Effect of Radial Resistance Gap on the Pressure Drop of a Compact Annular-Radial-Orifice Flow Magnetorheological Valve

Guoliang Hu, Jiawei Zhang, Mingke Liao and Ruqi Ding

(Key Laboratory of Conveyance and Equipment, Ministry of Education, East China Jiaotong University, Nanchang 330013, China)

Abstract: A compact annular-radial-orifice flow magnetorheological (MR) valve was developed to investigate the effects of radial resistance gap on pressure drop. The fluid flow paths of this proposed MR valve consist of a single annular flow channel, a single radial flow channel and an orifice flow channel through structure design. The finite element modelling and simulation analysis of the MR valve was carried out using ANSYS/Emag software to investigate the changes of the magnetic flux density and yield stress along the fluid flow paths under the four different radial resistance gaps. Moreover, the experimental tests were also conducted to evaluate the pressure drop, showing that the proposed MR valve has significantly improved its pressure drop at 0.5 mm width of the radial resistance gap when the annular resistance gap is fixed at 1 mm.

Key words: magnetorheological (MR) valve; annular-radial-orifice flow; pressure drop; radial resistance gap; finite element analysis

As a kind of smart material, magnetorheological (MR) fluid exhibits unusual characteristics in that its rheological properties can be continuously and reversibly changed within milliseconds by applying or removing a magnetic field[1]. This interesting property has inspired the design of a large variety of MR fluid-based devices in various engineering applications, such as MR shock absorbers and dampers, MR engine mounts, MR brakes and clutch systems. Since the working principles of most MR fluid-based devices are based on the manipulation of fluid flow rate in the resistance gaps, the key performance of MR fluid-based devices is determined by the performance of MR valve[2-4]. Therefore, a successful improvement of MR valve performance can significantly impact the development of other MR fluid-based devices.

In general, a typical MR valve consists of a valve body, a valve spool, an excitation coil and a fluid flow path. The detailed configuration of each MR valve could be different depending on the specific design, but the basic working principle is usually similar. The magnetic field of the excitation coil is applied to the MR fluid in the fluid flow path to make its rheological properties change. This leads to changes in the fluid flow resistance and therefore changes in the pressure drop of the valve that allows the MR fluid flow to be slowed or even stopped.

In recent years the research of MR valves aims to achieve large pressure drops or fast responses by either designing a novel valve structure or optimizing an existing valve structure. Among them, there are three typical fluid flow paths to configure the geometrical arrangements of the MR valves: the annular flow path, the radial flow path, and both the annular and radial flow paths.

The annular type MR valve is the most common type of valve. It has already been altered into several design varieties such as the inner coil design[5], the outer coil design[6-7]and the multiple-coil design[8]. Normally, the annular gap is characterized by the MR fluid flow channel longitudinal to the axial fluid flow, where it is usually parallel to the inlet and outlet of the valve. So, elongating the annular gap is the only way to increase the effective region as it will increase the pressure drop. Nevertheless, the elongation of the flow channel will enlarge the overall dimension of the valve as well, which might not be preferable in some valve designs.

Radial type MR valves have also been introduced as an alternative to the annular type MR valves with the capability of increasing the pressure drop capacity by providing modular stages[9-11]. It is characterized by the way MR fluid flow path is transversal in the valve; that is, the radial gap is placed perpendicularly to the inlet and outlet of the valve. The radial type MR valve can help generate a large pressure drop with a larger width and a shorter longitudinal flow channel length. For example, Aydar et al. developed a large-scale modular MRF bypass damper with a two-stage disk type bypass MR valve which can provide a pressure drop of over 9.6 MPa at 5A of activation electric input current[9]. Liao et al. developed a novel MR valve with multi-stage radial fluid flow paths, and an MR damper was also prototyped and integrated with this bypass MR valve. The simulation and experimental results showed that this new MR damper is superior to the traditional MR damper with annular damping channel[10].

