Rotordynamic Tests Of A Flexible Rotor On Flexure Pivot Journal Bearings And Stability Correlation With Frequency Dependent Characteristics.

A series of performance, unbalance response, and stability tests were performed on a flexible rotor incorporating two flexure pivot tilt-pad journal bearings, followed by a theoretical correlation using synchronous and frequency dependent bearing characteristics. The test data consisting of Bodé plots and frequency cascade plots are presented along with measured bearing performance data, including peak temperatures at different speeds. Unbalance tests consisted of applying a midspan unbalance. Effects of oil inlet flowrate and oil inlet temperature are examined. The measured peak responses are compared to the theoretical in five measurement planes. Stability tests consisted of running the balanced rotor up in speed to provide a high flexibility ratio and reduced logarithmic decrement. For these cases, the motion of the rotor was measured in five planes and results are presented in the form of cascade diagrams. The tests were conducted under a series of operation conditions by varying the speed, oil inlet temperature, and flowrates. High amplitude resonant whip instability did not occur; however, low amplitude limit cycle instability did occur, which aided in determining the stability threshold. Correlation of the test results to the theoretical logarithmic decrement was performed using both synchronous and nonsynchronous bearing coefficients, both with and without pivot rotational stiffness. Based on the results of this study, the theoretical model with the nonsynchronous bearing coefficients best represents the rotorbearing system. Pivot rotational stiffness had little effect. INTRODUCTION Dynamic characteristics of high-speed turbomachinery are largely dependent upon bearing dynamic characteristics both in terms of unbalance response and stability. This has resulted in numerous studies conducted on bearing dynamic characteristics for improved analysis and improved bearing design. One area that has not been adequately addressed, however, is the effect of frequency dependence in tilt-pad journal bearings. With regard to flexure pivot journal bearing applications, logarithmic decrements cited in literature have been fairly high and were cited to be in excess of 0.3 for two integrally geared applications (De Choudhury, et al., 1992; Chen, et al., 1994), and in excess of 1.4 for a turboexpander application (Kardine, et al., 1996). The analytical results that have been presented are limited to synchronously reduced coefficients and do not include the effect of frequency dependence on the tilt-pad journal bearing coefficients. In order to further determine the stability characteristics of these bearings and thus define the bearing application envelope, a series of tests was conducted. This paper details performance, unbalance response, and stability characteristics of a pair of flexure pivot journal bearings supporting a flexible shaft. The effect of speed (0 to 15,000 rpm), oil inlet temperature (110°F, 120°F, 130°F), and oil inlet flowrate (1.5 gpm, 2 gpm, 2.5 gpm) are examined. Steady-state performance is reported in the form of power loss and bearing metal temperatures. Unbalance response data are presented in the form of Bodé diagrams. Stability results are shown as cascade plots. A detailed theoretical analysis is performed, and results are compared to the test data. The flexure pivot tilt-pad journal bearings are modeled using both synchronous and nonsynchronous coefficients. While fixed geometry journal bearings have no 39 ROTORDYNAMIC TESTS OF A FLEXIBLE ROTOR ON FLEXURE PIVOT JOURNAL BEARINGS AND STABILITY CORRELATION WITH FREQUENCY DEPENDENT CHARACTERISTICS by Brian C. Pettinato Development Engineer and Pranabesh De Choudhury Senior Consulting Engineer Elliott Company Jeannette, Pennsylvania observable frequency dependent characteristics (Pettinato, et al., 2001), tilt-pad journal bearing coefficients are theoretically frequency dependent (Smalley, et al., 1975; Raimondi and Szeri, 1984; Barrett, et al., 1988), such that the bearing coefficients can be significantly different at the instability whirl frequency as compared to the operational speed of the machine. Consequently, from a standpoint of stability analysis, this can lead to significantly different results depending on whether synchronous or nonsynchronous reduction frequencies are used. Unfortunately, there has been little evidence either for or against the frequency dependent mathematical model (Nicholas, 2001). This has resulted in an ongoing debate as to whether synchronous or nonsynchronous coefficients should be used for stability analysis. But while the frequency dependence of tilt-pad journal bearing coefficients remains a controversial topic, the authors believe that this is primarily due to a lack of benchmarking using both methods. It should be noted that techniques involving the use of synchronous coefficients (Rouch, 1983; Wachel, 1986; Nicholas, 2001) and nonsynchronous coefficients (De Choudhury, 2001; Rouch, 1983) have been used for stabilizing flexible machinery. Depending on the bearings used, the use of one method over another could lead to either an overly conservative or overly aggressive limitation on logarithmic decrement. Given current state-of-the-art, it is beneficial to examine both methods. As such, the theoretical analysis consists of four bearing models—with and without pivot rotational stiffness, as well as with and without frequency dependence for purposes of benchmarking the series of tests performed. Test Stand Design and Configuration A highly flexible rotor was used to perform the stability tests. The test rig (Figure 1) consisted of a variable speed motor driving a shaft through a flexible coupling. The shaft was supported by two journal bearings 34 inches apart. The coupling end bearing is termed the DE (drive-end) bearing, while the free end bearing is termed the NDE (nondrive-end) bearing. The shaft consisted of 2.93 inch diameter journals, and a 2.375 inch diameter center section. One 9 inch diameter and two 12 inch diameter disks were mounted between bearings near the shaft center, thus providing a highly flexible shaft with first stiff support critical at 3937 rpm. An empirical parameter used as a stability criterion is the flexibility ratio defined as the ratio of shaft operating speed, N, to the first critical speed on stiff supports, Nc1 (Sood, 1979). The flexibility ratio of the test rotor, N/Nc1, is 3.81 at 15,000 rpm, which is well outside the typical experience range for operation without external damping. Figure 1. Flexible Rotor Test Stand. The rotor itself was incrementally balanced by first balancing the shaft alone, and then balancing the assembly as each successive disk was added. Table 1 describes the rotordynamic characteristics of the flexible shaft design. The test stand was instrumented with 10 eddy-current probes sensing in five planes. The sensor plane locations are shown in Figure 1 as hatched regions. Two probes were located at the shaft center ±45 degrees from bottom dead center. A pair of probes was Table 1. Shaft Design with Three Disks. also located inboard and outboard of each bearing, sensing in vertical and horizontal directions. Each bearing was instrumented with thermocouples embedded in the two loaded pads. Bearing inlet flowrates were monitored using positive displacement flowmeters. The inlet flowrate was adjusted by varying oil inlet pressure.