Construction of a Magnetorheological Damper For an Active suspension

Transcription

1 Construction of a Magnetorheological Damper For an Active suspension Eduarda Lectícia Martins da Costa Technical University of Lisbon, Instituto Superior Técnico, Lisboa , Portugal Abstract The development and progress of technology have taken some investigators and engineers to study the application of electroactives fluids, with the objective to apply them in the construction of devices that can be applied in vibrations control, using them in actives and semi-actives suspensions for damping systems. These fluids are characterized by presenting its viscosity dependent of the electric field (electrorheological fluid - ER) or of the magnetic field (magnetorheological fluid - MR) applied on the fluid. This work presents the theoretical and experimental study of a damping device based on magnetorheological fluid. The studied device consisted of a hollow cylinder, whose interior lodges a piston and is filled with magnetorheological fluid. There is a coil around piston where can circulate an electric current with the purpose of creating a magnetic field and thus have the possibility to command the viscosity of the fluid situated between the piston and the cylinder (gap). The theoretical and experimental results indicate the robustness of MR fluid and its effectiveness when applied in this type of devices, since with current very reduced it is possible to get high damping forces. Key Words: Electroactive fluid, magnetorheological fluid, viscosity, magnetorheological damper. 1 Introduction The new generations of active suspension systems for auto machine vehicles are based on electroactives fluids nominated electrorheological and magnetorheological fluids. These fluids can have its viscosity modified, depending on the intensity of the electric field (electrorheological) and magnetic field (magnetorheological) on them applied. Magnetorheological fluid consists of a fluid composed by small particles of iron (in the order of µm) magnetizable, suspended in oil, generally hydro-carbon. To the fluid it is also added some additives with objective to inhibit the deposit of iron particles, to promote its suspension, to modify viscosity and to diminish the consuming. The percentage of iron contained in this type of electroactive fluid varies between 0 to 40%. Magnetorheological fluid changes its rheological characteristics upon the application of a magnetic field. Thus, the viscosity of the fluid can then be commanded by the intensity of applied magnetic field. In last years it has had a great interest in the applications of the magnetorheological fluid in damping systems due to its fast response to the attenuation of vibration (~ ms) and due to the variation of its viscosity when submitted to a magnetic field. Other attractive feature is their small power requirement to produce maximum yield stress of about 50 to 150kPa, These systems have been applied mainly in truck seats, as suspension in vehicles automobiles, in braking systems and other applications not related with vehicles automobiles, for example, to stabilize buildings 1

2 during earthquakes, in watching machines, as well as above knee prosthesis. The MR fluid can be applied in damping systems in different operating modes in favor of adaptative vibration, depending on the objectives. In flow mode (figure 1a), the magnetorheological fluid is between two fixed parallel plates and is exerted an external difference of pressure on the fluid. A magnetorheological device operates in valve mode when a magnetic field is applied to command the fluid flow of one reservoir to another one. In direct shear mode (figure 1b), the fluid is sheared between two parallel plates and one of the plate is dislocated in relation to another one by an external force. in damping system based on the squeeze mode (figure 1c), the fluid is placed between two magnetic plates that vertically are pressure one on the other, this mode can generate very high damping forces, but the amplitude of the vibrations is restricted by the plate distance. a ) b) c) Figure 1 Operating mode of magnetorheological devices; a) valve mode, b) direct shear mode, c) squeeze mode. Fluid properties.1 Rheological properties The rheological properties are those that have influence in the transport of the amount of movement in a fluid, are related with the deformations occurred in this, due to the internal friction in the fluid (called shear stress), The rheological properties are related with the viscosity and elasticity of the fluid. In a magnetorheological fluid these properties depend on the concentration, density, size and form of iron particles, of the properties of the carrying fluid, the temperature, and external magnetic field (H) applied upon fluid. When there is no external magnetic field applied, the iron particles are suspended of random form and the fluid presents a behavior equal to an incompressible fluid (Figure a). When the fluid is submitted to a magnetic field, the suspended particles of iron is magnetized, forming a columnar structure parallel to the field as it can be visualized in the Figure b. These structures restrict the movement of the fluid in the direction perpendicular to the field, increasing the viscosity of the fluid. (a) (b) Figure Magnetorheological fluid; (a) no magnetic field applied, (b) magnetic field applied. It has some mathematical models that describe the behavior of the magnetorheological fluid, amongst them simplest is the Bingham Model that describes the dependence of the shear stress with the magnetic field. Figure 3 shows the relation between shear stress (τ ) and shear strain rate (γ& ) for values of increasing magnetic field, where the fluid presents a linear relation between the total shear stress (τ ) and the shear rate given for:.. τ = τ 0( H ) sgn γ + ηγ ( 1 ) H - Magnetic field amplitude. τ 0 - Yield Stress.. γ - Shear Strain rate.

