Active Control of Low-Frequency Sinusoidal Vibration Transmission of Ship Machinery

LI Yan,HE Lin,SHUAI Chang-geng,MA Jian-guo,WANG Fei,LIU Yong

(1a.Institute of Noise&Vibration;b.National Key Laboratory on Ship Vibration&Noise,Naval University of Engineering,Wuhan 430033,China;2 China Ship Scientific Research Center,Wuxi 214082,China; 3 China Ship Development and Design Center,Wuhan 430064,China)

Active Control of Low-Frequency Sinusoidal Vibration Transmission of Ship Machinery

LI Yan1a,b,HE Lin1a,b,SHUAI Chang-geng1a,b,MA Jian-guo1a,b,WANG Fei1a,2,LIU Yong1a,3

(1a.Institute of Noise&Vibration;b.National Key Laboratory on Ship Vibration&Noise,Naval University of Engineering,Wuhan 430033,China;2 China Ship Scientific Research Center,Wuxi 214082,China; 3 China Ship Development and Design Center,Wuhan 430064,China)

Aiming at the active control of low-frequency sinusoids in ship machinery vibration,noncontact electromagnetic actuator with large output force,flat frequency response,and excellent maneuverability is developed,and the electromechanical performance of such actuator with permanent magnet bias is analyzed.A dynamic model of active-passive vibration isolation system is presented, and the factors affecting system stability are analyzed.A passive-active vibration isolator consisting of electromagnetic actuator and air spring is developed,in which a disengageable suspended structure is designed to improve its adaptability to shock and swing in the ship environment.A multi-channel narrowband Fx-Newton algorithm with rapid convergence and good robustness to frequency fluctuation is also proposed.A passive-active vibration isolation system composed of such isolators is then installed on a 200 kW ship diesel generator for testing,and the experimental results show that under complex situations such as multiple sinusoids and frequency fluctuation of the targeted sinusoids, rapid convergence of the control algorithm and stable and effective control of vibration could be realized with this isolation system.Therefore,the developed passive-active vibration isolation system can satisfactorily meet the engineering requirement of attenuating low-frequency sinusoidal vibration excited by ship machinery.

low-frequency sinusoidal vibration of ship machinery;active control; electromagnetic actuator and air spring;Fx-Newton algorithm; frequency fluctuation;robustness

0 Introduction

In the vibration of ship machinery,energy-concentrated low-frequency sinusoids may lead to remarkable unwanted noise radiation under water and make the ship more vulnerable to sonar detection.On the other hand,these low-frequency sinusoids cannot be effectively eliminated with passive vibration isolation technology.

Passive-active vibration isolation can attenuate both broadband vibration and low-frequency sinusoidal vibration,which has been paid more attention in recent years.Related theoretical and experimental studies have made large progress[1-8],but its engineering applicationin ship machinery has scarcely been reported.

Active control of ship machinery vibration requires passive-active isolator with large carrying capacity,high reliability,and good adaptability to the ship environment.For such an isolator,electromagnetic actuator[9]is a good candidate with large output force,flat frequency response,and excellent maneuverability,but its poor adaptability to shock and swing is a longexisting problem awaiting solution.And further study of the control algorithm in ship engineering practice is also required to realize stable and rapid convergence in complex cases such as multiple sinusoids,MIMO coupling,and unstable magnitude and frequency fluctuation of the sinusoids.

In this paper,the electromechanical performance of electromagnetic actuator with permanent magnet bias is analyzed;a dynamic model of active-passive vibration isolation system is presented and analyzed.A new passive-active vibration isolator consisting of electromagnetic actuator and air spring is developed for ship machinery with good adaptability to shock and swing,and a multi-channel narrowband Fx-Newton algorithm with rapid convergence and good robustness to frequency fluctuation is proposed.The active-passive isolation system is then installed on a 200 kW ship diesel generator and the effect of attenuating the sinusoidal vibration of ship machinery is tested at stable and fluctuating shaft rotating speed.

