USING ROTOR KIT BENTLY NEVADA FOR EXPERIMENTS WITH AEROSTATIC BEARINGS

Transcription

1 USING ROTOR KIT BENTLY NEVADA FOR EXPERIMENTS WITH AEROSTATIC BEARINGS ŠIMEK, J. 1, KOZÁNEK, J., STEINBAUER, P., NEUSSER, Z. 3 1 TECHLAB Ltd., Prague, Institute of Thermomechanics AS CR 3 CTU in Prague, Faculty of Mechanical Engineering Introduction Aerostatic bearings are used both for low- and high-speed applications. For reliable operation of high-speed rotors it is necessary to have reliable data on bearing dynamic properties. Computational methods were developed for determination of aerostatic bearing stiffness and damping, but they were not experimentally verified. One of the possibilities of determining the bearing dynamic properties is external excitation of the bearing by harmonic force in two directions. Rotor Kit Bently Nevada (RKBN) enables controlled running of the shaft to speeds up to 1. rpm, which is sufficient for experiments with aerostatic bearings. That is why superstructure of RKBN, enabling identification of static and dynamic characteristics of aerostatic journal bearings, was designed, manufactured, tested and used for identification of aerostatic bearings stiffness and damping coefficients. Test stand Overall view of RKBN superstructure is presented in Fig. 1. Rigid test shaft 1 is supported in two precise rolling bearings 18. Test head 4 with aerostatic bearing is situated between rolling bearings. Piezoelectric piezoactuator 1 for excitation of test bearing by harmonic dynamic force is connected to the test head by means of butt hinge 7. The actuator is at its upper end connected to rigid frame, once more by butt hinge. Force transducer 13 is located between actuator and test head, which enables to record excitation force together Ing. Jiří Šimek, CSc. Techlab Ltd., Sokolovská 7, 19 Prague 9, j.simek@techlab.cz Ing. Jan Kozánek, CSc., Institute of Thermomechanics, Dolejškova, P8, kozanek@it.cas.cz Ing. Pavel Steinbauer, Ph.D., Ing. Zdeněk Neusser, CTU in Prague, FME, Technická 4, P6, pavel.steinbauer@fs.cvut.cz, zdenek.neusser@fs.cvut.cz

2 with pertinent responses. Static load, originally supposed to be exerted by differential screw, is applied by static offset of piezoactuator. Movement of test bearing relative to the shaft is measured by sensors S3, S4 14 orientated in vertical direction and other pair of sensors S1, S in horizontal direction. Fig. 1 Overall view of RKBN superstructure Initial tests showed, that test head movement was influenced by stiffness of cables and pressurized air hose, so that sliding surfaces of the bearing and shaft were not parallel one to another. The test stand was therefore modified by adding the test bearing suspension aimed at securing its purely transitional movement and disabling axial motion. Modifications are apparent from cross section in Fig.. Suspension consists of three thin strings anchored at test head disk 3 and two disks 31 fastened to the Rotor Kit frame. Proper alignment of the test head with the shaft can be achieved by means of threaded pins 33 and nuts 34. Fig. Detail of modified superstructure

3 During the process of testing the stand was equipped with another piezoactuator orientated in horizontal direction. This arrangement enables excitation of test bearing in both directions with the same adjustment of eccentricity, thus increasing repeatability and accuracy of measured results. Test aerostatic bearings and shafts already manufactured enable to make out a number of combinations of L/D ratio, number of feeding planes and clearance. Due to great number of variable parameters (speed, bearing load, air inlet pressure, frequency and amplitude of excitation force) it was necessary to define limited range of operating conditions. Measuring and controlling system was set up, enabling to save measured data and also to control motor speed and adjust piezoactuator characteristics. Some measured results The results presented here are test for bearing No. 1 with diameter of 3 mm, L/D=1,, radial clearance,4 mm and feeding planes of orifices, mm in diameter at distance L /4 from bearing boundary. Piezoactuators enabling dynamic excitation of test bearing in broad range of frequencies were used also for determination of quasi-static stiffness, which correlates bearing load with journal eccentricity. The test bearing was excited with frequency of, Hz and from its response were calculated values of quasi-static stiffness , MPa,, Hz horizontally,1,,3,4,,6,7,8,9 1,4 MPa,, Hz horizontally ,,1,,3,4,,6,7,8,9 1, Fig. 3 Response of test bearing to low frequency excitation without journal rotation 4 rpm,, MPa,, Hz horizontally 4 rpm,,4 MPa,, Hz horizontally ,1,,3,4,,6,7,8,9 1 -,,1,,3,4,,6,7,8,9 1, Fig. 4 Response of test bearing to low frequency excitation at 4 rpm

