Gear Research Articles

Study on the Tribological Properties of DIN 16MnCr5 Steel after Duplex Gas-Nitriding and Pack Boriding.

DIN 16MnCr5 is commonly used in mechanical engineering contact applications such as gears, joint parts, shafts, gear wheels, camshafts, bolts, pins, and cardan joints, among others. This study examined the microstructural and mechanical properties and tribological behavior of different surface treatments applied to DIN 16MnCr5 steel. The samples were hardened at 870 °C for 15 min and then quenched in water. The surface conditions evaluated were as follows: quenched and tempered DIN 16MnCr5 steel samples without surface treatments (control group), quenched and tempered DIN 16MnCr5 steel samples with gas-nitriding at 560 °C for 6 h, quenched and tempered DIN 16MnCr5 steel samples with pack boriding at 950 °C for 4 h, and quenched and tempered DIN 16MnCr5 steel samples with duplex gas-nitriding and pack boriding. Microstructure characterization was carried out using metallographic techniques, optical microscopy, scanning electron microscopy with energy-dispersive spectroscopy, and X-ray diffraction. The mechanical properties were assessed through microhardness and elastic modulus tests using nanoindentation. The tribological behavior was evaluated using pin-on-disc tests following the ASTM G99-17 standard procedure under dry sliding conditions. The results indicated that the surface treated with duplex gas-nitriding and pack boriding exhibited the highest wear resistance and a reduced coefficient of friction due to improved mechanical properties, leading to increased hardness and elastic modulus.

A numerical model for total bending fatigue life estimation of carburized spur gears considering the hardness gradient and residual stress

A numerical model for total bending fatigue life estimation of carburized spur gears considering the hardness gradient and residual stress

Model Analysis Of Worm Gear Pair System Using Finite Element Analysis

Spur gear, helical gear, worm gear, and bevel gear are all important components in industrial applications such as vehicles, pushes, conveyors, elevators, bowl mill, rolling mills, ribbon blender, machine tools, aeroplanes, and windmills. When various types of defects, such as wear, tooth breakage, corrosion, and scratches on bearings, appear in gearboxes, normal machine function may be abruptly terminated. As a result, output and dependability suffer. As a result, several quality tracking and evaluation approaches have been adopted by companies. Finite element analysis (FEA) is one of the approaches. This research paper presents the FEA of a ribbon blender worm gear pair by using Ansys 18.0 to identify the weak gear of the worm gear pair, natural frequency, and deformation. Proe-5 utilized for creation of three-dimensional geometry of threaded worm and toothed worm wheels, as well as other related elements such as shafts and bearings. Steel is used for the worm, shaft, and bearing, whereas bronze is used for the worm wheel. Ansys 18.0 is implemented to carry out worm gear pair model analysis. The results demonstrate that the worm wheel had the most deformation when compared to the worm, and that the natural frequency is greater than the operational frequency of the worm gear pair. The findings of the research study, worm wheel deteriorate early than worm, model analysis plays a significant role in vibration monitoring of worm gear pair, and this work is valuable for further fault analysis of ribbon blender worm gearbox utilising vibration response.

A Poly(Ionic Liquid)‐Based Polymer Binder for Endurable Lithium–Sulfur Batteries

AbstractThough polyvinylidene fluoride (PVDF) is widely‐used binder for conventional lithium‐sulfur (Li–S) batteries, it still encounters challenges of severe electrode fracture involved by drastic volume change upon repeating cycling, and lack of extended‐functions like trapping dissolved polysulfides and smoothing Li+ transfer. Herein, a methodology of grafting sulfophilic hydrogen‐bond donor and lithiophilic hydrogen‐bond acceptor to the polymer binder (named as PIL), function as gear teethes and tooth spaces, is reported. When cracks occur, the engaged gears driven by dynamic hydrogen bonds are separated, which are spontaneously reformed owing to the automatic meshing of gears, and thus accelerate the healing of cracks. At the molecular level, the synergetic effect of sulfophilic hydrogen‐bond donor and lithiophilic hydrogen‐bond acceptor enables polysulfides immobilization through “push‐pull effect”, facilitating the subsequent redox kinetics. Accordingly, the cross‐link network of hydrogen bonds endows the elaborated designed polymer binder with strong adhesive strength and rapid Li+ migration. Attributed to these beneficial properties, the PIL‐based sulfur cathode exhibits excellent rate performance and superior cycling durability (an ultralow capacity fading rate of 0.062% per cycle over 800 cycles at 2 C). Even with high sulfur loading of 9.27 mg cm−2, a high areal capacity of 8.71 mAh cm−2 can be achieved, verifying its potential application.

