Tooth Bending Stress Research Articles

Dynamic behaviours of rack vehicle-track system considering rack flexibility under gear-rack mesh impact

ABSTRACT There are complex and large gradients for the rack vehicle running on the large mountain slope line. Under such a circumstance, the driving gear-rack interactions will be more intensified and could induce the larger tooth bending stress of the rack. At present, the dynamics modelling of the rack in the existing literature is generally treated as a rigid body or an infinite beam model, however, which is inconsistent with reality. To accurately simulate the vibration characteristics and bending stress of the rack structure, it is necessary to establish a detailed dynamic model considering the flexibility of the rack structure. In this study, the free beam and rod models are, respectively, used to describe the vertical and longitudinal flexibilities of the rack with the finite length. Then, the proposed rack dynamics model is introduced into a rack vehicle-track coupled system, and the developed dynamics model is validated by comparing the results from the simulation with the tested data. Finally, the vibration and bending stress features of the driving gear-rack engagement are analysed under different mounting deviations. The simulated results can give theoretical references for the design and structure optimization of the rack track structure.

Investigating teeth root stresses of various spur gears using stress function and FEM

AbstractThe gear is the most efficient and reliable portion of the transmission system. In machine tools, gears are utilized to handle heavy loads. These gears are used indefinitely if the prerequisites are met. Gear tooth bending stress for numerous spur gears has been examined in this research. The influence of changing the pressure angles on the spur gear tooth root stress has been investigated. The purpose of this study is to look for a new way of finding the stresses generated in the roots of the gear teeth as well as the effect of changing pressure angles on these stresses. Solidworks 2021 uses parametric formulation to model gears, analyzed for deformation and maximum bending stress in ANSYS. The airy stress function is used to conduct the nominal root tooth stress. The enhancement percentages of modified cases are 5.92%, 1.70%, 10.70%, 17.22%, 10.86%, 24.32%, 20.91%, and 26.15% for the cases 2, 3, 4, 5, 6, 7, 8, and 9, respectively according to the stress function findings.

Fatigue and Wear Performance of Autoclave-Processed and Vacuum-Infused Carbon Fibre Reinforced Polymer Gears

This study focuses on investigating the fatigue and wear behaviour of carbon fibre reinforced polymer (CFRP) gears, which have shown promising potential as lightweight and high-performance alternatives to conventional gears. The gears were fabricated via an autoclave process using an 8-layer composite made of T300 plain weave carbon fabric and ET445 resin and were tested in pair with a 42CrMo4 steel pinion and under nominal tooth bending stress ranging from 60 to 150 MPa. In-situ temperature monitoring was performed, using an infrared camera, and wear rates were regularly assessed. The result of the wear test indicates adhesive wear and three-body abrasion wear mechanisms between the CFRP gears and the steel counterpart. A finite element analysis was performed to examine the in-mesh contact and root stress behaviour of both new and worn gears at various loads and a specified running time. The results point to a substantial divergence from ideal meshing and stress conditions as the wear level is increased. The fatigue results indicated that the CFRP gears exhibited superior performance compared to conventional plastic and composite short-fibrous polymer gears. The described composite gear material was additionally compared with two other composite configurations, including an autoclave-cured T700S plain weave prepreg with DT120 toughened resin and a vacuum-impregnated T300 spread plain weave carbon fabric with LG 900 UV resin. The study found that the use of the T700S-DT120 resulted in additional improvements.

Optimising the Geometric Parameters of a Gear in a Tractor Transmission Under Constraints Using Kisssoft

Abstract We optimise the speed gears in a tractor transmission with KISSsoft software under three constraints: input power torque, transmission system volume and the gear ratio for each speed. This study aimed to optimise the module, face width, gear quality, centre distance, number of teeth, helix angle, addendum modification coefficient and pressure angle for each speed while considering the above constraints based on an optimisation chart. Tooth bending stress, tooth contact stress, contact ratio and specific sliding were considered during optimisation. Additionally, the effects of changes in a module on the gear profiles, overlap ratio, number of teeth and weight of the gear pair were examined. Strength calculations of gear pairs that were optimised and defined for all geometric parameters with KISSsoft were calculated with the mathematical model described in ISO 6336, and results were then compared. Finally, backlash was minimised for all gear pairs as defined with geometric parameters, and all dimensions and tolerances were determined for gear inspection after manufacturing. A concept design was also presented. We conclude that both the KISSsoft results and mathematical model results are within the range of the target value.

