# Static Analysis of Spur Gear Using Finite Element Analysis – Mechanical Projects

ABSTRACT :

Gear is one of the most critical component in a mechanical power transmission system, and most industrial rotating machinery. A pair of spur gear teeth in action is generally subjected to two types of cyclic stresses: bending stresses inducing bending fatigue and contact stress causing contact fatigue. Both these types of stresses may not attain their maximum values at the same point of contact fatigue. These types of failures can be minimized by careful analysis of the problem during the design stage and creating proper tooth surface profile with proper manufacturing methods. In general, gear analysis is multidisciplinary, including calculations related to the tooth stresses and to tribological failures such as wear or scoring. In this paper, bending stress analysis will be performed, while trying to design spur gears to resist bending failure of the teeth, as it affects transmission error. First, the finite element models and solution methods needed for the accurate calculation of bending stresses will be determined. Then bending stresses calculated using ANSYS, were compared to the results obtained from existing methods.

Introduction

Gears usually used in the transmission system are also called speed reducer, gear head, gear reducer etc., which consists of a set of gears, shafts and bearings that are factory mounted in an enclosed lubricated housing. Speed reducers are available in a broad range of sizes, capacities and speed ratios. In this paper, analysis of the characteristics of spur gears in a gearbox will be studied using linear Finite Element Method. Gear analysis was performed using analytical methods, which required a number of assumptions and simplifications. In this paper, bending stress analysis will be performed, while trying to design spur gears to resist bending failure of the teeth, as it affects transmission error. As computers have become more and more powerful, people have tended to use numerical approaches to develop theoretical models to predict the effect of whatever is studied. This has improved gear analysis and computer simulations. Numerical methods can potentially provide more accurate solutions since they normally require much less restrictive assumptions. The finite element method is very often used to analyze the stress state of an elastic body with complicated geometry, such as a gear.

There are two theoretical formulas, which deal with these two fatigue failure mechanisms. One is the Hertz equation, which can be used to calculate the contact stresses and other is the Lewis formula, which can be used to calculate the bending stresses. The finite element method is capable of providing this information, but the time needed to create such a model is large. In order to reduce the modeling time, a 3D model created in solid modeling software can be used. One such model is provided by PRO-E. PRO-E can generate models of three-dimensional gears easily. In PRO-E, the geometry is saved as a file and then it can be transferred from PRO-E to ANSYS in IGES form.

In ANSYS, one can click File > Import > IGES > and check.

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The main focus of the paper is:-
1) To develop and to determine bending stresses using ANSYS and compare the results with conventional methods.
2) To generate the profile of spur gear teeth and to predict the effect of gear bending using a three dimensional model and compare the results with those of the Lewis equation.
3) To compare the accuracy of results obtained is ANSYS by varying mesh density.

Finite Element Analysis

In this finite element analysis the continuum is divided into a finite numbers of elements, having finite dimensions and reducing the continuum having infinite degrees of freedom to finite degrees of unknowns. It is assumed that the elements are connected only at the nodal points. The accuracy of solution increases with the number of elements taken. However, more number of elements will result in increased computer cost. Hence optimum number of divisions should be taken. In the element method the problem is formulated in two stages: 2.1 The element formulation It involves the derivation of the element stiffness matrix which yields a relationship between nodal point forces and nodal point displacements. 2.2 The system formulation It is the formulation of the stiffness and loads of the entire structure.