Week 1 Spur Gear Challenge

Objective:

To Perform Static Structural analyis of Spur Gear Using 3 different materials to determine:

Equivalent stress, Total deformation and Stress intensity

Solution:

Materials used:

Analysis set up details:

Contact:

The contact has been defined as frictional between the set of gears and only the required faces which come in contact are selected as contact and target faces as shown below.

These are having the frictional contact with symmetric behaviour. And the formulation is Augmented Lagrange whereas the interface treatment is set to adjust to touch.

Joints:

Revolute Joint has been set up between the gears wrt ground.

Mesh:

Meshing has been done using an element size of 1 mm.

The mesh metric graph has been represented above which confirms that most of the elements are of high Quality and thus acceptable.

Analysis Settings:

The analysis has been set up for 6 steps with specifying the initial, minimum and maximum time step. However, the time stepping is automatically controlled.

Also, the large deflection is kept on.

One of the gear rotates in the increament of 30 degree for 6 steps and the other Gear has been given a moment of 10 N-m at every step wrt revolute joint connection as shown below.

The results are evaluated for all the three materials as shown below:

Equivalent Stress Comparison :

Total Deformation Comparison:

Stress Intensity Comparison:

Stress Intensity:

The Stress Intensity Factor(KK {\displaystyle K} KK), is used in fracture mechanics to predict the stress state near the tip of a crack or notch caused by a remote load or residual stresses. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials, and is a critical technique in the discipline of damage tolerance. The concept can also be applied to materials that exhibit small-scale yielding at a crack tip.

In the above image we can see that all three materials exhibit stress intensity of smililar value at the same location.

Conclusion:

1. Considering the maximum stress value over time for strength requirement.

Maximum Over Load Steps	Equivalent Stress(Max)	Yield Strength	Difference
Cast Iron (Ductile)	396MPa	344MPa	52MPa
Cast Steel	427MPa	349MPa	78MPa
Cast Bronze	398MPa	144MPa	254Mpa

As we can see from above table as maximum Von mises stress value is exceeding the Yield strength, so plastic deformation will take place in all cases.

The Cast bronze with the lowest yield strength will be experiencing the maximum stress so it will not be a good choice for manufacturing. Also, the cast Iron will have more brittleness and low impact resistance as compared to Cast steel which is again not a good choice in this case.

Cast steel with the maximum Yield strength and better impact resistance (provides better fatigue resistance) will be the best choice.

2. Total Deformation value is same for all cases which is 30 mm.

3. The location of possible fracture would be near the root of the teeth where we can see the maximum stress below.