Tooth bending strength of gears with a progressive curved path of contact

Abstract The article presents a comprehensive study on the tooth bending strength of spur gears with a progressive curved path of contact, or so-called S-gears. Systematic gear meshing simulations were conducted to study the effects of S-gear geometry parameters on tooth bending strength. Different S-gear geometries were analysed in a systematically organized manner, and a comparison was made against a standard 20° pressure angle involute shape. Furthermore, different material combinations, e.g. polymer/polymer, steel/polymer, and steel/steel, of both drive and driven gear were analysed within a meaningful range of loads. The gear profile shape, material combination of the drive and the driven gear, and the transmitted load were found as the main parameters affecting gear tooth bending stress. Complex, non-linear relations between the recognized effects and the corresponding root stress were observed. Based on the numerical results, a shape factor, which considers the above-mentioned effects, was introduced, and a model for root strength control of S-gears was proposed and verified employing the finite element method (FEM).

Tooth bending stress analysis of high speed curve face gear of composite transmission

To promote the engineering application of composite transmission of high speed curve face gear, which consists of a cylindrical gear and a high speed curve face gear, the analysis of tooth bending stress should be taken into consideration. High speed curve face gear pair is a new type of curve face gear pair. Combined with the principle of high speed cam and curve face gear pair transmission, it can transfer the axial/rotation composite motion and power between two intersecting shafts. Based on the gear engagement principle, the gear meshing coordinate system was established and the fundamental of the high speed composite transmission was expounded. Combined with the tooth profile equation of generating gear, the tooth surface equation of high speed curve face gear was gained. Tooth force, contact ratio and normal load distribution were calculated. Then the tooth bending stress of high speed curve face gear during the transmission was calculated and analyzed in detail. Influence of basic parameters on tooth bending stress was discussed. Finally, the simulation and measurement experiment of tooth bending stress was carried out. By the comparison analysis of simulation, experiment and theory, the correctness of tooth bending stress calculation method was verified, which has important guiding significance for the further research of high speed curve face gear of composite transmission.

Real contact ratio and tooth bending stress calculation for plastic/plastic and plastic/steel spur gears

This paper presents an iterative method for calculating the effective contact ratio and the bending tooth stress for a pair of plastic/plastic and plastic/steel spur gears with an involute profile. In this method, the pinion and the gear are modeled, at each moment of the mesh cycle, as equivalent springs in parallel undergoing the same displacement along the line of action. This leads to the calculation of the bending stress by taking into account the number of teeth initially in contact and those which enter in contact prematurely. We also investigate the influence of certain gear parameters, such as, the number of teeth, the pressure angle, and the module on the behavior of a pair of meshed gears. In addition, the variation of the bending stress at the tooth fillet is investigated for a pair of plastic/plastic and a pair of plastic/steel spur gears, in order to determine the critical configurations for which the bending stress is maximum. In general, the results obtained from the present method also show that the stress variation in plastic/plastic gears differs markedly from that in plastic/steel gears.

Stress Analysis on Single and Herringbone Helical Gears

Abstract In the perspective of exploratory analysis into the theoretical concept and performance characteristics of helical gear design, a complete relationship between the design parameters and other working parameters remains to be clearly understood because of complexity. Gears are widely used to transmit mechanical power and where helical gears are known to have smoother transmission as compared to other gears. Often the stress generated on the tooth influences various operational parameters of a gear and where subjected to stresses which lead to failure. In helical the tooth failure occurs because of root bending stress acting on the gears. In this present work, a comparative study on helical gear design and its performance characteristics were made through Finite Element Analysis (FEA) as well as numerical method. Based on American Gear Manufacturing Association (AGMA) standards, theoretical analysis for single and herringbone helical gears have been evaluated in Matlab. The effect of tooth bending stress on single and herringbone helical gear system are studied through finite element analysis and compared with theoretical analysis. The comparison study is performed to determine the stress distribution on helical gears and it significantly increases the new variant design without considering design calculation by complex theoretical method which has scope of manual errors

Optimization of tooth modifications for spur and helical gears using an adaptive multi-objective swarm algorithm

Metaheuristic methods have proved to be suitable for solving complex multi-criteria optimization problems. In this paper, a modified particle swarm algorithm has been implemented in order to improve the quasi-static behavior of a power transmission gearbox, thus optimizing various objectives such as the maximum contact pressure on the gear flanks, the root-mean-square of the loaded transmission error signal, the tooth bending stress, and/or the pressure-speed factor. For narrow-faced spur gears, the comparison between optimal solutions found by the algorithm and the so-called master curve shows quite good agreements. The chosen form of the profile modifications, linear or quadratic, is then discussed. Finally, the robustness of the optimal solutions is tested to guarantee their efficiency against variable shaft misalignments.

