A review of resonance response in large, horizontal-axis wind turbines

Solar Energy, Vol. 29, No. 5, pp. 377-383, 1982 Prinled in Great Britain,

0038-092X182/110377~7503.00/0 © 1982 Pergamon Press Ltd.

A REVIEW OF RESONANCE RESPONSE IN LARGE, HORIZONTAL-AXIS WIND TURBINES TIMOTHY L. SULLIVAN National Aeronautics and Space Administration, Lewis Research Center, Cleveland, OH 44135, U.S.A.

(Received 1August 1981; accepted 24 February 1982) Abstract--Field operation of the Mod-0 and Mod-I wind turbines has provided valuable information concerning resonance response in large, two-bladed, horizontal-axis wind turbines. Operational experience has shown that 1/rev excitation exists in the drive train, high aerodynamic damping prevents resonance response of the blade flatwise modes, and teetering the hub substantially reduces the chordwise blade response to odd harmonic excitation. These results can be used by the designer as a guide to system frequency placement. In addition, it has been found that present analytical techniques can accurately predict wind turbine natural frequencies. 1. INTRODUCTION In any mechanical system, vibrations are undesirable and possibly dangerous if the vibratory motion becomes excessive. However, in a rotating system, such as a wind turbine, vibrations are unavoidable. Hence, one of the keys to good design of wind turbines is to minimize vibrations. This is done by avoiding resonance. Resonance is a phenomenon that occurs in a structure when an exciting or forcing frequency equals or nearly equals one of the natural frequencies of the system. It is characterized by a large increase in displacements and internal loads. In a rotating system the exciting frequencies are integer multiples of the rotational speed. In a wind turbine the important natural frequencies that must be considered are those associated with the blades, the tower (including yaw drive) and the drive train. The purpose of this report is to review what has been learned about resonance response from operation of the

Mod-0 [1] and Mod-1 [2] wind turbines (Figs. l(a,b), respectively). These two wind turbines are a part of the Federal Wind Energy Program directed by the Department of Energy. Based on field experience with these machines, conclusions will be made concerning when resonance will occur in a two-bladed, horizontal-axis wind turbine. In addition, analysis and design approaches to avoid resonance will be discussed. 2. ANALYTICALAPPROACHTO RESONANCE

A useful tool in the analysis of resonance potential of complex rotating systems is the frequency plot or Cambell diagram. A Campbell diagram for a hypothetical wind turbine, typical of wind turbines such as the Mod-0 and Mod-l, is shown in Fig. 2. In this diagram system natural frequencies are plotted versus rotational frequency. The radial lines are plots of integer multiples of the rotational frequency and represent exciting

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frequencies. Therefore, a potential for resonance exists whenever lines cross. This type of diagram is particularly useful in analyzing wind turbines designed to operate at variable rotational speeds. System natural frequencies such as those shown in Fig. 2 can be calculated using finite element computer codes such as NASTRAN. Modeling considerations and natural frequency results for the Mod-0 tower, bed plate and blades are presented in Chamis and Sullivan[3] and for the Mod-0 drive train in Sullivan et aL [4]. Experimental methods using vibration analyzers[5] are available for verifying calculations. Agreement between measured and calculated frequencies within 5 per cent are not uncommon for the lower frequency modes that are of primary interest in wind turbines. For a wind turbine with a single operating speed, another type of frequency diagram can be constructed: this is illustrated in Fig. 3. This diagram was presented at the detailed design review of a "second generation" wind

turbine, the Mod-2. The radial "per-rev" lines of Fig. 2 are now vertical lines with an avoid range applied. The required width of the avoid ranges is not precisely known. Here they were conservatively set at -+0.5 per rev for the even harmonics and -+0.25 per-rev for the odd harmonics. Calculated system frequencies are also shown. All the system frequencies for the Mod-2 are clear of the avoid ranges except the off-line drive train frequency. Because the rotor is a node point for this mode, the rotor cannot excite it. Therefore, it is permissible to be within the avoid range for this case. In Table 1 the most-recently calculated system frequencies are compared to measured frequencies, showing the degree of correlation that can be expected. As can be seen, the agreement is excellent. The avoid ranges shown in Fig. 3 are relatively wide, resulting in rather small windows for the designer to place system frequencies. Another point to note in this figure is that no drive train avoid range is shown for the odd harmonics. However, experimental evidence discussed in the following section shows that avoid ranges should also be provided for odd harmonics. A similar diagram for the Mod-1 wind turbine for 35 rpm operation is shown in Fig. 4 (a). Here a slightly different approach to the avoid ranges was taken. The avoid ranges are not as wide, allowing the designer greater flexibility in frequency placement. The Table 1. Comparison of calculated and measured natural frequencies for the Mod-2 wind turbine Frequency, per rev at 17.5r.p.m. Calculated Measured

