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    Take a good look at these pictures. This shaft is exactly the way it came out of a Linde MPR-63L hydraulic pump. Notice anything wrong? Yes, that's  right, the front bearing is looking the wrong way! This pump was mounted and put in service (not for long) with the front bearing mounted the way you see on these pictures. Apparently some mechanics get a real kick out of defying common sense! Or, maybe, it was a well planned joke? Accident? Or, maybe, the pump was mounted as a part of a kindergarten project, and, surely, the poor four year olds just didn't know how to assemble a shaft which works with two tapered roller bearings?  I am betting this mystery will never be sold...

     If you ever "by accident" mount a shaft bearing like this, try using mathematics as an excuse.
This assembly has three pieces - the shaft itself, the bearing and the seal sleeve, so, mathematically speaking, as the bearing and the sleeve can be mounted only on one side of the shaft, but have two sides themselves, there are 2x2x2=8 ways the three parts can be combined together, so you have only a small 12.5 percent chance to mount it right!