I understand there will be exact multiple of fundamental frequency based bearing rotation with respect to fundamental, based on gear rotation with respect to fundamental. But what exactly means for multiples of bearing rotations, multiples of blade passes like 1x, 2x, 3x etc.,
Honestly, it depends...
It depends on the specific machinery and source mechanism.
It can be nonlinearities in the system (e.g., nonlinearities in linear drives like speakers), it can be (periodic) elements in the system (e.g. number of teeth in gears), it can be wear in components (which needs to be periodic on rotating parts, e.g. higher harmonics on railcar wheels - polygonalization), it can be impulsive behaviour triggered periodically by a rotating part (e.g. combustion impulses in internal combustion engines), it can be linearly moving parts that are not rotating (e.g. pistons), it can be some additional higher order torque components from inbalances, ...
The key point is that for all of these processes (except of some non-linearities that might generate subharmonics), you can only get integer multiples of the base period.
Nevertheless, it is important to mind the base period. For a 4-stroke engine, for example, this is 2 rotations, which is why you might also find "half orders" at internal combustion engines (and only full and half orders, no third or something...).
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