model was developed using the slice method and the Hertz contact model, exploring the spatial coupling effects between the gear contact interface and the train–track interface. Subsequently, the dynamic model was employed to extract essential contact mechanical parameters of the transmission gear under the influence of wheel defects, including gear meshing load, gear contact stress, and sliding velocity. Furthermore, an analysis was conducted to uncover and elucidate the mechanism by which wheel flatness and polygonal wear impact the dynamic contact behaviour of the transmission gear. This study underscores the importance of considering wheel defects when assessing the contact fatigue and wear performance of high-speed train transmission gears.

Modeling and Simulation of the Induction Hardening Process: Evaluation of Gear Deformations and Parameter Optimization

This study aimed to analyze and optimize the thermal induction hardening process applied to toothed transmission gears, focusing on thermal aspects, structural deformation, and topology optimization, while exploring the feasibility of various materials and operating conditions. The research simulated thermal and deformation behavior using a computer model, comparing results with experimental data through the Ansys® platform 2022 R1. The methodology encompassed thermal and deformation analyses, topology optimization to identify removable regions without compromising part integrity, and a sensitivity study to evaluate the different materials and operating conditions. This study validates the precision of computational models in predicting thermal and deformation behavior in toothed gears under thermal induction hardening, introducing topology optimizations and alternative materials, and providing novel perspectives for the more efficient and cost-effective manufacturing of these components. Comparative thermal analysis revealed a maximum relative error of less than 6% between temperatures from the computer model and experimental results, while deformation comparisons exhibited a maximum relative error of less than 7%, affirming the simulation model’s accuracy in predicting and managing deformations within acceptable thresholds. Topology optimization successfully pinpointed removable regions without compromising structural integrity, enabling the production of lighter and more economical devices. Future endeavors should concentrate on additional tests to verify the feasibility of reducing power and cooling temperature without compromising product specifications. Furthermore, it is advisable to explore alternative materials and apply the developed methodology in diverse industrial settings to generalize the findings and amplify the impact of the proposed optimizations.

Analytical method for time-varying meshing stiffness and dynamic responses of modified spur gears considering pitch deviation and geometric eccentricity

Pitch deviation and geometric eccentricity are almost inevitable in gear transmission systems. Tooth profile modification (TPM) is a common method used to improve gear contact properties. However, the coupling interaction between the tooth profile deviation introduced by TPM and manufacturing errors is complex. There is a lack of an analytical model that can clarify the dynamic behaviors of the modified gear pair affected by multiple manufacturing errors, specifically pitch deviation and geometric eccentricity. To fill this gap, a comprehensive analytical gear mesh model is proposed considering TPM, pitch deviation, and geometric eccentricity. The calculation formulas for the time-varying meshing stiffness (TVMS) and load sharing factor (LSF) are derived considering the iterative change of gear pair meshing parameters with phase under the influence of multiple manufacturing errors. Then, the translation-torsion coupling dynamic model of the spur gear pair based on the lumped mass method is established to investigate the dynamic transmission error (DTE) and vibration characteristics. Results show that TPM is an effective method for improving the comprehensive stiffness of a gear pair within the meshing range containing pitch deviation, but it reduces the meshing phase that includes only geometric eccentricity. Compared with the unmodified gear pair, the suppression effect of changing the modification length on the maximum DTE and vibration acceleration is more significant than that of the modification amount. TPM increases the overall fluctuation threshold range of DTE for gear pairs with only geometric eccentricity. It is expected that the proposed method can provide a theoretical basis for exploring vibration suppression in gear pairs with geometric eccentricity and pitch deviation errors.

Research on gear life reliability analysis based on accelerated life test

AbstractAs one of the key components of marine reducer, the life reliability of gear is of great significance to the safe operation of the reducer and even the whole transmission system. However, due to economic and testing constraints, executing extensive fatigue life tests on complex and costly gears presents a formidable challenge, resulting in inadequate reliability assessments. In this paper, the gear life reliability analysis method based on the accelerated life test is proposed. By conducting the gear bending fatigue accelerated life test, the life distribution and failure mechanism are determined based on the accelerated life data. Furthermore, the gear life distribution parameters and acceleration model are solved by least squared method. This allows us to derive a reliability index specific to the service conditions, facilitating the evaluation of gear life reliability. The method proposed in this paper provides data and theoretical support for the accelerated life tests, lays a foundation for the gear reliability evaluation under small samples, and improves the efficiency of the gear fatigue life evaluation. It has significant engineering significance in saving test costs, reducing test times and shortening development cycle.