The latest advance for MR valves is a combination of annular and radial type valves, which has shown promising performance by effectively multiplying the number of effective gaps. For example, Wang and Ai proposed an MR valve simultaneously possessing annular and radial fluid flow resistance channels with the assumption that the magnetic flux densities at the annular and radial fluid flow gaps are identical[12-13]. The results showed that the radial fluid flow gaps in the MR valve were more efficient in providing a larger, controllable range than those with annular fluid flow gaps. Imaduddin and Mazlan further developed a compact MR valve with multiple annular and radial gaps[14-16]. The simulation and experimental results revealed that this novel design could increase the achievable pressure drop of the valve by more than 2.5 MPa.

As mentioned above, the performance of the valve with the combination of radial and annular fluid flow paths was the best, followed by the valve with the single radial fluid flow path, and then the worst was the valve with the single annular fluid flow path. This was based on the assumption that the valves were constrained in a specific volumetric dimension and the annular and radial resistance gaps or both of them were fixed. The thickness of the fluid flow resistance gap is an important factor that affects the performance of the valves, especially the pressure drop. Because the magnetic resistance in the fluid flow gap is one thousand times that of the magnetic materials used in the valve spool and body, a large gap thickness will change the magnetic circuit of the MR valve and decrease the magnetic flux density, which in turn will decrease the MR effect. If the gap thickness is too small, it will be difficult for the MR fluid to pass through the gaps even without the magnetic field being applied to the gaps due to the oil film effect. In a word, the feasible gap thickness should be determined when an MR valve is designed. In general, the reasonable gap thickness ranges between 0.5 mm and 1.5 mm[12].

In this paper, a compact MR valve with annular-radial-orifice flow paths was developed. First, the fluid flow paths were composed of a single annular flow channel, a single radial flow channel and an orifice flow channel through compact structural design. This valve structure not only guarantees a larger pressure drop but also reduces the geometry of the proposed MR valve to some extent. Then the effect of the radial resistance gap of the proposed MR valve on the pressure drop was investigated through simulation analysis and experimental verification. Finally, the effects of the radial resistance gaps on the pressure drop using experimental methodology is being discussed.

1 Structure Design and Model of the Annular-Radial-Orifice Flow MR Valve

1.1 Structural analysis of the proposed MR valve

The structure of the annular-radial-orifice flow MR valve is shown in Fig.1. In the MR valve, the right and left end covers are made from stainless steel materials, and they have six threaded holes as a holder for the screw and one fluid flow channel port acting as the inlet/outlet port of the MR valve. The flow guiding plate, which is made from stainless steel material, acts as a connecting passage between the inlet port and the annular flow channel, and it can allow the fluid to be in a state of laminated flow so as to avoid turbulence. The excitation coil was wound onto the groove formed by the fixed plate and the valve spool and protruded out through a hole in the right end cover. The assembly between the fixed plate and the valve spool was dependent on the screw joints at the left end of the valve spool. The screw was used to fix the magnetic plate, the washer and the fixed plate together. The radial resistance gap was guaranteed by the thickness of the washer. The radial resistance gap can be changed by replacing the different sizes of the washers. Here, four different sizes of washers were manufactured to investigate the effects of radial resistance gaps on the pressure drop in the following experimental tests.

1—left end cover; 2—flowguiding plate; 3—screw; 4.magnetic plate; 5—washer; 6—fixed plate; 7—valve body; 8—excitation coil; 9—valve spool; 10—right end cover Fig.1 Schematic diagram of the annular-radial-orifice flow MR valve

The MR fluid flow paths in the proposed MR valve were comprised of a single annular flow path, a radial flow path and an orifice flow path. In detail, the annular flow path was formed between the outer circumference of the magnetic plate and the inner circumference of the valve body, and the annular resistance gap was fixed at 1.0 mm[12]. The radial fluid flow path was looped between the right surface of the magnetic plate and the left surface of the valve spool. There was a through hole with a diameter of 4 mm in the middle of the valve spool, and it formed the orifice flow path of the MR valve. In addition, the proposed MR valve has an outer diameter size of 62 mm and an overall length of 80 mm.