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A review of resonance response in large, horizontal-axiswind turbines

modeling assumptions that were not realized in the as-built wind turbine. For instance, the difference in the off-line drive train frequencies comes from the assumption of no backlash in the drive train. The difference in the tower bending frequencies is related in part to the assumption of a flexible foundation, when the actual wind turbine was attached to bed rock. A condensed version of Fig. 4 (a) is shown in Fig. 4(b) for the present operating speed of the Mod-1, 23 rpm. The measured natural frequencies are clear of the avoid ranges except for the blade flatwise mode. Because of high aerodynamic damping, this is no concern. Note that the calculated drive train mode now is very close to l/rev. The implications of this are discussed in the following section.

justification for the very narrow avoid range for the flatwise blade mode is the high aerodynamic damping associated with this mode. Only odd harmonic avoid ranges are shown for the blade chordwise mode because no even harmonic excitation is expected. The theoretical basis for this can be found in Den Hartog[6]. The blade torsion/pitch change mechanism (PCM) mode requires high stiffness to avoid flutter. The natural frequency of this mode should be designed to be so high that resonance is not a consideration. Measured and calculated system frequencies for ModI are compared in Fig. 4(a). The calculated blade frequencies include the effect of centrifugal stiffening. The measured blade frequencies were obtained by applying an analytically-derived correction factor to the measured non-rotating frequencies. In general the agreement between measured and calculated values is good, which is typical of experience to date. When differences do occur, they can usually be explained by

3. FIELD EXPERIENCE WITH RESONANCE

Because it is a research machine the Mod-0 wind turbine has provided much experience with resonance.

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The Mod-1 has provided additional experience. In this section this experience will be reviewed for the drive train, rotor support (tower and yaw drive) and blades. Drive Train. For a perfectly balanced rotor, only even harmonic excitation would be expected in the drive train of a two-bladed rotor. For this reason avoid ranges in Fig. 3 and 4 are shown only on the even harmonics. However, mass, stiffness or aerodynamic unbalance from blade to blade can cause odd harmonic excitation as well. This was vividly demonstrated when the Mod-1 rotor speed was reduced from 35 to 23 rpm, which placed its natural frequency close to 1/rev. The output power of a wind turbine can vary about a mean power level. Figure 5 compares the amplitudes of cyclic power variation for 23 and 35 rpm operations. Examination of the real time data for 23 rpm operation showed the cyclic frequency was close to l/rev. The source of the i/rev excitation in the drive train is presently being investigated. However, the response seen here is not peculiar to the Mod-1. Synchronous operation of the Mod-0 at 35 rpm placed its drive train natural frequency close to l/rev. A time history of output power is shown in Fig. 6. The response here is very similar to that seen with the Mod-1. During early operation of the Mod-0, one mode of operation was with the alternator output connected to a resistive load bank. At this time the low-speed end of the drive train contained a hardening spring coupling[4]. The nonlinear nature of this coupling resulted in a significant increase in drive train natural frequency with increasing power as shown in Fig. 7. The calculated frequency coincided with 4/rev at a power of about 35 kW. Figure 8 shows the low-speed shaft torsional response as a function of power. The peak response occurs close to 35 kW and the shape of the data envelope is typical of resonance response in systems containing hardening springs.

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A review of resonance response in large, horizontal-axiswind turbines

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40rpm. Because of interest in more flexible towers, primarily for economic reasons, the frequency of the Mod-0 truss tower was reduced by placing the tower on a spring fixture. The details of this fixture are given in Ref.[10]. With the fixture the tower bending frequency was reduced to about 0.8 Hz or 1.5/rev at the present operational speed of 31 rpm. Towers with bending frequencies between l/rev and 2/rev are classified as "firm" towers. One of the operational characteristics of firm towers is that the machine passes through a 2/rev tower resonance going up to and coming down from operational speed. The effect of this resonance on blade and tower loads was a concern. Figure 10 shows the envelope of peaks from a time history of the response of the Mod-0 with a firm tower during a typical start-up, shut-down cycle. In summary, this test showed that when passing through the tower resonance, blade loads were not adversely affected and tower deflections were not excessive. More details of this test can be found in Keith et a/.[12]. Initial operation

