The Low-frequency Compensation of the Vibration Sensor s Amplitude-frequency Characteristics

Transcription

1 Senor & Tranducer, Vol. 8, Iue, October 4, pp. -7 Senor & Tranducer 4 by IFSA Publihing, S. L. The Low-frequency Compenation of the Vibration Senor Amplitude-frequency Characteritic Lifeng Pan School of Electrical & Information Engineering, Hunan International Economic Univerity, Changha, 45, China Tel.: matlab_wjf@6.com Received: 4 June 4 /Accepted: 3 September 4 /Publihed: 3 October 4 Abtract: The hydropower generating unit vibration parameter i an important indicator to monitor it rolltabilization. To meaure the low-frequency vibration of the large and middle cale of hydropower generating unit, according to frequency characteritic compenation principle of the vibration enor, a low-frequency compenating circuit wa deigned to etend the frequency characteritic to the low frequency region. The mathematical model of the magnetoelectric dromometer vibration enor and the deign of the compenation circuit were detailed. The amplitude-frequency characteritic of the enor and it mathematical model were comparatively analyzed before and after compenation repectively. The eperimental reult how that the deign could etend the amplitude-frequency characteritic to the low frequency region, and have good enitivity and linearity. Copyright 4 IFSA Publihing, S. L. Keyword: Senor, Vibration, Amplitude-frequency characteritic, Compenating circuit, Tranfer function, Senitivity.. Introduction Hydro accident howed vibration fault []. Medium-ized hydro group tranfer frequency i low, about - Hz, and unit water vorte-induced vibration which hydro draft Tube produce i lower, about /5 to /3 of rotation frequency. In addition, once the accident occurred during hydropower unit operation, which load hedding and load rejection tranition proce, vibration ignal frequency will be lower []. In magnetic vibration velocity enor, maller natural frequency, the greater the volume. Conidering the eae of intallation of the enor, the magnetic vibration velocity enor i widely ued in engineering, and it natural frequency limit of i about.5 Hz, but alo the meaurement frequency i higher and to 3 time than the natural frequency of vibration enor [3]. If the enor i without compenation, and the direct the meaurement i operated, the meaurement i not accurate. How to deign compenation circuit, and the vibration frequency characteritic i allowed to epand the low-frequency or to meet the requirement of the low-frequency tet, it i the focu of the tudy.. Etablih and Validate of the Vibration Senor Model.. Operating Principle of the Ocillation Senor Magnetic vibration velocity enor have been widely applied in low-frequency enor, becaue of

2 Senor & Tranducer, Vol. 8, Iue, October 4, pp. -7 thee advantage which their output ignal i large, the follow-up circuit i imple, anti-jamming capability i trong. A hown in Fig., the vibration enor i fied with a permanent magnet inide, and in the outer caing, the magnetic circuit of the magnet i encloed within the houing. Two circular pring upper and lower i fied between the magnet and the houing. They upport the coil, and are urrounded by the coil with ma m and without touching the magnet. When the eternal action of the vibration enor, the relative motion i made between the magnet and the coil, the coil i cutting magnetic induction line, and i generating a voltage ignal. i the abolute diplacement of the inertial body; i the peed of the bae houing; ' ' i the peed of the inertia body; " i the acceleration of the inertial body; F() t i the force acting on the inertial body; Take Ft () ; c/ m, i the characteritic angular frequency; ξ μ /m, ξ i the damping ratio; r, Ma diplacement i relative to vibration enor houing. () by the Laplace tranform a follow: X ( ) H( ) X r ( ) + ς + () Vibration enor coil i are cutting magnetic induction line, the output voltage i: u Bl (3) ' r Fig.. Magnetic vibration enor tructure diagram... Model Building It i an inertial enor, the mechanical model can be implified a a ingle ytem with the degree of freedom, which i compoed of three-part ytem of a pring with elatic coefficient k, inertial ma m and damping C [4] a hown in Fig.. By Laplace tranform a follow: U () BlX () k X (), (4) r which B i the magnetic field trength; l i the length of the coil which i cutting magnetic field line; k i the enor enitivity coefficient. By the Formula (), (4), a vibration enor output repone: r U ( ) k H( ) X ( ) k + ξ + X ( ) (5) Vibration enor tranfer function i: The motion equation i Fig.. Mechanical model. m + μ( ) + c( ) F( t), () " ' ' where m i the inertial body ma (coil); C i the pring tiffne; μ i the Damping; i the abolute diplacement of the bae houing; k () + ξ + G (6) In CDJ-Z.5C vibration enor a a reference, to etablih the mathematical model. Natural frequency f.5± % Hz, take value.5. Damping i ξ.7 ± %, take value.75. ( π f) 46.74, ξ If k 8, the Formula (6) can be written a: G ( ) (7) 3

