Week 1 Spur Gear Challenge
Objective :
To carry out a static structural analysis on Spur gear to find out Equivalent stress, Total deformation and Stress intensity and the location for possible fracture for the following materials -
- Cast Iron(ductile)
- Cast Steel
- Cast Bronze
Prinicple :
The stress intensity factor describes the stress state at a crack tip, is related to the rate of crack growth, and is used to establish failure criteria due to fracture.
Given by the general formula
k = ασ√(πa)
where σ = far feild stress
a = cracked length
Apparatus :
Two Spur Gears having 13 teeth each, contact region being the sides of the teeth.
Materials :
1. Cast Iron(Ductile)
The material posseses excellent strength to weight ratio, superior castability and machinability and provides a designer with an exceptional combination of toughness, low cost manufacturing, and reliability.
2. Cast Steel
The physical properties of cast steel change significantly depending on chemical composition and heat treatment.
3. Bronze, Cast
Simulation :
1. Cast Iron (Ductile)
a) Stress Intensity
Stress Intensity min : 4.2002e-5 MPa
Stress Intensity max : 375.97 MPa
b) Equivalent stress
Equivalent stress min : 3.6621e-5 MPa
Equivalent stress max : 359.58 MPa
c) Total deformation
Total deformation min : 18.5 mm
Total deformation max : 30 mm
2. Cast Steel
a) Stress Intensity
Stress Intensity min : 3.8798e-5 MPa
Stress Intensity max : 380.71 MPa
b) Equivalent stress
Equivalent stress min : 3.8458e-5 MPa
Equivalent stress max : 362.15 MPa
c) Total deformation
Total deformation min : 18.5 mm
Total deformation max : 30 mm
3. Bronze, Cast
a) Stress Intensity
Stress Intensity min : 5.9964e-5 MPa
Stress Intensity max : 376.85 MPa
b) Equivalent stress
Equivalent stress min : 5.8172e-5 MPa
Equivalent stress max : 354.28 MPa
c) Total deformation
Total deformation min : 0.9682 mm
Total deformation max : 30 mm
Location for possible facture:
The region colored with red experiences the maximum stress.
Observations:
| Material | total | deformation | Elastic | Stress | Stress | Intensity | ||
| min | max | min | max | min | max | |||
| Cast Iron | 18.5 | 30 | 3.6621e-5 | 359.58 | 4.2002e-5 | 375.97 | ||
| Cast Steel | 18.5 | 30 | 3.8458e-5 | 362.15 | 3.8798e-5 | 380.71 | ||
| Bronze, Cast | .9682 | 30 | 5.8172e-5 | 354.28 | 5.9964e-5 | 376.85 |
Conclusion :
On the basis of comparison, we can see that all the tests for each material differs by a small amount in terms of stress intensity and elastic stress. Comparing with the materials respective Young Modulus values we can use any of the three material. Since there is a need for mass production, Bronze should not be favourable due to its cost and availablity. considering all other aspects as in the table the ideal material will be cast steel as steel is superior in tension, and does not rust leading to longer life.