Gear Contact Stress Research Articles

Analytical Calculation of the Tooth Surface Contact Stress of Cylindrical Gear with Variable Hyperbolic Circular-Arc-Tooth-Trace

In order to theoretically research the tooth surface maximum contact stress of a Cylindrical Gear with Variable Hyperbolic Circular-Arc-Tooth-Trace (VH-CATT), the computing formula of maximum contact stress of VH-CATT cylindrical gear is investigated according to Hertz formula in this paper. Insufficient contact fatigue strength will lead to pitting corrosion, plastic deformation of tooth surface and other damages. Therefore, the maximum contact stress of tooth surface must be carried out. The contact stress calculation formula is particularly considering the effect of normal force, total carrying length, synthetical curvature radius, and position angle. The present work establishes analytical solutions to research the effect of different parameters for the contact stress of VH-CATT cylindrical gear incorporating elastic deformation on the tooth surface, and which have shown that the different module, transmission ratio, pressure angle, tooth width, and the cutter head radius have a crucial effect on the contact stress and contact ellipse of VH-CATT cylindrical gear along the tooth width direction. Moreover, a finite element analysis is carried out to verify the correctness of the theoretical computing formula of contact stress of VH-CATT cylindrical gear. By contrast with the theoretical calculated value and the stress value of finite element analysis, its error is very small. It is indicated that the derived formula of contact fatigue strength of VH-CATT cylindrical gear has high accuracy and can accurately reflect the real contact stress value of tooth surface, which is beneficial for research on tooth break reduction, pitting, wear resistance and fatigue life improvement of the VH-CATT cylindrical gear. The study results also have a certain reference value for the design and check calculation of the VH-CATT cylindrical gear.

Correlation between surface roughness parameters and contact stress of gear

To reveal the relationship between rough tooth surface microstructure characteristics and contact performance, contact analysis is carried out based on the measured surface topography of the tooth surface of ultrasonic grinding by utilizing the elastic-plastic contact mechanics and statistical correlation analysis theory. Simple correlation analysis and partial correlation analysis are adopted for the gear three-dimensional surface roughness parameters and the maximum Mises stress and maximum shear stress. Then, the method of stepwise regression analysis and path analysis is used to construct the best fitting linear model of 3D roughness parameters and the maximum Mises stress and maximum shear stress, and the parameters’ decision coefficient is obtained. The research shows: (1) the rank of comprehensive influence factors of the maximum Mises stress is as follows: arithmetical mean height ( Sa), peak material portion ( Smr1), maximum peak height ( Sp), reduced peak height ( Spk), and minimum curvature radius and height ratio ( K), where Smr1, Spk, and K are negatively correlated with the maximum Mises stress; (2) the comprehensive influence variables of the maximum shear stress are in the order of Sa, Spk, and Vmp, among which Spk and Vmp are inversely related to the maximum shear stress.

Design and Fatigue Analysis of an E-Drive Transmission System of Single-Speed Gear for Electric Vehicle

Design an e-drive transmi ssion gear , it is very crucial, to understand the failure modes since gears should be sized correctly to withstand loads that will expect to act on the gear teeth and make sure that still be within reasonable load-carrying capacity, compact and light weight. Fatigue failure can happen on gears under repeated loading due to fatigue such as tooth root bend ing and contact stress of gear. M aterials used in this study were two candidate alloy steels of Cr-Mo and Cr-Mo-Ni and methods employed to design the e-drive transmission gear were by iteration through KISSsoft gear simulation software as well as AGMA of Matlab script, it approaches various parameters such as helix angle, face- width , and input torque . Investigations on safety factors of root bending and contact , stresses of contact and bending , weight, compactness, qui e t and smooth functioning have been done by altering the variable design parameters . To conclude that by increasing face width and helix angle both safety factors were increased uniformly regardless of the in put torque as we calculated by both approaches. Similarly , the results showed that by increasing the helix angle and face width it brings to reduce the contact and bending stress es of transmission gear . As we comparing the results , the KISSsoft values are a little higher than the analytical (AGMA) values as proven in all fatigue of safety factors versus variable gear design parameter. Based on the sa fety factor, compactness, light weight and quiet for smooth function of the designed e-drive mating gears are proven as the face width is 24.5 mm and the helix angle is 25 o .

