2d fem analysisof spurgeartooth

8/12/2019 2D FEM AnalysisOf SpurGearTooth

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2 D FEM analysis of spur gear tooth

Group Members: Ajay Vora , Nakul Nuwal , Prateek Nyati

Introduction and motivation

Spur gears having involute profile are designed to transmit torque in parallel shafts. These gears

have teeth that experience bending stresses.

In the case of intricate geometries like this, where shape of the gear tooth profile is veryimportant, the type and size of elements in FEM analysis will play an important role in accuracy

of final results. Capturing the boundary of the involute profile of gear tooth is very important if

we want to get the correct results. It is expected that when we decrease the element size to

smaller and smaller value, we will get better and better approximation to the profile and

consequently, better results. Parametric study with respect to mesh size and type of elements

is very important in this case.

Also, in the problems like this where we have localized stress concentrations at the point of

application of load and high amount of localized deformations, choice of higher order shape

functions might give significantly different results. Study of effect of using different quadrature

rules on the final results will help to improve understanding of the importance of order and

type of different kinds of shape functions.



Figure 1 Triangular finite element

Displacements u and v at any point inside the element

Figure 2 triangular parent element



Relationship between Cartesian and parent co ordinates

Element Strain matrix

Using rules of prtial derivatives we will find jacobians for transformation matrix



Element stress recovery for homogeneous isotropic material



Element Stiffness matrix

Using gauss quadrature

For any parameter inside the element

Body forces

due to body forces



Boundary conditions

Analysis using Ansys

Mesh 1

Results



Results



Formulation and governing equations reference

1. Finite elements analysis procedures in engineering by H.V. Lakshminarayanana

2d fem analysisof spurgeartooth

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