An analytical approach for predicting the fillet and contact stresses in symmetric and asymmetric spur gears under frictional mesh assumptions

A precise estimation of the bending and contact stresses, as well as the true friction value during the gear mesh, are critical aspects of a cost-effective and safe gear design. Previous studies have usually neglected friction by assuming a frictionless contact. Additionally, the impact of friction on the bending stress of spur gears has rarely been addressed. Moreover, to the authors' best knowledge, the impact of friction on the weakest section, stress concentration factor, and Lewis form factor remain unexplored for both symmetric and asymmetric gears. This study presents an analytical model incorporating friction at different contact locations to calculate the variables related to the tooth's weakest section. This model facilitates the evaluation of the stress concentration factor, Lewis form factor, and maximum tensile stress for symmetric and asymmetric gears. The proposed model is especially beneficial for assessing the load-carrying capacity of spur gears operating in challenging conditions. The results showed that the asymmetric spur gear is superior to its equivalent symmetric counterpart in terms of tooth form factor; however, this superiority decreases as the coefficient of friction increases. In addition, friction has been found to have a greater effect on fillet stress than contact stress. For μ = 0.2, at the HPSTC, the contact load and tooth form factor decreased by 7 % and 12 %, respectively, and the fillet stress worsened by 13 % compared to the frictionless assumption. Meanwhile, at the LPSTC, the stress concentration factor and contact stress increased by 9 % and 3 %, respectively.

Crowning dressing wheel based closed-loop topology modification approach for internal-meshing power gear honing

Crowning dressing wheel based closed-loop topology modification approach for internal-meshing power gear honing

Addendum To: Geometric design, modelling and finite element analysis of spur gear pairs having normal teeth based on the modification of the pressure angle

Addendum To: Geometric design, modelling and finite element analysis of spur gear pairs having normal teeth based on the modification of the pressure angle

Addendum To: Manufacturing of spur gears having normal teeth on different pressure angles by module disc milling cutter

Addendum To: Manufacturing of spur gears having normal teeth on different pressure angles by module disc milling cutter

A high-speed gear reshaping method for electric vehicles combining the effects of input torque and speed variation.

In this study, we introduce an optimization method for high-speed gear trimming in electric vehicles, focusing on variations in input torque and speed. This approach is designed to aid in vibration suppression in electric vehicle gears. We initially use Tooth Contact Analysis (TCA) and Loaded Tooth Contact Analysis (LTCA) to investigate meshing point localization, considering changes in gear tooth surface and deformations due to load. Based on impact mechanics theory, we then derive a formula for the maximum impact force. A 12-degree-of-freedom bending-torsion-axis coupled dynamic model for the helical gear drive in the gearbox's input stage is developed using the centralized mass method, allowing for an extensive examination of high-speed gear vibration characteristics. Through a genetic algorithm, we optimize the tooth profile and tooth flank parabolic modification coefficients, resulting in optimal vibration-suppressing tooth surfaces. Experimental results under various input torques and speeds demonstrate that the overall vibration amplitude is stable and lower than that of conventional gear shaping methods. Specifically, the root mean square of vibration acceleration along the meshing line under different conditions is 58.02 m/s2 and 20.33 m/s2, respectively. The vibration acceleration in the direction of the meshing line is 20.33 m/s2 and 20.02 m/s2 under varying torques and speeds, with 20.33 m/s2 being the lowest. Furthermore, the average magnitude of the meshing impact force is significantly reduced to 5015.2. This high-speed gear reshaping method not only enhances gear dynamics and reliability by considering changes in input torque and speed but also effectively reduces vibration in electric vehicle gear systems. The study provides valuable insights and methodologies for the design and optimization of electric vehicle gears, focusing on comprehensive improvement in dynamic performance.

Vibration Analysis of the Double Row Planetary Gear System for an Electromechanical Energy Conversion System

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.