Investigation on contact and bending stress of face-hobbed and face-milled hypoid gear

The tooth strength performance of face-hobbed and face-milled hypoid gears under the same work condition is a controversial research hotspot. In this paper, the load capacity of face-hobbed and face-milled hypoid gears has been studied based on finite element analysis method and conventional international standards. The stress comparison for contact and bending stress between two types of gears have been conducted. The accurate mathematical model of face-hobbed and face-milled hypoid gear were established based on the generating and forming process. The statistical method was used to assess the contact and bending stress. Results show that the values of bending stress of face-milled gear are about 20–30% larger than those of face-hobbed gear. For the contact area with high stress (800–1300 MPa), the proportion of face-milled hypoid gear is much more than that of face-hobbed gear. The standard deviation values of contact point stress for face-milled hypoid gear are 7.1% higher than those of face-hobbed gear. The strength results by standards and finite element analysis results can verify with each other consistently. Both results contribute that face-hobbed hypoid gear has better tooth strength under the same condition.

Contact Stress and Fatigue Analysis of Spur Gear

Spur gear is the most basic type of parallel-axis gear. In this study, contact stress and fatigue life of spur gear for different modules and for different materials were studied. The commercially available Solidworks 2016 is used for modelling and ANSYS Workbench tool for discretizing and solving. The analysis has been performed on the gear models of modules 1mm, 2mm and 3mm to observe the distribution of contact stress and life. The graphic results obtained were compared and it was found that contact stress decreases as the module increases and also aluminium alloy was having the least stress and high fatigue life among the selected materials. Hence from the finite element analysis, it’s found that the contact stress depends on the module and material used. Similarly fatigue life of gear purely depends on the material chosen.

Power loss prediction in asymmetric spur gear considering gear tooth dynamic load

In many gear drives, one side of the flank is subjected to relatively higher load for a longer duration than the other side. Asymmetric spur gears with drive side pressure angle higher than the coast side reflects this functional difference. Conventional design criteria and procedures followed for symmetric spur gears are suitably modified and applied to predict the gear tooth bending, contact stress and power loss in asymmetric spur gears. Quasi-static gear tooth load and empirical friction coefficient formulae were applied in the past to predict the sliding power loss in asymmetric spur gears. In the present work, Finite element method is used to determine the time varying mesh stiffness of the normal contact ratio asymmetric spur gear tooth. Computed gear tooth stiffness is used to predict the dynamic load at two different speeds under non-extended contact condition. Sliding power loss during the course of meshing is analytically calculated under quasi static and dynamic load conditions. Study demonstrates the difference in sliding power loss computed based on friction formulae and empirical friction coefficient formulae under static and dynamic load.

Contact stress and bending stress calculation model of spur face gear drive based on orthogonal test

As the stress of gears determines the reliability of transmission, the stress research of face gear drive has great significance from the perspective of both theory and practice. The finite element model of orthogonal spur face gear meshing is attained via root-top section lofting method. The geometry parameters (include modulus, teeth number of face gear, teeth number of pinion and pressure angle) and transmission parameter (nominal contact force) are considered in the stress modeling. This paper, respectively established the empirical equations for contact stress and bending stress of face gear and pinion through stepwise regression by using single factor test and orthogonal test. The empirical equations have been validated by comparing them with results obtained from FEA.