Comparative Analysis of Different Starter Driven Gear Materials Using Finite Element Method

Gear is an essential element in motor vehicles. Bending stress and gear surface strength are two factors contributing to a gear failure. Therefore, calculating precisely the bending stress and total deformation of the gear tooth is profoundly important for the development of modern gear design industry. This study aimed to investigate the strength, deformation, and crack in gears. The Finite Element Method (FEM) was used in the ANSYS simulation. The simulation was performed on three gear materials, i.e. alloy steel, structural steel, and carbon steel. The results showed that among the three materials, the highest strength with the equivalent stress of 921.63 MPa was structural steel, with the maximum principal stress of 407.33 MPa and maximum shear stress of 407.33 MPa.

Concave and convex modifications analysis for skewed beveloid gears considering misalignments

The mathematical models of beveloid surface with concave and convex modifications were derived. The finite element and analytical mesh models were developed considering the shaft deformation and misalignments including pinion axial position, center distance and shaft angle errors. Then, tooth contact analysis were conducted to study the impacts of loads and misalignments on contact characteristics. Results show that the higher load applied has stronger effects for enlarging contact pattern and lowering transmission error with the concave and convex modifications. Moreover, the proposed tooth modifications can decrease the sensitivity of contact characteristics to misalignments. The shaft angle error has the greatest impact on the mesh behaviors. The contact path and pattern are prone to shift the location along tooth trace direction due to shaft angle and center distance errors. The contact stress, bending stress and transmission error are seen to increase due to these two assembly errors. Pinion axial position error does not affect the location of the contact path and pattern significantly. However, it can increase the magnitude and change the location of the maximum tooth bending stress in the axis direction. Finally, it only produces minimal effect on the contact stress, contact area and transmission error.

Effects of Hob Tip Radius and Addendum Modification Coefficients on Tooth Bending Stress of Spur Gears under Dynamic Conditions

The paper presents a bending stress analysis of spur gear pairs in order to enhance the effects of the tooth root influence factors in relation to the hob tip geometry and addendum modification coefficients. These factors are evaluated in accordance with ISO 6336 for the basic rack profiles. In order to improve the accuracy of this analysis, a dynamic model is considered to analyse the shared dynamic load for a meshing cycle. All these influence factors are included in a global factor Yd. A comparative study has been performed to investigate the effects of the hob tip radius, addendum modification coefficients and pinion speed on the variation of the factor Yd on the meshing cycle. The approach makes for improved in predicting the tooth bending stress at the design stage.

Stress Concentration factor Analysis of Helical Gear Drives with Asymmetric Teeth Profiles

This study investigates the influence of asymmetric involute teeth profiles for helical gears on the bending stress. Theoretically, bending stress has been estimated in spur involute gears which have symmetric teeth profile by based on the Lewis, 1892 equation. Later, this equation is developed by, Abdullah, 2012. to determine the effect of an asymmetric tooth profile for the spur gear on the bending stress. And then these equations are applied with stress concentration factor once for symmetric and once other for asymmetric teeth profile. In this paper, the bending stresses for various types of helical gear with various types of asymmetric teeth profile are calculated numerically for defined the stress concentration factor. The numerical solution based on the finite element method technique which that done by using the software simulation SolidWorks 2016. The results of this study indicate that the helical gear drive with asymmetric teeth profile having 'loaded side pressure angle' of ( ) and 'unloaded side pressure angle' of ( ) is better than a helical gear with standard teeth profile having pressure angle of ( ) from the regarding of tooth bending strength. Also, notes that the great enhancement in the results of maximum tooth bending stress for modified involute of tooth profile compared with the standard teeth profile. In addition to, predict the equation of stress concentration factor which is a function of both unloaded side pressure angle and helix angle and then it used with Abdullah equation for to determine the nominal stresses in the root fillet.

Search method applied for gear tooth bending stress prediction in normal contact ratio asymmetric spur gears

Various analytical methods have been developed by designers to predict gear tooth bending stress in asymmetric spur gears with an intention to improve the accuracy of predicted results and to reduce the need for time consuming finite element analysis at the early stages of gear design. Asymmetry in the drive and coast side of asymmetric spur gears poses difficulty in direct application of well-known procedures like American Gear Manufacturers Association and International Organization for Standardization in the prediction of gear tooth bending stress. In earlier works, ISO-6336-3 methodology was suitably modified and adapted to predict asymmetric spur gear tooth bending stress. This approach is based on certain assumptions on the location of critical section which could introduce error in the predicted maximum bending stress. The present work is to analytically predict gear tooth bending stress in normal contact ratio asymmetric spur gears based on a more rigorous analytical approach. This includes a fundamental study on the gear tooth orientation used to define the coordinate system, determination of maximum bending stress by search along the fillet profile and to obtain stress profile along the fillet. Gear tooth bending stress obtained from the present work using Search method is compared against the results obtained from earlier adapted International Organization for Standardization method and Finite Element Analysis. This study recommends a new coordinate system and method for analytical prediction of gear tooth bending stress in normal contact ratio asymmetric spur gears.

