Helical Gears Research Articles

An Effective Method for Identifying Uneven Load Distribution on the Tooth Faces of Misaligned Wide-Faced Helical Gear Pairs

An Effective Method for Identifying Uneven Load Distribution on the Tooth Faces of Misaligned Wide-Faced Helical Gear Pairs

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.

Enhancing wind turbine energy efficiency: Tribo-dynamics modeling and shape modification

The performance of wind turbine gearbox planetary bearing systems directly influences the turbine's reliability, energy production efficiency, and economy. However, the lack of a comprehensive model to accurately predict the dynamic meshing load of helical gears and temperature effects hinders a deeper understanding of the transient performance of gearbox planetary sliding bearings. Additionally, research on shape modification for gearbox planetary sliding bearings remains inadequate. This study develops a comprehensive tribo-dynamics model that considers the dynamic meshing forces of helical gears and temperature effects. The model's effectiveness is validated by the concordance between experimental data from a full-size test bench and simulation results on oil film thickness and temperature. Transient simulation analysis indicates insufficient lubrication, high-temperature rise, and severe contact that reduce electricity production efficiency and reliability, all of which occur at bearing axial edges. Therefore, three modified bearing designs (super-elliptical, trapezoidal, and quadratic shapes) are introduced, and their improved performance is thoroughly compared. The super-elliptical design increases the minimum oil film thickness by 2.60 μm. The trapezoidal design reduces cumulative friction energy losses by 4.34 %. Each modified design successfully reduces the edge wear and oil temperature. The underlying enhancing mechanisms are revealed to be oil film uniform redistribution and lubrication states' alteration. This work can contribute to the reliability, electricity production efficiency, and economy of global wind turbines and support the achievement of net-zero emission goals.

Investigations on mesh stiffness functions in three-dimensional spur and helical gear models. Definitions and numerical simulations

A definition of mesh stiffness as a scalar function connecting spur and helical three-dimensional pinions and gears is presented along with its conceptual limitations. Since it relies on global parameters namely, variations in torque and transmission errors, it can therefore be applied to the vast majority of the models found in the literature. In parallel, a multi-foundation (MF) model of mesh interface is introduced with the objective of being as accurate as three-dimensional finite element (FE) simulations for highly reduced computational costs. Numerous results on mesh stiffness and tooth contact conditions are presented for unmodified spur and helical gears. It is shown that the proposed mesh stiffness functions based on global parameters are sound and that the MF and FE results compare well, particularly when gear body deflections are limited. The contributions of off-line of action contacts, elastic couplings when several tooth pairs are loaded and axial deflections in helical gears are analysed. Finally, the notion of mesh stiffness function representative of the elasticity of a pinion-gear pair for static and dynamic conditions is examined.

Dynamic Analysis of Helical Gears Considering Friction

The use of high contact ratio (HCR) gears is an effective method to reduce single tooth loads, as well as vibration and noise, making the application of helical gears increasingly widespread. Although the presence of helix angles can cause significant relative sliding, the presence of more teeth in contact makes HCR gears more sensitive to surface quality. The existing literature mainly investigates geometric optimization, load distribution, or efficiency calculation of helical gears. The research on the influence of rough surfaces on the dynamic performance of helical gears is very limited. To this end, a multi degree of freedom mathematical model of static transmission error was established based on the 2-DOF system. The relative sliding friction was studied using different friction coefficients, and the influence of different friction coefficients on the gear system was analyzed in detail. The numerical results indicate that surface roughness has a relatively small impact on the dynamic transmission error of the system, but has a significant impact on the motion and friction in the direction of departure.