3 Senor & Tranducer, Vol. 8, Iue, October 4, pp. -7 Matlab imulating curve with the amplitudefrequency characteritic, a hown in Fig. 3, curve B i the imulation reult. can be een that the imulation and meaured curve are ame when frequency i larger than.3 Hz, almot eactly. The vibration frequency i le than.3 Hz, output of the enor itelf i mall, and becaue of the floor and all noie, the relative output i high. The lower the frequency, the larger the error. Comprehenive aement i that model i feaible. 3. Deign of Compenation Apect 3.. Compenation Principle Fig. 3. Amplitude-frequency characteritic curve..3. Verify Model Equipment ued in the eperiment: one CDJ-Z.5C vibration enor, an integrated vibration teter. The vibration enor i put vertically on the vibration generator, the output of the enor i directly connected to the teter' input. Set the output vibration level, vibration level i.5 cm/. Table how the raw data which i collected by the vibration. Table. Original vibration data..5 Vibration level data (before compenation) the meaured Voltage vibration level (mv) (cm/) Senitivity (mv/cm - ) Note: Senitivity voltage / vibration level, the unit i mv/cm -. In Table, the enitivity i the voltage which i normalized by dividing the vibration level, unit i mv/cm -. The meaured amplitude-frequency characteritic curve i curve A which i hown in Fig. 3. Comparion of the curve A, B in Fig. 3, it In order to etend the frequency repone of the low-frequency magnetic vibration velocity enor, the circuit compenation method i required. There are two compenation form in the circuit compenate, which are feedback compenation and erie compenation, and the feedback compenation i with lower natural frequency, while the damping ratio i reduced, tability i poor, but alo it i eay to produce ocillation [5]. It i ued in erie compenation. The enor output voltage i in erie with a compenation network C(), o that the pole of the original tranfer function G() i eliminated by the C() zero point, C()' pole become the pole of the tranfer function G() after paing compenation, o the low-frequency output characteritic of the enor can been changed by changing the compenation network' pole. The tranfer function of the compenation apect were given in Literature [5-8], equation (8) below, thi tranfer function can be decompoed by three parallel filtering part, namely all-pa, low-pa, band-pa filtering link. C () + ξ+ + ξ + ( ξ ξ ) + ξ+ + ξ+ + +, (8) where ξ i the damping ratio of compenation apect, which reflect the frequency characteritic in the ocillation link, and doe not directly reflect the frequency repone of the filter circuit. So in thi paper, the damping ratio ξ i replaced by the equivalent quality factor, i a parameter which reflect the frequency repone of the filter circuit. A hown in Formula (9): C () + ξ +, + + (9) where π f i the characteritic angular frequency which i compenated. After the compenation, tranfer function G() of the vibration enor i: 4

4 Senor & Tranducer, Vol. 8, Iue, October 4, pp. -7 G () G() C () k + + () Compenation circuit C() i deigned, o that <, and i the bet equivalent quality factor. Compenated ytem maintain the original vibration enor high mechanical propertie unchanged, and the natural frequency depend entirely on the compenation circuit which i connected in erie, thu in compenated enor ytem, the original enor volume i mall, and performance characteritic i good, but alo low-frequency output characteritic i improved. The ratio between thee three gain i adjuted, zeroof the compenation link and pole of the original ytem are made offet, allowing the ytem to achieve the deired frequency characteritic. Becaue of the integrated operational amplifier module feature itelf, little DC offet will been produced, after amplification, thi can t be ignored, o after the filter circuit, the DC offet i removed in erie with a firt-order high-pa filter circuit. The cutoff frequency hould be much le than. Hz. Fig. 5 i compenation circuit wiring diagram. 3.. Vibration Senor Compenation Circuit Deign To meet the meaurement requirement of hydroelectric generating low-frequency vibration, the natural frequency of the enor i needed to epand from.5 Hz to the low-frequency. Hz, to maintain the bet quality factor. That i f. Hz,.7. The compenation link C() i divided into: kavf kavf C () + + in the formula, ξ A, k AVF VF k, () Among them, A VF for the ame phae caling circuit voltage gain. By Formula (), it can be een that the compenation apect i the parallel together with allpa, low-pa, band-pa three apect, the tructure i hown in Fig. 4. Fig. 4. Compenation link tructure figure. Fig. 5. Compenation circuit wiring diagram. Wherein: R, R, R A, R F, C, U contitute a econd-order low-pa filter circuit; R, R, R, R A, R F, C, U contitute a econd order band-pa filter circuit; R3 i an all-pa circuit; R 3, R 3, R 3, R 33, U 3 contitute an addition circuit; R 4, R 4A, R 4F, C, U4 form a firt order high pa filter. To reduce ytem circuit noie, each reitor in the circuit hould be trillion level and below, o the capacitance value C uf to implify the calculation, o that R R R R R; R R; R 3 R 3 kω. The deign requirement were: R A R A R A ; R F R F R F. And RF 3 VAF +, R A ǁ RA R F R, πf / RC, R 3 R 3 /k, R 33 R 3 /k, o the parameter value of the circuit i about R 8 kω, R A 44 kω, R F 5 KΩ, R 3 kω, R 33 9 kω. For a firt-order high-pa filter, parameter i not trictly required to achieve the blocking effect. Due to the low ignal to noie ratio of low frequency enor output voltage, lowfrequency amplitude of the original ytem i bigger than the theoretical value. R, R, R reitance can be increaed, o that the amplitude-frequency characteritic of the band rejection filter circuit i tranlated to the high frequency. In order to increae the output voltage of the enor ytem, the voltage drop of the circuit i compenated. The meaured data i howed in Table after compenation. 5