3 In the figure 5 the presented values of temperature and respective viscosity correspond to the interval of operation of the fluid that is used in this work. Having in consideration the device studied in this work, it can be considered that the viscosity of the fluid will be only function of the magnetic field. Figure 3 Shear stress versus Shear rate. Each magnetorheological fluid presents an electromechanical characteristic shear stress x magnetic field, which is obtained by laboratorial assays through a rheometer. Figure 4 presents the magnetorheological fluid electromechanical characteristic shear stress x magnetic field, τ (H ), of the fluid used in this work. It is verified that the shear stress increases with linear form with the increase of the magnetic field until a field close to the 100 ka/m. Figure 5 Viscosity versus Temperature with no applied field.. Magnetic properties The magnetorheological fluid presents magnetic properties that are related with the properties particles of iron dispersed in it. Thus, Figure 6 presents curve B (H) of the used magnetorheological fluid in this work. Figure 4 Electromechanical characteristic shear stress x magnetic field of the fluid used in this work MRF-1-EG. Table 1 Two principal rheological properties of the fluid, density and viscosity, both gotten without applied magnetic field.rheological properties of the fluid MRF-1EG Properties Value / Limits Carried fluid Hydrocarbon Operation temperature -40ºC a +130 ºC Density (H=0) Kg/m 3 Viscosity (H=0, 40ºC) 0,07 (±0,0) Pa.s Figure 6 Magnetization curve of the fluid MRF-1EG. Fluid MR approximately shows linear magnetic until an applied field near 100kA. 3

4 3 Damper components v c r The studied device (Figure 7a) consists of a mobile piston inside a fixed cylindrical container (Figure 7b), which is filled with a electroactive fluid of the magnetorheological type. The piston and the cylinder are made of steel, being that, as it shows the figure 8c, the piston presents a central rabbet where is inserted a bobbin. The conducting wire of the bobbin passes through an orifice elaborated in the center of the piston axle (Figure 7d), thus allowing linking to the external current source. The inferior and superior part of the cylinder was closed by a transparent acrylic cover (Figure 7e). R d Figure 8 Project of the considered electromechanical device with the respective cylindrical coordinates. Figure 9 presents the magnetic field lines, from simulation of magnetic circuit in FEEM (Finite Element Method Magnetics) program. l 1 l l 1 z r θ θ v r r (a) (b) (c) Figure 9 Magnetic field lines. 5 Mathematical Model (d) (e) Figure 7 Damper components: a) Cylinder; b) cylinder interior part with piston inside; c) and d) piston, piston rod and coil; e) acrylic covers. 4 Magnetic circuit An optimal design for magnetic circuit requires maximizing magnetic field energy in the fluid gap while minimizing magnetic energy lost in the steel flux conduit. The magnetic flux path, as seen in figure 9 and 10, goes from piston core, through the piston end disc, through the fluid, through the cylinder, through the other piston end disc and back through the piston core. In figure 8 R=4cm,l 1 =l =l=1cm. Figure 8 presents an image in cut of the damping device and respective cylindrical coordinates( r,θ, z). The bobbin with N spires is in piston and is covered by a current i, the magnetic circuit establishes a magnetic field H uniform and constant in the radial direction r along the gap, H = H r. Being the device symmetrical in relation to the axle z, it is admitted that properties of the system vary in the direction = = 0. z θ z e θ : ( ) The magnetorheological fluid is considered homogeneous and uncompressible, then v = 0 ( 3) 4