When a direct current is applied to the excitation coil, the closed loop magnetic circuits will be generated in the valve body, the annular flow resistance gap, the magnetic plate, the radial resistance gap and the valve spool. The intense magnetic fields will generate in the annular and radial resistance gaps that are perpendicular to the gaps. Finally, a pressure drop between the inlet port and the outlet port of the MR valve will be produced because of the shear stress in both of the resistance gaps. Therefore by adjusting the direct current, this pressure drop can be controlled.

1.2 Magnetic circuit of the proposed MR valve

Fig.2 shows the simplified magnetic circuit of the proposed MR valve. According to the principle of the continuity of magnetic flux that is used to determine the magnetic flux density throughout its conduit, the magnetic flux can be considered as

ΦMR,r=ΦMR,a=Φsteel=Φ

(1)

whereΦis the magnetic flux of the circuit,ΦMR,aandΦMR,rare the magnetic flux of the MR fluid in the annular fluid flow path and radial fluid flow path, respectively, andΦsteelis the magnetic flux of the valve body, valve spool and magnetic plate in the primary magnetic path.

Fig.2 Simplified magnetic circuit of the proposed MR valve

The magnetic circuit is analyzed using the magnetic Kirchhoff’s law as

(2)

whereNcis the number of turns of the excitation coil, andIis the current applied to the excitation coil;Hiis the magnetic field intensity in theith link of the circuit, andliis the overall effective length of that link.

On the other hand, the magnetic flux conservation rule of the circuit is given by

Φ=∮cBdS=BiSi

(3)

whereBiandSiare the magnetic flux density and cross-sectional area of theith link, respectively.

For the proposed MR valve that is shown in Fig.1 and Fig.2, the effective length of theith link of the circuit can be defined as

(4)

The cross-sectional area of theith link in the magnetic flux path can be calculated by

(5)

According to electromagnetic theory, the magnetic flux density,B, can be approximately expressed in terms of the magnetic field intensityHas

Bi=μ0μiHi

(6)

whereμ0=4π×10-7T·mA-1is the magnetic permeability of free space, andμiis the relative magnetic permeability of magnetic materials.

Rirepresents the magnetic resistance of theith link in the magnetic flux path, and the equation ofRicab be expressed as

(7)

So, the equation of magnetic Kirchhoff’s law can be rewritten as

(8)

The magnetic flux density of each part of the MR valve can be expressed in the following formand respectively upper bounded by the magnetization property of the used magnetic materials.

(9)

whereBjsatis the saturated magnetic flux density of the corresponding material in thejth link.

According to Eqs.(7) (9), the magnetic flux density of the MR fluid in the annular fluid flow path and radial fluid flow path can be obtained, respectively. They are expressed as

(10)

(11)

1.3 Control model of the MR valve

In general, the performance of an MR valve can be determined by its capability to create and regulate pressure drop between the inlet port and the outlet port; although, the other capabilities of MR valve such as time constant, linearity and hysteresis are also important.

Ignoring the pressure drop induced in the left and right end covers and the flow guiding plate, it can be seen that the flow paths consist of one annular gap, one radial gap, and one orifice gap together in the MR valve from Fig.2. So the pressure drop Δpof the MR valve can be defined as

Δp=Δpa+Δpr+Δpo

(12)

where Δpa, Δpr, Δporepresent the pressure drop through the annular fluid flow path, radial fluid flow path and the orifice flow channel, respectively. The pressure drop Δpain the annular resistance gap is expressed as[12]

(13)

where Δpa,ηand Δpa,τare the pressure drop from the viscous properties of the fluid and the pressure drop from the field dependent yield stress of the fluid in the annular resistance gap, respectively.ηis the viscosity without the magnetic field,qis the system flow rate,gais the thickness of the annular resistance gap,Ris the radius of the valve, andthandLaare the thickness of the valve body and magnetic plate, respectively.τy,ais the change of yield stress in the annular resistance gap that responds to an applied magnetic field, andcis the coefficient which depends on the flow velocity profile and ranges from a minimum value of 1 to a maximum value of 3.

