Fillet Stresses Research Articles

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.

Finite Element Analysis of Rail-End Bolt Hole and Fillet Stress on Bolted Rail Joints

A rail joint typically is one of the weakest elements of a track superstructure, primarily because of discontinuities in its geometric and mechanical properties and the high-impact loads induced by these discontinuities. The development of continuously welded rail has significantly reduced the number of rail joints, but many bolted joints remain installed in rail transit systems. Because of the unique loading environment of a rail transit system (especially high-frequency, high-repetition loads), defects related to bolted rail joints (e.g., joint bar failures, bolt hole cracks, and cracks in the upper fillet) continue to cause service failures and can pose derailment risks. Recent research in the Rail Transportation and Engineering Center at the University of Illinois at Urbana–Champaign has focused on investigating crack initiation in the bolt hole and fillet areas of bolted rail joints. Stress distribution was investigated at the rail-end bolt hole and upper fillet areas of standard, longer, and thicker joint bars under static loading conditions. Numerical simulations were organized into a comprehensive parametric analysis performed with finite element modeling. Preliminary results indicated that the longer joint bar performed similarly to the standard joint bar but the thicker joint bar reduced rail vertical displacement and rail upper fillet stresses compared with the standard joint bar. However, the thicker joint bar also may generate higher stresses at the rail-end bolt hole. Additionally, joint bar performance was dependent on the rail profile and bolt hole location.

Stress concentration of transition groove induced by a press-fitted part in railway axles

The design guides of railway axles prescribe these axles to have an infinite life based on fatigue limit and to estimate the local stresses in transition fillets or grooves by using the nominal stresses derived by beam calculations. Our previous report described that the press-fitted wheel induced stress concentration on the adjacent transition. In this study, the effect of interference fitting on stress concentration of the transition was experimentally and analytically evaluated using scaled specimens. Finite element analyses of realistic wheelsets based on Japanese and European axle transition geometries were conducted to assess the interference fitting effect on full-scale axles.

STUDY OF FILLET STRESSES ON CRANKSHAFT AND ITS NATURAL FREQUENCY

Present research paper “Study of Fillet Stresses on Crankshaft and Modal Analysis” is a complete Finite Element Analysis of Crankshaft and validate results are theoretical analysed for 4-cylinder, 4-stroke, turbocharged diesel engine with in-line through crankshaft that used the most of automobile companies for the model analysis. In this study the Crankshaft torsional vibrations are analyzed by using the numerical simulation methods and Causes of failures of Crankshaft. For this research Holzer method is used to determine the natural frequency and mode shape of multi-rotor torsional vibration system. Various Pressures at different crank angles are also taken in the account of analysis. .This study is an important effort to develop the scientific and technical understanding for the failure Crankshaft of any Engine under the line of laws of mechanics.

Design of asymmetric normal contact ratio spur gear drive through direct design to enhance the load carrying capacity

Maximum fillet and contact stresses of asymmetric normal contact ratio spur gears designed by direct design method are evaluated based on the load sharing ratio, using finite element method. For a direct gear design, area of existence diagrams are developed for known input gear parameters such as number of teeth, coefficient of asymmetry, top land thickness coefficient and drive side contact ratio. A unique Ansys parametric design language code is developed to find the load sharing ratio, maximum fillet and contact stresses. The fillet stress is calculated in terms of non-dimensional stress. The influence of gear drive parameters such as drive and coast side pressure angles, top-land thickness coefficients, contact ratio, coefficient of asymmetry, gear ratio and teeth number on load carrying capacity has been studied extensively on non-dimensional fillet stress and maximum contact stress and compared with that of the conventionally designed gears. Through parametric study, suitable suggestions are made for the design of asymmetric gear drive for an enhanced load carrying capacity with constant contact ratio and constant drive side pressure angle separately.