5 As the piston moves only in the direction z, v = 0 e v = 0 ( 4 ) θ r The total force density Ftotal acting in each elementary volume of the magnetorheological fluid is defined by the relation 5 Ftotal = ρg p + ( FH + µ ) ( 5 ) ρ g is the force density of the gravitical force; p, is the force component resultant of v the gradient of internal pressures in fluid, and; FH +µ v is the total force density corresponding to the shear stress which appear in interior of the fluid due to its viscosity. F H, correspond to the constituent relation of the fluid, which is characterized by efforts of shear between layers of the fluid as function of applied magnetic field (nonnewtonian fluid); and µ v, corresponds to τ τ( H) F H = r d ( 7 ) p p z l ( 8 ) where p is the pressure difference between the extremities of the canal with length l. Borders conditions are: in r = R, v z in r = R+ d, = v v z c, = 0. Then, substituting 7 and 8 in 5, for a balance situation: vc v ( r ) = ( R+ d r ) + ( 9 ) z d 1 p τ( H) + + ρg + ( r (R + d) r + R( R+ d)) µ l µ d Figure 11, shows the velocity profile through the gap. the force density that appear when the magnetic field H is null equal to the relation presented by a newtonian fluid, µ is the fluid viscosity with no magnetic field applied. To findf H, it s considered figure 10 where it is represented a volume element of the fluid centered r in and submitted to two shear stress in r e r+. Figure 11 Velocity profile v z through the gap. The total force resistant to the movement of the piston, is: F Total F p + F µ F p = ( 10 ) = pπ ( R r ) ( 11 ) To calculate F µ let s consider figure 1, where Figure 10 representation of an element volume of the fluid centered r in and submitted to two shear stress in e r. r + the piston is submitted upon a magnetic field H 1 and the fluid upon a magnetic filed H. F vol = τ( r ) θ z τ( r+ ) θ z ( 6) 5

6 Admitting in the linear region of the curve τ (H ), τ ( H ) = KH ( 15) Where, K is the slot of the τ(h ) in linear zone. Ni H = ( 16 ) d The equation 13 can be write by: Figure 1 - Piston is submitted upon a magnetic field H 1 and the fluid upon a magnetic filed H. 1 Fµ = ηct(πrl ) = ηc µ H.(πRl ) ( 1 ) F πrln =. η c 4d Total µ i π R r ) KNl + i + gl ( R ρ π d + ( r ) ( 17 ) Substituting H = Ni d in 1: The total force resistant to the piston movements F πrln Total = pπ( R r ) +. η cµ i (13) 4d The curves in figures 14 and 15 shows that F total x current varie with the value of coefficient de atrito η c between fluid and the piston surface and with gap size, respectively. Figure 13 - Curve that represents the total force resistant to the movement of the piston in function of the applied current. Figure 14 - Curve F total x current for different values of the coefficient of attrition between the fluid and the surface of the piston. Stationary regime is a particular functioning mode of the system where a load with constant value F1 is submitted to the piston, being however stopped in balance with v = 0 and c the fluid withv = 0. z In this conditions, the force in piston who must to balance with F 1, assume the quadratic form given by equation 14. Figure 15 - Curve F total x current for different gap sizes. F Total πrln π( R r ) l =. η + ( ) + cµ i τ H 4d d + ρ glπ( R r ) ( 14) 6 Experimental setup An experimental set up depicted in figure 16 was built, to produce force to move the piston. 6