Computerised design, simulation of meshing and stress analysis of bionic logarithmic spiral spur gear drives

Inspired by the inherent properties of logarithmic spiral in nature, a new cylindrical spur gear drives using logarithmic spiral as a gear tooth profile is proposed. The logarithmic spiral property is explored, and then the equation of meshing, conjugate tooth profile and contact path of the proposed gear pairs are derived. The meshing characteristics of the new pair are investigated, such as pressure angle, contact ratio and sliding ratio. Simulation analysis of the strength, transmission error and transmission efficiency are used to validate the performance of the gear pairs before production of the proposed gear, followed by gluing load capacity and bending fatigue strength testing of the fabricated gear pairs. The results show that the pressure angle at any point of the tooth profile on the proposed gear is constant and equal to the logarithmic spiral strike angle. The contact ratio of the gear decreases with the increase of the strike angle. Compared with that of involute gears, logarithmic spiral gears have better performance in terms of strength, transmission error, transmission efficiency and lifetime.

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.

THE INFLUENCE OF THE OPTIMIZATION OF THE SPUR GEAR BODY ON THE MESHING STIFFNESS

The design of the body shape of spur gears has an effect on the deformation and thus also the stiffness of the gearing. The stiffness of the gearing is a parameter that significantly affects the noise level of transmission mechanisms. Determining the gear stiffness is difficult due to the shape of the gear teeth. The paper examines the influence of the shape and size of individual gear body parameters on gear deformation. Deformation is solved by finite element method. On the basis of the deformation of the gearing, the stiffness of the gearing is determined.

Method for a Comprehensive Analytical Study of Contact Pressures, Wear, and Durability of Metal-Polymer Helical and Spur Gears with Steel Pinion and Polyamide Gear

An analytical complex study of metal-polymer (MP) helical and spur gears by a new author's analytical method was carried out. The influence of the helix angle on the contact pressures in the engagement, the teeth wear, and the durability of the MP gears of different polymers has been established. MP gears with a pinion made of carbon steel (0.45% C) and gear made of basic polyamides PA6, PA66, and their composites with the following fillers: fiberglass (PA6+30GF), carbon fiber (PA6+30CF), molybdenum disulfide (PA6+MoS2), and oil filled cast polyamide (PA6+Oil) are studied. According to the developed procedure for determination of the angles of engagement parity change, it is shown that there is two-one-two-pair or three-two-three-pair engagement depending on the helix angle. Quantitative and qualitative regularities of changes in the initial maximum contact pressures and their reduction due to tooth wear over the time from the moment of the entrance of teeth to engagement up to their exit from it are established. In particular, at a helix angle of β = 10°, the contact pressures reduce to 33% compared to spur gears. The linear wear of the gear polymer tooth profile at selected points of engagement and different helix angles has been investigated, and the influence of the pressure angle on it is shown. It is established that its regularities of change during the engagement phase are the same for all polymeric materials studied. The durability of transmissions is calculated, and its comparative evaluation is given. At the helix angle β = 5°, a slight increase in durability is achieved compared to spur gears, and at β = 10° the durability of MP gears increases by about 1.5 times for all polymeric materials studied.

Study on multi-state of meshing-impacting dynamic characteristics of spur gear systems considering friction under localized tooth breakage

Localized tooth breakage is one of the common failures of spur gears, which affects the smooth and safe operation of spur gear transmission systems. The tooth collision cannot be neglected, and it is especially important to reveal the meshing-impacting dynamic characteristics of the gear system under localized tooth breakage to improve the safe and stable operation of the gear system. Based on the gear meshing principle and the dissipative collision contact force model, the drive-side tooth meshing model and back-side tooth impacting model are established with considering the transient nature of tooth back-side contact. The tooth surface meshing model and tooth back collision model under partial breakage are established. According to the contact state and force environment of the gear pair, the multi-state meshing-impacting behaviour under local breakage is classified, and the discrete meshing-impact dynamics model of an involute spur gear system under local breakage is established to explore the influence of local breakage on the meshing stiffness and load distribution. The mechanism of contact force under partial tooth breakage is revealed, and the influence of load coefficient and meshing frequency on the nonlinear dynamics is studied by defining two Poincaré maps. It is found that local tooth breakage affects the contact force of single-and double-tooth meshes and reduces gear load carrying capacity. Larger loads inhibit back-side impact, and smaller loads induce the coexistence behaviour and back-side impact. Larger or smaller meshing frequency induce back-side impact behaviour. The coexistence of chaotic and periodic motions induces back-side impact behaviour, and localized tooth breakage affects the coexistence phenomenon and aggravates the complexity of the dynamic behaviour. The dynamic model of gear system considering energy dissipation and nonlinear vibration under the presence of local tooth breakage of the pinion is explored, and the conditions of back-side impact are studied. This research provides new methods and ideas for nonlinear dynamic modelling and analysis of faulty gear systems.