Optimization of fillet stress to enhance the bending strength through non-standard high contact ratio spur gears

The present study aims to determine the improvement in the bending strength of the non-standard high contact ratio spur gears based on the balanced (optimum) fillet stress of the pinion and gear. The average number teeth in contact is more than two for high contact ratio gear drives. In the non-standard high contact ratio spur gears, the rack cutter tooth thickness factor is more than 0.5, whereas the standard rack cutter tooth thickness factor is 0.5. The maximum fillet stresses of the pinion and gear is not equal for non-standard high contact ratio spur gear drives when the gear ratio increases. In order to avoid the fatigue failure of the gear, the fillet stresses of the pinion and gear should be balanced. This balanced stress is predicted as the optimum fillet stress. Hence, the present study focuses to optimize the fillet stress with respect to the rack cutter tooth thickness factor of the pinion and gear through finite element analysis. Also, a parametric study is carried out to obtain the influence of some gear parameters, such as gear ratio, teeth number in the pinion, pressure angle, addendum height and corrected gear drives (S+, S− and So) on the optimum fillet stress with respect to the rack cutter tooth thickness factor of the pinion and gear.

Optimization Design for Spur Gear with Stress-Relieving Holes

By designing stress-relieving holes in the stressed zone, an optimization design for reduction of root fillet stress in spur gear is presented based on the stress redistribution techniques. The design method consists of two parts as follows. In the first part, a finite element model that is combined with two gear segments for pinion gear and driven gear is built and the bending stress is analyzed. In the second part, the sizes and the locations of the stress-relieving holes of the gear teeth are optimized in order to reduce the root fillet stress. In the procedures of optimization design, the numerical simulation results by using Ansys Workbench are first used to construct the metamodels which can reduce the computational cost of the finite element analysis (FEA). In the metamodeling process, the optimal Space-Filling design (SFD) method is employed for the selection of sampling design points in design space, and the polynomial response surface (PRS) is utilized to formulate the design objective σmax. Based on the metamodels of the design objective, the genetic algorithm (GA) methodology is employed to find out the optimized locations and sizes of the holes at the root fillet. An illustrated example shows that the maximum principal stress in gear root fillet has been reduced by 14.69% based on the proposed optimization design. This implies the feasibility of the optimization design for increasing the life of gear by designing stress-relieving holes.

A Balanced Maximum Fillet Stresses on Normal Contact Ratio Spur Gears to Improve the Load Carrying Capacity Through Nonstandard Gears

This article presents an idea to remove the inequality in maximum fillet stresses developed between pinion and gear of a step up gear drive. This uniform fillet strength of the gear drive can be achieved by using nonstandard pinion and gear with appropriate addendum modifications generated by nonstandard basic racks of respective tooth thickness not equal to 0.5πm at the pitch circle. The influence of gear parameters such as gear ratio, pressure angle, addendum factor, pinion teeth number, and addendum modifications on the maximum fillet stress on the nonstandard pinion and gears of different tooth thickness has been analyzed through finite element method and finally the optimum value of rack tooth thickness coefficients (k pc and k gc ) are suggested for the given gear drive (defined by i) that improves the fillet capacity in bending. This study has been extended for various drives like S std , S o , S +, and S − drives.

Adaptive grid-size finite element modeling of helical gear pairs

A method for solving the contact problem for generic helical gear pairs (either external or internal) is described. Gear profiles are obtained by means of numerical simulation of the cutting process and an accurate description is provided in terms of NURBS curves or surfaces. A new method for finding the enveloping profiles for a generic tool (e.g. from a measured topography) is proposed. The minimum number of parameters needed to describe the profile in the presence of tip and root reliefs, helix modification and crowning is discussed. A reference structured grid is defined on the tooth, then refinement criteria are applied in order to obtain accurate solutions in terms of tooth deflection, contact pressure and fillet stress. The method allows to automatically perform a Loaded Tooth Contact Analysis (LTCA) starting from the design data of a gear pair. Results from the LTCA include contact pressure and contact pattern maps, as well as maximum fillet stress and fatigue strength. Combining several analyses within a mesh cycle, information about the Static Transmission Error (STE) and mesh stiffness is provided. The whole procedure has been implemented in a software called helical pair. A comparison with other approaches is given.

