ROTOR DYNAMICS ANALYSIS AND VIBRATION MEAS- UREMENT OF THE COMPOSITE FLYWHEEL BEARING SYSTEM FOR ENERGY STORAGE Xingjian Dai, Kai Zhang and Xiao-Zhang Zhang Tsinghua University, Department of Engineering Physics, 100084, Beijing, China email: daixj@mail.tsinghua.edu.cn A composite flywheel energy storage system with energy of 1300 Wh and power of 20kW is built for the experimental study on the power quality application in electricity grid. The vibration dynamics model of the composite flywheel bearing system in vertical installment is presented. The rotor dynamics analysis using the transfer matrix method and FEM method predict the model shape and the varying behavior of the mode frequency with the rising rotational speed. The calculation results show that two critical speeds locating in the ranges of 22-54 rps and 45-172 rps. The high value of the critical speed means that the feild balancing with high precision is very necessary to the speeding up of the flywheel bearing system. The composite flywheel bearing system passed through two critical speeds and ran to the speed of 13500rpm after the balancing process at the speed of 2300 rpm and 4600 rpm. Tow mode resonant frequencies of the casing in the flywheel energy storage system is observed in the vibration measurement. 1. Introduction Flywheels are electro-mechanical storage devices that store kinetic energy in a rotating mass socalled rotor coupled with an electric machine working as a motor in charging or generator in discharging. Flywheels present good features regarding high efficiency (around 90% at rated power), long cycling life and high power [1]. However, flywheels are not adequate devices for long-term energy storage due to high landing loss. The advantageous features make ESS based on flywheels a very suitable option for different applications such as wind power smoothing, transportation or quality power applications [2-4]. For example, flywheel based energy storage systems (FESSs) are used as short-term ESS in Wind diesel power systems (WDPSs) in isolated micro-grids to improve the logistic and the dynamic operation [5]. The kinetic energy stored in a flywheel is proportional to the inertia and the square of its rotating speed. The maximum stored energy is ultimately limited by the tensile strength of the flywheel material. Until now, most composite flywheels were made from circumferentially wound fibers pulled through a wet bath of resin [6, 7]. To design a high rotational speed machine, rotordynamics is very important [8].An optimal control system is proposed by incorporating cross-coupling technology into the control architecture to improve the synchronization performance of the rotor in the radial direction [9]. Squeeze film damper was employed to suppress the unbalance response and improve the stability at high speed [10]. The developed FESS has been designed to output 5kW power at 15,000rpm and the operating test [11]. The sub-critical rotor dynamics design and pivot-jewel bearing proved to be good solutions to the spin test for the composite flywheel [12]. The primary contributors to bearing loads are shown to be vehicle shock, vibration, and gyro-dynamics [13]. For the low speed flywheel bearing system, the rotordynamics is not hard to be solved. However, for the case of high speed exceeding 10000 rpm, the vibration problem becomes difficult. To study the rotordynam- 1
ics in flywheel energy storage system, a high speed composite flywheel energy storage system with energy of 1300 Wh and power of 20kW was built. 2. Flywheel bearing system configuration 2.1 Flywheel configuration The flywheel was composed by composite rim, aluminum alloy hub and steel shaft, as shown in figure 1. The composite rim is manufactured from wet filament winding by carbon fibers and glass fibers. The length of the rim is 600 mm and its diameter is 500 mm. The weight of the flywheel is 78 kg with rotational inertial of 5kgm 2. Figure 1: Composite flywheel shaft configuration. 