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Mechanical Systems and Signal Processing Mechanical Systems and Signal Processing 22 (2008) 10081015 Infl uence of magnetic fl uids on the dynamic characteristics of a hydraulic servo-valve torque motor Songjing Lia,?, Wen Baob aDepartment of Fluid Control and Automation, Harbin Institute of Technology, Box 3040, Science and Technology Park, 150001 Harbin, China bSchool of Energy Science and Engineering, Harbin Institute of Technology, Box 458, 150001 Harbin, China Received 13 December 2006; received in revised form 27 September 2007; accepted 27 September 2007 Available online 6 October 2007 Abstract The aim of this paper is to investigate the infl uence of magnetic fl uids on the dynamic characteristics of a hydraulic servo-valve torque motor. As a kind of functional materials, magnetic fl uids are fi lled into the working gaps of a hydraulic servo-valve torque motor in this paper. Forces on the torque motor due to magnetic fl uids are studied. The dynamic mathematical models of the torque motor with magnetic fl uids are introduced. After that the dynamic characteristics of the torque motor with magnetic fl uids are analyzed and tested. Analysis and experimental results are compared with the results when magnetic fl uids are not applied in the motor. r 2007 Elsevier Ltd. All rights reserved. Keywords: Magnetic fl uids; Hydraulic servo-valve; Torque motor; Hydraulic control systems 1. Introduction As magnetic fl uids show higher saturation magnetizations when they are exposed to magnetic fi elds, they are widely applied in the areas of sealing, bearing, grinding, speaker, damper and so on 1,2. Investigations in 35 showed that the magnetic fi eld strength infl uenced the viscosity of magnetic fl uids when magnetic fl uids were exposed to a magnetic fi eld. The application of magnetic fl uids in an electric motor was also studied in 6 because of the higher magnetic permeability of magnetic fl uids. The application of magnetic fl uids in hydraulic servo-valves was studied recently in 7. Hydraulic servo- valves are the necessary components in hydraulic control systems. The characteristics of hydraulic servo-valves signifi cantly infl uence the performance of hydraulic control systems. As the electro-mechanical mechanism in hydraulic servo-valves, torque motors are used to stroke the valves from electric signals. If the dynamic characteristics of a torque motor can be modifi ed, the performance of a hydraulic servo-valve can be improved. ARTICLE IN PRESS 0888-3270/$-see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2007.09.016 ?Corresponding author. Tel./fax: +8645186418318. E-mail addresses: lisongjing (S. Li), baowen (W. Bao). Self-excited high-frequency noise and pressure oscillations appear very frequently in the fl ow fi eld of a fl appernozzle or a jet pipe servo-valve due to cavitations and shear-layer instabilities if the construction parameters were not selected correctly, as shown in 8. The self-excited pressure oscillations may irritate the oscillations of the torque motor armature and the spool of a servo-valve so that the servo-valve may lose its stability. As magnetic fl uids have a higher saturation magnetization and a larger viscosity when they are exposed to magnetic fi elds, magnetic fl uids can be fi lled into the working gaps of a hydraulic servo-valve torque motor to introduce damping into the motor and the servo-valve. In this paper, the application of magnetic fl uids in a hydraulic servo-valve torque motor is introduced. Mathematical models for forces due to magnetic fl uids on the torque motor are studied. Dynamic characteristics of a hydraulic servo-valve torque motor are simulated and tested when magnetic fl uids are applied in the motor. 2. Construction of a hydraulic servo-valve torque motor with magnetic fl uids The construction of a hydraulic servo-valve and torque motor with magnetic fl uids is shown in Fig. 1. The equivalent magnetic circuit of the torque motor is shown in Fig. 2. A hydraulic servo-valve can usually be divided into the valve part, the fl appernozzle part and the torque motor. The valve part includes a spool and a valve body. The fl appernozzle part includes a fl apper and two nozzles. The torque motor usually consists of cores, an armature supported by a spring pipe, two coils and two permanent magnets. The fl apper and the armature are connected with each other and therefore named armaturefl