Determination of optimal position for both support bearing and unbalance mass of balance shaft

A balance shaft module is a smart device that removes harmonic vibrations of rotating machinery directly by generating an excitation with the same magnitude and an opposite phase of the vibration. However, the unbalance of a balance shaft causes a considerable bending deformation of the balance shaft as well as measurable power consumption. This paper presents an optimal conceptual design of a balance shaft by determining locations of both unbalance and supporting bearing. The optimal strategy is to minimize a normalized energy sum of both the elastic strain energy and the kinematic energy of a balance shaft. Then, an optimal design of the balance shaft is derived by the explicit formulation of the global optimum location of both the supporting bearing and the unbalance mass. The optimal design is verified with a simulation of a conceptual design of a balance shaft for a specific target engine.