1 An active-passive isolator for ship machinery

1.1 Mechanism of active-passive isolation system using electromagnetic actuator

The mechanism of the active-passive isolation mounting using electromagnetic actuator is shown in Fig.1.In the system,the passive isolators bear the machinery’s weight and isolate the transmission of vibration from machinery to the lower frame,and the non-contact actuator bearing no static load is driven by the controller and power amplifier to attenuate low-frequency sinusoidal vibration of the lower frame.

Fig.1 Mechanism of the active-passive isolation mounting

Fig.2 Schematic structure of electromagnetic actuator

An electromagnetic actuator with permanent magnet bias[10]is designed with the structure shown in Fig.2,which does not require static power consumption;and is convenient for installation.Before the control current is input to the coil,the attraction force caused by permanent magnet bias[10]is：

After the alternating control current i is input to the coil with N turns,the generated electromagnetic field is superposed on the permanent magnetic field,and the resultant force of actuator is：

According to Eqs.(1)and(2),the electromagnetic force of actuatorFg（）is：

Then the dynamic equation of the active-passive isolation system can be derived as：

where m is the machinery’s weight;kaand caare the stiffness and damping ratio of air spring, respectively;fdis the exciting force;and x is the relative vibration displacement of the machinery and lower frame.

Hence the dynamic model of the active-passive isolation system can be linearized at the equilibrium point：

Since Eq.(6)is similar to the system using electromagnetic actuator with electromagnet bias[9],the proposed system using actuator with permanent magnet bias also have the following characteristics：

(1)Negative stiffness of actuator may reduce the whole stiffness of the hybrid isolation system,thus enhancing the broadband isolation effect even if the active controller is shut down.

(2)When the frequency ratio γ(excitation frequency divided by the natural frequency)is smaller than 1,the required active control force is greater than the excitation force;when γ= 1,the required force will be close to the excitation force;when γ＞1,the required force is smaller than the excitation force,and the greater is γ,the smaller force will be required.

(3)When γ＞1,the amplitude of machinery vibration will not be increased after active control.

1.2 Development of active-passive vibration isolator

Fig.3 The mechanics of the active-passive isolation mounting

Fig.4 Structure of active-passive isolator composed of electromagnetic actuator and air spring (a)Active-passive isolator;(b)Disengageable suspended structure

In this hybrid isolator,the actuator iron core is mounted on the lower plate of air spring, and the actuator armature is mounted on the upper plate of air spring through a disengageable suspended structure.Magnetic conductive rubber is filled into the air gap between the actuator armature and permanent magnet on top of iron core,serving the function of reducing the air-gap reluctance and improving the electro-mechanical efficiency of actuator.The structure of this hybrid isolator has the merits of small size and ease of installation,and it is convenient for application in ship air spring vibration isolation devices[11].

1.2.1 Stiffness matching and stability design for hybrid isolator

In section 1.1,it is indicated that the actuator demonstrates negative stiffness.To ensure the stability of mounting under disturbances,such as those caused by ship motion(shock and swing),stiffness matching is considered in the design of active-passive isolator.

where ARis a function of the lower flange deflection angle β and upper flange deflection angle α;pais the atmosphere pressure;p is the air spring pressure;Se,V and Reare the effective area,internal volume and effective radius of air spring,respectively.The initial values of these parameters are given at the rated height and they all vary with x.

According to the stiffness criterion of stability,if the isolator stiffness is always positive within the air gap working range：

then the mounting will not be unstable in case of large ship motion.

Since the electromagnetic field of electromagnetic actuator is located in multiple media and has complicated shape;has nonlinear properties;and may be affected by magnetic leakage and the edge effect,the theoretical‘-kp’derived in Eq.(7)is not very accurate.The finite element method is therefore used to predict the total stiffness“k”.The input parameters of the finite element model are the structural and electromagnetic parameter of actuator and the structural and air pressure parameters of air spring;these parameters are adjusted for stiffness matching so that the isolator stiffness is always positive within the air gap working range and the stability condition is satisfied.