2.2 Bearings design The vertical rotor-bearing system is ordinary employed in flywheel energy storage system. At the top of the flywheel motor shaft, a permanent magnetic bearing bears 90% of the weight of the flywheel and motor. The small roller bearings are used to bear the 10% of the weight of the flywheel and motor and bear the radial unbalance fore of the shaft due to rotation. The roller bearings are supported to the casing through elastic element such as O rubber rings. The elastic element regulates the critical speed of the flywheel bearing system. To bear the bias magnetic force of the permanent motor, the top support has bigger stiffness than that of the bottom support. In the design analysis, the top support stiffness varies from 10 8 N/m to 10 7 N/m, and the bottom support stiffness varies from 10 7 N/m to 10 6 N/m. The inner diameter of the mechanical bearing is set as 20 mm. The top bearing is a pair of angular contact bearings. A cylindrical roller bearing is used at the bottom of the shaft. 3. Theoretical dynamics predictions 3.1 Transfer Matrix Methods Both the transfer matrix method and finite element method were used to calculate the critical speeds of the flywheel bearing system. Nine lumped parameters model was presented to calculate the critical speed and vibration shape. The calculation resulted that the first critical speed was 23 rps and the second critical speed was 85 rps. 2 ICSV23, Athens (Greece), 10-14 July 2016
Figure 2: Lumped parameters mode of flywheel-shaft system. Mode 1: 23 rps Mode 2: 85 rps Figure 3: Mode frequencies and mode shape. The support stiffness is the key parameter affecting the critical speeds greatly. Table 1 illustrates varying of the values of the critical speed according to the changing of the support stiffness at the top and the bottom. Table 1: Stiffness s effects on the critical speeds. K1( N/m) K2(N/m) Critical speed 1 Critical speed 2 Mode 10 9 10 9 54 172 Translational/tilt 10 8 10 8 53 159 Translational/tilt 10 7 10 7 42 106 Translational/tilt 10 6 10 6 19 45 Translational/tilt 10 8 10 7 46 112 Translational/tilt 10 8 10 6 23 85 Translational/tilt 10 7 10 6 22 74 Translational/tilt 3.2 Finite Element Methods ANSYS was used to calculate the mode frequencies and mode shapes. The computation parameters are top support stiffness being 10 8 N/m, bottom support stiffness being 10 6 N/m, and the rotational speed is 0-400 rps. The calculation results were shown in following figures. ICSV23, Athens (Greece), 10-14 July 2016 3
Figure 4: Translation motion mode shape (22Hz). Figure 5: Ttilt mode shape (63Hz). Figure 6: Hub axial mode shape(192hz) and Hub twist mode shape (756Hz). Finite element method analysis presented that the natural frequencies would change with the speed rising as shown in the following Campell diagram. Figure 7: Campell diagram. Figure 8: Flywheel and casing for experiment. 4 ICSV23, Athens (Greece), 10-14 July 2016
From the above figure 7, one can find that two critical speeds are 25rps and 125 rps respectively. The calculation predicted that the second critical speed was locating in the range of 85-125 rps from different analytical methods, which was difficult to pass through. Therefore, the in-site balancing is necessary for the flywheel running to high speed. 4. Vibration measurement 4.1 Test instruments The composite flywheel was designed and manufactured for experiments. The flywheel rotor was driven by a permanent synchronic motor in 20 kw power. All the rotational parts are set in a chamber casing in which the vacuum in pressure of 2 Pa was sustained by a vacuum pump. The power controller give power or get power from the flywheel motor by power electronics technology. The vibration is measured through vibration sensors whose signals are checked and processed by a data analyser named SYNERY. 