4 Fig. 3 shows bearing response to harmonic excitation with frequency of, Hz in horizontal direction for two values of inlet pressure, and,4 MPa without journal rotation. It can be seen, that exciting force and both responses are purely harmonic. Corresponding quasi-static stiffness values are 1, and 1,4.1 6 N.m -1 respectively. Diagrams in Fig. 4 illustrate bearing response at low frequency excitation with journal rotation at 4. rpm for the same values of inlet pressure as without rotation. Response of the test bearing is once more harmonic, but superimposed on it is frequency of rotation with amplitude of about 3 µm. With increasing speed amplitude of synchronous component grows with maximum of about µm at. rpm. Coefficients of stiffness and damping matrix were identified from dynamic model, which was presented e.g. at [1]. The real part of the time-response ~ x( t) q ( t) = of the test y( t) bearing relative to the shaft on the complex harmonic excitation force f x ( t) f x i Ωt i Ωt f ( t) = = =,, = 1, Ω > ( ) e f e f R i (1) f y t f y was evaluated from measured discretized signal in the first step as the simple linear (in real parameters q, q q R ) and non-linear (related to Ω ) least squares regression problems S, C q ~ ( t) = q + q S sin( Ωt) + qc cos( Ωt) and transformed into complex amplitude form i Ωt q( t) = q e, q = q i q C C S corresponding to the complex excitation force (1). The equation of motion in harmonic regime is K q + i ΩBq Ω Mq = f, (4) where real matrices M the matrix M =, K, B, M R are matrices of stiffness, damping and mass. In our case M, where M is mass of test head with aerostatic bearing, is known. K x x K x y Bx x Bx y The unknown parameters elements of matrices K =, B = K y x K can be y y By x By y identified from the equations (4) for two orthogonal excitation forces f and for one or more corresponding excitation frequencies Ω using least squares method see [1]. Higher number of excitation frequencies, especially in regions near resonance, should increase robustness of solution. In ideal case it would be also advisable to identify eigenvalues by indirect identification method and to confront these values with eigenvalues corresponding to stiffness and damping matrices. It is also possible to determine at first step diagonal elements of stiffness and damping matrices, which are less sensitive to measurement errors, and only in further phase of evaluation to deal with cross coupling terms. Use of additional vibration sensors accelerometers is considered for further test, which can be advantageous for higher frequencies. Accelerometers could be located in bearing centre plane, thus eliminating necessity of averaging deviations measured at both bearing sides. () (3)

