a b s t r a c t  The variable critical speeds and resonances of a geared parallel-rotor system with five shafts effected by changing oil bearing stiffness due to different external loads are investigated in this paper。 The rotor system of a modern centrifugal compressor is taken as the research object firstly。 A finite element (FE) model of it is established by using rotating beam elements with 6 degrees-of-freedom (DOFs), and linear mesh stiffnesses of the engaged helical gears are involved。 The changing stiffness and damping of the oil bearings effected by different loads are calculated based on traditional oil-film fluid formula。 Then, the Campbell diagrams of the whole rotor system under different loads on three output shafts are calculated based on the above model。 Finally, comparing the obtained critical speeds, the load ranges are revealed to lead possible resonances of the rotor system near the operating speeds。84918

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1。Introduction

Integrally geared centrifugal compressor is one of the most attractive developed and important equipments in recent years and used in many patrol processing factories, which has merged the speed-increasing gearbox with the compression sections to create a compact and efficient package [1]。 The rotor system of the integrally geared centrifugal compressor is always composed of some paralleled and geared shafts including one input shaft and three or even more output ones supported by the tilting pad journal bearing (TPJB)。 Due to the complicated dynamic characteristics, dynamic modeling of com- pression system has received significant attention over the years。 However, the studies in this field are still inadequate because of its complexity。 Among the limited modeling studies, most works in this field are done for axial compressors and fewer results are available from literatures on centrifugal compressors especially for the integrally geared ones。 Morini et al。 [2] developed a non-linear one-dimensional modular dynamic model of bio-gas compression system and which is used for the simulation of compression system transient behavior。 Jiang [3] presented an analytical model for the centrifugal compressor which can be used to predict the compressor performance curves of outlet pressure, efficiency and losses and obtain surge line for defining stable operation range。 Lee [4] conducted an investigation on the suppression   of   sub-synchronous   vibrations   due   to aerodynamic

response and surge in a two-stage centrifugal compressor with airfoil bearings。 Gruntfest et al。 [5] discussed the rotordynamic instability of an integrally geared compressor that initially had problems with high bearing pad temperatures and investigated its causes。 Moore [6] conducted full-load, full-pressure rotordynamic stability  measure- ments on a seven-stage,  back-to-back  centrifugal  compressor。  Kim [7] investigated the fundamental aeromechanics of compressor flow instabilities through experiments in a three-stage axial  flow compres- sor, and pointed out that aerodynamically forced vibration in a centrifugal  compressor  should  be  considered。

Nowadays, many interesting papers on the dynamic analysis of geared rotor system have been presented。 Choi [8] and Park [9] studied analytical modeling method for a helical geared system respectively and the dynamics of gears were investigated。 Choi [10] presented a model of geared one-stage rotor bearing system by transfer matrix method where the gear mesh was modeled as a pair of rigid disks connected by a spring-damper。 Baguet [11] applied an iterative Newmark scheme to a single stage geared system, and demonstrated the gear-bearing dynamic interactions through the analysis of dynamic gear loads, dynamic bearing loads and bearing displacements。 Kang [12] investigated the dynamic behaviors of a two-shaft gear-rotor system with viscoelastic supports。 Maliha [13], Eritenel [14] and Walha [15] analyzed the nonlinear behaviors of the geared rotors, and the dynamic gear loads and dynamic bearing forces were calculated。 Lee [16] presented a 5-DOFs models for obtaining the unbalance response of a 600 kW turbo-chiller rotor- bearing system based on the finite element    approach。