Spur Gear Challenge
Spur Gear Challenge
Aim: To understand effects acting on two spur gears which are in a mesh, when in revolute motion with respect to each other.
Introduction: A spur gear is a gear with teeth that project outwards from a cylindrical surface. In spur gears, the edge of each tooth is parallel to the axis of rotation and they mesh together when they are fitted to parallel shafts. Each time a gear tooth engages a tooth on the other gear, the teeth collide, and this impact makes a noise. It also increases the stress on the gear teeth.
Stress Intensity is an important parameter in fracture mechanics. It is represented by Stress Intensity Factor, K, which I used in fracture mechanics to predict the stress state near the tip of a crack or notch caused by a remote load or residual stress.
Stress Intensity Factor, K = σ √π a
Where σ = Applied Stress, a = Crack Width
Geometry:
Spur gears in mesh with each other are shown above.
Contacts:
Frictional Contact between the maximum contacting surfaces. Augmented Lagrange to stop the part from moving off from its location when the teeth come in contact & also to damp the vibration.
Adjust to touch Interface treatment is used.
Both the gears are treated to be revolute joints.
Mesh:
Element Size : 0.5mm
No of elements: 19232
No of nodes: 96672
Analysis Setting:
Large deflection is turned on.
Boundary Conditions:
Left Spur Gear revolute joint has been assigned with the rotational load as shown above.
Right Spur Gear revolute joint has been assigned with momentum as shown above
Case 1: Cast Iron
Material Data:
All the important mechanical properties of the material have been defined in the table above.
Convergence & Time Increment Plot:
Total Deformation:
Max deformation of about 30mm as seen above.
Equivalent Stress:
Max Stress of about 460 Mpa as seen above.
Equivalent Elastic Strain:
Max Equivalent Elastic Strain of 0.00528 mm/mm as seen above.
Stress Intensity:
Max Stress Intensity of 520 Mpa at the crack tip as seen above.
Contact Status:
Contact status for the tooth surfaces in motion has been described above.
Contact Pressure:
Max Contact Pressure of 476Mpa at the denoted point as shown above.
Case 2: Cast Steel
Material Data:
All the important mechanical properties of the material have been defined in the table above.
Convergence & Time Increment Plot:
Total Deformation:
Max deformation of about 30mm as seen above.
Equivalent Stress:
Max Stress of about 458 Mpa as seen above.
Equivalent Elastic Strain:
Max Equivalent Elastic Strain of 0.00528 mm/mm as seen above.
Stress Intensity:
Max Stress Intensity of 517 Mpa at the crack tip as seen above.
Contact Status:
Contact status for the tooth surfaces in motion has been described above.
Contact Pressure:
Max Contact Pressure of 533 Mpa at the denoted point as shown above.
Case 3: Cast Bronze
Material Data:
All the important mechanical properties of the material have been defined in the table above.
Convergence & Time Increment Plot:
Total Deformation:
Max deformation of about 30mm as seen above.
Equivalent Stress:
Max Stress of about 441 Mpa as seen above.
Equivalent Elastic Strain:
Max Equivalent Elastic Strain of 0.00694 mm/mm as seen above.
Stress Intensity:
Max Stress Intensity of 494 Mpa at the crack tip as seen above.
Contact Status:
Contact status for the tooth surfaces in motion has been described above.
Contact Pressure:
Max Contact Pressure of 461 Mpa at the denoted point as shown above.
Comparison:
|
Total Deformation (mm) |
Equivalent Stress (Mpa) |
Stress Intensity (Mpa) |
|
|
Cast Iron |
30 |
460.97 |
520 |
|
Cast Steel |
30 |
458.92 |
517.1 |
|
Cast Bronze |
30 |
441.46 |
494.13 |
From the above comparison, Cast Bronze has equivalent stress of 441Mpa & Stress Intensity of 494Mpa which is way beyond its Ultimate Strength of 267 Mpa & hence, Cast Bronze Spur Gear will fail. On the contrary, even though equivalent stress & stress intensity of Cast Steel is slightly below as compared to Cast Steel, the ultimate strength of Cast Iron (820Mpa) is higher than Cast Steel (505Mpa) & hence will run for few more no of cycles.