Investigation on meshing characteristics of spiral bevel gear under wear fault evolution with assembly errors

Spiral bevel gears have the advantage of transmitting high torque and power comparing to helical gear and straight bevel gear. However, they are susceptible to wear due to factors such as high loads, poor lubrication, and surface imperfections resulting from machining. In this study, we propose an autonomous model for predicting tooth wear and analyze the meshing characteristics of spiral bevel gear (SBG) pairs under different assembly errors. Concurrently, we establish a finite element model to validate the accuracy of our meshing characteristic analyses. We also compare the distribution patterns of wear depth on the tooth surface with existing literature. Our investigation delves into meshing characteristics, encompassing transmission errors and Time-varying mesh stiffness (TVMS), considering wear evolution under assembly errors. The results demonstrate that the fluctuations in TVMS remain consistent across all four types of assembly errors examined. Gear tooth wear leads to an increase in gear backlash and fluctuations in unloaded transmission error. The meshing stiffness fluctuation of the SBG pair enlarges under wear evolution. Assembly errors result in shifts in the initial contact line and contact pattern, subsequently altering the distribution of wear depth. Different forms of assembly errors may cause a similar effect on the distribution of wear depth and meshing characteristics.

Exploring Fatigue Crack Initiation in Helical Gears: Impact of Carburization and Frictional Influences

A computational model is presented to analyze the fatigue crack initiation period in helical gears, incorporating considerations for heat treatment via carburization and friction effects. The aim is to determine the number of stress cycles necessary for the initiation and growth of initial cracks, while investigating the impact of dynamic behavior. This study employs a dynamic gear model with two degrees of freedom in torsion, developed using MATLAB, and incorporates the Papadopoulos criterion for fatigue analysis. The computational results are benchmarked against the strain-life method. The findings underscore the significant influence of the friction coefficient between surfaces, heat treatment, and dynamic loads on the growth of initial fatigue cracks. For instance, with a friction coefficient (μ) of 0.5, the initial crack forms on the tooth surface (y=0) in both methods, with the (ε-N) method suggesting 28-65 cycles and the Papadopoulos criterion indicating 101-156 cycles. The latter accounts for the greater influence of residual stresses. Additionally, untreated gears exhibit a minimum number of loading cycles for initial crack appearance at 1.07 × 104 cycles. In contrast, carburized gears demonstrate an extended lifespan, requiring 1.45 × 105 loading cycles for crack initiation in our example. This emphasizes the efficacy of carburization in enhancing gear durability.

Loaded tooth contact analysis for helical gears with surface waviness error

Meshing characteristics are crucial for the transmission performance of vibration noise and strength of gear systems. Gear transmission error has been acknowledged as a prominent excitation in vibration systems, but the surface waviness deviations that directly affect it in contact analysis are generally ignored. This study proposes a comprehensive model for quasi-static analysis of tooth surfaces with waviness error. The model reconstructs the actual tooth surface in reverse based on the gear Fourier measurement principle. Instead of solving the meshing equations to pre-assume contact position, the problem of normal contact between surfaces with deviations is solved by an innovative multiscale grid and a local iterative numerical algorithm. Combining the finite element numerical method and surface integral of the Boussinesq solution determines gear deformation and develops a loaded contact model. The validity of the model is verified through numerical examples. Furthermore, the proposed model is applied to discuss the tooth surfaces with different waviness amplitudes, frequencies, and distribution angles for the first time. It explains the interaction between local microscale and global scale introduced by waviness error on tooth surfaces and reveals the mechanism of the waviness error on meshing performance.

Geometry strategies for the repair of cylindrical gears teeth using laser-directed energy deposition

Gears are essential components in power transmission systems. The replacement of the transmission of a wind turbine can reach more than $300 000 and face long lead times. Previous studies have shown that laser-directed energy deposition (L-DED) has the potential to be used in the repair of gears. However, there is a lack of understanding of the appropriate toolpath planning strategies and their impact on the performance of the gears repaired by L-DED. In this work, we study several strategies for the repair of cylindrical (straight and helical) gears. The strategies consider several types of gear tooth failures, allowing for the repair of a portion of the tooth and the reconstruction of the whole tooth. The studied strategies encompass planar and nonplanar slicing procedures. We manufactured several gear teeth to demonstrate the geometrical and kinematic feasibility of some strategies. We performed destructive analyses on the manufactured teeth to check for manufacturing faults. We used AISI 316L for these experiments, although we are assessing and testing powdered materials for their potential use in gear repair using L-DED. Future work will be devoted to the evaluation of the mechanical performance (e.g., wear resistance and bending fatigue) of the teeth manufactured with L-DED.

