Spur Gears- Comparing the Structural Analysis results for different materials and Stress Intensity

Spur Gears- Comparing the Structural Analysis results for different materials and Stress Intensity

Objective

Conducting Static Structural Analysis for 3 different materials- Cast Iron (ductile), Cast Steel, Cast Bronze, and evaluating the results for Total Deformation, Equivalent Von-Mises Stress, and Stress Intensity. As well as identifying the region where fracture will occur.

Case 1

For the first case, Cast Iron (ductile) material is assigned to the model in ANSYS. The material data is available is added from the ANSYS Engineer Data and following are the material properties for Cast Iron.

In ANSYS mechanical, the material is assigned simply by selecting the geometry and replacing the default assigned material to Cast Iron (ductile)

After defining appropriate contacts and joints, meshing is generated at default element size and solution is run. No errors occurred and solution finished successfully, after which the element size was reduced to 1 mm. The Hex-dominant mesh is generated as shown below.

Following results are obtained upon the completion of analysis.

Case 2

For case 2, Cast Steel material is assigned to the model and rest of the process is conducted in similar way as the previous case. The mesh is generated at the 1mm element size.

Following are the properties for the Cast Steel material.

Following results were obtained from the analysis for the Cast Steel material.

Case 3

For this case, Cast Bronze is assigned material for the analysis and the rest of the process is carried out in the similar way as previous cases. Mesh is generated at 1mm element size.

Following are the properties for the Cast Bronze.

From the analysis, following results are obtained for the Cast Bronze material.

Discussion

Once all the results have been obtained, comparing the results shall provide clear picture on which material should be selected for the manufacturing of the gears.

Below is the comparison of the results.

On comparing the obtained results, it is observed that there is no difference in the Total deformation values as all the cases have 30 mm maximum deformation.

All these materials are used for the manufacturing of gears based on their applications.

Amongst the three material, Cast Steel has the highest Equivalent Stress and Cast Bronze experiences lowest Equivalent Stress. So, prima facie, Cast Bronze is the suitable material since it experiences least Stress amongst the three. But, the Stress of 402.94 MPa is way beyond its Yield Strength and Ultimate Tensile Strength. Therefore, Cast Bronze cannot be recommended for this loading. Besides, it also has high density, therefore it would weigh very heavy compared to other materials, if it were to modify to resist the given loading.

The Equivalent stress developed in both Cast Iron (ductile) and Cast Steel exceed their Yield strengths significantly. Therefore, plastic deformation will take place. It can be concluded that in both the cases, the material will fail after some time, unless modifications are made in the designs.

But before suitable material can be recommended, lets look at Stress Intensity.

Stress Intensity

In Fracture Mechanics, stress intensity plays a crucial role. When a fracture occurs, cracks develop to form an opening where stresses are concentrated more than other areas. So, it is important to identify if the max stress near crack tip exceeds fracture toughness. But it is difficult t identify the stresses in these zones, so Stress Intensity Factor, K, is used to determine whether crack will grow rapidly or not.

It is given by the formula, K=σ √πa

Where ‘σ’ is applied stress and ‘a’ is the crack width.

Now, from the obtained results, max Stress Intensity for Cast Iron (ductile) is 480.33 MPa and for Cast Steel is 539.55 MPa. For Cast Steel, this value exceeds even its UTS of 505 MPa. Therefor, the cracks will propagate rapidly after failure occurs.

For Cast Iron (ductile), this value is still below its UTS of 548 MPa. So even though the material fails, it can last longer compared to Cast Steel. Therefor, Cast Iron (Ductile) shall be used for this application.

From the picture below, Max stress is concentrated at the root of the tooth. Therefore, fracture will occur at this place and developed crack will grow.