apper group sometimes. ARTICLE IN PRESS Nomenclature aradius of armature from pivot to center of pole face Ag area normal to fl ux path in air gap Amf working area of damping force on armature due to magnetic fl uid Ba viscous damping coeffi cient of mechanical armature mounting and load F1, F2 damping force due to magnetic fl uid, resistance due to magnetic fl uid g, xlength of gap at neutral, displacement of the end of armature H magnetic fi eld strength h thickness of magnetic fl uids surrounding armature Jainertia of armature Kamechanical torsion spring constant of spring pipe Km, Ktmagnetic spring constant and torque constant of torque motor K0m,K0t magnetic spring constant of magnetic fl uid, torque constant of magnetic fl uid Ms saturation magnetization of magnetic fl uid M0magnetomotive force due to permanent magnet Ncturns of coil Tdoutput torque of torque motor Tpload torque due to spring pipe TLload torque of armature Tmf1 load torque due to viscosity of magnetic fl uid Tmf2 load torque due to saturation magnetization of magnetic fl uid Z0 viscosity of magnetic fl uid in the absence of a magnetic fi eld Zmf viscosity of magnetic fl uid exposed to a magnetic fi eld yrotation angle of armature o0rotation speed of armature Didifference current of coils Dp1, Dp2 stress on armature due to magnetic fl uids in gaps 1 and 2 S. Li, W. Bao / Mechanical Systems and Signal Processing 22 (2008) 100810151009 There are four working gaps between the cores and the armature where magnetic fl uids can be fi lled into. As a hydraulic servo-valve torque motor works under the cooperation between the permanent magnets and the electric magnets, there are always magnetic fi elds due to the permanent magnets inside the working gaps of the torque motor, even if the electric power of the torque motor is turned off. Therefore magnetic fl uids will always stay inside the working gaps after they are applied. As the rotation angle of the armature is small, magnetic fl uids can hardly be scattered out from the gaps when the armature rotates. When the power of the coils is turned off, the torque motor will stay at the middle position under the working of the permanent magnets. If the four working gaps are almost the same in dimension, the distributions of magnetic fi elds will be the same in the four working gaps. Theoretically, there will not be any output torque from the motor because the torque balance is achieved at this time. Then the hydraulic servo- valve will work at the middle position. If the electric power of the coils is turned on, the torque motor will work under the cooperation between the electromagnets and the permanent magnets. As shown in Fig. 2, the magnetic fl ux densities in the working gaps 1 and 3 will be increased and become larger than those in the other two working gaps 2 and 4. There will be an output torque supplied by the torque motor to the servo-valve. The torque motor armature will rotate and drive the fl ap to introduce a pressure difference to both sides of the spool. The spool will move to a new position until the output torque of the motor equals the sum of the load torque from the spring pipe and the ARTICLE IN PRESS N S Magnetic fluids Permanent magnet Armature Spring pipe Core Return PS Supply PS Supply QL QL Valve body Feedback rod Spool Flapper Nozzle Fig. 1. Construction of a hydraulic servo-valve with magnetic fl uids. N S N S N S 1 2 3 4 g+x gx a Fig. 2. Torque motor equivalent magnetic circuit. S. Li, W. Bao / Mechanical Systems and Signal Processing 22 (2008) 100810151010 feedback torque from the feedback rod due to the movement of the spool. The displacement of the spool is proportional to the input electric current of the torque motor. As magnetic fl uids show a higher saturation magnetization and larger viscosity when they are exposed to the magnetic fi elds inside the working gaps of the torque motor, large damping forces or resistance will be exerted on the torque motor armature due to the special properties of magnetic fl uids. The damping forces or resistance will be helpful to improve the dynamic performance, especially the stability, of the torque motor and the servo-valve. 