Analysis and formulation of spur gear stresses with different tip modifications

Spur gears are widely used in the power transmission mechanism of several machines. Due to the transmitted torque, spur gears experience high stresses which could cause gear tooth failure by surface pitting or root fracture. Tip relief and other gear profile modification have been considered for reducing the induced stresses in the gear tooth. In this work, the influence of tip relief on stresses on a pair of identical spur gear was analyzed using commercial FEA software ANSYS, and formulae for estimating contact and bending stresses were derived. Three cases of gear sets were analyzed; a non-modified pair and another two sets with linear and parabolic tip relief profiles. The non-modified gear set frictionless contact stress was validated against the calculated AGMA pitting resistance, Hertzian contact stress and a reported contact stress value in the literature. The four methods agreed well with each other. Similarly, bending stress was also compared with the AGMA bending strength and Lewis bending stress for validation. Then, friction coefficient was varied from 0.0 to 0.3 with increment of 0.1. The gear contact stress increased up to 11% relative to the frictionless case, whereas bending stress decreased by 6%. Linear tip relief modification was carried out for increasing normalised tip relief values of 0.25 to 1.0 with increment of 0.25. The gear frictionless contact and bending stresses decreased by a maximum of 4% and 2%, respectively. Frictional contact stress increased by up to 7.1% and the bending stress is almost identical with the frictionless case. Parabolic tip relief was also carried out with similar normalised tip relief values. Frictionless contact stress decreased by 5% while frictional contact stress increased by up to 11.5% and the bending stress is also almost identical with the frictionless case. Finally, four formulae were introduced for estimating the contact and bending stresses for a tip modified spur gear.

Meshing performance of spiral bevel gear with different loads and modules considering edge contact by finite element method

To analyze the edge contact of spiral bevel gears, owing to its effect on meshing performance, batch processing is performed based on a static solver and the finite element method (FEM) because of its computational speed advantage. A series of programs automatically perform the functions of modeling, analysis, and extraction of performance indexes. Starting from the entrance meshing position to the exit meshing position, a series of models was built and analyzed to describe the whole meshing process of the gear pair. For a specific gear pair, contact and bending stresses, contact stress patterns, loaded transmission errors, contact forces, and load sharing coefficients are calculated under five different load conditions and the change rules are summarized. Edge contact phenomenon occurs as the load increases to a critical value, resulting in a sharp increase in contact stress. As the load increases, the load sharing coefficient decreases gradually and the absolute value of transmission error increases, but the fluctuation of transmission error first decreases and then increases. In addition, the effect of modules is discussed and the results show that large modulus will decrease stress, contact ratio, and edge contact, but there is a certain module to minimize the fluctuation of transmission error.

Contact Stress Analysis of Spur Gear Under the Different Rotational Speed by Theoretical and Finite Element Method

In this study that spur gears are chosen, contact stress of spur gear is presented under the effect of rotational speed. Three-dimensional simulation of dynamic analysis of gears designed and modeled using ANSYS software. The dynamic analysis included in the determination of dynamic stresses analysis. Contact stress is theoretically calculated and analyzed and numerically estimated using both Hertzian mathematical model and finite element method respectively. Different values of rotational speed used to study its effect on contact stress. Both methods compared by evaluating the percentage error of contact stress, and the modeling of the spur gear and stress analysis of spur gear carried out using SOLID WORK and ANSYS V14, respectively. The most significant note in this study concludes that increasing speed causes vibration and pitting failure due to repetitions.

An Approximate Solution Method of Dynamic Reliability for Wind Turbine Gear Transmission with Parameters of Uncertain Distribution Type

The reliability evaluation of wind turbine system is the theoretical basis for engineering design, and how to deal with its complex wind loads is the technical challenge for it. Considering the distribution type of wind loads is uncertain, the stress-strength interference model based on the assumption of normal distribution can’t be applied to the reliability of wind turbine gear transmission. For this, the dynamic reliability model for wind turbine transmission with uncertain distribution parameters is established firstly with the deterioration of gear contact stress and strength degradation being considered. Then, the dynamic reliability is solved by approximate expansion of the model function into standard normal distribution function based on the stochastic perturbation theory and the Edgeworth series method. In the absence of experimental data, the first four moments of the random parameters with uncertain distribution are obtained by Monte Carlo method. Meanwhile, the dynamic reliability sensitivity to gear parameters is derived by the same method and the sensitivity variation is given which effectively reflecting the influence of gear parameter changes on the system reliability of wind power gear drive, and providing an accurate theoretical basis for the optimal design of the project.