The pressure drop Δprin the radial resistance gap is defined as[12]

(14)

where Δpr,ηand Δpr,τare the pressure drop from the viscous properties of the fluid and the pressure drop from the field dependent yield stress of the fluid in the radial resistance gap, respectively.τy,ris the change of yield stress in the radial resistance gap that responds to an applied magnetic field,gris the thickness of the radial resistance gap,R0is the radius of the central hole of the valve spool,Wcis the thickness of the groove of the valve spool,Rcis the radius of the valve spool at the left end without screw thread, andRdis the radius of the valve spool at the left end with screw thread.

The pressure drop Δpoin the orifice resistance gap is defined as

(15)

whereLis the length of the valve spool.

By substituting Eqs.(13)-(15) into Eq.(12), the pressure drop Δpof the proposed MR valve is obtained. In order to make it clear whether pressure drop is controllable or not, the range change is defined as the ratio of active pressure drop Δpτand passive pressure drop Δpη.

(16)

2 Modeling and Simulation of the Annular-Radial-Orifice Flow MR Valve

The MR fluid with the type MRF-J01T provided by the Chongqing Instrument Material Research Institute in China was used in the following simulations and experiments[11].

Fig.4 Magnetic flux density of the defined path

Fig.3 shows the axisymmetric two-dimensional finite element model of the proposed MR valve using ANSYS/EMAG software. The magnetic plate and the valve spool and body were made from No.10 steel, which has a saturated magnetic flux density of 2.4 T when the applied magnetic field intensity exceeds 320 kA/m. The excitation coil is made of copper with a relative permeability of 1. The annular and radial resistance gaps are full of MR fluid whose permeability is defined by the B-H curve of MRF-J01T. In the simulation, the annular resistance gap was set to 1.0 mm, while the radial resistance gap was set to 1.5 mm, 1.0 mm, 0.8 mm and 0.5 mm, respectively. The current density in the excitation coil was set at 2.51 A/mm2when the applied current to the excitation coil equaled 2.0 A. The diameter of the excitation coil was 0.6 mm, and the number of the turns was 400. In the figure, the entity model was meshed using a quadrangular element with a total number of elements of 1 629 and a total number of nodes of 5 036.

In order to investigate the distribution of the magnetic flux density in the fluid flow paths clearly, the pathP1along the annular fluid flow path and the pathP2along the radial fluid flow path were defined separately. The dimensions of the path position along the fluid flow paths are also listed, as shown in Fig.3.

Fig.3 Two dimensional finite element model of the MR valve

Fig.4 shows the magnetic flux density along the defined paths in the annular fluid flow path and in the radial fluid flow path, respectively. It can be seen that the magnetic flux density, both in the annular fluid flow path and in the radial fluid flow path, distributes evenly though it decreases sharply at the end of the defined path. In addition, the magnetic flux density at the radial fluid flow path is larger than that at the annular fluid flow path under the same radial resistance gap. Moreover, the less the radial resistance gap is, the bigger the magnetic flux density is, both in the radial resistance gap and in the annular resistance gap. The average magnetic flux density in the annular fluid flow path is 0.737 T, and the average magnetic flux density in the radial fluid flow path is 0.837 T, when the current applied to the excitation coil is 2.0 A, the radial resistance gap is 0.5 mm, and the annular resistance gap is 1.0 mm.

Fig.5 shows the distribution of the magnetic flux density along the fluid flow paths under the different radial resistance gaps when the applied current is 2.0 A. It can be seen that the magnetic flux density increased both in the annular and radial resistance gaps when the radial resistance gap decreased from 1.5 mm to 0.5 mm, and the magnetic flux density in the radial fluid flow path was bigger than that in the annular fluid flow path. However, the deviation of the magnetic flux density in the radial and annular resistance gap is not big, which shows the high utilization of the magnetic flux density through the compact design for the proposed MR valve.

Fig.5 Magnetic flux density along the fluid flow paths under the different radial resistance gaps

Fig.7 Simulations of the magnetic flux density under different applied currents

Fig.6 shows the changes of yield stress along the fluid flow paths under four different radial resistance gaps. Here,currents of 0.8 A and 2.0 A were applied to the excitation coil, respectively. Observing the figure, the trend of the yield stress variation is shown to be similar to the trend of the magnetic flux density variation as depicted in Fig.5 when the applied current is 0.8 A. However, the values of the yield stress remain stable when the applied current exceeds 2.0 A; the reason is that the change of yield stress is saturated under this applied current.