5 Senor & Tranducer, Vol. 8, Iue, October 4, pp. -7 Table. Meaured data after compenated..5 vibration level data (after compenation) Meaured Voltage vibration level (mv) (cm/) Senitivity (mv/cm - ) Table 3. Linearity relative error. Before compenation After compenation 4. Analyi 4.. Development of Low-frequency The amplitude-frequency characteritic curve before and after the ytem compenation can be drawn from Table and, a hown in Fig. 6. The curve A, B i repectively the amplitude-frequency characteritic curve before and after the ytem compenation [9-]. The linearity relative error are hown in Table 3. And generally, the-3db frequency correponding about 7 % of the flat area i the natural frequency of the ytem. For eample, the compenation i not increaed in circuit, if frequency i equal to Hz, the enitivity i 993, and it 7 % i 395. From the data in the table, the natural frequencie are howed between -3 Hz, about.5 Hz, and it i the actual match. After adding the compenation circuit, if frequency i equal to Hz, the enitivity i 945 and it 7 % i 36, it natural frequency hould be between.-. Hz which i een from Table, approimately.8 Hz. It can be een in Fig. 6 that curve A natural frequency i about.5 Hz, the natural frequency of curve B i about.8 Hz, thu the ytem i epanded to 3.8 time of low frequency, that i.8 Hz, the deign requirement are meet Senitivity Vibration data.5 cm/ i for a tandard vibration level, the relative error of the enitivity i calculated by a vibration data acquiition another.8 cm/ vibration level, o the enitivity tability of the compenated ytem i the aeed. Table 4 how that the relative error i.5 or le in the enitivity, a enitivity of the ytem remain table after compenation. Table 4. Senitivity relative error..5 cm/.8 cm/ Relative error Concluion and Outlook Fig. 6. Compenated amplitude-frequency characteritic curve. In the deign of the compenation apect, the equivalent quality factor i cited by, o that the compenation circuit deign of the magnetic vibration velocity enor i imple and traight victory. The low-frequency ytem i developed to low-frequency after compenated, there are 6

6 Senor & Tranducer, Vol. 8, Iue, October 4, pp. -7 enitivity, linearity, more comprehenive analyi, thee are indicating that the enor ytem performance i good after compenating, the deign of the compenation apect i proved reaonably practicable. Acknowledgement Thi paper i ponored by the Scientific Reearch Project (No. 4C655) of Department of Education of Hunan Province. Reference []. Shen Dong, Chu Fu-Tao, Chen Si, Diagnoi and Identification of Vibration Accident for Hydrogenerator Unit, Journal of Hydrodynamic, 5,,, pp []. Zheng Jinju, Yu Shuibao, Sun Xiaoqin, A New Magnetic Senor, Chinee Journal of Scientific Intrument, 6, 8, 5, pp [3]. Xiao Mingwei, Yang Yongming, Zhong Yulin, Reearch on the meaurement of low-frequency vibration of water turbine generator, Tranducer and Microytem Technologie, 3, 5,. [4]. Liu Yu, The Etablihment of Vibration Senor Verification Device, Metrology & Meaurement Technique, 39,,. [5]. Yuniao Fan, Hua Liu, Nong Wang, Study on Ultra- Low Vibration Senor by Uing Magnetoelectric Speedometer, Journal of Univerity of Science and Technology,, 3,, pp [6]. Li Ming-Guo, Sun Rong-Xiang, Li Yong, Reearch on Vibration Senor of Ultra Low, Colliery Mechanical & Electrical Technology, 3, 8, pp [7]. Along Yu, Weiyi Huag, Reearch on Method of Improvement for Amplitude/ Characteritic of Vibration Velocity Tranducer, Proce Automation Intrumentation, 3, 4, 4, pp. 89-9, 95. [8]. Yu Shuibao, Study on optimizing technique for tranfer function of the ULF abolute vibration enor, Chinee Journal of Scientific Intrument, 7, 8, 6, pp [9]. Yang X. S., Low-frequency characteritic etenion technique reearch for velocity vibration enor, Earthquake Engineering and Engineering Vibration,, 4, pp []. A Bedoor B. O., Blade Vibration Meaurement in Turbo-machinery: Current Statu, Shock and Vibration Diget, 6,, pp []. Wang Chao, Tang Huang, Xiao ian, The Application of Wide Spectrum Laer in Noncontact Vibration Meaurement, Microwave and Optical Technology Letter,, 9, pp Copyright, International Senor Aociation (IFSA) Publihing, S. L. All right reerved. ( 7