ACTIVE VIBRATION CONTROL OF AN INTERMEDIATE MASS: VIBRATION ISOLATION IN SHIPS

Transcription

1 ACTIVE VIBRATION CONTROL OF AN INTERMEDIATE MASS: VIBRATION ISOLATION IN SHIPS Xun Li, Ben S. Cazzolato and Colin H. Hansen Shool of Mehanial Engineering, University of Adelaide Adelaide SA 5005, Australia. 1 INTRODUCTION The traditional approah for isolating the transmission of vibratory energy from a vibration soure, suh as a reiproating engine, to a flexible support struture is to plae passive isolators between the vibration soure and the reeiving struture. The seleted vibration isolator must support the stati load of the mahine and must also have a suffiiently low stiffness so that the translational and rotational resonane frequenies of the mahine, mounted on the isolators, are onsiderably less than the frequenies of the dominant disturbanes generated by the mahine. A passive isolator apable of adequate isolation at low frequenies an sometimes result in insuffiient support stability for the equipment. One promising way around these problems is to use ative vibration isolation with passive isolators to redue the vibratory energy transmission. Ahn et. al. 1 proposed a hybrid-type ative vibration isolation system using an eletromagneti atuator and air-springs. In their work, the eletromagneti atuator was used as an ative element and the air spring ated as the passive element. It was demonstrated that this hybrid ontrol system ould provide a better isolation performane than the passive system alone. Gardonio et. al. 2-5 studied the theoretial effetiveness of various ontrol strategies for ative vibration isolation. In their work 3, the minimisation of the total power transmission through the mounts to the reeiver was ompared with several ontrol strategies: the minimisation of the axial veloities or fores; the minimisation of the axial power transmission and the minimisation of the sum of the squared axial veloities and weighted squared fores. It was onluded that the anellation of the total power transmitted from the soure to the reeiver through the mounts was the optimal ontrol strategy for the ases they studied. In this paper, the feasibility of using ative vibration isolation to minimise the motion of an intermediate mass of a two stage passive ship engine mount is investigated in the laboratory. The work involved the use of a feedforward ontroller to anel the total vibratory energy of the intermediate mass of a test rig simulating one of diesel engine mounts in a ship. The motion of the intermediate mass (a total of six degrees of freedom) was sensed using aelerometers to provide the error signals and several inertial shakers were mounted to the mass to at as ontrol atuators. Both numerial simulation results and real time ontrol results are provided.

2 2 TEST RIG MODEL Figure 1 shows the setup of the test rig, whih represents a two-stage hybrid vibration isolation system. In the figure, for the passive system, the top plate is onneted to the intermediate mass through 4 rubber isolators and another 6 isolators are mounted between the intermediate mass and the bottom plate. The intermediate mass was from top mass z y x rotating mahine primary disturbane simulated with simulated primary shakers with shakers intermediate mass aelerometers bottom mass ontrol shakers Figure 1: Two stage hybrid vibration isolation system an atual ship isolator. Suffiient rubber bloks were used on eah side of the intermediate mass to provide a similar stati defletion to that ahieved by installed isolator. The number of bloks used in the tests was onsiderably less than the number used on the ship, as the mass of the top plate was muh less than the mass of engine supported in the atual installation. The speifiations of the system are detailed in previous work 6. For the ative ontrol system, seven error sensors (E 1 E 7 ) and seven pairs of ontrol atuators (A 1 A 7 and AA 1 AA 7 ), whih allowed ontrol at a total of six degrees of freedom of the rigid mass were loated on the intermediate mass as mapped in Figure 2. Two atuators of eah pair (A i and AA i ) were wired in series and onneted to the ontroller through one hannel. In Figure 2, M 1 -M 7 indiate the monitor sensor loations whih were used to evaluate the ontrol performane for numerial simulation and R, P and T represent pith, rotation and torsional motion of the mass about the X, Y and Z axes respetively. P Z T R Y e6 m6 A2 (AA2) e2 m2 A3 (AA3) e3 m3 A5 AA5 A1 (AA1) m1 e5 m5 e1 A6 AA6 e4 m4 A4 (AA4) e7 m7 A7 AA7 X Figure 2: Error sensor, monitor sensor and ontrol atuator loations To inrease the mehanial output of the ontrol shakers within the frequeny range of interest, two sets of ontrol shakers A i and AA i were tuned to resonate around the fundamental and 2.5 th order of the engine operating speed respetively 7. A simulated primary disturbane was generated by feeding vibration signals that were reorded on a ship into the primary inertial atuators attahed to the top mass.

