Pergamon Mech. Mach. Theory Vol. 31, No. 6, pp. 771-779, 1996 Copyright © 1996 ElsevierScienceLid 0094-114X(95)00109-3 Printed in Great Britain. All rights reserved 0094-114X/96 $15.00 + 0.00 STABILITY CHARACTERISTICS OF ROTATING SYSTEMS WITH JOURNAL BEARINGS ON VISCOELASTIC SUPPORT J. K. DUTT Department of Mechanical Engineering, I.I.T. Kharagpur, India 721 302 B. C. NAKRA Department of Mechanical Engineering, I.I.T. Delhi, India l l0 016 (Received 1 June 1994) Abstract--An analysis for determining the stability limit of the rotor speed of a rotor shaft system, is given. The system consists of a single rotor disc in the middle of an elastic shaft having identical plain cylindrical journal beatings at the ends, supported on viscoelastic supports. The influence of support parameters on the stability limits of the rotor shaft system has been studied. Copyright © 1996 Elsevier Science Ltd 1. INTRODUCTION Support damping is considered to be useful for improving the dynamic characteristics of a rotor shaft system [1]. The influence of flexible and viscously damped supports on the stability of a rotor shaft system mounted on journal bearings using the above mentioned types of supports has been studied in [2-4]. Viscous damping at the supports is seen to improve the dynamic instability due to oil film forces in hydrodynamic journal bearings. On the other hand, viscoelastic polymeric supports present certain operational advantages [5] and the use of such supports has been seen as giving a higher stability limit compared to that given by elastic or viscously damped elastic supports in the case of instability due to material damping of the rotor shaft system [6]. Recently, detailed results on the influence of viscoelastic supports on unbalance response of a rotor shaft system on rolling element or journal bearings and also some preliminary results on stability characteristics of such systems on journal bearings have been reported using the finite element method [7, 8]. In this work, studies have been carried out on stability characteristics of the rotor shaft system mounted on identical plain cylindrical journal bearings at the ends supported on viscoelastic supports. The support mass has been taken into account while deriving the equations of motion. The shaft mass has been ignored. Detailed results on the stability limit of the rotor speeds for different values of the viscoelastic material constants and support mass ratios have been given. Results are found to have good agreement with those obtained by the finite element method as in [7, 8] after incorporating the effect of support mass. 2. ANALYSIS Figure 1 shows the schematic diagram of the system taken for the analysis. For modelling the journal bearings all the direct and cross coupled stiffness and damping terms have been taken into consideration. For the study of stability of the rotor shaft system on journal bearings and viscoelastic supports, the viscoelastic support material has been modelled as a 4-element viscoelastic solid since the complex modulus representation is only applicable for the cases of harmonic oscillations [9]. The 4-element viscoelastic solid is represented as a parallel combination of a Maxwell element and a Voigt element and can be shown schematically as in Fig. 2. Using the above model for the support, the system may be represented as shown in Fig. 3(a) and (b). For finding out the stability of the rotor-shaft system, the equations of motion for free vibration of the system are first written down as follows: M2.ii2 + K~x~ = 0 (1) 771