Predictive Model for Scuffing Temperature Field Rise of Spiral Bevel Gears under Different Machining Conditions

Spiral bevel gears are extensively employed in mechanical transmissions; however, they are prone to adhesive wear when operating under high-speed and heavy-load conditions. Research indicates that the tooth surface roughness of gears significantly influences the friction and wear of the meshing gears. The present study delves into the origins of tooth surface roughness through the integration of the W-M function and fractal theory. Utilizing an involute helical gear with surface roughness for tooth cutting, a three-dimensional model is established with roughened tooth surfaces. This paper introduces an approach to developing three-dimensional gear models with roughness and applies the finite element method to perform thermodynamic analysis on gears exhibiting diverse levels of surface roughness. The thermal analysis of gears with varying degrees of roughness was conducted using the finite element method. Comparative analysis of the results under specific operating conditions elucidated the impact of roughness on tooth surface temperature rise. In order to validate the simulation model, an experimental test platform for spiral bevel gears of identical size was established. This model integrates tooth surface roughness with thermodynamic analysis, allowing for the rapid assessment of tooth surface temperature rise under different machining conditions, and reducing the cost of validating predicted tooth surface load-carrying capacity.

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.

Integrated analysis strategy for detecting gear contact fatigue before reaching failure interruption criterion

Identifying the occurrence of gear contact fatigue failure as early as possible is essential for condition-based maintenance (CBM). Vibration signals can be used to identify gear contact fatigue. However, the use of vibration signals can be challenging due to its complexity, compounded by lower levels of vibration during the initial stages of contact fatigue. The present study details a new algorithm that integrates stand-alone features to correlate the vibrational signal with early failure occurrence. The study aim is to identify the failure in the early stages, before reaching the ISO 6336-5 stopping criterion of 4% damaged area. A damage induction on the flank of helical gears is applied to simulate and characterize the failure occurrence. Damping characteristics with impact evaluation, Kurtosis analysis and the monitoring of the Gear Meshing Frequency are applied to characterize the failure signature. This strategy stands out by the integration of these stand-alone features and their behavior. The algorithm's capacity is verified through durability tests, promoting the natural evolution of this failure mode. Results show a success rate of above 80% at identifying the failure presence before the stopping criterion limit.

Mathematical model and generation analysis for crossed helical gear system

Purpose Crossed helical gears have point contact and their surfaces are subject to high surface stress. Contact stress and root tooth stress are the most common sources of failure in crossed helical gear. This paper aims to study the load-carrying capacity and performance of crossed helical gear teeth with different gear tooth profiles. To overcome defects and reduce the sensitivity to small shaft angle changes. The combined tooth profile is designed to reduce the bending stresses, contact stresses and tooth deflection, and prevent pinion failure in the gearbox. Design/methodology/approach The principle of the method is a line contact is introduced instead of a point contact between two teeth in mesh with each other. The tooth surface of the helical gear is designed and cut by a modified tool. Higher normal pressure angles like 25° and 35° are used. The modified involute is accomplished to eliminate interference between the teeth. Engineering software packages have been applied to generate all crossed helical gears gear profiles. The modification is compounding curves consisting of an epicycloid-involute-hypocycloid gear teeth profile generated by the cutter modified. Findings The stresses in the crossed helical gear teeth profile were reduced by increasing the normal pressure angle values. Using a 35° pressure angle the enhancement percentage in contact stress and teeth fillet region will be about 29.345% and 15.421%, respectively. The best enhancement in a gear’s resistance is the epicycloid-involute-hypocycloid gear teeth profile. The enhancement was 32.610% and 18.588%. The skew in line of action in skewed helical gear will be sensitive when the crossing angles are small. Their teeth surface tends to be easily worn out; however, the wearing process will be reduced by using a proposed gear teeth profile. Practical implications The gear teeth to be modified are cut by a shaper process. The modifying rack cutter of this study can be used as a reference for creating a different helical gears sample. The helical teeth surface is modified to become an envelope of the other. This makes an original point contact change into a line contact. The epicycloid-involute-hypocycloid gear teeth profile is preferred for a higher contact ratio and a large load capacity. This work explicitly introduces a new method of kinematic consideration to improve the load capacity of crossed helical gear. Originality/value This paper showed some novel results by the unique shape of the rack-cutter designed to generate different helical angles and different gear positions. In the future, it will make valuable contributions to the further development of the dynamic performance of a crossed helical gear system through the study in the field of using asymmetric teeth profiles of helical gears with tip relief as the manner to enhance the crossed helical gear performance. Investigation of crossed helical gear by applying a predesigned parabolic function of transmission error enables the absorption of linear discontinuous functions caused by misalignment.