1.2.2 Shock and swing adaptability design for hybrid isolator

Complex ship operation conditions(such as shock,swing,and tilt)may cause large displacement of the isolator,resulting in the collision of iron core with armature.This problem has

The stiffness[11]of air spring can be calculated as：not been well solved yet;the‘smart spring’[3]improved the environmental adaptability of hybrid isolator by leaving a large air gap(about 9mm high)in the electromagnetic actuator, which,however,also increased the power consumption.

A disengageable suspended structure is proposed to improve the shock and swing adaptability of hybrid isolator.It connects the armature of actuator and the upper cover plate of air spring,as shown in Fig.4.In normal working state,this structure rigidly connects the actuator armature with the upper plate of air spring,the actuator force can be directly output,thus behaves small phase shift and flat amplitude-frequency characteristics.

In the state of shock or swing,the actuator armature will contact with the magnetic conductive rubber,and when the force between them exceeds a threshold,the upper and lower seats of the suspended structure will be swiftly disengaged.The mechanics of the active-passive isolation system at this state is shown in Fig.5,where kris the stiffness of magnetic conductive rubber; ksis the stiffness of spiral spring;and ks<

Fig.5 Mechanics of the mounting after the structure is disengaged

Compared with the normal working state in Fig.3,the total stiffness of the isolator is just increased by a small amount‘ks’.Thus,after the suspended structure is disengaged,the lowstiffness deformation allowance is increased by 5-7 mm,so rigid contact is prevented.Furthermore,the magnetic conductive rubber can also prevent the collision of actuator armature with permanent magnet.When large displacement has diminished,the suspended structure is automatically restored to the original position.

The above-mentioned designs help to improve the stability and adaptability of the proposed active-passive vibration isolator to the ship environment.

1.3 Performance testing of the active-passive vibration isolator

A variety of electromagnetic actuators with rated output force in the range of 20-300 N have been developed,and the test results of 300 N-actuator are shown in Fig.6.The magnitudes of fundamental force at different frequencies are shown in Fig.6(a),which keep almost the same for a given input current.Fig.6(b)shows that the nonlinearity of force increases with current,but even at the allowed maximum current of 7 A,it is still lower than-23 dB.

The static stiffness of this active-passive vibration isolator is measured on an MTS-landmark370.50 testing machine when the isolator is inflated and loaded up to about 8.6 kN, and the measured displacement is plotted vs the applied vertical static load in Fig.7.Since the rated air gap between the magnetic conductive rubber and the armature is 2 mm wide,when the displacement under compression is less than 2 mm,the static stiffness of the isolator is about 282.0 N/mm;when the displacement reaches about 2 mm under compression,the arma-ture contacts with the magnetic conductive rubber and the static stiffness is increased to 2 939 N/mm;however,when the displacement under compression is larger than 2.2 mm, the static stiffness swiftly decreases to 653 N/mm,suggesting that in case of large displacement caused by shock or swing, the suspended structure in the isolator has automatically disengaged and rigid contact is prevented.

The dynamic stiffness and natural frequency of this active-passive isolator are also measured and the results are shown in Tab.1.The dynamic stiffness and natural frequency under the rated conditions(with 0 mm static displacement)are listed in Tab.1(a).In this state,the natural frequency of the isolator is very low,about 3.59-3.84 Hz.When the isolator is pressed 4 mm down(in simulating the condition of tilted hull),the measured dynamic stiffness and natural frequency are listed in Tab.1(b).The natural frequency is about 4.27-4.48Hz,only slightly higher than the natural frequency of the isolator working at the rated height.This result suggests that large deformation caused by shock,swing or tilt would not lead to short-cut transmission of vibration,and the isolator could still maintain highly effective broadband vibration isolation.

Fig.6 Measured results of actuator’s characteristics(a)fundamental output force of actuator；(b)the nonlinearity of force,which is defined as the energy difference between the second and fundamental component of force

Fig.7 Measured static properties of the active-passive vibration isolator

Tab.1 The dynamic stiffness and natural frequency of the active-passive vibration isolator(pp-peak excitation magnitude,fe-excitation frequency,Kd-dynamic stiffness,fn-natural frequency) (a)The isolator is at rated height with 0 mm static displacement

(b)The isolator is pressed down 4 mm(simulating ship tilting)

2 The narrowband control algorithm

In active control of machinery vibration,some major problems have been encountered.The Fx-LMS algorithm[1,6-10,12]has been widely used in active noise and vibration control.However, in active-passive machinery vibration isolation systems with strong cross-coupling,large eigenvalue dispersion results in low convergence rate and the control effect may be poor under unstable vibration excitation.Furthermore,the frequency and amplitude of machinery vibration may fluctuate,so the control algorithm requires good real-time performance,fast convergence rate and good robustness to these fluctuations.

