Static Structural Analysis of Spur Gear

OBJECTIVE:

To carry out static structural analysis on the given spur gear model for three different materials (a) Cast iron (ductile) (b) Cast Steel (c) Cast Bronze, and evaluate the (i) equivalent stress (ii) total deformation (iii) stress intensity and (iv) find location of possible fracture, for all three cases.

To perform a detailed comparison of the results and recommend the best material for the application.

SOLUTION:

Step 1: Part Design

The spur gear model was given.

Step 2: Material

The study on the spur gears has to be carried for three different materials.

1. Cast iron (ductile)

2. Cast steel

3. Cast bronze

Step 3: Connections

Since the spur gear simulation consists of two bodies coming in contact, it is important to define necessary contacts between the bodies.

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

Contact type - Frictional

Formulation - Augmented Lagrange

Interface treatment - Adjust to touch

Further, joints were defined for the model. Both the gears are revolute joints 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 utilising the maximum capacity of ANSYS academic version.

The below parameters were taken same for all the cases. The element quality was found to be very good with average quality in the range of 0.906.

Step 5: Boundary conditions

All models were subjected to the same boundary conditions, as illustrated below.

The analysis was carried out over 6 steps defined by time, with initial time step = 0.1s, minimum time tep = 0.05s and maximum time step = 0.2s. The large deflection option was turned on.

The joints were also defined accordingly. A moment of 100Nm was given on one of the gears and a rotation of 120 degree was given on the other.

Step 6: Results

The equivalent stress, stress intensity and the total deformation were evaluated for each of the above cases.

1. Equivalent stresses

	Maximum stress (MPa)	Average stress (MPa)	Minimum stress x 10-8(MPa)
Cast iron	327.39	144.51	1.9
Cast steel	326.73	144.21	2.35
Cast bronze	325.66	144.74	5.3

2. Stress Intensity

	Maximum Stress Intensity (MPa)	Average Stress Intensity (MPa)	Stress Intensity x 10-8(MPa)
Cast iron	343.19	152.53	2.239
Cast steel	344.83	153.26	2.714
Cast bronze	347.87	154.61	6.1407

3. Total deformation

	Maximum deformation (mm)	Minimum deformation (mm)
Cast iron	25.985	16.04
Cast steel	25.984	16.021
Cast bronze	25.996	16.021

4. Possible fracture point

From the above figure, 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 per the simulation, this point has the highest possibility for fracture.

5. Best material for the application

The best material for this application can be decided taking into consideration two factors, maximum stresses developed and cost of the material.

Based on the simulations carried out, the maximum stress is developed for cast iron model with 327.39MPa and the minimum stress is for cast bronze model, 325.66MPa. It should be noted that the stress values does not have a significant difference. So based on the analytical results, cast bronze might be preferred material. But for any application cost is also an important factor. The below table gives the cost comparison for the three materials.

Material	Cost (USD per kg)
Cast Iron (ductile)	1.31 – 1.42
Cast Steel	2 – 2.45
Cast bronze	8 – 12

The cost of cast bronze is very high compared to cast iron, and this increase in cost may not be justifiable for the very small change in stress value offered by cast bronze.

Hence cast iron is recommended for the spur gear application.

CONCLUSIONS:

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 it is worth noting that the difference in these values are not significant.
2. The stress intensity values showed a different trend, with cast bronze having the highest value and cast iron having the least value. The difference in the values were not very significant.
3. The deformation developed in the model for all three materials were found to be similar (almost equal).
4. The maximum equivalent stress and maximum stress intensity were found at the end of the tooth face, more specifically at the flank and dedendum circle. Hence this point has the highest chance of failure.
5. Considering the maximum stress values developed and the cost of different materials, it is concluded that cast iron is the best material for the spur gear application.