Gear tooth stress analysis by the complex potentials method

Meccanica ◽  
1992 ◽  
Vol 27 (2) ◽  
pp. 105-110 ◽  
Author(s):  
Gianni Nicoletto
Keyword(s):  
Stress Analysis ◽  
Gear Tooth ◽  
Complex Potentials

Numerical Implementation of Complex Potentials for Gear Tooth Stress Analysis

1981 ◽  
Vol 103 (2) ◽  
pp. 460-465 ◽  
Author(s):  
A. Cardou ◽  
G. V. Tordion
Keyword(s):  
Mathematical Programming ◽  
Conformal Mapping ◽  
Stress Analysis ◽  
Gear Tooth ◽  
Spur Gear ◽  
Complex Potentials ◽  
Numerical Implementation ◽  
Gear Teeth ◽  
Transformation Parameters

Stresses in spur gear teeth can be calculated by the complex potentials method, using a generalization of Hirano’s conformal mapping. Mathematical programming is used to fit the transformation to a given profile as closely as desired. Complete formulas for stresses and displacements are given in terms of the transformation parameters. Results are compared with other published values.

Computer Implementation of an Optimal Conformal Mapping for Gear Tooth Stress Analysis

1989 ◽  
Vol 111 (2) ◽  
pp. 297-305 ◽  
Author(s):  
M. J. Richard ◽  
D. Pare ◽  
A. Cardou
Keyword(s):  
Conformal Mapping ◽  
Stress Analysis ◽  
Computer Aided Design ◽  
Gear Tooth ◽  
Spur Gear ◽  
Concentrated Load ◽  
New Approach ◽  
Gear Teeth ◽  
Aided Design ◽  
Mapping Theory

This paper describes a computerized version of the complex potential approach which is a comprehensive mathematical model for the stress analysis of spur gear teeth. The entire procedure is a basic application of Hirano’s conformal mapping theory in which laws of elasticity have been combined. The main concepts of the method have been explained in previous publications but the work described herein is an appreciable extension of this relatively new approach. The algorithm is eminently well-suited for computer-aided-design of gear teeth; it serves as the basis for an interactive computer program which can model a gear tooth and can calculate the stresses and displacements within the tooth when subjected to a concentrated load. Results are compared with AGMA’s and other published values.

Body Force Method for Melan Problem With Hole Using Complex Potentials

2007 ◽  
Author(s):  
B. S. Manjunath ◽  
D. S. Ramakrishna
Keyword(s):  
Stress Analysis ◽  
Body Force ◽  
Infinite Plate ◽  
The Body ◽  
Complex Potentials ◽  
Actual Condition ◽  
Principle Of Superposition ◽  
Concentrated Load ◽  
Force Method ◽  
Body Force Method

The problem of a half plane with concentrated load acting at an interior point is known as melan problem as shown in Fig.1. In the present case melan problem with hole is considered as shown in Fig.2. The body force method is developed for the above case. Body force method is a method based on principle of superposition [1]. In the body force method the actual condition is treated as an imaginary condition i.e. the semi-infinite plate with hole and interior load is treated as a plate without hole; the actual hole is regarded as imaginary on whose periphery boundary forces are applied. The problem is solved by superimposing the stress fields of the boundary forces and concentrated force acting at an arbitrary point to satisfy the prescribed boundary conditions so that the stress condition of the actual plate is approximately equal to that of the imaginary plate [2]. The complex variable method of stress analysis is a versatile technique for stress analysis Problem. The formulas for melan problem are derived and described [3]. Complex potentials are used for stress analysis.

Global Local Finite Element Method (GLFEM) in Gear Tooth Stress Analysis

1993 ◽  
Vol 115 (4) ◽  
pp. 1008-1012 ◽  
Author(s):  
I. Moriwaki ◽  
T. Fukuda ◽  
Y. Watabe ◽  
K. Saito
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Analysis ◽  
Dimensional Analysis ◽  
Gear Tooth ◽  
Three Dimensional ◽  
Critical Section ◽  
Energy Principle ◽  
Analysis Technique ◽  
Element Method

The present study is concerned with an application of the global local finite element method (GLFEM) to a gear tooth stress analysis. The GLFEM is a numerical analysis technique which combines finite element solutions and classical analytical ones on the basis of the energy principle. In this method, the classical analytical solutions give an almost exact stress field to the elements in which the stress varies very rapidly and/or the stress concentration is found. A fine subdivision, therefore, is not required. In the application of the conventional finite element method to the gear tooth stress analysis, the fine subdivision is required especially at the positions near tooth bottom and the load applied point. Hence, only two-dimensional analysis is available for common use. Furthermore, in order to determine an exact location of a critical section on which a fillet stress is maximum, we must use complicated procedures, e.g., an iteration of subdivision for searching the maximum nodal stress. In the present paper, the GLFEM is applied to the gear tooth stress analysis to show that even the rough subdivision enables us to make the precise three-dimensional analysis. It also guarantees an easy determination of the critical section. Thus, we show the effective future of the GLFEM to the gear tooth stress analysis.