A REVIEW ON STUDY OF BENDING STRESS AND CONTACT STRESS OF HELICAL GEAR AS CALCULATED BY AGMA STANDARD AND FEA

Gears are one of the most critical components in mechanical power transmission systems. The bending and surface strength of the gear tooth are considered to be one of the main contributors for the failure of the gear in a gear set. Thus, analysis of stresses has become popular as an area of research on gears to minimize or to reduce the failures and for optimal design of gears. The helical gears can fail due to excessive bending stress at the root of gear tooth or surface contact stresses. This can be avoided only by minimizing bending stresses and contact stress or by modifying the geometry or parameters of the gear tooth. This paper presents the comparative study of bending stress and contact stress of helical gear using AGMA standard and FEA. Ultimately results of two methods compared with respect to each other.

Characteristics of Reduction Gear in Electric Agricultural Vehicle

In electric agricultural machine a reduction gear is needed to convert the high speed rotation motion generated by DC motor to lower speed rotation motion used by the vehicle. The reduction gear consists of several spur gears. Spur gears are the most easily visualized gears that transmit motion between two parallel shafts and easy to produce. The modelling and simulation of spur gears in DC motor reduction gear is important to predict the actual motion behaviour. A pair of spur gear tooth in action is generally subjected to two types of cyclic stress: contact stress and bending stress. The stress may not attain their maximum values at the same point of contact fatigue. These types of failure can be minimized by analysis of the problem during the design stage and creating proper tooth surface profile with proper manufacturing methods. To improve its life expectation in this study modal and stress analysis of reduction gear is simulated using ANSYS workbench based on finite element method (FEM). The modal analysis was done to understand reduction gear deformation behaviour when vibration occurs. FEM static stress analysis is also simulated on reduction gear to simulate the gear teeth bending stress and contact stress behaviour.

A Comparative Study between a Pair of Cosine Gears and a Pair of Involute Gears: Contact Stress, Root Fillet Stress, and Contact Ratio

Contact stresses, root fillet stresses, and contact ratios of a pair of cosine gears and a pair of involute gears are analyzed and compared in this paper. The mathematical models of pinions and gears are created based on the coordinate transformation theory and the theory of gearing. Static structural finite element analysis is performed by using ANSYS. The assumption of contact of one tooth is not adopted in order to comply with the real situation of meshing. Numerical results have shown that maximum contact stress and maximum root fillet stress of cosine pinion are smaller than those of involute pinion, maximum contact stress of cosine gear is approximately equal to that of involute gear, and maximum fillet stress of cosine gear is smaller than that of involute gear. The pair of cosine gears has a higher strength but a lower contact ratio in comparison with the pair of involute gears. Maximum contact and root fillet stresses can be reduced largely when the number of teeth in contact is increased from 1 to 2.

RESEARCH OF SURFACES OF RESPONSE OF INDEXES OF DURABILITY OF THE HAULING GEARING WITH THE DIFFERENT DEGREES OF WEAR OF PROFILES OF POINTS

The urgency of developments aimed at further improvement of repair technologies for traction gears of railway rolling stock is substantiated. As one of the promising areas of such works, studies have been made of the characteristics of gear engagement with the established wear profiles of gear teeth and wheels using generalized mathematical models of the corresponding indicators. Such dependencies, in addition to calculations and evaluation of the considered variants of completing the repair gears, make it possible to obtain the response surfaces of the corresponding indicators of traction gears. The study of such surfaces, the determination of their appearance, and the construction and analysis of binary sections is important for the justified choice of pinion-wheel pairs in the repair of traction gears. It is proposed to determine the form of the response surfaces and study them on the basis of canonical transformations of generalized mathematical models of the corresponding indicators. The article presents the results of analysis of the surfaces of the response of flexural stresses of gear teeth and contact stresses of teeth of traction gears of electric trains of ER2R series. It is concluded that in order to obtain a comprehensive picture of the effect of the degree of wear of the tooth and gear tooth profiles on the strength indices, it is necessary to analyze their response surfaces.

