Week 1 Spur Gear Challenge

Stress Concentration on a Spur Gear

OBJECTIVES:

To carry out a Static Structural Analysis on Spur Gear for the given three cases which uses different material for the spur gear and determine the stress, deformation and location of possible failure.

CASE-1:

            For Case-1, Static Structural Analysis was carried out with the given spur gear model. The material used for this analysis was CAST IRON and the analysis was carried out using ANSYS Mechanical Enterprise. The model for the case-1 was imported to ANSYS Workbench software and is shown in the figure below.

Fig.1 Case-1 Spur Gear Model

Later the material was assigned and the material and its properties used for this analysis are specified below for both gears.

Material	Cast Iron
Density	6.999e-6 kg/mm3
Young’s Modulus	89440 MPa
Thermal Conductivity	0.06 W/mm°C
Specific Heat	4.996e+5 J/tonne°C
Tensile Yield Strength	79.81 MPa
Tensile Ultimate Strength	141.4 MPa

 Then the model was meshed in ANSYS Mechanical Enterprise with an element size of 1.0mm and using Tetrahedrons and Hexahedrons was employed. This was done to get better mesh.

Fig.2 Element Quality

A mesh metric that identifies elements according to their quality was employed and it can be seen that the elements of lowest quality are minimal. Most of the elements have very high quality in the range of 0.8 to 1. Hence, the mesh is of acceptable quality. The meshed model is shown below.

Fig.3 Meshed Model

Then Contacts were provided with FRICTIONAL type, SYMMETRIC behaviour and using AUGMENTED LAGRNGIAN formulation method and ADJUST TO TOUCH Interface Treatment. Later REVOLUTE Joints was assigned to both the gears with BODY-GROUND Connection Type. The Simulation is then run with the applied Joint Loads of i) ROTATION for one gear with 180-degree rotation angle and ii) MOMENT for other gear with a magnitude of 10Nm for 6 number of steps for the entire analysis run.  It was ensured that both the gears rotate in Opposite Direction and simulation was carried out and results were obtained for Equivalent Stress, Total Deformation and Stress Intensity where stress intensity predict the stress state near the tip of a crack or notch caused by a remote load or residual stresses.

Fig.4 Frictional Contact

Fig.5 Revolute Joint

Fig.6 Load Applied (Rotation and Moment)

CASE-2:

            For Case-2, Static Structural Analysis was carried out with the given spur gear model. The material used for this analysis was CAST STEEL and the analysis was carried out using ANSYS Mechanical Enterprise. Later the material was assigned and the material and its properties used for this analysis are specified below for both gears.

Material	Cast Steel
Density	7.82e-6 kg/mm3
Young’s Modulus	20.3e+04 MPa
Thermal Conductivity	0.06 W/mm°C
Specific Heat	4.996e+5 J/tonne°C
Tensile Yield Strength	349 MPa
Tensile Ultimate Strength	505 MPa

 The same contacts and load used in Case-1 was used in Case-2 also with only change in Material of the Spur Gear. Then the analysis was run and results were obtained.

CASE-3:

            For Case-3, Static Structural Analysis was carried out with the given spur gear model. The material used for this analysis was CAST BRONZE and the analysis was carried out using ANSYS Mechanical Enterprise. Later the material was assigned and the material and its properties used for this analysis are specified below for both gears.

Material	Cast Iron
Density	8.810e-6 kg/mm3
Young’s Modulus	8e+05 MPa
Thermal Conductivity	0.06 W/mm°C
Specific Heat	4.996e+5 J/tonne°C
Tensile Yield Strength	144 MPa
Tensile Ultimate Strength	267 MPa

 The same contacts and load used in Case-1 was used in Case-3 also with only change in Material of the Spur Gear. Then the analysis was run and results were obtained.

RESULTS:

The Total Deformation at last (6s) for all the three cases was obtained from the analysis and compared below.

Case	Minimum [mm]	Maximum [mm]	Average [mm]
1	0.96822	30	23.995
2	0.96822	30	23.712
3	0.96822	30	23.995

 The Equivalent (Von-Mises) Stress at last for all the three cases was obtained from the analysis and compared below.

Case	Minimum [MPa]	Maximum [MPa]	Average [MPa]
1	4.3325e-009	374.86	8.2382
2	9.2784e-009	369.30	9.3215
3	1.1482e-008	371.94	8.3036

The Stress Intensity at last for all the three cases was obtained from the analysis and compared below.

Case	Minimum [MPa]	Maximum [MPa]	Average [MPa]
1	4.8515e-009	397.02	8.9269
2	1.0318e-008	395.71	10.103
3	1.2543e-008	399.13	9.0045

 The Total Deformation for all the three cases obtained from the analysis is shown below.

Fig.7 Total Deformation Contour Plot

The Equivalent (Von-Mises) Stress for all the three cases obtained from the analysis is shown below.

Fig.8 Equivalent Stress Contour Plot

The Stress Intensity for all the three cases obtained from the analysis is shown below

Fig. 9 Stress Intensity Contour Plot

The Total Deformation graph/table plot is shown below.

Fig.10 Total Deformation Table Plot

The Equivalent (Von-Mises) Stress graph plot is shown below.

Fig.11 Equivalent Stress Table Plot

The Stress Intensity graph plot is shown below

Fig. 12 Stress Intensity Table Plot

LOCATION OF POSSIBLE FACTURE:

            The Spur Gear, for the given load may facture or start to fail at the location of High Stress Regions or High Stress Intensity area which is as shown in the figure below.

Fig. 13 Possible Facture Location

This is the region where the stress is higher and it tends to crack/expand on the opposite side of high stress shown in the above figure as the gear rotates for longer cycles, due to the Moment acting on the gear, high force or torque acts on the mating gear tooth thus pushing or rotating the other gear. This results in breaking or cracking of the tooth gear where the stress is more. This is same for all the three cases.

CONCLUSION:

            The analysis was run successfully for all three cases and results were obtained and tabulated.

While comparing the Total Deformation sustained by the models, there is a slight variation in the average deformation by an order of 0.28mm. From the both model cases, Case-2 (Cast Steel Spur Gear) has lesser average deformation compared to Case-1&3.

            While comparing the Equivalent Stress obtained by all the models, there is a least noticeable variation in the average, minimum and maximum stress by an order of 0.1 to 2 MPa. From the all three model cases, Case-2 Model has lesser deformation compared to Case-1&3.

I. Recommended Material:

From Analysis point of view, Case-2 (CAST STEEL) design model can be selected and used because for the given load Case-2 model has lesser Stress when compared to the other materials. Also, the total deformation is quite close similar.

II. Order of Materials for Spur Gear:

Cast Steel << Cast Bronze ≤ Cast Iron. In case of Stress Intensity Cast Steel << Cast Iron.