Analysis and formulation of spur gear stresses with different tip modifications

7 - Detailed Gear Stressing

Loaded tooth contact analysis (LTCA), deformation, and stress calculations of three types of thin-rimmed spur gears with inclined webs at the left side, the center, and the right side of the tooth are conducted in this paper with finite element methods (FEM) combined with a mathematical programming method when these gears are engaged with a solid mating gear. The contact stresses on the tooth surfaces, the bending stresses at the tooth roots, and the joint stresses of the rim and the web are analyzed as the web position and the web angle are changed. It was found that the web position and the web angle of the thin-rimmed gears have a significant effect on the tooth contact stresses, the root bending stresses, and the joint stresses. The maximum contact stress of the right web gear becomes very small when the web is inclined from 0 to 30 deg, and it increases again when the web angles are changed from 45 to 60 deg. This interesting relationship between the web angle and the tooth contact stresses of thin-rimmed right inclined web gears is used to absorb the misalignment errors in the gears and improve the partial tooth contact pattern resulting from the misalignment errors. A calculation example is provided to illustrate how to improve the partial tooth contact patterns in gears with misalignment errors.

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.

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.

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.

There are two types of curvilinear cylindrical gear drives: those with point contact and those with line contact. In this paper, a mathematical model, tooth contact analysis and stress analysis are investigated for curvilinear cylindrical gears with line contact. Here, fixed-setting face-milling cutters are used for the generation of the tooth surfaces of the gears and their matching gears. Based on the theory of gearing, a mathematical model of curvilinear gears is derived, and the instantaneous contact lines on the gear tooth surfaces are examined under ideal assembly conditions. Meanwhile, the instantaneous contact points on the gear tooth surfaces and transmission errors under assembly error conditions are investigated by a tooth contact analysis algorithm. Finally, contact and bending stresses for curvilinear cylindrical gears with tip relief and without tip relief are explored by the finite element method. This research result shows that (1) under ideal assembly conditions, the length of the instantaneous contact lines is greater than the tooth face width, but the effect is very weak. (2) In terms of the transmission errors, crossing shaft angle errors are more sensitive than intersecting shaft angle errors; axial displacement errors are more sensitive than centre distance errors. (3) Severe contact stresses caused by edge contact are eliminated by the tip relief. (4) The maximum bending stress at every contact position is always distributed in both ends of the gear tooth surfaces.

This article used ANSYS, the software of finite element analysis, to analyze the contact stress between the wheel gear and the rack the two locking devices, which called in the switch. While through adding the necessary conditions, such as restrain methods, element types, coefficient of friction, Poisson ratio, damping ratio, contact conditions etc, We are also testing the simulation meshing run of contact between gears. Then according to load the rated power to make calculations, we can get cloud map of prototype gear's contact stress. Finally, on the preliminary study basis, we build the reliability model of the gear lever transformation locks up, which use the Weibull distribution.

Tooth root bending stress and surface contact stress are two major determinants of the load carrying capacity of gear drives. Generally, a high contact ratio has the potential to enhance the gear strength. In this paper, the basic procedures and methods for constructing a high-contact-ratio (HCR) internal spur gear pair with the arc path of the contact are presented. The effects of design and modification parameters such as deflection angle, modification angle, and addendum coefficient on gear drive are analyzed in detail based on 2D finite-element models (FEMs). A comparison of experimental and finite-element analyses (FEA) of the bending stress, contact stress, and contact ratio between HCR and involute internal spur gear drives was conducted to demonstrate the advantages of the HCR gear drive in terms of load capacity. The results show that appropriately increasing the deflection angle and addendum coefficient is beneficial for reducing bending and contact stresses. It was also observed that the bending and contact stresses of a HCR pinion are lower than those of an involute one. Moreover, the contact ratio increases with input torque.

Planetary gear trains are widely applied in various transmission units. Whether strengths of all gears are accurately calculated or not can affect reliability of the entire system significantly. Strength calculation method for planetary gear trains usually follows the method for cylindrical gears, in which the worst meshing positions for both contact stress and bending stress cannot be determined precisely, and calculation results tend to be conservative. To overcome these shortcomings, a kinematics analysis for a planetary gear train is firstly performed, in which the influence of relative speed is investigated. Then the finite element strength analysis of a planetary gear train based on its transient meshing properties is carried out in ANSYS. Time–history curves of contact and bending stresses of sun gear, planetary gears and ring gear are respectively obtained. Also the accurate moment and its corresponding position of the maximum stress are precisely determined. Finally, calculation results of finite element method (FEM) and traditional method are compared in order to verify the effectiveness. Simulation and comparison show the stability of the proposed method in this paper. Researches in this paper establish the foundations for fatigue analysis and optimization for a planetary gear train.