THE ANALYSIS OF THE SLIPPAGE AND CONTACT STRESS IN THE MESHING OF THE POWER-SHIFT TYPE GEAR

This work is an analysis of gear slippage and contact stresses in toothed gears of a six-shaft power shift gearing. Gear meshing contains 5 characteristic contact points located within the active surface of a tooth. The contact points are as follows: A – beginning of a tooth involute profile located within double-tooth engagement area; B – the end-point of double-tooth engagement constituting the beginning of single-tooth engagement area; C – pitch point, referred to also as the central contact point; D – the last point of the single-tooth engagement being at the same time the starting point of the double-tooth engagement area, which is a part of the tooth tip; and, E – point at the tooth tip that closes the double-tooth engagement area. The location of individual contact points and the resulting slippage and contact stress values depend on the geometrical parameters of cooperating gear wheels. The inter-relationship suggests that, in power shift gearings, the contact points have as many positions within the active surface as there are cooperating gear wheels.

Multi-Condition Contact Stress Analysis of High Speed Train Helical Gear

Taking traction helical gear of CRH380A high speed train for example, not only analyzing the meshing process characters of the high speed train helical gear and the tractive performance curve, but also using Pro/E to complete a three-dimensional model, combining with ANSYS workbench, helical gear contact finite element model is built in start-up, continuous and high speed conditions. A meshing period equivalent stress and contact pressure distributions of gear tooth surface are obtained by solving the model. And so are the changing regularity of gear contact state and stress on the meshing process. The result shows that based on ANSYS workbench, dynamic contact stress analysis about traction helical gear of high speed train can reflect the realistic contact stress state among the meshing process. It provides some certain references and foundations to calculate the gear’s strength analysis and modification design.

Contact Stress and Shear Stress Analysis of Spur Gear Using ANSYS and Theoretical

Contact Stress and Shear Stress Analysis of Spur Gear Using ANSYS and Theoretical

Frictional Contact Stress Analysis of Spur Gear by Using Finite Element Method

Spur gear is used to transfer rotary motion between parallel shafts. The simplicity in its design is one of the advantages of the spur gear. However higher frictional force that is accumulated on the gear teeth will influence the spur gear performance. Many previous papers elaborated extensively on the contact stress in the spur gear but few of them gave the details on how friction affects the gear teeth. There are insufficient frictional effect data in the gear and thus should be regarded as an important research parameter. In this paper, the contact stress of spur gear has been evaluated with and without friction by employing the Hertz theory, AGMA standard and finite element method (FEM). The frictionless contact stress result has been validated with both the theoretical methods with minimum deviation. Frictional coefficient range of 0.0 to 0.3 was selected and the corresponding contact stress is directly proportional to the friction coefficient. The work also involves the variation of face width of the gear set under the influence of friction. The contact stress of spur gear was found to be inversely proportional to the face width.

Analytical and Experimental Study of Gear Surface Micropitting Due to Variable Loading

This paper presents an investigation of the effect of load variation on gear tooth surface micropitting, for an application in planet gears in a wind turbine gearbox. To study the effect of load variation, two methods are employed: an experimental testing of gear micropitting under variable loading and a probabilistic analysis of gear contact stress and specific lubricant film thickness variations using the ISO Technical Report ISO/TR 15144-1:2010. The load variation of wind turbine gearbox is derived from SCADA (Supervisory Control and Data Acquisition) data recorded in operation. Both experimental and analytical results show that high levels of contact stress, load variations and repeated load cycles are determinant factors for the initiation and propagation of micropitting of gear tooth surfaces.