To avoid the waste of the energy and the impact load on the starting process of the centrifugal compressor, the compressor is always speeding-up without load until stabilizing at the working speed firstly, which is beyond the first several critical speeds of its rotor system, and then increasing the load to the rated load。 During the speeding-up process, it sometimes needs to accelerate through the critical points in order to avoid the increasing vibration。 While during the load increasing process, it frequently occurs that the vibration of the system also increases as the rotor system speeding- up across critical speed。 That is, when the load increases near to a certain value, the vibration increases significantly, while after this certain load, the vibration decreases to the normal range, which is often called “critical load” by the operations staff。 Sometimes, the vibration is so violent that makes the operations staffs have to stop the compressor。 This phenomenon is quite common, including the compressor designed by some well-known companies in the world, and confuse the users and  designers。

Due to the nonlinear dynamics of the oil film bearing and gear mesh, there is no accurate critical speed for a gear-bearing-rotor system。 Most researches focus on the nonlinear dynamics of rotor system, and few works focus on the changing dynamic character- istic caused by the load variation from the critical speeds perspec- tive。 But the critical speed of the geared rotor-system after linearization is useful, and the appropriate working speed of the

Fig。 2。  The dynamic model of the five shaft geared rotor  system。

high speed rotating  machineries  is also designed by critical   speed

analyzing。 Meanwhile, many famous compressor manufacturing companies still treat the rotor system of the whole machine with many geared shafts as different single-rotor systems pidedly nowadays, and make the critical speed of the shaft perge from the working speed at the design stage without considering the variable load。 Sometimes, however, the vibration problems of the rotor system occur when increasing loads even though the rotat- ing speed is steady in the start-up process of centrifugal compres- sor, which makes the compressor inoperable, or even causes dangerous risk in the machine operation。 It is necessary to study the changing dynamic characteristic of the geared rotor system in the centrifugal compressor caused by the loads, and find out the possible cause of “critical load”, which would be a guidance in the integrally geared  centrifugal  compressor design。

In this paper, the dynamics of an integrally centrifugal com- pressor with five parallel shafts is investigated, where the chan- ging parameters of TPJBs are considered as the main causes of the severe vibrations mentioned above。 Admittedly, the “critical load” may not be caused only by the changing parameters of TPJB, but it is certain that it is one of the most important reasons。 Based on the finite  element  (FE)   model   of   the  rotor  system,   the    response

Fig。 1。  A geared rotor system composed of five shafts。

Fig。 3。 Rotating beam element。

reproduced the vibration phenomenon in the starting-up process。 These results will provide guides for the integrally centrifugal compressor design。

2。Geared rotor system in the integrally centrifugal compressor with five parallel shafts

A schematic of the geared parallel-rotor  system  is  shown in Fig。 1, which is a prototype of an integrally geared centrifugal compressor with 5 shafts coupled by helical gears in parallel arrangement。 Each shaft is supported by two TPJBs。 The test rig is driven by an AC motor connected to the input shaft (I)。 The dummy impellers or discs are fixed on the three output shafts (O1, O2, O3)。 These shafts are all connected to a big main gear (M) by different gears。 The transmission ratios of the three output shafts are 2。72 (I to O1), 3。25 (I to O2) and 5。10 (I to O3)。