Week 1 Spur Gear Challenge

Stress concentration on spur Gear

Case 1

For case 1 static structural analysis is carried out on spur gear. The material used is cast iron and analysis is carried out in ANSYS workbench. The model is taken from the challenge it self.

The material properties of cast iron as below

Density: 7200 Kg m^-3

Coefficient of thermal expansion: 1.1E-05 C^-1

Young modulus: 1.1E+11 Pa

Poisson’s Ratio: 0.28

Bulk Modulus: 8.3333E+10 Pa

Shear Modulus: 4.2969E+10 Pa

Tensile Ultimate strength: 2.4E+08 Pa

Compressive Ultimate strength: 8.2E+08 Pa

We had assign both the gear as cast iron for case 1 as shown in below figure

The model has meshed using ANSYS mesher with an element size 0.5 mm. Suing smoothing quality as low,

A Mesh metric that identifies elements according to their quality was employed and it can be seen that the elements of the lowest quality are the minimal. Most of the elements have very high quality in the range of 0.5 to 1. Hence, the mesh is of acceptable quality. The meshed model is as shown in image below

We made the connection one gear is as contact other gear as target, and we made connection as frictional type and use the formulation as augmented Lagrange’s, behaviors as symmetric.

We created 2 joints for one for each gear, and used the connection type as body to ground and type as revolute.

Analysis setting was done as number of step put as 6 and we defined it by time in second, initial time step was 0.2 second, minimum time step was 5e-2 second and maximum time step was 0.5 second.

We has used 2 joint load, one for each gear, one is rotational (driver gear in our case right gear) other is moment (Driven Gear in our case left gear) of 10 N-m at each step, total revolution was divided into 6 step so each step was 30 degree.

And we had solve the simulation for total deformation, equivalent stress & stress intensity and elastic strain & total strain, contact status and pressure.

The simulation is then run with the setting applied and the result obtained.

Case 2

For case 2 we had duplicate the project which was prepared in case 1, and change the material from cast iron to cast steel,

Material Properties of Cast Steel as below

Density: 7820 Kg m^-3

Coefficient of thermal expansion: 1.1E-05 C^-1

Young modulus: 2.03E+11 Pa

Poisson’s Ratio: 0.3

Bulk Modulus: 1.6917E+11 Pa

Shear Modulus: 7.8077E+10 Pa

Tensile Yield strength: 3.49E+08 Pa

Tensile Ultimate strength: 5.5E+08 Pa

The simulation is then run with the setting applied and the result obtained.

Case 3

For case 3 we had duplicate the project which was prepared in case 1, and change the material from cast iron to cast steel,

Material properties of Cast Bronze as below

Density: 8810 Kg m^-3

Coefficient of thermal expansion: 1.68E-05 C^-1

Young modulus: 8E+10 Pa

Poisson’s Ratio: 0.345

Bulk Modulus: 8.6022E+10 Pa

Shear Modulus: 2.974E+10 Pa

Tensile Yield strength: 1.44E+08 Pa

Tensile Ultimate strength: 2.67E+08 Pa

The simulation is then run with the setting applied and the result obtained.

Result:

The total deformation for the three cases are compared below:

Material	time (s)	Min(mm)	Max(mm)	Ave(mm)
Cast Iron	6	18.5	30	23.567
Cast steel	6	18.5	30	23.576
Cast bronze	6	18.5	30	23.576

The equivalent stress for the three cases are compared below

Material	time(s)	Minimum (MPa)	Maximum (MPa)	Average (MPa)
Cast Iron	6	3.8424e-005	462.57	9.0436
Cast steel	6	3.7904e-005	457.75	9.07
Cast bronze	6	8.594e-005	443.07	9.084

The Stress intensity for the three cases are compared below

Material	time(s)	Minimum (MPa)	Maximum (MPa)	Average (MPa)
cast iron	6	4.4368e-005	520.76	9.861
cast steel	6	4.3753e-005	513.92	9.9133
Cast bronze	6	9.5124e-005	493.89	9.9387

The Elastic strain for the three cases are compared below

Material	time(s)	Min	Max	Ave
Cast Iron	6	4.565e-010	5.1125e-003	8.6285e-005
Cast Steel	6	2.5428e-010	6.3005e-003	8.8398e-005
Cast bronze	6	1.0748e-009	6.6925e-003	1.1909e-004

The total strain for the three cases are compared below

Material	time(s)	Min	Max	Ave
Cast iron	6	4.565e-010	5.1125e-003	8.6285e-005
Cast steel	6	2.5428e-010	6.3005e-003	8.8398e-005
Cast bronze	6	1.0748e-009	6.6925e-003	1.1909e-004

The Pressure for the three cases are compared below

Material	time(s)	Minimum (MPa)	Maximum (MPa)	Average (MPa)
Cast Iron	6	0	461.99	17.008
Cast steel	6	0	452.88	17.082
Cast bronze	6	0	456.41	456.41

Pictures of result:

Case 1 : Cast Iron

Total deformation

Equivalent Stress: Cast Iron

Stress intensity: cast Iron

Elastic Strain: cast iron

Total STrain: Cast Iron

Pressure: Cast Iron

Contact Status : Cast Iron

Case 2: For using material Cast Steel

Total deformation: Cast steel

Equivalent stress: Cast steel

Stress Intensity: Cast steel

Elastic strain: Cast Steel

Total strain: Cast steel

Pressure: Cast steel

Contact Status: Cast Steel

Case 3: Cast Bronze

Total deformation: Cast Bronze

Equivalent Stress: Cast Bronze

Stress Intensity : Cast bronze

Elastic Strain : Cast Bronze

Total strain: Cast bronze

Pressure: Cast Bronze

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Contact status: Cast bronze

Conclusion:

The analysis was run successfully. Within the limit of academic license, the simulation for the 3 cases were examined. The mesh size of all cases are kept same as 0.5 mm.

On Comparison of the total deformation experience by the model in all 3 cases, we had found not any difference in any cases. We had found minimum deformation as 18.5 mm, maximum deformation as 30 mm and average deformation as 23.576 mm in all cases.

On comparison of equivalent stress experience by the model in all three cases, we found maximum stress (462.57 MPa) on cast iron material and minimum stress (443.07 MPa) on cast bronze model. As we know the mechanical properties of all three model and cast iron have maximum ultimate tensile stress which is 820 MPa , and fro cast bronze ultimate tensile strength is 267 MPa, thus comparing with Ultimate tensile stress cast bronze model is not fit for maximum pressure as it exceed the limit . rest two material are in limit but cast iron is more safe then cast steel.

On comparing the pressure experience by all the cases we had found that pressure have slightly difference in all three model, in case of cast iron we received max pressure thus it will generate more torque to the system

On comparing various factor of all three cases we came on conclusion that we will select cast iron material for