4.2 In-site balancing Before installed into the vacuum chamber, the composite flywheel motor shaft was balanced on a balancing machine. However, the actual bearings and the installation have great impacts on the dynamics behaviour. Therefore, in-site balancing is necessary to high speed machinery such as turbomachines, compressors, blowing machines and flywheels. Table 2 indicated that the in-site balancing decreased the unbalance response greatly. Balancing speed 2300rpm 4600rpm Original vibration 16.1um 314 17.2um 300 19.7um 68 3.62um 235 Table 2: In-site balancing results. Balancing weight Residual vibration W1: 5.75g 138 13.74g 332 4.3um 94 W2: 2.2g 68 3.3 210 4.7um 81 W1: 6.82g 250 3.81g 177 0.91um 67 0.58um 226 4.3 High speed running After the balancing, the flywheel test system could be accelerated to higher speed up to 13500 rpm. The vibration test results in figure 9 shows that the resonance is obviously for the critical speeds. Figure 9 indicates that the translational mode frequency is about 43 Hz and the tilt mode frequency is 140Hz higher. The other resonance frequencies being 20Hz and 183Hz are due to the natural frequency of the vacuum chamber as casing structure. Figure 9: High speed running. ICSV23, Athens (Greece), 10-14 July 2016 5
5. Conslusion The vibration dynamics model of the composite flywheel bearing system in vertical installment is presented. The rotor dynamics analysis using the transfer matrix method and FEM method predict the model shape and the varying behavior of the mode frequency with the rising rotational speed. The calculation results show that two critical speeds locating in the ranges of 22-54 rps and 45-172 rps according to the different support stiffness. The high value of the critical speed means that the in-site balancing with high precision is very necessary to the speeding up of the flywheel bearing system. The composite flywheel bearing system passed through two critical speeds and ran to the speed of 13500rpm after the balancing process at the speed of 2300 rpm and 4600 rpm. Tow mode resonant frequencies of the casing (vacuum chamber) in the flywheel energy storage system is observed in the vibration measurement. REFERENCES 1 Genta, G. Kinetic energy storage Theory and practice of advanced flywheel systems, Butterworth s, (1985). 2 Dai, X., Deng, Z., Liu, G., Tang, X., Zhang, F. and Deng, Z., Review on advanced flywheel energy storage system with large scale. Trans China Electrotech Soc., 26, 133 40, (2011). 3 Tzeng, J., Emerson, R. and Moy. P. Composite flywheels for energy storage. Compos Sci Technol, 66, 2520 2527, (2006). 4 Abrahamsson, J. and Bernhoff, H. Magnetic bearings in kinetic energy storage systems for vehicular applications. J Electr Syst, 7, 225 236, (2011). 5 Sebastián, R. and Peña-Alzola, R. Control and simulation of a flywheel energy storage for a wind diesel power system. Electrical Power and Energy Systems, 64,1049 1056, (2015). 6 Arvin, A.C. and Bakis, C.E. Optimal design of press-fitted filament wound composite flywheel rotors. Compos Struct, 72, 47-57, (2006). 7 Dai, X., Li, Y., Yu, H. Design of high specific energy density flywheel. Journal of Tsinghua University (Sci & Tech), 48(3), 379-382, (2008). 8 Vance, J., Zeidan, F. and Murphy, B. Machinery Vibration and Rotor dynamics, John Wiley & sons, Inc., (2010). 9 Zhu, K.Y., Xiao, Y. and Rajendra A.U. Optimal control of the magnetic bearings for a flywheel energy storage system, Mechatronics, 19(8), 1221-1235, (2009). 10 Dai, X., Shen, Z., Wei, H. On the vibration of rotor-bearing system with squeeze film damper in an energy storage flywheel, International Journal of Mechanical Sciences, 43(11), 2525-2540, (2001). 11 Park, C.H., Choi, S.K., Lee J.P. and Han Y.H. On the Dynamic Behavior of a 5kWh FESS Mounted on AMBs, the 11th International Conference on Mechatronics Technology, Ulsan, Korea, 416-420. (2007). 12 Tang, C., Dai, X., Zhang, X. and Jiang, L. Rotor dynamics analysis and experiment study of the flywheel spin test system, Journal of Mechanical Science and Technology, 26(9), 2669-2677, (2012). 13 Murphy, B.T. Bresie, D. A. and Beno J. H. Bearing loads in a vehicular flywheel battery, SAE Special Publications, v 1243, Feb, 1997, Electric and Hybrid Vehicle Design Studies, Proceedings of the 1997 International Congress and Exposition, Feb 24-27 1997, Detroit, MI 6 ICSV23, Athens (Greece), 10-14 July 2016