Spur Gear Challenge

Stress intensity :The stress intensity, K_I, represents the level of “stress” at the tip of the crack and the fracture toughness, K_IC, is the highest value of stress intensity that a material under very specific (plane-strain) conditions that a material can withstand without fracture. As the stress intensity factor reaches the K_IC value, unstable fracture occurs.

Engineers are interested in the maximum stress near the crack tip and whether it exceeds the fracture toughness. Thus, the stress intensity factor K is commonly expressed in terms of the applied stresses at and . For example, for a through crack in an infinite plate under uniform tension , the stress intensity factor is

where a is one half of the width of the through crack. The dimension of K is In the last few decades, many closed-form solutions of the stress intensity factor K for simple configurations were derived. Some of the common ones are listed in the following three categories: classic, specimen, and structure.

Objective : To run analysis of spur gear mated to each other and compute the stress, deformations and possible crack location for the the three kinds of materials:

1. Cast Iron

2. Cast Steel

3. Cast Steel

Geometry : Spur Gear Geometry imported from provided file.

Cases: The material properties are taken as follows for the three cases as follows:

Contacts : The contact type provided is frictional with the mating surfaces of gears selected as Contact and Target. The Behaviour is changed to symmetric and the Formulation type used is Augmented Lagrange. The interface treatment is set to Adjust to Touch.

Joints : The joints are set to Ground to Body for both the bodies as both the gears are rotating along their axes.

Joint Load : One of the gears is given rotation for six time steps and the other is given a constant moment of 10 N-m.

Joint Moments

Mesh : The body is meshed with adaptive sizing off. 1mm element size. The node count is 16586 and element count is 2808.

Stress Plots :

CASE 1 (CAST IRON) - 327.74 MPa

CASE 3 (CAST Bronze) - 318.55 MPa

CASE 2 (CAST STEEL) - 327.37 MPa

Deformation Plots:

CASE 3 -CAST BRONZE

CASE 1- CAST IRON

CASE 2 - CAST STEEL

Stress Intensity Plots:

CASE 3 -CAST BRONZE - 330.28 Mpa

CASE 1- CAST IRON - 335.75 MPa

CASE 2 - CAST STEEL - 336.88 MPa

LOCATION OF CRACK : The crack is approximated to initiated at gear root and land of the mating tooth. This leads to maximum Stress Intesnity and thus fracture is approximated to occur at this location.

Pressure Plots :

Result Comparison :

	Equivalent Stress Max (Mpa)	Total Deformation Max (mm)	Stress Intensity (Mpa)
CASE 1 ( CAST IRON)	327.74	30	335.75
CASE 2(CAST STEEL)	327.37	30	336.88
CASE 3(CAST BRONZE)	318.55	30	330.28

As Visible from the results Stress Intensity is maximum in CAST STEEL there for it is very likely to fail under same loading. So Cast Bronze should be used for usage. But Casr bronze is very costly. So considering both the factors I would recommend using Cast Iron which is economically feasible and having Stress Intensity in between both Cast Steel and Cast Bronze.

Attachments - Model File and Animation for one Run