ROTOR DYNAMICS ANALYSIS AND VIBRATION MEASUREMENT 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: [email protected]
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 45172 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-
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The 23rd International Congress on Sound and Vibration
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 5kgm2.
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 108N/m to 107N/m, and the bottom support stiffness
varies from 107N/m to 106N/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.
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ICSV23, Athens (Greece), 10-14 July 2016
The 23rd International Congress on Sound and Vibration
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)
Critical speed 1
Critical speed 2
10
9
54
172
Translational/tilt
10
10
8
53
159
Translational/tilt
107
106
108
108
107
107
106
107
106
106
42
19
46
23
22
106
45
112
85
74
Translational/tilt
Translational/tilt
Translational/tilt
Translational/tilt
Translational/tilt
9
10
8
K2(N/m)
Mode
3.2 Finite Element Methods
ANSYS was used to calculate the mode frequencies and mode shapes. The computation parameters are top support stiffness being 108 N/m, bottom support stiffness being 106N/m, and the rotational speed is 0-400 rps. The calculation results were shown in following figures.
ICSV23, Athens (Greece), 10-14 July 2016
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The 23rd International Congress on Sound and Vibration
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.
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Figure 8: Flywheel and casing for experiment.
ICSV23, Athens (Greece), 10-14 July 2016
The 23rd International Congress on Sound and Vibration
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.
Table 2: In-site balancing results.
Balancing
speed
2300rpm
4600rpm
Original vibration
16.1um∠314°
17.2um∠300°
19.7um∠68°
3.62um∠235°
Balancing weight
Residual vibration
W1: 5.75g∠138°13.74g∠332°
W2: 2.2g∠68°3.3∠210°
W1: 6.82g∠250°3.81g∠177°
4.3um∠94°
4.7um∠81°
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
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The 23rd International Congress on Sound and Vibration
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 45172 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.
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