Fig.8 Schematic diagram of the time domain filtered-x Newton narrowband algorithm

The proposed algorithm has been improved in the following aspects to address the problems mentioned above：

(1)The proposed algorithm uses narrowband pass filters(NBPF)to extract target sinusoids from the broadband signal and control them in multi-controllers with different step sizes and running in parallel,thus multiple sinusoids can be effectively controlled with fast convergence rate.This method does not require frequency estimation,so frequency mismatch is avoided.

(2)The frequency of sinusoids in machinery vibration may fluctuate within a certain range.However,the frequency-domain narrowband algorithms[15]based on FFT or demodulation,and the time-domain narrowband algorithms[16]based on internal reference signal generator,are not good for vibration with frequency and amplitude fluctuations.And for time-domain narrowband algorithms based on the NBPF,because of the steep phase-frequency characteristics of the NBPF,significant phase shift would exist between the extracted sinusoidal signal and original broadband signal,so this frequency fluctuation may lead to fluctuating optimum controller response（Wopt）in the algorithm and deteriorate the control performance.Hence an adaptive phase-shift compensator is proposed to eliminate this variation of Wopt,and improve the robustness of control system to frequency fluctuation.

where the filter coefficients cRand cIcan be adaptively updated online,and the updating equations are：

Fig.9 Adaptive phase-shift compensator for the NBPF

Fig.10 The structure of the inverse secondary-path filter

(3)In the proposed algorithm,the sinusoidal reference signal is first processed by inverse secondary path filtering based on the Newton iteration method[1,13-14],and then the output signal is used to update the controller,so the convergence rate[14]is almost unaffected by the strong cross-coupling in active-passive machinery vibration isolation systems and can be much faster than the Fx-LMS algorithm.

According to Eq.(14)and Fig.10,for an L-channel system,the secondary-path inverse filtering can be realized in time-domain by an L×L matrix of 2nd-order filters.Such a system has small workload and does not need time-frequency transformation;both merits favor good real-time performance of the control algorithm.

(4)Even though the actuator only has weak nonlinearity,it still needs to be compensated to avoid structural resonance of ship frame caused by nonlinear harmonics.The improved algorithm with nonlinear inverse-model compensator is proposed.

3 Experiments and results discussion

3.1 Experimental setup and algorithm setting

The developed active-passive vibration isolators are installed in a single-deck vibration isolation system on which a 200 kW ship diesel generator is mounted,as shown in Fig.11.The generator weighs 3.6 t,supported by six active-passive isolators.The electromagnetic actuators(actuator 1#-6#)integrated in air spring act as the secondary vibration sources.Six accelerometers are mounted near the six isolators on the lower supporting frame and the signals recorded by them are used as error signals(these accelerometers are called error sensor e1-e6).The diesel generator can act as the primary source to excite broadband vibration with multiple harmonics,and the accelerometer mounted on the upper supporting frame records the reference signal.

The control system works at 1 000 Hz sampling rate.The time-domain Fx-Newton algorithm with NBPF is run to investigate the performance of the isolator in controlling real machinery vibration,with the following settings：the Hilbert transformation is realized by a 21-order FIR filter and the corresponding time-delayer is 10 points;the controllers for each sinusoid are 15-order FIR filters,and the inverse secondary-path filtering is implemented witha 6×6 matrix of 2nd-order filters in the time domain;the controller coefficients are updated and the control signals are also generated in the time domain;the phase-shift compensator is realized by a 2nd-order filter.