5 Up to now identified direct stiffness and damping coefficients of test bearing No. 1 are summarized in Table 1. Cross coupling terms are not presented because they have at least one order lower magnitude than direct terms and their scatter is therefore much greater. The only realistic values of cross coupling stiffness were measured without journal rotation, when the perturbation effects are minimum. For inlet pressures of, MPa and,4 MPa respectively the evaluated values were: K xy 1,3.1 4 and 1,7.1 4, K yx 1,.1 4 and 1,8.1 4 N.m -1. Tab. 1 Identified coefficients of stiffness and damping inl. pres. speed exc. frequency K xx K yy B xx B yy (MPa) (rpm) (Hz) (N/m) (N/m) (N.s/m) (N.s/m), 31/6 9,E+6 9,6E ,E+ 9,6E ,88E+ 9,79E ,3E+ 9,79E ,E+6 9,66E ,84E+ 9,77E ,1E+ 9,71E+ 48,4 31 1,4E+6 1,41E ,43E+6 1,4E ,43E+6 1,44E ,4E+6 1,4E ,44E+6 1,4E ,3E+6 1,43E It can be seen from the table, that identified stiffness is in good accordance with above presented quasi-static stiffness values. The agreement between theory and experiment can be observed when comparing the tabulated values with diagrams of computed values in Fig. and 6. Calculation was carried out for relative eccentricities of,3 and,. stiffness (N/m) 4,E+6 3,E+6 3,E+6,E+6,E+6 1,E+6 Direct stiffness vers. speed inlet pressure, MPa Kxx - rel. ecc.,3 Kyy - rel. výstř.,3 Kxx - rel. ecc.., Kyy - rel. ecc., 1,E damping (N.s/m) 1,E+3 9,E+ 8,E+ 7,E+ 6,E+,E+ 4,E+ 3,E+ Direct damping vers. speed inlet pressure, MPa Bxx - rel. ecc.,3 Byy - rel. ecc.,3 Bxx - rel. ecc., Byy - rel. ecc.,,e Fig. Calculated direct stiffness and damping coefficients for inlet pressure, MPa

6 stiffness (N/m),E+6,E+6 4,E+6 4,E+6 3,E+6 3,E+6,E+6 Direct stiffness vers. speed inlet pressure,4 MPa,E+6 Kxx - rel. ecc.,3 Kyy - rel. ecc.,3 1,E+6 Kxx - rel. ecc., Kyy - rel. ecc., 1,E damping (N.s/m) 9,E+ 8,E+ 7,E+ 6,E+,E+ 4,E+ 3,E+ Direct damping vers. speed inlet pressure,4 MPa Bxx - rel. ecc.,3 Byy - rel. ecc.,3 Bxx - rel. ecc., Byy - rel. ecc.,,e Fig. 6 Calculated direct stiffness and damping coefficients for inlet pressure,4 MPa It is evident, that calculated values of stiffness are somewhat higher than experimental ones; the agreement of measured damping with results of calculation is quite good with the exception of zero speed and,4 MPa inlet pressure. Small differences between measured terms K xx and K yy indicate, that the measurement was carried out with journal in vicinity of bearing centre. Due to relatively big clearance the effect of journal rotation is very small. The next bearing tested will have smaller clearance, so that aerodynamic effect will show up much sooner. Conclusions Test stand was designed and identification of the 1 st test aerostatic journal bearing dynamic properties was carried out. The agreement of measurement and calculation can be generally considered as reasonably good, some modifications of the computer program are proposed after more measured data will be available. Some possibilities of improving the methods of identification of dynamic coefficients from measured data were suggested and more bearings types will be measured. REFERENCES [1] Šimek, J. Kozánek, J. Steinbauer, P. Neusser, Z.: Determination of aerostatic journal bearing properties. Colloquium Dynamics of Machines 8, p. 169 ACKNOWLEDGEMENT This work was supported by Czech Scientific Foundation under project No. 11/6/1787 Dynamic properties of gas bearings and their interaction with rotor. SUMMARY Superstructure of Rotor Kit Bently Nevada was designed for identification of aerostatic journal bearing dynamic properties. The test stand enables to run the test shaft up to 1. rpm and to excite test bearing by forces with frequency from,1 Hz to about 1 Hz. Up to now measured results show reasonable agreement with calculation as concerns quasi-static stiffness and direct elements of stiffness matrix. The agreement between theory and experiment of main elements of damping matrix is somewhat worse and cross-coupling elements of stiffness and damping have considerable scatter. More sophisticated methods of dynamic coefficients identification are elaborated to improve credibility of results.