Static structure analysis of Spur Gear

OBJECTIVE: To perform a static structural analysis on the given spur gear model for the three different materials (a) Cast Iron (ductile) (b) Cast Steel (c) Cast Bronze, and the results for (i) equivalent stress (ii) total deformation (iii) stress intensity and find the location of possible fracture. And then compare the results for all the cases and recommend the best material for the application.

SOLUTION:

STEP 1) Part Design

The spur gear model was already given.

STEP 2) Material Assignment

The study on the spur gear is carried out for three different materials.

1) Cast Iron (ductile)

2)Cast Steel

3)Cast Bronze

STEP 3) Connections

In this stimulation two bodies are coming in contact with each other so it is important to define the necessary contacts between the bodies.

The given model has 13 teeth on each gear. The contact and target faces were defined under contact type, with each body having 26 faces and the below conditions were given.

Then joints were defined for the model. The joint type is revolute joint and the connection type is Body-Ground.

STEP 4) Meshing

The models were meshed using the ANSYS mesher. Element size of 0.8mm was used for all the cases, thus utilizing the maximum capacity of ANSYS academic version.

The below parameter were taken same for all the cases. The element quality was found to be very good with average quality in the range of 0.86795.

STEP 5) Boundary conditions

In every case same boundary conditions were applied, as illustrated below.

STEP 6) Results

The total deformation, equivalent stress and stress intensity were evaluated for all the cases.

• Total deformation

Material	Maximum value over time	Minimum value over time
Cast Iron (ductile)	30 mm	0.24216 mm
Cast Steel	30 mm	0.24216 mm
Cast Bronze	30 mm	0.96822 mm

• Equivalent stress

Material	Maximum value over time	Minimum value over time
Cast Iron (ductile)	417.45 MPa	5.4758e-009 MPa
Cast Steel	416.48 MPa	7.2328e-009 MPa
Cast Bronze	409.96 MPa	6.6384e-009 MPa

• Stress intensity

Material	Maximum value over time	Minimum value over time
Cast Iron (ductile)	445.22 MPa	5.9635e-009 MPa
Cast Steel	446.39 MPa	7.4762e-009 MPa
Cast Bronze	444.19 MPa	7.5655e-009 MPa

• Possible fracture point

Stress intensity is the term used in study of fracture mechanics to analysis the concentration of stresses along the tip of a crack or notch.

From the above fig, it can be seen that the maximum equivalent stress and maximum stress intensity for the model is developed at the end of the tooth face. Hence as pe the stimulation, this point has the highest possibility for fracture. And from above case we can see the in practical also the fracture will occurs in that part of gear also.

• Best material for the application

The two factors will decide the best material for the gear, first one is the maximum stress developed in the tooth of the gear and the material cost.

Based on the stimulation carried out we can see that the maximum stress is developed in case of cast iron with 417.45 MPa and the minimum stress for cast Bronze with 409.96 MPa. We can see that the stress developed in all case have very minimum difference. So based on the results cast bronze will be the best material for the gear. But if we see on the prospective of cost, the material cost of cast bronze is very high as compare to other materials. As I stated that there is very minimum difference between the stresses. So in my opinion cast iron (ductile) the best material on the prospective of cost and strength.

CONCLUSION:

From the above results following conclusions can be inferred.

1. The equivalent stress for different materials was found and it was observed that the maximum stress was highest for cast iron and the minimum for cast bronze, but there is not significant difference between them.
2. The stress intensity value for different materials was found and it was observed that stress intensity is maximum in case of cast steel and minimum for cast bronze, but there is not significant difference between them.
3. The total deformation for all the cases is almost same.
4. The maximum equivalent stress and maximum stress intensity was found at the end of the tooth face, more specifically at the fillet of the flank. Hence, that point has the highest chance of failure.
5. Then from the above data and on the practical point of view we stated that the best material for the gear is cast iron.