3.2 Passive isolation effect of broadband vibration

The effect of broadband vibration isolation is evaluated at shaft rotating speeds of 1 000-1 500 r/min without active control.Signals recorded by six accelerators mounted on the upper frame and the other six accelerators near the isolators on the lower frame are used to calculate the vibration level difference,in range of 20-8 000 Hz.The results indicate that the isolator has excellent passive isolation effect on broadband vibration at each rotating speed,with vibration level difference larger than 32.8 dB.The 1/3-octave test result at the shaft rotating speed of 1 300 r/min is shown in Fig.12.

Fig.11 Experimental setup and layout of measuring points for active vibration isolation

Fig.12 Experimental result of passive broadband isolation at 1 300 r/min

3.3 The attenuation effect on multiple sinusoidal vibrations excited by diesel generator

In this test,the reference signal comes from the accelerometer mounted on the upper frame.The control algorithm is designed to effectively attenuate 10-11 outstanding sinusoids of vibration on the lower frame.

Firstly,experiments are conducted at constant shaft rotating speeds of about 1 400 r/min and 1 200 r/min.The proposed Fx-Newton algorithm with NBPF(without compensator)is tested.

Fig.13 Power spectrum density of acceleration on lower supporting frame before and after active control (a)At rotating speed of about 1400r/min;(b)At rotating speed of about 1 200 r/min

Fig.13(a)and(b)show the power spectra of the vibration acceleration on the lower frame, before and after active control.Before active control,despite the good passive isolation effect introduced in Section 3.2,the vibration of lower frame still contains significant harmonic sinusoids.After active control,in additional to the passive isolation effect,the most outstanding 10-11 harmonics in the range of 20-150 Hz are further effectively attenuated by 15-37 dB until being merged into the background noise.

The evolution of normalized error power at 110 Hz and 140 Hz at stable rotating speed of 1 200 r/min is also shown in Fig.14, which further demonstrates that the algorithm can rapidly,stably and effectively attenuate harmonics with amplitude-fluctuation.These results suggest that the proposed Fx-Newton algorithm with NBPF(without compensator)have very good vibration isolation effect on a real machine with stable rotating speed.

Then,rotating speed fluctuation of±20 r/min around 1 200 r/min is manually driven by a fuel pump suction valve,and the Fx-Newton algorithms with NBPF and phase-shift compensator are tested.

The test results in Fig.15(a)and(b)suggest that the proposed Fx-Newton algorithm with both NBPF and compensator has good robustness to frequency fluctuations and can effectively suppress frequency-fluctuating harmonics in a real machine.Fig.15(a)shows that the frequency-fluctuating harmonics are suppressed by about 15-32 dB at the 1st,1.5th,2nd,3.5th,4th order harmonics and about 10-18 dB at the 4.5th,5.5th,6th,6.5th,7th,7.5th order harmonics.Fig.15(b)shows the evolution of the average power spectrum of errors(based on STFT), which suggests that this algorithm could accomplish rapid and effective vibration suppression,and almost no significant low-frequency harmonics would appear in the error signals under control started at the 20th second.

Fig.14 Evolution of normalized error power when control vibration at stable rotating speed of about 1 200 r/min

Fig.15 The acceleration on the lower supporting frame before and after control,obtained by the narrowband Fx-Newton algorithm with phase-shift compensator,at fluctuating rotating speed of about 1 200±20 r/min(a)Power spectrum density;(b)Evolution of the power spectrum,based on STFT

4 Conclusions

It is important to control low-frequency sinusoidal vibration transmission of ship machinery.In this paper,an active-passive vibration isolator which contains an electromagnetic actuator integrated in an air spring isolator is developed for this purpose;it has the merits of small size,large carrying capacity,good broadband vibration isolation effect,and low power consumption for active control.

A disengageable suspended structure is designed,which can automatically separate the actuator armature from the plate of air spring when shock or swing occurs on ship,to prevent rigid contact and give the isolator good adaptability to the ship environment.

A time-domain MIMO Fx-Newton narrowband algorithm and modified algorithm with narrowband-pass filter(NBPF)and phase-shift compensator are proposed for the isolation system.This control algorithm can realize rapid convergence,and high control effect of low-frequency sinusoids in ship machinery vibration under complex situations such as multiple sinusoids,MIMO coupling,and amplitude and frequency fluctuation.

