spur gears analysis
Objective: Simulation of spur gears using different materials and to find equivalent stress, deformation, and stress intensity.
Pre-processing steps: Using all the listed material given in the objective from engineering material library we perform the analysis on the spur gears one by one.
The material used are cast iron, cast steel and bronze cast.
first, we have imported the cad model in the design modeler and checked to see if there is some error.
In the mechanical model cell, we have assigned materials to the gears, set frictional contact of coefficient “0” between the gear tooths and with symmetric behavior. Here we use augmented LaGrange formulation to avoid penetration between the bodies and for interface treatment we use \"adjust to touch.\"
To rotate the gears along the z-axis, we are using revolute joint(body- ground) for each gear.
Mesh: Default mesh is used to mesh the gears with smoothing set to \"medium\" and adaptive sizing to \"yes\". As we are using academics version, the no. of nodes and element were kept below the limit imposed by academic version. The figures below show the meshed body and statistics of the meshed element.
Analysis settings: This setup was run in six steps with large deflection \"on\".
Joints: The revolute joint in the left gear was given rotation in 6 steps with an increment of 30 degrees (anticlockwise) and moment of constant -10Nm was given to right gear (clockwise).
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Post-processing :
Case 1: Cast iron ductile
- Equivalent stress Max stress :302.77 MPa
- Stress intensity Max stress intensity: 333.45MPa
- Total deformation Max deformation:30mm
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Case 2: Cast steel
- Stress Max stress: 300.89 MPa
- Stress intensity Max stress intensity: 333.39MPa
- Deformations Max deformation:30mm
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Case 3: Bronze cast
- Stress Max stress: 314.86 MPa
- Stress intensity Max stress intensity: 352.04MPa
- Deformations Max deformation:30mm
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Graph-comparison:
- Average-Deformations vs time
- Average Stress vs time
- Average Stress intensity vs time
Conclusion:
Yield strength Ultimate strength Young mod (MPa)
Cast iron 344 548 171000
Cast steel 349 505 203000
Bronze cast 144 267 80000
Maximum deformation of 30mm is seen at the tooth land in all the cases due to the meshing of two teeth which is indicated by red color and minimum deformation is seen at gear inner surface.
From the above avg stress vs time graph, it can be seen stress is maximum for cast steel and ranking the above material in term of stress developed in the gear: Cast steel>Cast iron>Bronze cast. This stress is maximum at the point of contact between two gears. To stop the material from going to the plastics region, the stress should be under yield limit and the material won\'t crack until it reaches the ultimate limit of stress.
The reason cast steel has the highest stress is mainly due to high young modulus than the other two. Ranking in terms of young modulus: cast steel>cast iron>cast bronze. For cast iron and cast steel, the max stress is below the yield limit so it hasn\'t gone plastics deformations but, for the bronze cast, it has crossed its yield limit so it has undergone plastics deformations.
Stress intensity: The term stress intensity factor is used in fracture mechanics of materials to predict the propagation rate of crack and the state stress. This theory has some assumption like material has to be homogeneous and linear elastics in nature when loaded. Whenever a part with some discontinuity is loaded ununiformly more stresses are developed near the discontinuity which may fail the material by creating a crack and propagating. Engineers are more concerned with the stress generated near the tip of the crack whether it crosses the fracture toughness. The stress are very difficult to estimate practically so we use stress intensity factor.
From the above graphs and contours, we can draw a conclusion that the cast steel will be better for gear material because of its high young modulus. Cast iron is brittle in nature and will have less resistance to impact. Cast bronze has the lowest young modulus and is very ductile.