Gear design and analysis are fundamental aspects of mechanical engineering, particularly due to their extensive applications in industries such as automotive, aerospace, and marine. In power transmission systems, gears must meet strict performance requirements to ensure efficiency and durability. Recent advancements in materials science have led to increased research on composite materials in gear design, offering improved performance over conventional materials. This study examines the comparative effectiveness of contact and bending stress in pure HDPE spur gears versus HDPE reinforced with TiO 2 and SiO 2 composites. Using ANSYS Workbench, the contact and bending stresses between polymer gear pairs are analyzed through simulation, modeling their behavior under applied torque loads. The study provides a detailed three-dimensional analysis of gear tooth interactions, treating the contact between teeth as a dynamic engagement. Torque is applied to the driving gear under controlled loads, while the driven gear is constrained to facilitate an in-depth stress evaluation around the gear teeth. The results indicate that HDPE-TiO 2 -SiO 2 composite spur gears exhibit significantly improved performance in managing contact and bending stresses compared to pure HDPE gears, demonstrating their potential for enhanced durability and reliability in demanding applications

<h2>ABSTRACT</h2> <p><strong>Objectives:</strong> To carry out dynamic state analysis of asymmetrical helical gears for contact stresses using photo stress technique and suitable finite element software.<strong> Methods:</strong> Currently the Hertz contact stress equation is used to calculate the contact stress which is based on certain speculations. The value of load transmitted by a gear may be known but whether it is taken by a single or more pairs of teeth are based on some assumptions and stresses thus calculated may not be true stresses. To get precise evaluation of stress field in gear tooth it is decided to carry out experimental work on asymmetric helical gear in actual working condition. The photo stress method not only provide magnitude of stress but also gives idea about stress distribution in gear. Finite element method is used for asymmetrical helical gear to validate experimental results. <strong>Findings:</strong> The stress values obtained by photostress method and FEA method has minimum error of 2.17% and maximum of 8.89% respectively. The error values are less than 10% and within the limit. We can observe close agreement between these two methods.<strong> Novelty:</strong> This study has provided a more accurate result than theoretical method of stress calculation. Photostress analysis method is one of the best test methods for evaluation of contact stress of asymmetric helical gear with different torque condition in actual working that is dynamic condition. Maximum error of 8.89% has been found with photostress method.</p>

Among all the common mechanical transmission elements, gears still playing the most dominant role especially in the heavy duty works offering extraordinary performance under extreme conditions and that the cause behind the extensive researches concentrating on the enhancement of its durability to do its job as well as possible. Contact stress distribution within the teeth domain is considered as one of the most effective parameters characterizing gear life, performance, efficiency, and application so that it has been well sought for formal gear profiles and paid a lot of attention for moderate tooth shapes. The aim of this work is to investigate the effect of pressure angle, speed ratio, and correction factor on the maximum contact and bending stress value and principal stresses distribution for symmetric and asymmetric spur gear. The analytical investigation adopted Hertz equations to find the contact stress value, distribution, and the contact zone width while the numerical part depends on Ansys software version 15, as a FE solver with Lagrange and penalty contact algorithm. The most fruitful points to be noticed are that the increasing of pressure angle and speed ratio trends to minimize all the induced stresses for the classical gears and the altered teeth shape with larger loaded side pressure angle than the unloaded side one behave better than the symmetric teeth concerning the stress reduction.
 

Contact mechanics of two elastic spheres reinforced by functionally graded materials (FGM) thin coatings

Spur gears for many applications make use of profile shapes that are modifications of the mathematically defined involute to avoid premature tooth contact and unfavourable transmission error. It is well known that specification of the involute modification is important as it relates to the resulting performance, vibration and gear noise. In this research, a hybrid analysis method using finite elements and contact mechanics was used to investigate the effects of linear, parabolic and exponential tooth profile modifications on performance of an involute spur gear pair. For each type of modification, 10 different magnitudes of tip relief were used to study its influence on static transmission error (STE), tooth loads, root stresses and contact stresses. Peak-to-peak transmission error, root mean square transmission error and total area per cycle transmission error were used to characterise STE. Multiple output responses were calculated including the STE characteristics, tooth loads, tooth root stresses, contact stresses, gear moments and bearing forces to compare and contrast the type and magnitude of the tooth modification. Results show that linear modification produced low root stresses; parabolic modification produced low STE, contact stress, gear moment variations, and bearing force variations; exponential modification produced nearly the same STE characteristics over a wide range of tip modification magnitudes.

A study on the design of asymmetric spur gears in gear pump applications