Design and Analysis of Asymmetrical Spur Gear Drive for Automobile Gear Box Application

This work mainly aims to explore the actual load, fillet and contact stresses induced during a mesh cycle in a spur gear tooth. As the mesh stiffness differs at different contact points along the path of contact, it significantly affects the load sharing between the simultaneously meshed contact pairs hence stresses. Comparative study has been made between existing symmetric spur gear pair used in light motor vehicle gear box and asymmetric spur gear. Finite element multi pair contact model has been used to explore the load sharing behavior and related stresses in this work.

Application of Finite Element to Spur Gear Stress Reduction Using Stress Relieving Feature

The aim of this study was to create stress relieving features to reduce the root fillet stress in spur gear. A pilot model was established to predict von Mises stress at the root fillet of the gear without holes and was used as a reference model. Finite element modeling was adopted using Abaqus® package. The predicted stresses were compared with stresses obtained by AGMA analytical solution. A good agreement was found in the comparison between the calculated and predicted stresses. Then, another model, namely hole model, was built to investigate the effect of various hole parameters (number, diameter, location, angle). The hole model was performed by creating hole/holes in the gear body. The results obtained showed that increasing the diameter size of hole/holes resulted in higher percentage of stress reductions compared to the pilot case. Furthermore, increasing the number of holes resulted in higher percentage of stress reductions compared to the pilot case, but gear rigidity in this case was highly affected.

Load sharing based maximum fillet stress analysis of asymmetric helical gears designed through direct design — A parametric study

Direct gear design method is one of the most effective gear design approaches, which provides the high performance gears without concern for any predefined tooling parameters. In the present work, the load sharing ratio (LSR) and the corresponding LSR based maximum fillet stresses in terms of non-dimensional stress number have been estimated for the conventionally designed and direct designed symmetric helical gears. It is also extended for direct designed asymmetric helical gears. The area of existence procedure is developed and using the same, the possible existence of design solutions for a drive of required constant transverse contact ratio and different addendum pressure angles is chosen to develop the rack dimensions. Finally, the influence of a few parameters such as gear ratio, transverse contact ratio, top land thickness coefficient and the pinion teeth number on area of existence, load sharing ratio and the corresponding values of non-dimensional stress number in the asymmetric helical gear drives designed through the direct design method has been carried out and discussed.

EMPIRICAL RELATION TO ESTIMATE THE REDUCTION OF ROOT FILLET STRESS IN SPUR GEAR DUE TO ELLIPTICAL STRESS RELIEF FEATURES

This work is an attempt to establish the empirical relations to predict the percentage of reduction of the root fillet stress in a spur gear due to elliptical stress relief features (SRF). To modify the stress field in a spur gear to reduce the stress concentration using elliptical stress relief feature has added advantage over the circular stress relief features, because it has more parameters such as major diameter, ratio of major to minor diameter and orientation of its axis to regulate stress field. An investigation on roo t fillet stress is in a spur gear with an elliptical stress relieving feature is carried out using finite element method. Based on the finite element analysis carried out nine empirical relations are proposed. With these relations it is possible to predict the percentage of reduction of root fillet stress in spur gear within 2percentages of deviation.

Effect of Face Contact Ratio on Load Sharing Based Fillet Stress in Asymmetric Helical Gear Drives

The gear smoothness in the transmission of power mainly depends on the contact ratio. When the contact ratio is higher, the load shared by the pair of teeth in mesh will be lower. In the helical gear, the additional contact ratio is created due to face advance which is called face contact ratio and it provides the higher contact ratio than that of spur gear. The face contact ratio can improve by changing the few parameters such as helical lead and face width. In the present work, the face contact ratio is improved by altering those parameters and their effects on the load sharing based fillet stress are also determined for one mesh cycle in the asymmetric helical gear designed through direct design procedure using finite element method.