3 3 CONTROL STRATEGIES The quadrati optimisation tehnique, whih has been doumented thoroughly by Nelson and Elliott 8 and Hansen and Snyder 9, has been widely used in ative noise and vibration ontrol simulations and is summarised in Table 1 for the ase study. In the table, for kineti energy ontrol, Z e is the matrix of transfer funtions from the ontrol soures to the error sensors; Q is the vetor of the ontrol fores and V p is the vetor of the primary disturbane signals at the error sensors. For modal ontrol, Z m is the matrix of modal transfer funtions from the modal ontrol atuators to the modal error sensors; and V m is the vetor of the primary disturbane for eah mode. Control Strategies Kineti Energy Control Modal Control H H H Error Criterion J = Q AQ + Q b + b Q + -1 Optimum Control Fores Q,opt = A b A Z H Z H = e e ; b = Z e Vp ; A Z H = Z m m ; b Z H = V m m ; H = V p V p = V H V m m Table 1 Control strategies The minimum ost funtion at the error sensing loations an be obtained by substituting the expression for optimum ontrol fores into the expression for the error riterion in Table 1. 4 NUMERICAL SIMULATION Initially, off-line ontrol was done to evaluate only the physial system onfiguration without any limiting effets due to the ontrol system, so that the maximum ahievable ontrol results ould be ahieved. This involved taking measurements of the transfer funtions from the ontrol soures to the error sensors and measurements of the primary disturbane at the error sensors. To evaluate the ontrol performane at a set of monitor sensors, the transfer funtions from the ontrol atuators to the monitor sensors were measured as well. The optimum ontrol inputs, orresponding to the minimum ost funtion at the error sensors, were alulated and the vibratory energy redution at the monitor sensors was then alulated using these optimum ontrol inputs. Table 2 shows the numerial results using both ontrol strategies. Both sets of ontrol atuators loated on the top and bottom of the intermediate mass were used. Harmoni order of engine speed fundamental 1.5 th 2 nd Overall redution at Kineti energy ontrol monitor sensors (db) Modal ontrol Table 2 Predited overall vibratory energy level redution at the monitor sensors

