Modal balancing of flexible shafts without trial weights

Most balancing procedures for flexible shafts involve the use of trial weights. The few techniques purporting to predict the shaft unbalance mathematically rely on modelling the system from measured characteristics. The bearings are dfficult to model and the technique presented in the present paper evades the necessityfor doing this. A technique is presented whereby the unbalance on a rotating shaft can be directly calculated from running Vibration; no explicit representation of the bearing characteristics is required. NOTATION generalized inertia matrix bearing damping matrix bearing stiffness matrix bending stiffness property of beam section shaft stiffness matrix length of two-bearing beam elemental beam length elemental mass mass of supported beam resolved components of unbalance distribution column matrix of generalized forcing generalized coordinates of rigidly supported shaft modes bending stiffness of shaft element rth displacement at ith bearing position in direc-tion x bearing impedance matrix generalized support impedance matrix generalized coordinate of free shaft modes resolved components of displacement of mass rth eigenfrequency of supported beam rth free mode of shaft rth rigidly supported mode of shaft forcing frequency or running speed rth rigidly supported shaft natural frequency displacement vector modal components of shaft forcing