Effect of Backup Ratio and Cutter Tip Radius on Uniform Bending Strength Design of Spur Gears

In the higher speed ratio and profile shifted gear drives, the maximum fillet stress in the pinion and the gear is not equal. The load-carrying capacity of the gear drives can be improved by removing this unbalanced maximum fillet stress. This paper has explained an idea to remove this unbalanced maximum fillet stress and design the spur gear drives with uniform fillet strength. This uniform fillet strength of the gear drive can be achieved by changing the tooth thickness of basic racks on the pitch lines from the standard tooth thickness (0.5πm) in to a non-standard one (kgcπm, kgc≠0.5). The influence of gear parameters such as backup ratio, cutter tip radius and addendum modification factors on the maximum fillet stress has been analyzed through FEM with different values of tooth thickness coefficient and finally the optimum value of tooth thickness coefficient are suggested for the given spur gear drive that improve the fillet capacity in bending.

Optimum Profile Shift Estimation on Direct Design Asymmetric Normal and High Contact Ratio Spur Gears Based on Load Sharing

Abstract In direct design method, gear pair is selected from area of existence diagram. This area of existence diagram gives N number of possible gear pairs. From this possible gear pairs it is important to optimize the fillet strength of pinion and gear with respect to the optimum profile shift. Optimum design of gear drive means the maximum fillet stresses developed at the pinion and gear are to be equal. Hence the present work attempts for a reasonably accurate estimation of optimum profile shifts based on pinion and gear tooth fillet strength for a load at critical loading point considering the load sharing between the gear pair on asymmetric normal and high contact ratio asymmetric spur gear through direct design.

Load Sharing Based Fillet Stress Analysis of Involute Helical Gears

The tooth fracture occurs due to high fillet stress developed at the root fillet region along the face width, when the tooth is normally loaded. Hence, an accurate estimation of critical loading position on the tooth along the line of contact for maximum fillet stress and its location along the face width become important to reduce the tooth fracture. In the present work, the maximum fillet stress is evaluated based on load sharing ratio using the finite element method through the multi pair loaded model and using the results, the influence of cutter tip radius and addendum height on the load sharing ratio and respective maximum fillet stress is evaluated. The maximum fillet stress is lesser in the gear drives which is generated by the full round cutter and it increases due to increase the addendum height. The location at which the maximum fillet stress occurs along the face width is determined, when the load is applied at the critical loading position in the helical gear drive.

Influence of Pressure Angle on Load Sharing Based Stresses in Asymmetric Normal Contact Ratio Spur Gear Drives

The aim of this paper is to investigate the influence of pressure angle on drive and coast sides in conventional design asymmetric normal contact ratio spur gear, considering the load sharing between the gear teeth pair. The multi pair contact model in finite element analysis is used to find the load sharing ratio and respective stresses. It has been found out that the predictions through multipoint contact model are in good agreement with the available literature. A unique Ansys parametric design language code is developed for this study. It is found that, the maximum fillet stress decreases up to the threshold point for drive side (35o) and coast side (25o) pressure angles, beyond this point it increases. The load share based maximum fillet and contact stresses are lower in the high pressure angle side than that of the low pressure angle side, when it is loaded at the critical loading points.

Effect of the design of the lap welded joint on its stress–strain state

The results of calculation of the stress–strain state of lap welded joints confirm that the design of the joint in bending of the welded layers has a strong effect on the value of the maximum working stresses in longitudinal fillet welded joints.

Design of face-hobbed spiral bevel gears with reduced maximum tooth contact pressure and transmission errors

The aim of this study is to define optimal tooth modifications, introduced by appropriately chosen head-cutter geometry and machine tool setting, to simultaneously minimize tooth contact pressure and angular displacement error of the driven gear (transmission error) of face-hobbed spiral bevel gears. As a result of these modifications, the gear pair becomes mismatched, and a point contact replaces the theoretical line contact. In the applied loaded tooth contact analysis it is assumed that the point contact under load is spreading over a surface along the whole or part of the “potential” contact line. A computer program was developed to implement the formulation provided above. By using this program the influence of tooth modifications introduced by the variation in machine tool settings and in head cutter data on load and pressure distributions, transmission errors, and fillet stresses is investigated and discussed. The correlation between the ease-off obtained by pinion tooth modifications and the corresponding tooth contact pressure distribution is investigated and the obtained results are presented.