Gear Selection for Spur Gear
Spur Gear Simulation
Analysis of Spur Gear:
Carried out Analysis of spur gear with 6-time steps.
One gear with a rotation of 30 degrees for each time step and the other gear with a constant moment of 10 N-m.
Assigned only the mating surfaces as contact surface in order to reduce computation time.
The simulation was carried out for three different materials, Cast Iron(ductile), Cast Steel and Cast Bronze.
Reduced mesh size until the stress converged to a similar value.
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Location of Fracture:
The location of fracture for the Spur gear for the given problem is the root of the gear, because the tooth of the gear acts like a cantilever beam.
It is indicated as Max. in the image below.
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Results for Spur Gear- Cast Iron (Ductile):
Max. Equivalent stress: 3.86E8 Pa
Max. Equivalent strain: 0.00227
Total Deformation: 0.03 m
Stress Intensity: 4.1033E8 Pa
Mesh Convergence:
|
Mesh Size (mm) |
Max. Equivalent Stress (Pa) |
Max. Equivalent Strain |
Total Deformation(m) |
|
2 |
3.26E8 |
0.00192 |
0.03 |
|
1.9 |
3.39E8 |
0.00201 |
0.03 |
|
1.2 |
3.43E8 |
0.00203 |
0.03 |
|
1 |
3.86E8 |
0.00226 |
0.03 |
|
0.9 |
3.86E8 |
0.00227 |
0.03 |
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Results for Spur Gear- Cast Steel:
Max. Equivalent stress: 3.86E8 Pa
Max. Equivalent strain: 0.00192
Total Deformation: 0.03 m
Stress Intensity: 4.1194E8 Pa
|
Mesh Size (mm) |
Max. Equivalent Stress (Pa) |
Max. Equivalent Strain |
Total Deformation(m) |
|
1.2 |
3.75E8 |
0.00220 |
0.03 |
|
1 |
3.88E8 |
0.00192 |
0.03 |
|
0.9 |
3.86E8 |
0.00192 |
0.03 |
|
0.8 |
3.75E8 |
0.00296 |
0.03 |
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Results for Spur Gear- Cast Bronze:
Max. Equivalent stress: 2.76E8 Pa
Max. Equivalent strain: 0.0034
Total Deformation: 0.03 m
Stress Intensity: 2.94E8 Pa
Mesh Convergence:
|
Mesh Size |
Equivalent Stress (Pa) |
Equivalent Strain |
Total Deformation(m) |
|
1.7 |
2.96E8 |
0.0037 |
0.03 |
|
1.6 |
2.20E8 |
0.0027 |
0.03 |
|
1.55 |
2.76E8 |
0.0035 |
0.03 |
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Choosing material for the gear:
On comparing the simulation results from the three material we can eliminate Cast Bronze since maximum stress for Cast Bronze is 2.76E8 Pa which is substantially lower than Cast Steel and Cast Iron (Ductile).
Comparing the values of Cast Steel and Cast Iron (Ductile) below,
|
Cast Iron (Ductile) |
Cast Steel |
|
|
Equi. Stress value |
3.86E8 Pa |
3.75E8 Pa |
|
Equi. Strain value |
0.0023 |
0.003 |
|
Total Deformation |
0.03 |
0.03 |
|
Stress Intensity |
4.103E8 Pa |
4.118E8 Pa |
|
Young’s Modulus |
1.71E11 Pa |
2.03E11 |
|
Tensile Ultimate Strength |
5.48E8 Pa |
5.05E8 Pa |
|
Tensile Yield Strength |
3.44E8 Pa |
3.49E8 Pa |
We want to select the material that is more Brittle among the two since, we want the gear to fail through brittle fracture. If the gear fails by ductile fracture, the gear material will plastically deform before failure, which will affect the mating of gears.
Comparing the values of Cast Iron(Ductile) and Cast steel, we notice that,
1) The stress intensity of the Cast Steel gear is higher than the Cast Iron(Ductile) gear
Brittle materials have sharper crack in comparison to ductile material i.e., brittle materials have smaller crack tip radius then ductile material.
From the equation and the Stress intensity values we can conclude that Cast Steel(with higher stress intensity) is more brittle.
2) The difference between Ultimate strength and Yield Strength is higher for Cast Iron (ductile) then Cast Steel. Also, indicating Cast Steel is more brittle.
Conclusion: Thus, we can choose Cast Steel as the gear material.