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of the first Mod-2 wind turbine at Goldendale, Washington, confirms the results of the Mod-0 firm tower tests. Blades. Blade resonance response can be determined by running a speed survey in which the wind turbine is operated over a wide range of rotor speeds. The results of a speed survey between 10 and 40 rpm for Mod-0 in the stiff tower configuration are shown in Fig. 11. In general the chordwise loads respond to the odd har-

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monics as expected. Peak response was expected to occur very close to the odd per-revs. However, the 5/rev peak response occurs about 2 rpm higher than expected. The reason for this displaced response is not presently understood. The response to harmonics greater than 5/rev does not appear to be significant. Examination of flatwise blade loads during this same speed survey showed no load amplification at any rotor speed. High aerodynamic damping prevents the blades from responding in the flatwise direction. The primary reason for teetering a rotor is to reduce flatwise blade loads and torsional tower loads. As a result, hub motions are reduced, which in turn should reduce the blade resonance response. This indeed is the case as shown in Fig. l 1 for a 5/rev resonance. The load amplification for the teetered hub was about half that for the rigid hub. Typical time histories of blade chordwise response to 5/rev excitation are shown in Fig. 12 for both rigid and teetered hub. The data shown in Fig. 11 have certain implications with respect to multispeed operation of a wind turbine. Operation on 5]rev and above for a teetered rotor and 7/rev and above for a rigid rotor could probably be tolerated. This is based on the fact that the load magnification for these resonances is less than 20per cent.

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A review of resonance response in large, horizontal-axis wind turbines 4. COSCLUSIOSS Based on the operation of the Mod-0 and Mod-I wind turbines, the following conclusions concerning resonance response in large, two-bladed, horizontal-axis wind turbines can be made: 1. The important natural frequencies of wind turbines can be calculated with reasonable accuracy. 2. Odd harmonic content is present in the drive train and can cause significant resonance response. 3. Resonance associated with yaw drive flexibility causes blade load amplification; resonance associated with tower bending flexibility does not cause blade load amplification. 4. Odd harmonic excitations up to and including 5/rev can cause significant blade chordwise resonance response; teetering the rotor will reduce this response substantially. 5. High aerodynamic damping prevents resonance response in the blade flatwise direction at all frequencies. REFERENCES

1. R. L. Thomas and T. R. Richards, ERDA/NASA 100-kW Mod-0 wind turbine operations and performance. NASA TM-73824 (1977).

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2. Mod-I wind turbine generator analysis and design report. NASA CR-159495,(1979). 3. C. C. Chamis and T. L. Sullivan, Free vibrations of the ERDA-NASA 100 kW wind turbine, NASA TMX-71879 (1976). 4. T. L. Sullivan, D. R. Miller and D. A. Spera, Drive train normal modes analysis for the ERDA/NASA 100 kW wind turbine generator. NASA TM-73718(1977). 5. Walter Edgerly, Instant replay for vibration analysis. Machine Design, 22 Nov. (1979). 6. J. P. Den Hartog, Mechanical Vibrations, 2nd Edn. p. 313. McGraw-Hill, New York (1940). 7. K. R. V. Kaza, D. C. Janetzke and T. L. Sullivan,Evaluation of MOSTAS computer code for predicting dynamic loads in two bladed wind turbines. NASA TM-79101 (1979). 8. D. A. Spera, D. C. Janetzke and T. R. Richards, Dynamic blade loading in the ERDA/NASA 100 kW and 200 kW wind turbines. NASA TM-73711 (1977). 9. Mod-2 wind turbine system concept and preliminary design report. Volume II, Detailed Report. NASA CR-159609(1979). 10. J. R. Winemilleret al., Design, fabrication and initial test of a fixture for reducing the natural frequency of the Mod-0 wind turbine tower, NASA TM-79200(1979). 11. J. C. Glasgow and D. R. Miller, Teetered, tip-controlled rotor: preliminary test results from Mod-0 100kW experimental wind turbine. NASA TM-81445(1980). 12. Theo G. Keith, Jr., Timothy L. Sullivan and Larry A. Viterna, Performance of a steel spar wind turbine blade on the Mod-0 100 kW experimental wind turbine. NASA TM81588 (1980).