Crack initiation life of aviation gear pair

Abstract The gear transmission system is an important part of the aero-engine. The most serious fault is tooth root fatigue fracture. This paper mainly discusses the time of fatigue crack initiation stage of aviation gear tooth root position. The crack initiation state can be evaluated by analyzing the root stress. The static contact analysis is solved by using the generated aviation gear pair model. The maximum stress in the bending direction of gear teeth is calculated. The changing pattern of tooth root stress with meshing position is described in detail. According to the multi-axial stress fatigue theory, the surface damage parameters and fatigue life of the gear tooth root position are calculated, and the location of the crack initiation is obtained. Fatigue cracks often appear at half of the gear tooth width and near the tooth root circle.

Accelerated testing of the Wear Behavior of 3D-printed Spur Gears

This paper presents the results of an in-depth investigation of 3D-printed plastic gears made of ABS, PLA, and annealed PLA. Wear tests performed on a specialized rig underscore the superior wear resistance of ABS gears, while the annealing process shows a modest improvement in PLA gear durability. The novelty of this study is a comprehensive evaluation of the wear behavior of different 3D printed materials under different loading conditions. This study introduces an innovative accelerated testing method, emphasizing efficiency in product development through reduced testing durations and adaptability to various scenarios.

Analysis of crack propagation and life estimation of spiral bevel gears with root cracks

Abstract In order to study the effect of tooth root cracks on the fatigue life of spiral bevel gears, a certain spiral bevel gear was taken as the research object, and the mechanism of tooth root fatigue cracks was analyzed based on crack propagation theory; By combining the extended finite element method and the level set method, an initial crack propagation finite element model is established. The crack location of the gear teeth is determined through static analysis of the gear pair, and the influence of alternating loads on the initiation and propagation life of tooth surface cracks is studied. The analysis results indicate that the number of load cycles required for each crack propagation after its first occurrence gradually decreases; The crack propagation path of gear cracks under fatigue load is consistent with the actual tooth surface fracture surface; Realize life estimation from crack propagation to fracture failure.

Robust phase unwrapping algorithm for gear interferometry based on mutual information and adaptive spin-inpainting approaches

An enhanced robust phase unwrapping algorithm for gear tooth flank measurement by laser interferometry is proposed. The method integrates wrapped phase mutual information estimation with an adaptive spin-inpainting strategy, resulting in improved quality phase maps to guide the phase unwrapping process. Mutual information estimation is employed to investigate potential phase relationships among interference fringes in the wrapped phase map, forming the foundation for the suppression and recovery of abnormal fringes. The adaptive spin-inpainting method, which adjusts in response to fringe density, plays a crucial role in efficiently addressing the restoration of abnormal fringes and obtaining the optimized quality map. With the enhanced new quality map, the approach yields optimized results, enabling a concurrent assessment of unwrapping process efficiency and quality. Several simulations and experiments were conducted to validate the effectiveness of the proposed method. Comparative analyses against commonly employed methods consistently demonstrate the superior performance of the proposed algorithm.

Instantaneous mesh load factor (Kγ ) measurements in a wind turbine gearbox using fiber-optic strain sensors

The mesh load factor, Kγ , describes how loads are shared between planet gears and has become one of the key design challenges in modern wind turbine gearboxes. Planet load sharing directly impacts tooth root stresses, a critical driver of torque density and gearbox reliability. Experimental evaluation of Kγ is typically performed from sun gear tooth root strain gauge measurements, which are complex. Furthermore, such measurements can only provide an average value of load sharing. The present study describes an alternative method to evaluate the mesh load factor in wind turbine gearboxes based on fiber-optic strain sensors installed on the outer surface of the fixed ring gear. We present the results of an extensive measurement campaign to evaluate this novel sensing solution installed on the input planetary stage of a 2-MW wind turbine gearbox at the National Renewable Energy Laboratory’s Flatirons Campus (Colorado, USA). The number of strain sensors on the ring gear was selected as an integer multiple of the number of planets, which has enabled an instantaneous evaluation of the mesh load factor. The effect of operating conditions on the planet load-sharing behavior of the gearbox has been investigated. The mesh load factor measured for operating conditions close to rated was below 1.05, well below IEC 61400-4 standard requirements.