Identification of the Asymmetric Transmission Error and Gear Mesh Dynamic Parameters using Full-Spectrum Responses in a Geared-Rotor System

A dominant source of vibration in geared-rotor systems are the gear mesh fault parameters. They include the asymmetric transmission error, phases of transmission error, the gear mesh stiffness, the gear mesh damping and the gear runouts. The present work deals with the experimental identification of aforementioned parameters. A mathematical model of geared-rotor system has been developed using Lagrangian dynamics. Equations of motion are transformed into frequency domain using the full-spectrum response analysis. These transformed equations are used to develop an identification algorithm based on least-squares fit to estimate the transmission error and gear mesh dynamic parameters. The system identification algorithm is initially verified using numerical simulations. The robustness of the algorithm is checked by introducing white Gaussian noise in the simulated responses. A geared-rotor experimental rig was developed and used to measure responses at gear locations in two orthogonal directions. Measured responses are transformed in frequency domain using the full-spectrum analysis and used in the present novel identification algorithm to identify the gear parameters. The identified parameters are validated by comparing the numerically generated full-spectrum response using experimentally estimated parameters and that from the experimental rig. Conflict of Interest Statement The authors declare no conflicts of interest.

Experimental Analysis of Spur Gear Pair with Geometrical and Operating Parameters

Abstract This study presents experimental work to analyze spur gear pair with geometrical and operating parameters. The spur gear pair accommodates the correction in tooth addendum, gear backlash, and linear tip relief profile modification with three levels. As per Taguchi L9 orthogonal array, nine test spur gear pairs are precisely manufactured to analyze the combined influence of these three geometrical parameters on gear dynamics. Other basic gear design parameters and operating parameters were held at a constant level. RMS acceleration in the vertical direction to quantify the dynamic response of test gear pairs. Experimental data are analyzed by using the Taguchi method to investigate the rank of influencing parameters to minimize vibration response. Finally, the confirmation test was performed by using a simulation study to validate the experimental results. The simulation results are similar to the experimental results. Similarly, 20 experiments were conducted with different speed and load combinations to check the effect of operating conditions on gear dynamics. From this experimental study, it is observed that the rank of influencing parameters and optimum level of geometrical are varied with respect to operating conditions. It may be concluded that typically optimized spur gear pair operated at one particular combination of load and speed may not show good performance at other operating conditions. Therefore, this study suggests that the realistic range of operating conditions should be considered while selecting suitable geometrical parameters.

Study on the Parameter Influences of Gear Tooth Profile Modification and Transmission Error Analysis

Gear transmission systems are widely used to transfer energy and motion and to guarantee the accuracy of the entire machine system. The modification technique is a common method that improves the gear profile and reduces the transmission error. Based on the parametric model, a modified gear can be established for the evaluation of static and dynamic characteristics. The influences of profile modification parameters and gear parameters are investigated while changing the rules of different kinds of factors. Based on sensitive parameters, a two-stage profile modification curve is proposed to improve the performance of gear pairs. Thus, considering the time-varying mesh stiffness and backlash, a novel, dynamic modified gear model is established to analyze the dynamic performance, such as the dynamic transmission error. Based on the proposed curve, the range and amplitude of the transmission error can be decreased. Additionally, the vibration displacement and noise can be reduced to improve the running characteristics.

Research on optimal design method of dynamic stress parameters of helical gear based on orthogonal experimental design

Aiming at the reliability optimization design problem of two-grade helical cylindrical gear transmission system, the UG parameterized model based on expression and ADAMS dynamic simulation model under real working conditions are integrated in ISIGHT platform, and the distribution law of peak contact force on the tooth surface of helical gear pair in the transmission system at different meshing times is obtained. Considering the uncertainty of material properties, load conditions and geometric parameters, the sample set was generated according to the orthogonal experimental design method, and the Kriging approximation model was established. On this basis, the contact strength reliability of helical gear was analyzed. The mathematical model of meshing efficiency reliability optimization of helical gear pair was established and solved by Hooke-Jeeves Direct Search method. The results show that the meshing efficiency and reliability of the optimized helical gear pair are improved, and the peak value of the contact force is obviously reduced.

Analysis of landing gear walk vibration characteristics excited by aircraft anti-skid brakes

Currently, there is not enough research on the mechanism that causes the vibration of landing gear walk when an aircraft anti-skid brake is activated. This paper aims to provide a comprehensive analysis of the characteristics of the landing gear walk and the associated research. It shows that the walk vibration is caused by a cantilever beam’s tip mass and that the study should focus on the landing gear walk’s characteristics. Firstly, according to the transverse vibration theory of cantilever beams, the transcendental equation for calculating the natural frequency of the landing gear can be obtained. After that, the influence of the structural parameters of the landing gear on each order of the natural frequency is analyzed. To ensure that the conclusions derived are applicable to all landing gear structures, the structural parameters are selected to cover both small unmanned aerial vehicles and large civil aircraft. Finally, the influence of the axial pressure of the landing gear on its inherent frequency is analyzed.