How to design a shaft under different loads and stress? What's the formula to calculate length and diameter?
For the shaft calculation this might be useful:
But, sometimes you might have to make a compromise, depending on the construction you need to make.
The shaft of an electric motor where the bearing section (diameter) needs to be smaller than the diameter of the rotor section. If is bigger you won't be able to mount the rotor on the shaft. The best example are low rpm motors where the bearing section can be for example 4 times smaller than the inside diameter of the rotor, there for you have to design a ribbed shaft (see https://www.researchgate.net/figure/274634472_fig10_Figure-10-Partial-longitudinal-section-through-a-rotor-cage-induction-motor-with-ribbed)
Hope this helps!