Hi Samyak,

If you want to study Herztian stresses, you don't want Explicit Dynamics, you want Statics. If the 3D Statics model was taking too long, use a 2D Statics plane strain model. That will reduce time much more than a 2D Explicit Dynamics model would.

I also want to plot the variation of stresses with respect to time for different depths. 

When you say "depths" what do you mean?  Do you mean face width?

The variation in stress with respect to time is the same as different angles of the gears in a static solution to get the contact point to one side or the other of the pitch circle.