3. Forces due to magnetic fl uids The working state of magnetic fl uids inside the air gaps of a torque motor are shown in Fig. 3. It can be seen that the cross-section of the armature is surrounded by magnetic fl uids entirely. Therefore there are forces working on the upside and downside surfaces of the armature due to the saturation magnetization of magnetic fl uids. And there are damping forces working on the left side and right side of the armature due to the viscosity of magnetic fl uids. 3.1. Forces due to the viscosity of magnetic fl uids If the cross-section of an armature along the magnetic fl ux inside the air gaps is surrounded by magnetic fl uids entirely, as shown in Fig. 3, there will be forces working on the armature due to the viscosity of magnetic fl uids when the armature rotates. The force on the armature due to the viscosity of magnetic fl uids is shown in Fig. 4. The forces work as the damping against the rotation of the armature. It can be calculated as F1 ZmfAmf do dy .(1) Assuming the distribution of rotating speed is uniform along the y-axis, the gradient of rotation speed do/dy can be simplifi ed as do/dy o0/h, where the rotation speed of the armature o0can be written as o0 dy/dt. ARTICLE IN PRESS 0 F2 F2 F1F1 core magnetic fluid armature 0 Fig. 3. Forces on the torque motor armature due to magnetic fl uids. h 0 +d x y F1 ArmatureMagnetic fluid Fig. 4. Force due to the viscosity of magnetic fl uids. S. Li, W. Bao / Mechanical Systems and Signal Processing 22 (2008) 100810151011 Therefore formula (1) can be written as F1 ZmfAmf h dy dt .(2) The relationship between the viscosity of magnetic fl uids and the magnetic fi eld strength is studied in 3,5. It was shown that the viscosity of magnetic fl uids becomes larger when the magnetic fi eld strength working on magnetic fl uids increases. The viscosity of magnetic fl uids under magnetic fi elds is named magnetoviscosity. Magnetoviscosity is a function of magnetic fi eld strength. It is also a function of shear rate or armature rotation speed because of the non-Newton properties of magnetic fl uids. In order to simplify the simulation, the magnetoviscosity of a magnetic fl uid is taken as a constant in this paper when the magnetic fl uid gets saturated. 3.2. Forces due to the magnetization of magnetic fl uids As shown in 9, when magnetic fl uids are exposed to a magnetic fi eld, the magnetizations of magnetic fl uids work as stress on the armature. As we know from 10, the stress developed by magnetic fl uids can be written as Dp Z H2 H1 MsdH.(3) As the saturation magnetization of magnetic fl uids is nearly a constant, formula (3) can be simplifi ed as Dp Ms Z H2 H1 dH.(4) If the magnetic fi eld strength inside the working gaps of the torque motor is assumed to be everywhere the same and the lowest magnetic fi eld strength is almost negligible at the outside surface of magnetic fl uids, formula (4) can be written as: Dp MsH. The forces F21and F22working on the torque motor armature due to the saturation magnetization of magnetic fl uids, respectively, in the gaps 1 and 2 can be calculated as F21 Dp1Ag MsH11Ag,(5) F22 Dp2Ag MsH12Ag.(6) The magnetic fi eld strength H inside the air gaps of a torque motor is a function of the difference electric current of the torque motor coils Di and the rotation angle of the armature y. If the magnetic fl ux leakage from the gaps is omitted, the magnetic fi eld strength through the gaps 1 and 2 can be expressed as H11 M0 NcDi 2g ? x ,(7) H12 M0? NcDi 2g x ,(8) where x ay. When the rotation angle of the armature y is increased, the heights of the two gaps 2 and 4 will be increased and the heights of the other two gaps 1 and 3 will be decreased. Thus, the magnetic fi eld strength H11through the gaps 1 and 3 will be increased. The magnetic fi eld strength H12through the gaps 2 and 4 will be decreased. 4. Torques due to magnetic fl uids The load torque on the armature due to the viscosity of magnetic fl uids can be expressed as Tmf1 4 ZmfAmf h dy dt a.(9) ARTICLE IN PRESS S. Li, W. Bao / Mechanical Systems and Signal Processing 22 (2008) 100810151012 The load torque working on the armature due to the saturation magnetization of magnetic fl uids can be calculated as Tmf2 2F21? F22 ? a MsAga M0 NcDi g ? x ? M0? NcDi g x ? .(10) Usually, in order to simplify the simulation, the output torque of a hydraulic servo-valve torque motor is linearized as T KtDi Kmy when the condition x/go1 3 is satisfi ed 8. Under this condition, the torque motor works with in the zone around the balancing point. Therefore the linearization is acceptable. For the same reason, the load torque due to the saturation magnetization of magnetic fl uids can also be simplifi ed as Tmf2 K0tDi K0my, where the constants K0tand K0mare functions of Ms, Ag, M0, g, Ncand a. 5. Dynamic mathematical models of a torque motor The motion equation of a torque motor can be written as Td Ja d2y dt2 Ba dy dt Kay TL.