Design And FEM Analysis of Helical Gear

In this paper the problem of the failure of gear in speed reduction gearbox developed by Laxmi Hydraulic Pump (LHP) Pvt Ltd, Solapur is resolved by replacing the existing material by a material SAE8620. The Gear and Pinion using AGMA and FEM analysis Method. In the gear design, the bending stress and surface strength of the gear tooth are considered to be one of the main factors to the failure of the gear. In this paper bending and contact stresses are calculated by using analytical method as well as Finite Element Method. To estimate bending stress modified Lewis beam strength method is used as well as AGMA method. Software is used to generate the 3-D solid model of helical gear. Ansys software package is used to analyze the bending stress. Contact stresses are calculated using modified AGMA contact stress method. Ansys software package is used to analyze the contact stress and bending stress. The main objective of this study has to investigate the stresses induced by gear tooth profile. Finally, the results obtained by theoretical analysis and Finite Element Analysis are compared to check the correctness. Estimated stress is used to calculate module of gear which can withstand easily at given loading conditions. A conclusion has arrived on the material which is best suited for helical gear based on the results.

Optimisation of Effective Design Parameters for an Automotive Transmission Gearbox to Reduce Tooth Bending Stress

Optimisation of effective design parameters to reduce tooth bending stress for an automotive transmission gearbox is presented. A systematic investigation of effective design parameters for optimum design of a five-speed gearbox is studied. For this aim contact ratio effect on tooth bending stress by the changing of contact ratio with respect to pressure angle is analysed. Additionally, profile modification effects on tooth bending stress are presented. During the optimisation, the tooth bending stress is considered as the objective function, and all the geometric design parameters such as module, teeth number etc. are optimised under two different constraints, including tooth contact stress and constant gear centre distance. It can be concluded that higher the contact ratio results in a reduced tooth bending stress, while higher the pressure angle caused an increase in tooth bending stress and contact stress, since decreases in the contact ratio. In addition, application of positive profile modification on tooth reduces tooth bending stress. All of the obtained optimum solutions satisfy all constraints.

A Review of Bending and Contact Stress Analysis of Helical Gear

This paper reviews Bending and Contact Stress Analysis of Helical Gear. In this paper the bending stress and contact stress of the gear tooth are examined and are to be one of the main contributors for the failure of the gear in a gear set. Thus, the 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.

Contact Stress Analysis of a Helical Gear

The main factors that cause the failure of gears are the bending stress and contact stress of the gear tooth. Out of these, failure of gears due to contact stress is high compared to bending stress. Stress analysis has been a key area of research to minimize failure and optimize design. This paper gives a finite element model for introspection of the stresses in the tooth during the meshing of gears. Specifically, helix angle is important for helical gears. Using modeling software, 3-D models for different helix angles in helical gears were generated, and the simulation was performed using ANSYS 12.0 to estimate the contact stress. The Hertz equation and AGMA standard was used to calculate the contact stress. The results of the theoretical contact stress values, using Hertz and AGMA are compared with the stress values from the FEA for different helix angles and the results are tabulated and discussed.

Research on the Maximal Bearing Capacity Calculation of a New Double Ring Reducer Based on MATLAB

The bearing capacity of a new double ring reducer increases with the increase of load because of the elastic deformation of the gear tooth. In order to solve the problem of its bearing capacity quantificationally, the concept of the maximal bearing capacity is put forward. Starting with that the single tooth bending stress is up to the bending fatigue strength, a mathematical model to determine the normal backlash of the gear teeth has been established, the maximal deformation of the single tooth has been determined. The mathematical relationships have also been setup between the normal backlashes of the tooth pairs, the maximal deformation and number of contact points, a corresponding MATLAB program is designed. The maximal bearing capacity of the reducer has been estimated through examples and proved by experiment. The results show that the calculation method is more effective and fully considers the factors that the elastic deformation of the gear tooth can increases its bearing capacity, so the structure of the reducer is more compact, which establishes the theory foundation for designing the reducer.

Minimizing tooth bending stress in spur gears with simplified shapes of fillet and tool shape determination

The strength of a gear is typically defined relative to durability (pitting) and load capacity (tooth-breakage). Tooth-breakage is controlled by the root shape and this gear part can be designed because there is no contact between gear pairs here. The shape of gears is generally defined by different standards, with the ISO standard probably being the most common one. Gears are manufactured using two principally different tools: rack tools and gear tools. In this work, the bending stress of involute teeth is minimized by shape optimization made directly on the final gear. This optimized shape is then used to find the cutting tool (the gear envelope) that can create this optimized gear shape. A simple but sufficiently flexible root parameterization is applied and emphasis is put on the importance of separating the shape parameterization from the finite element analysis of stresses. Large improvements in the stress level are found.