How does one go about calculating what the best diameter axel would be for a givin application? An axel too small with bend and de-shape but an axel to big will have too much rotational inertia?
The ASME and Westinghouse shaft codes are often used to determine what diameter is required to keep stresses below a specified level, with a particular factor of safety. These codes can be found in many engineering text books. In some applications, torsional and bending deflections will also be an important consideration.