IMPROVING CRITICAL SPEED CALCULATIONS USING FLEXIBLE BEARING SUPPORT FRF COMPLIANCE DATA

Sean D. Franklin is an Analytical Engi­ neer with the Stress Analysis Group of Turbodyne Division, Dresser Industries in Wellsville, New York. Mr. Franklin graduated from Clarkson C allege of Technology in 1980. His experi­ ence includes six years of stress and vi­ bration analysis, using classical and finite element methods and modal testing. He has experience in vibration testing of components of steam turbines and other The importance of including flexible supports in rotordynam­ ic analyses is discussed. Various methods of including the support in rotordynamic calculations are reviewed. A method is described in which actual compliance frequency response func­ tion, FRF, data are used directly in a rotordynamic forced response computer program to accurately predict a steam turbine rotor's critical speed. The flexible support model is described as two single degree of freedom, SDOF, spring-mass­ damper systems per bearing support. The methodology of acquiring the FRF data via impact hammer testing is described, and the equations are summarized that incorporate the FRF data into the flexible support model. Three flexible support models of increasing sophistication are used to analytically predict the rotor and support resonances. These results are compared to the actual steam turbine speed-amplitude plots. Modelling the support as many speed dependent SDOF sys­ tems acccurately predicts the location of the rotor's first critical speed and also the split critical peaks and several support resonance speeds. JNTRODUCTION It has become increasingly important in recent years to accurately predict the location of rotor lateral critical speeds. Most of this emphasis is due in part to the stringent rotordynam­ ics user specifications to which rotating equipment manufactur­ ers must adhere. This is particularly true for the petrochemical 70 PROCEEDINGS OF THE FIFTEENTH TURBOMACHINERY SYMPOSIUM industry where a typical standard prohibits critical speeds to be located between 15 percent below the minimum speed to 20 percent above the maximum continuous speed [1]. The same standard limits critical speed amplification factors to be below 8.0, while stating that amplification factors below 5.0 are preferable. As the amplification factor decreases, the critical speed becomes less severe, with a much more gradual change in vibration amplitude with speed. This type of design requires the rotor shaft to be relatively rigid to permit sufficient shaft movement at the bearings thereby allowing the bearing damping to be effective in vibration suppression. Furthermore, the bearing flexibility plays a predominant role in locating the rotor's critical speed. For flexible shaft rotors with higher amplification factors, critical speeds can be accurately predicted by carefully modelling the shaft. The bearing flexibility plays a very small role in locating the critical speed. Thus, for low amplification factor rotors, critical speeds are less severe, but are much more difficult to predict analytically, since they depend greatly on the stiff ness and damping prop­ erties of the bearing fluid film and the bearing supporting structure. This support includes the pad and pad pivots for tilting pad bearings, the bearing housing, the housing support feet, the baseplate and the foundation. The flexibility of the bearing support beyond the fluid film can dramatically alter the effective bearing stiffness and damping properties acting on the rotating shaft [2, 3, 4]. The analysis of machine vibration response based on rigid bearing supports predict critical speeds that are substantially higher than actual values [2, 3]. Nicholas and Barrett [2] found that for the four rotors analyzed, neglecting support flexibility resulted in pre­ dicted first critical errors that range from 14 percent to 21 percent high and second critical errors that range from 40 percent to 88 percent high. Since rotating machinery is de­ signed, marketed and sold, for the most part, based on analytical prediction, an accurate method of easily incorporating the support flexibility effect into rotordynamic analyses is of para­ mount importance. To this end, several researchers have included the effects of support flexibility into rotordynamic analyses. The method usually used is to model the supports with stiffn ess and damping coefficients which are constant over the entire speed range [2, 5, 6, 7, 8]. In most cases, the support stiffn ess is based on static deflections of the bearing pedestal (experimentally and/or ana­ lytically calculated). This method also requires values for the support mass and damping which require additional calculations and approximations. While this approach can be successfully utilized to predict both the location and amplification of rotor critical speeds [2], it will not show more than a single support or foundation resonance. Recently, detailed models of support structures have been incorporated into rotordynamic analyses in an effort to predict the support-rotor resonance interactions. The usual approach has been to use either an approximate beam model [9] or a modal model from finite element analysis of the structure [10, 11, 12]. Some studies use component mode synthesis tech­ niques [10, 11] whereas Queitzsch [12] uses analytical frequency response functions (FRF) to represent the supporting structure. These methods have proven successful, but they are time­ consuming and costly. The method proposed here utilizes experimental FRF data to represent the bearing support structure. The experimental data is determined from modal analysis techniques where the re­ sponse of the structure to a known force is recorded. The resulting FRF data, both magnitude and phase, are plotted as a function of frequency. If the magnitude of the FRF function is displacement divided by the force, the resulting data is called dynamic compliance [13]. The application of experimental FRF data to rotordynamic analyses has been discussed previously [3, 14, 15]. One of the biggest advantages of this method is that the support mass and damping is included implicitly in the FRF data along with the support stiffness. The FRF data can easily be incorporated into the rotordynamic support model used in references [2, 5, 6, 7], either as a constant dynamic stiffness over a narrow speed range or as a speed dependent dynamic stiffn ess over the entire speed range. The modal analysis technique used in determining the dy­ namic compliance data is detailed herein. The data is then employed in a forced response rotordynamic analysis, using various levels of flexible support model sophistication. The results will be compared to actual test stand speed amplitude plots from a steam turbine, running on the test stand with a known midspan unbalance. FLEXIBLE SUPPORT MODEL A typical outline drawing of a steam turbine case is shown in Figure 1. The steam end bearing is housed in a bearing case that is supported by a flex plate to allow for axial thermal expansion. The exhaust end bearing case is supported within the exhaust casing which sits on two sets of thick horizontal plates with gussets for added stiffness. These plates along with the flex plate are attached to the baseplate. EXHAUST 1 END �� BEARING � CASE