Using Modern Engineering Tools to Efficiently Solve Challenging Engineering Design Problems: Analysis of the Stepped Shaft

There is an inarguable elegance to the efficiency gains from the gear-driven compressor of an aircraft engine presently being developed or to a natural gas-fired power plant with a bottoming cycle that achieves 45% thermodynamic efficiency. But in considering the design as a whole it is easy to forget the most basic components. The shaft is an important rotating component used for the transmission of power and motion. The design considerations of a shaft can be broken down into three areas, fatigue, deflection, and critical frequency. During operation it can be subject to minimum and maximum axial, transverse and torsional loads leading to mean and alternating stress states. The effects of such stresses can be addressed during a fatigue analysis, a topic which is well covered in texts on machine component design and in governing standards. Critical frequency prediction is reasonably straightforward once the deflection of the shaft is known along with the attendant masses. As long as the loading is not complicated and the shaft has a constant diameter, determining the deflections of a shaft is simple and well covered in texts on mechanics of materials and machine component design. However, when the shaft cross section becomes practical it includes changes of diameter to provide steps that can be used to accurately mount bearings and gears. It can have overhanging ends and tapered cross sections. The determination of the deflection of these practical shafts has been historically cumbersome and intractable. Until now. A method of solution for these practical shaft geometries and loadings is presented. The method stays generalized, using an engineer’s knowledge of free body diagrams, writing moment equations, and Castigliano’s theorem to set up the problem solution into a form that is solved in an engineer’s favorite computer program. Thus far we have evidence that it is straightforward to implement this solution method in programs such as EES © , TK Solver, and Matlab ® .