Global Local Finite Element Method (GLFEM) in Gear Tooth Stress Analysis

1992 ◽  
Author(s):  
I. Moriwaki ◽  
T. Fukuda ◽  
Y. Watabe ◽  
K. Saito
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Analysis ◽  
Dimensional Analysis ◽  
Gear Tooth ◽  
Three Dimensional ◽  
Critical Section ◽  
Energy Principle ◽  
Analysis Technique ◽  
Element Method

Abstract The present study is concerned with an application of the Global Local Finite Element Method (GLFEM) to a gear tooth stress analysis. The GLFEM is a numerical analysis technique which combines finite element solutions and classical analytical ones on the basis of the energy principle. In this method, the classical analytical solutions give an almost exact stress field to the elements in which the stress varies very rapidly and/or the stress concentration is found. A fine subdivision, therefore, is not required. In the application of the conventional finite element method to the gear tooth stress analysis, the fine subdivision is required especially at the positions near tooth bottom and the load applied point. Hence, only two dimensional analysis is available for common use. Furthermore, in order to determine an exact location of a critical section on which a fillet stress is maximum, we must use complicated procedures, e.g. an iteration of subdivision for searching the maximum nodal stress. In the present paper, the GLFEM is applied to the gear tooth stress analysis to show that even the rough subdivision enables us to make the precise three dimensional analysis. It also guarantees an easy determination of the critical section. Thus, we show the effective future of the GLFEM to the gear tooth stress analysis.

Influence of Different Gear Generation Methods on Contact Stress Analysis of Spur Bevel Gears in PSD

2013 ◽  
Vol 448-453 ◽  
pp. 3476-3480
Author(s):  
Xin Peng Hu ◽  
Jing Wen Yan ◽  
Yan Liu ◽  
Chao Xu ◽  
Ji Xin Wang
Keyword(s):  
Finite Element ◽  
Stress Analysis ◽  
Contact Stress ◽  
Gear Tooth ◽  
Axial Direction ◽  
Element Model ◽  
Bevel Gears ◽  
Power Split ◽  
Curve Method ◽  
Coarse Meshes

This paper summarizes three methods of gear tooth profile generation. Geometry coordinate positions on their profile are compared. A detailed finite element model of mating gear pairs, containing fine meshes and coarse meshes, is presented. Contact stress analysis of three finite element models are conducted to investigate the influence of different generation methods on contact stress. Then, a spur bevel gears pair in Power Split Device is generated by CATIA Law Curve method, and contact stress under the special operating condition is analyzed. The results show few differences of three methods in geometry coordinate positions and tooth contact stress, and the displacement of spur bevel gear in axial direction may cause uneven stress distribution.

Calculation of Spur Gear Tooth Flexibility by the Complex Potential Method

1985 ◽  
Vol 107 (1) ◽  
pp. 38-42 ◽  
Author(s):  
A. Cardou ◽  
G. V. Tordion
Keyword(s):  
Singular Point ◽  
Complex Potential ◽  
Gear Tooth ◽  
Contact Point ◽  
Spur Gear ◽  
Potential Method ◽  
Complex Potentials ◽  
Spur Gears ◽  
Tooth Contact ◽  
Complex Potential Method

Complex potentials have already been used to calculate analytically spur gear stresses. However, their application to the calculation of tooth flexibility is not so straightforward since displacements of interest are at the tooth contact point, which is a singular point for the equations being used. A method has been devised to circumvent this difficulty and to obtain the value of the displacement at each point of the line of action, and thus, the flexibility of a given pair of spur gears.

Fatigue and Life Prediction

2005 ◽  
pp. 293-309
Keyword(s):  
Fatigue Life ◽  
Stress Analysis ◽  
Fatigue Failure ◽  
Contact Stress ◽  
Life Prediction ◽  
Gear Tooth ◽  
Gear Train ◽  
Tooth Surface ◽  
Bending Stress ◽  
Surface Durability

Abstract This chapter summarizes the various kinds of gear wear and failure and how gear life in service is estimated and discusses the kinds of flaws in material that may lead to premature gear fatigue failure. The topics covered are alignment, gear tooth, surface durability and breakage of gear tooth, life determined by contact stress and bending stress, analysis of gear tooth failure by breakage after pitting, and metallurgical flaws that reduce the life of gears. The chapter briefly reviews some components in the design and structure of each gear and/or gear train that must be considered in conjunction with the teeth to enhance fatigue life.

Sign in / Sign up

Export Citation Format

Share Document