7 The MR damper was filling with MRF-1-ED. Figure 16 damper connected to DC machine. Stationary tests were conducted to measure the current necessary to stop the piston movements for an applied force. The damper was submitted to force F=mg, with m=[0-5]kg, and g=9,98m/s the gravity acceleration. Figure 17 shows the current value for an applied load on damper. (a) (b) Figure 18 - Curva F(v), a) g=1mm, b) g=mm. Figure 17 - Curve F(i) with no damper velocity. Another tests, figure 18, was made in permanent regime where the damper was connected to DC machine. The linear velocity of the damper was measured through angular velocity of the machine, and the force through the torque considering that the force developed by the machine is the same applied unto damper piston. Using figure 18, the damping coefficient, β=df/dv can be obtained from the slop of the best linear curve fitting, it s equal to 94,5Fs/m to a gap of 1mm and equal to 30Fs/m to a gap of mm. The maximum force of MR damper at 0,A is approximately equal to two times of that without magnetic field, for g=1mm, and for g=mm. These values have any error due the measure method used, the DC machine was considered working in nominal regimen, but during tests it wasn t verified. But comparing with mathematical model can be concluded that this error isn t significant. 7

8 7 Power dissipated As the bobbin are constituted of copper wires there is waste of power in the form of heat for Joule effect. P J = r i ( 18 ) The resistance, r, of the bobbin was measured with an ohmmeter, and is equal the 4Ω. Table Power loss from Joule effect. I [A] P [W] 0,1 0,4 0, 0,8 0,3 1, 0,4 1,6 The another power is due the movements of damper. P v = F v cosα ( 19) The total power is P P + P T = ( 0) v J Being the used currents very small the power due to the Joule loss can be disdained and having only in consideration movement of the damper. Figure 19 presents the value of the power as damper velocity function, for constants values of current i=0 A; 0,1 A ; 0,15 A e 0, A. Figure 19 Power dissipated by MR damper. The maximum power dissipated by damper is when it moves with velocity 1,35 cm/s with i=0,15a that corresponds to 4,6 W. 8 Conclusion and recommendations This work was based on the construction and study of the prototype of a magnetorheological damper that functions in direct mode. In this type of damper, the damping is generated by the difficulty of fluid pass through gap. The magnetic circuit is responsible for controlling the movement of the damper through the variation of the viscosity of the fluid that is regulated by the magnetic field strength. How much lesser the gap lesser will be the energy consumption, being able, in this case to have a magnetic field in the order of 0kA/m with a current of 0,A to a gap of 1mm, while to a gap of mm this value of magnetic field it s gets with a current of 0,4A. Therefore, for the same applied current, the magnetorheological fluid offers greater resistance to the movement of the piston when gap is lesser. According to experimental results, the constructed prototype, absorb vibrations of force until 350N with a current of 0,A for when gap d=1mm and with a current of 0,3 for gap d=mm. I recommend that to increase the volume of an extremity of the cylinder for the other, without harming the size of gap, some punctures in the piston are made thus allowing one better draining of the fluid and in this way lesser will be the pressure in the interior of the cylinder and greater the easiness of the movement of the piston. For winning the pressure that is created inside of the cylinder, also it is solution, to do an longer exterior cylinder allowing with that having a bigger freedom in the space to be covered by the piston, and to make 8

9 punctures in the cover for ticket of the air without that the fluid overflows. This solution is only applicable for experimental assays of the dumper. The use of one better method of measure (measure instruments), allows to get better results. 9 References - Mark R. Jolly, Jonathan W. Bender, J. David Carlson, Properties and Applications of Commercial Magnetorheological Fluids, Lord Corporation. - Jung-Hoon Kim, Jun-Ho Oh, Development of an Above Knee Prosthesis using MR Damper and Leg Simulator, Proceedings of the 001 IEEE International Conference on Robotics & Automation Seoul, Korea. May 1-6, Rotordynamics & Squeeze Film Damper Lord Corporation Magnetorheological (MR) Fluid for Automotive Damping Systems. Presentation to the IIR Suspension and Damping Conference. - Releases_006/pr_006_11_30_ J. David Carllson, What makes a good MR fluid?, presented at the 8 th International Conference on Electrorheological (ER) Fluids and Magnetorheological (MR) Suspensions, Nice, July 9-13, Mark R. Jolly, Jonathan W. Bender, and J. David Carlson, Properties and Applications of Commercial Magnetorheological Fluids, Thomas Lord Research Center