Evaluation of Scuffing Load Capacity of Helical Gear Based on the Tribo‐Dynamic Model

ABSTRACTThe scuffing load capacity of gear is closely related to the meshing temperature rise of tooth surface. The key to predict the temperature rise is to establish an accurate meshing temperature rise model. In the paper, a tribo‐dynamic model of helical gear is established through coupling of tooth surface lubrication parameters, and the influence of temperature rise on ambient temperature during meshing process is considered. Then, the effects of oil supply temperature, input speed and torque on tooth surface temperature rise, film thickness, friction excitation and gear dynamic characteristics are discussed. The results show that the temperature rise of the gear is higher during the engaging‐in and engaging‐out regions. Meanwhile, there is local high temperature at the end of the contact line due to the end effect. The vibration of gear along the off‐line‐of‐action direction is mainly determined by friction excitation. With the increase of oil supply temperature, input speed and torque, the risk of scuffing failure increases and the influence of oil supply temperature and input load is more significant. The conclusions of this paper may provide some valuable suggestions for the anti‐gluing failure design of gear in engineering.

Geometric Parameter Optimization for Axial Modification in Helical Gear Form Grinding

During the axial modification in helical gear form grinding, the contact line between the grinding wheel and the gear constantly changes, and the additional radial motion can cause a “tooth surface twist” phenomenon. An optimization method for tooth surface twist error was proposed to address this. Based on the gear meshing principles, a mathematical model for axial modification in form grinding was established to solve for the instantaneous contact lines at various positions on the actual modified tooth surface. By analyzing the influence of the grinding wheel installation angle on the axial modification contact line, an optimization model was constructed to reduce the twist of the transverse profile, reduce the twist of the flank profile, reduce the helix deviation, and improve the form grinding efficiency. The practical implications of this research are significant, as the Particle Swarm Optimization (PSO) algorithm was employed to optimize the form grinding parameters, leading to a method that effectively reduced tooth surface twist error and improved the form grinding accuracy of the modified tooth surface.

Computerized generation, deviation correction and rapid tooth contact analysis of helical face gear

This paper delves into the generation of helical face gears using a grinding worm. It investigates the computerized generation process and explores the inherent geometric constraints associated with the application of a grinding worm for helical face gears. An approximate grinding method, tailored for helical face gears featuring large helix angles, is proposed, with an evaluation of the resulting theoretical deviations. Furthermore, a novel rapid computational approach for determining the bearing contact of helical face gear pairs is introduced and validated through Finite Element Analysis (FEA). The subsequent analysis comprehensively examines the effects of the machine tool positioning errors on tooth flank deviations, bearing contact, and transmission errors. A sensitivity matrix is developed to elucidate the relationship between machine tool positioning errors and the tooth flank deviations, leading to the proposition of a correction method for theoretical generating deviations. Finally, the paper introduces a tooth flank modification method for helical face gears and the meshing performance is highly improved.

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.

