No Penetration Troubleshoot

Also, you cannot run the study without any external loads.

Correct. You could add a dummy load to get the analysis to run though (something like 0.001 g of gravity).

What I found was that running the study with both brake torques prompted a warning for large displacement. Now, I understand that stressing the material beyond its yield is an indication that a nonlinear study should be done....

Generally speaking, yes. However, if the above-yield stresses are due to singularities, then you don't need to run a nonlinear analysis; you'll just need to handle the singularities in the appropriate manner. If you do have above-yield stresses that aren't due to singularities, then you'll need to define the appropriate elasto-plastic material model (perfectly plastic, linear hardening, etc.) Be aware that if you decide do go down the elasto-plastic route, your displacements will get larger due to the decrease in the Young's Modulus when you go into the plastic region. I'm not sure what the purpose of your project is, but if it's to design a spindle to handle the applied loads, then I'd stay away from a elasto-plastic material model and large-displacement formulation and modify the geometry of the model to bring the stresses to a sub-yield level.

...instead of a static study, yes?

Nonlinear and static are two different categories. Linear and Nonlinear refer to the assumptions used in the formulation of the model. Linear assumes purely constant material properties (no plasticity, temperature dependent CTE, etc.), small strains and displacements (no second order terms), no contact (path dependent solution), etc. Nonlinear doesn't necessarily make these assumptions (it depends on how you set up the model), and can account for some or all of these effects. Static and Dynamic refer to whether your solution is time-independent or time-dependent. As such, you have four analysis types:

1. Linear Static
2. Linear Dynamic
3. Nonlinear Static
4. Nonlinear Dynamic.

mroe than likely you have a load issue, probably too high rather than needing nonlinear

nonlinear is only needed for large displacement (doubt you want this) or plastic deformation (doubt you want this either)

suggest you sit down and figure out how you came up with your loads

what your expectations are regarding those loads

if your loads are right, your design is poor and needs adjustment