(11) When the torque motor is not installed in a hydraulic servo-valve, the viscous coeffi cient due to the mechanical friction of the supporting and the viscous friction of air is usually negligible. If magnetic fl uids are not fi lled into the working gaps of the torque motor, the load torque TLshould be omitted. If magnetic fl uids are applied to the torque motor, the load torque TLcan be described as: TL Tmf1+Tmf2. 6. Dynamic characteristics of a torque motor with magnetic fl uids Dynamic characteristics of a torque motor with magnetic fl uids are analyzed using Matlab Simulink software. The construction parameters of the torque motor are shown in Table 1. The saturation magnetization of magnetic fl uids Msis 400Gs in the simulation. The viscosity of magnetic fl uids Z0 is 1.9Pas in the absence of a magnetic fi eld. The viscosity of magnetic fl uids exposed to the magnetic ARTICLE IN PRESS Table 1 Construction parameters of the torque motor ParametersValue Width of permanent magnet Wp(mm)18.8 Length of permanent magnet in polar direction Lp(mm)10.4 Length of armature La(mm)32.2 Width of armature Wa(mm)3 Thickness of armature Sa(mm)1.4 Length of core Lc(mm)32.2 Thickness of core Sc(mm)3 Area of gap normal to fl ux path Ag(mm?mm)3.9?3 Contact area between armature and magnetic fl uids Amf(mm?mm)3.9?2 Length of working gap at neutral g (mm)0.3 Armature radius from pivot to center of pole face a (mm)16 Turns of coil4000 Inertia of armature Ja(Nms2/rad)3.12?10?7 Spring constant of spring pipe Ka(Nm/rad)12.7 Rated difference electric current of coil Di (A)0.01 Torque constant of torque motor Kt(Nm/A)1.08 Magnetic spring constant of torque motor Km(Nm/rad)1.615 Damping coeffi cient Ba(Nms/rad)0.000036 Torque constant of magnetic fl uid K0t(Nm/A)0.15 Magnetic spring constant of magnetic fl uid K0m(Nm/rad)0.625 S. Li, W. Bao / Mechanical Systems and Signal Processing 22 (2008) 100810151013 fi elds in the working gaps of the torque motor Zmf is 3.0Pas when the magnetic fl uids get saturated. The analyzed dynamic characteristics of the torque motor are shown as bode diagrams in Fig. 5. The dynamic characteristics of the torque motor with magnetic fl uids are tested using an optical displacement sensor. The displacements of the armature under different frequencies are recorded when sinusoidal signals with different frequencies are supplied to the torque motor. The dynamic amplitude response of the torque motor armature is shown in Fig. 6. ARTICLE IN PRESS Bode Diagram Frequency (Hz) 101102103 270 180 90 0 Phase (deg) 60 40 20 0 20 Magnitude (dB) Fig. 5. Analyzed dynamic characteristics: without magnetic fl uids; - - - with magnetic fl uids. 101102103 Frequency (Hz) 40 35 30 25 20 15 10 Magnitude (dB) Fig. 6. Tested dynamic characteristics: without magnetic fl uids; - - - with magnetic fl uids. S. Li, W. Bao / Mechanical Systems and Signal Processing 22 (2008) 100810151014 Fig. 5 shows that the simulated resonance frequency of a hydraulic torque motor is about 900Hz when magnetic fl uids are applied or not in the torque motor. Fig. 6 shows that the tested resonance frequency of the torque motor is about 1000Hz when magnetic fl uids are applied or not in the torque motor. The agreement between the simulated and tested resonance frequencies is acceptable for the application in this paper although there are about 10% errors between them. The difference between the simulated and tested resonance frequencies is most probably caused by the simulation and experimental errors. There are some factors in the torque motor that cannot be included properly in the simulation models, for example, the magnetic fl ux leakage and noise which cause the simulation errors. The frequency step (10Hz) may also somehow contribute the experimental errors on the resonance frequency when the experiment was done. It is diffi cult to quantify the errors between the simulated and tested resonance frequencies. When magnetic fl uids are fi lled into the torque motor, the resonance peak is reduced signifi cantly because of the damping force on the armature due to magnetic fl uids. The damping force due to magnetic fl uids relates to the damping ratio of the torque motor which can be calculated from the resonance peak. Figs. 5 and 6 show the same infl