This paper presents a theoretical model for analytical study of internal friction-induced whirl instability due to shrink fit and interference fit joints in rotating machines. It is the theoretical continuation of an experimental study on the effects of internal friction published in a companion paper. The theoretical study shows that the follower force internal friction model proposed by Gunter in 1965 is a physically incorrect model due to its inconsistency with Newton’s Third Law of Motion. The internal moments model proposed by Lund in 1976 to explain unstable sub-synchronous vibrations due to micro-slip in interference and shrink fit joints is physically consistent with the basic principles of mechanics and can explain rotordynamic instability due to internal friction in rotating machines. Rotordynamic simulations of the experimental single-disk and two-disk rotor based on an internal moments model are carried out using finite element based rotordynamics software. Rotordynamic simulations of the unstable experimental rotors using the linear viscous form of the internal moments model, with selected moment stiffness and damping parameters at the interface, result in correct prediction of the instabilities (negative real part of the damped eigenvalues).

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