Evolution of tooth surface morphology and tribological properties of helical gears during mixed lubrication sliding wear

In mixed lubrication, the interplay of lubricant flows, solid asperity contact, and material wear between tooth surfaces creates complex and unpredictable contact states on tooth surface. To comprehensively understand the interaction between the lubrication and wear characteristics of the rough tooth surfaces of helical gears, this study established a mixed lubrication sliding wear calculation model for helical gears based on the mixed elastohydrodynamic lubrication model and Archard’s model. Specifically, the study aimed to examine the effects of surface topography features on average film thickness, contact area ratio, and accumulated wear at the meshing point. The findings demonstrated that the texture and power spectral density distributions of a non-Gaussian reconstructed surface closely resembled those of the actual ground surface. Furthermore, for non-Gaussian rough surfaces, a larger wavelength ratio enhanced microwedge motion, which increased film thickness and reduced wear. Additionally, a negatively skewed surface demonstrated better lubrication performance compared to both positively skewed and Gaussian surfaces. This improved performance is evident in the smaller contact area ratio and lower accumulated wear value of the negatively skewed surface.

Analytical investigation on load sharing characteristics and speed difference of coaxial reverse closed differential herringbone gear transmission system with floating gear and errors

To investigate the influence of gear floating on the load sharing characteristics of the Coaxial Reverse Closed Differential Herringbone Gear Transmission System (CRCDHGTS) and the rotational speed difference between the upper and lower rotors, a dynamic Bending-Torsional-Axial-Pendular (BTAP) model of the CRCDHGTS was established using the centralized parameter method, which considers various excitation factors such as gear floating, errors, Time Varying Meshing Stiffness (TVMS), gyroscopic effect, and tooth friction. It considers the interaction between the closed-stage gear set and the differential-stage gear set, treating the herringbone gear as a symmetric helical gear connected through a receding slot. The dynamic model was solved using the Runge-Kutta method to obtain the dynamic meshing forces for each gear pair under single and combined floating modes. The Dynamic Load Sharing Coefficient (DLSC) of the system, which characterizes the Load Sharing Performance (LSP), was deduced. The load sharing characteristics of different floating modes were analyzed, as well as the influence of different floating displacement on the DLSC. The motion path of the gear floating was also determined. Additionally, the impact of manufacturing error and assembly error of each component on the DLSC under combined floating mode was analyzed. Finally, the influence of gear floating on the output rotation speeds of the upper and lower rotors of the system was investigated. The results indicate that both free-floating of the center gear and combined floating can effectively improve the LSP of the system. When the system adopts combined floating mode, the DLSC of inner and outer meshing changes between 0.91 and 1.09, demonstrating a significant improvement in the LSP. The DLSC of the system increases with the increase in error, with the eccentricity error having a greater impact on the DLSC compared to the assembly error. The optimal floating value for the sun gear is between 0.6 mm and 0.8 mm, while for the planetary gear, it is between 0.4 mm and 0.6 mm. The rotational speed difference between the upper and lower rotors can be controlled within 1r/min. These research findings provide a theoretical basis for further analysis of the dynamic stability and reliability of the system.

The Design and Analysis of the Helical Gear in the Car Gear Box for the Slag Port Transfer

The design and analysis of helical gears with involutes profiles is the primary focus of this study. The most widely utilized gearing system in use today is the involutes gear profile. Power and torque are typically transmitted through them. When compared to other forms of transmission, the efficiency of power transmission via gears is extremely high. Bending and contact stress are the main causes of gear tooth failure. The current study examines helical gear, which has to do with slag transfer in the steel production sector. The most affected stress concentrated location of any set of gears in the slag port transfer car (SPTC) gear box is identified by examining the contact stresses for the current design set of gears. The high stress concentration gear set was redesigned with a constant (45mm) face width at various Helix angles (14, 15, 16, 17, 19^, 20 ̊, 25^, and 30 ̊) and a constant pressure angle (20). To calculate the contact stresses between two gears that are mating. The robust and cutting-edge solid modeling program AUTODESK FUSION 360 creates a three-dimensional solid model. The ANSYS Workbench module was utilized to do the numerical analysis. The outcomes of the workbench module for ANSYS. The current study is helpful in quantifying the previously mentioned factors, which aids in the safe and effective design of the helical gear in the SPTC Gearbox.