Teaching shaft balancing as a parameter estimation problem

Abstract

One of the typical topics on Mechanisms and Machine Theory subject is shaft or rotor balancing. The unbalance is produced by an inadequate mass distribution of the rotating part. It can be said that static unbalance exists when the mass centre does not lie on the rotation axis and that dynamic unbalance happens when the rotating axis is not a principal inertia axis of the shaft. Making use of this point of view, the way to correct an unbalanced shaft is to cancel its inertia products involving the rotation axis. If these inertia products are known, it is easy to calculate the mass to be added or eliminated in order to cancel them. Instead, if the inertia products are unknown, they must be experimentally estimated in order to balance the shaft. This work presents a way to balance an unknown shaft as a parameter estimation problem. The formulation of least-square parameter estimation has been used in order to estimate the inertial properties of a shaft. Then, the balancing of the shaft is easily carried out. This approach has been explained to students of a Degree on Mechanical Engineering at the Public University of Navarra. By means of a virtual model of an unbalanced shaft, students have estimated the inertial properties of the unbalanced shaft and then calculated the masses to be added in order to balance it. I has been a satisfactory experience in order to improve the students skills on the Mechanism and Machine Theory and they have also learned a formulation that can be used for other kind of problems.