4 From Table 2, one an see that the vibratory energy redutions at the fundamental frequeny and the frequeny orresponding to the 1.5 th order are 40.9 db and 28.6 db, respetively, for kineti energy ontrol and 40.2 db and 34.3 db, respetively, for modal ontrol. As the supported mass may be assumed rigid in the frequeny range of interest, the seven monitor sensors (M 1 M 7 ), whih are mapped in Figure 2, an measure all degrees of freedom of the mass. Therefore the vibratory energy level redution at the monitor sensors is representative of the total vibratory energy level redution of the mass. 5 REAL TIME CONTROL To verify the predited results, real time ontrol was arried out with an EZ-ANC II multihannel ontroller. A simulated primary disturbane was generated by feeding the signals that were reorded on a ship into the primary inertial atuators attahed to the top mass. Both kineti energy and modal ontrol strategies were evaluated. 5.1 Experimental set-up For kineti energy ontrol, seven ontrol atuators and seven error sensors were used. The signals from the error sensors were input into the EZ-ANC II ontroller and also into a Brüel & Kjær PULSE system (multi-data aquisition system). The average redution of the sum of the squared signals at the error sensors was measured using the PULSE system. Monitor sensors were not used for this part of the work as the intermediate mass was suffiiently rigid that the measured overall vibration level redutions at the error sensors were representative of the total vibration redution of the rigid intermediate mass. Control adaptation eased one the overall vibration level redutions at the error sensors reahed a maximum. The power spetra at the error sensors were then reorded. For modal ontrol, eletroni summers between the ontroller and ontrol atuators were used to onstrut the modal atuators. Figure 3 shows a blok diagram of the experimental set-up for real time ontrol. In the figure the summers are used only for modal ontrol. primary atuators power amplifiers DAT reorder aelerometers harge amplifiers EZ-ANC II PC omputer B & K PULSE ontrol atuators power amplifiers summers 5.2 Control results Figure 3: Blok diagram of the experimental setup for real time ontrol For kineti energy ontrol, the ost funtion to be minimised was the sum of the squared error signals at the 7 error sensor loations. This quantity is proportional to the kineti energy of the intermediate mass; thus minimisation of the ost funtion implies minimisation of the vibratory energy. Figure 4 shows aeleration levels before and after kineti energy ontrol. Only the set of ontrol atuators with a resonane frequeny around the fundamental of the engine speed were used. From the figure it an be seen that the large aeleration level

5 redutions of 30.1 db and 30.4 db were ahieved at frequenies orresponding to the fundamental and 1.5 th order respetively, but poor ontrol performane was obtained at the 2 nd order frequeny. Aeleration level (db re: 1m/s 2 ) st 1.5 th 2 nd 2.5 th 3 rd engine operating speed and harmonis before ontrol after kineti energy ontrol 1 =30.1 db; 1.5 =30.4 db; 2 =3.1 db; 2.5 =1.6 db; 3 =6.8 db Figure 4: Overall aeleration levels before and after kineti ontrol; the resonane frequeny of the ontrol atuators was around fundamental of engine speed The reason for this phenomenon is that the ontrol atuators resonated at a frequeny orresponding approximately to the engine running speed, so that a large portion of the energy used to model the anellation path was distributed around the fundamental and 1.5 th orders, shown as the dotted line in Figure 5. On the other hand, poor anellation path modelling as a result of the low S/N ratio at the seond order frequeny resulted in poor ontrol performane at this frequeny. To improve ontrol performane at the seond order frequeny, an additional set of seven atuators, all of whih were tuned to resonate around the 2.5 th order engine operating speed, were introdued into the system. The onfiguration of the ontrol atuators for this ase was desribed previously. The response of the intermediate mass with both sets of atuators present is shown as the solid line in Figure Aeleration levels (db re: 1 ms 2 ) engine operating speed and harmonis one set of atuators resonant at the 1st harmoni two sets of atuators resonant at the 1st and 2.5th harmonis Figure 5: Response of the intermediate mass during anellation path modeling Figure 6 shows the ontrol results ahieved with the additional seven ontrol atuators. By omparing the results shown in Figure 6 with those in Figure 4, one an see that the vibration level redution at the 2 nd order frequeny is slightly inreased but a further 18 db redution is ahieved at the 2.5 th order. This is partly beause the additional set of ontrol atuators resonated at a frequeny that was loser to the 2.5 th order frequeny than the 2 nd order. Another reason for the ontinued poor performane at the seond order frequeny is the presene of eletroni noise in the system around the 2 nd order frequeny due to an earth loop