Experiments conducted on an 200 kW ship diesel generator mounted on this isolator system show that when active control function is turned off,passive isolation larger than 32.8 dB can be achieved;when active function is turned on,in addition to passive vibration isolation, the most outstanding 10-11 sinusoids can be further attenuated by 10-37 dB,and almost no vibration is boosted at adjacent frequencies.Furthermore,the proposed Fx-Newton algorithm with NBPF and phase-shift compensator demonstrates very good robustness and large suppression effect in active control of frequency-fluctuating harmonics generated by the diesel generator.

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船舶機(jī)械低頻線譜振動(dòng)傳遞的主動(dòng)控制

李彥1a，b，何琳1a，b，帥長(zhǎng)庚1a，b，馬建國(guó)1a，b，王飛1a，2，柳勇1a，3
（1海軍工程大學(xué)a.振動(dòng)與噪聲研究所；b.船舶振動(dòng)噪聲重點(diǎn)實(shí)驗(yàn)室，武漢430033；2中國(guó)船舶科學(xué)研究中心，江蘇無(wú)錫214082；3中國(guó)船舶設(shè)計(jì)研究中心，武漢430064）

針對(duì)船舶機(jī)械振動(dòng)的低頻線譜主動(dòng)控制，文章采用輸出力大、頻響平直、無(wú)接觸式的磁懸浮作動(dòng)器，分析了永磁偏置式作動(dòng)器的電-磁-力耦合特性，推導(dǎo)了磁懸浮主被動(dòng)隔振系統(tǒng)運(yùn)動(dòng)方程和系統(tǒng)穩(wěn)定性影響因素；研制了滿足船舶應(yīng)用要求、具有沖擊搖擺適應(yīng)能力的磁懸浮-氣囊主被動(dòng)混合隔振器。采用收斂快速的窄帶多通道Fx-Newton算法，并針對(duì)線譜頻率波動(dòng)時(shí)的控制魯棒性，提出了窄帶濾波相位差的自適應(yīng)補(bǔ)償環(huán)節(jié)。在船用200 kW柴發(fā)機(jī)組上進(jìn)行了主被動(dòng)混合隔振實(shí)驗(yàn)，未開啟線譜控制時(shí)，可獲得＞32.8 dB的寬頻隔振效果；控制開啟后，可進(jìn)一步有效衰減傳遞到基座的多根線譜振動(dòng)，并且在柴發(fā)機(jī)組的轉(zhuǎn)速波動(dòng)工況下依然能實(shí)現(xiàn)快速收斂、穩(wěn)定和高效控制。該主被動(dòng)混合隔振系統(tǒng)可滿足船舶機(jī)械低頻線譜控制的工程實(shí)用要求。

船舶機(jī)械低頻線譜振動(dòng)；主動(dòng)控制；磁懸浮—?dú)饽遥籉x-Newton算法；轉(zhuǎn)速波動(dòng)；魯棒性

TB533+.1

：A

李彥（1984-），女，海軍工程大學(xué)振動(dòng)與噪聲研究所博士研究生；

1007-7294（2015）12-1549-15

TB553+.1

：A

10.3969/j.issn.1007-7294.2015.12.011

何琳（1957-），男，海軍工程大學(xué)振動(dòng)與噪聲研究所教授；

帥長(zhǎng)庚（1976-），男，海軍工程大學(xué)振動(dòng)與噪聲研究所教授；

馬建國(guó)（1990-），男，海軍工程大學(xué)振動(dòng)與噪聲研究所碩士研究生；

王飛（1987-），男，中國(guó)船舶科學(xué)研究中心工程師；

柳勇（1982-），男，中國(guó)船舶設(shè)計(jì)研究中心高級(jí)工程師。

Received date：2015-09-08

Biography：LI Yan(1984-),female,doctoral candidate of Institute of Noise&Vibration,Naval University of Engineering;Corresponding author：HE Lin(1957-),male,professor/tutor of Institute of Noise& Vibration,Naval University of Engineering,E-mail：helin202@vip.sina.com.