6 problem. Thus, there is no doubt that good ontrol performane an be ahieved at the 2 nd order frequeny if properly tuned atuators are used and the ground loop problem is eliminated by proper insulation of the aelerometers. Aeleration level (db re: 1m/s 2 ) st 1.5 th 2 nd 2.5 th 3 rd engine operating speed and harmonis before ontrol after kineti energy ontrol 1 =31.1 db; 1.5 =17.6 db; 2 =5.2 db; 2.5 =19.9 db; 3 =6.5 db Figure 6: Overall aeleration levels before and after kineti ontrol; the resonane frequenies of ontrol atuators were around 1 st and 2.5 th order engine speed. For modal ontrol, eletroni summers were used to ombine the ontroller outputs so that the modal ontrol atuators, whih ontrolled eah of six degrees of freedom, ould be onstruted. The overall vibration levels before and after modal ontrol are shown in Figure 7 when both sets of atuators were used. Aeleration level (db re: 1m/s 2 ) st 1.5 th 2 nd 2.5 th 3 rd engien oerating speed and harmonis before ontrol after modal ontrol 1 =29.3 db; 1.5 =14.3 db; 2 =9.7 db; 2.5 =15.4 db; 3 =1.6 db Figure 7: Overall aeleration levels before and after modal ontrol; both sets of ontrol atuators loated on the top and bottom of the intermediate mass. As expeted, overall vibration levels were redued at the required frequenies and espeially good results were ahieved at the frequenies that were lose to the resonane frequenies of the ontrol atuators. These results are similar to those ahieved using kineti energy ontrol, as shown in Figure 6.

7 6 CONCLUSIONS The feasibility of using ative ontrol to minimise the vibration levels of an intermediate mass of an existing two-stage passive isolation mount used in a ship has been investigated. The ontrol objetive was to minimise the overall vibration levels of the intermediate mass for all six degrees of freedom. To ahieve ontrol, seven error sensors and seven ontrol atuators were used. Two ontrol strategies were evaluated; namely, kineti energy ontrol and modal ontrol. Numerial simulations were onduted using the measured disturbane at the error sensors and the measured transfer funtions from the ontrol atuators to the error sensors. To verify the predited results, real time ontrol was arried out using an EZ-ANC II ten-hannel ontroller. The real time results demonstrated that overall vibration levels of the intermediate mass ould be redued by 31.1 db, 17.6 db and 5.2 db for kineti energy ontrol, and the overall vibration levels of the mass ould be redued by 29.3 db, 14.3 db and 9.7 db for modal ontrol at frequenies orresponding to the fundamental, 1.5 th and 2 nd orders respetively. ACKNOWLEDGEMENT The finanial support of AMRL, Defene Siene and Tehnology Organisation, Australia is gratefully aknowledgement. REFERENCES 1. K. G. Ahn, H. J. Pahk, M. Y. Jung and D. W. Cho, A hybrid-type ative vibration isolation system using neural networks, Journal of Sound and Vibration, 192(4), (1996) 2. P. Gardonio, S. J. Elliott and R. J. Pinnington, Ative isolation of strutural vibration on a multiple-degree-of freedom system, Part I: The dynamis of the system, Journal of Sound and Vibration, 207(1), (1997) 3. P. Gardonio, S. J. Elliott and R. J. Pinnington, Ative isolation of strutural vibration on a multiple-degree-of freedom system, Part II: Effetiveness of ative ontrol strategies, Journal of Sound and Vibration, 207(1), (1997) 4. P. Gardonio and S. J. Elliott, A study of ontrol strategies for the redution of strutural vibration transmission, Journal of Vibration and Aoustis, 121, (1999) 5. P. Gardonio, S. J. Elliott, Passive and ative isolation of strutural vibration transmission between two plates onneted by a set of mounts, Journal of Sound and Vibration, 237(3), (2000)

8 6. J. W. Lee, X. Li, B. S. Cazzolato and C. H. Hansen, Ative vibration ontrol to redue the low frequeny vibration transmission through an existing passive isolation system, Proeedings of ICSV8, Hong Kong, (2001) 7. X. Li, J. Cordioli, B. S. Cazzolato, X. Qiu and C. H. Hansen Tuneable inertial shakers for ative ontrol, International Journal of Aoustis and Vibration, 6(4), (2001) 8. P. A. Nelson and S. J. Elliott, Ative Control of Sound. (Aademi Press, 1995) 9. C. H. Hansen and S. D. Snyder, Ative Control of Noise and Vibration. (E & FN SPON, 1997)