Fig.6 Changes of yield stress along the fluid flow path under the different radial resistance gaps

Fig.7a shows the relationships between the magnetic flux densities at the radial resistance gap under different applied currents with four different radial resistance gaps, and Fig.7b shows the relationships between the magnetic flux densities at the annular resistance gap. Both figures show that the magnetic flux density increased as the applied current increased when the resistance gap was fixed but decreased as the radial resistance gap increased. This occurred because the magnetic resistance increased as the resistance gap became wider, which in turn led to a decrease in the magnetic flux density.

Fig.8 is the estimation of the pressure drop under four types of radial resistance gaps. The pressure drop increased with the increase of the applied current, and the pressure drop of the MR valve increased with the decreasing of the radial resistance gaps. Moreover, the less applied current was needed for the saturation of the pressure drop when the radial resistance gap changed from 1.5 mm to 0.5 mm.

Fig.8 Effect of radial resistance gap size on the pressure drop

3 Performance Analysis of the Annular-Radial-Orifice Flow MR Valve

3.1 Prototype of the MR valve

In order to make full use of magnetic flux density in the resistance gap, the magnetic flux density in the radial flow channel was designed to be roughly equal to that in the annular flow channels, so the reasonable resistance length ofLrandLacan also be obtained.

From Eq.(3), it can be deduced as

BMR,rSMR,r=BMR,aSMR,a

(17)

As mentioned above,BMR,ris roughly equal toBMR,a, soSMR,ris also roughly equal toSMR,a. According to Eq.(5), the relationship ofLrandLacan be determined. Here,Lris 11 mm andLais 4.2 mm.

Fig.9 shows the prototype of the proposed MR valve with annular-radial-orifice fluid flow paths.

3.2 Experimental test rig setup

In order to validate the valve performance of the proposed MR valve, an experimental test rig was built up and shown in Fig.10. A motor-driven fixed gear pump was used as a power unit. Pressure transducers (a) and (b) were used to measure the inlet pressure and the outlet pressure of the MR valve, respectively. A relief valve (a) was used as a safety valve to protect the hydraulic system, and a relief valve (b) was adopted to simulate the load cases in the hydraulic system. A DC power (a) was used to supply power to the two pressure transducers, and the DC power (b) was applied to supply power to the excitation coil of the proposed MR valve. A data acquisition board was used to capture the pressures. A host computer was used to monitor the relevant test parameters of the hydraulic system in real time.

Fig.9 Photograph of the manufactured MR valve

Fig.10 Experimental test rig of the proposed MR valve

3.3 Effect of different radial resistance gap sizes on the pressure drop

In order to investigate the effects of radial resistance gaps on the pressure drop of the proposed MR valve, four different widths of washer were manufacturedas shown in Fig.11. In other words, four different radial resistance gaps from 0.5 mm to 1.5 mm can be obtained by changing the washers shown in Fig.11.

Fig.11 Four sizes of washers used in the experiment

Fig.12 shows the experimental pressure of the MR valve under applied currents with four different radial resistance gaps.The inlet port pressure and the pressure drop increased as the applied currents increased under the four different radial resistance gaps, while the outlet port pressure remained at a value of 500 kPa. The reason

is that the pressure drop equals a subtraction of the inlet port pressure and outlet port pressure, while the outlet port pressure was held at a certain value by adjusting the outside valve knob of the relief valve (b) in Fig.10. However, the outlet port pressure fluctuated a little because the gears in the fixed gear pump were worn out due to long operating time and the abrasive nature of the MR fluid.

Fig.12 Pressure change under applied currents with four different radial resistance gaps

Fig.13 shows the experimental pressure drop of the MR valve under applied currents with four different radial resistance gaps. Itcan be seen that the pressure drop increased as the applied current increased. In addition, the pressure drop also increased as the radial resistance gap decreased from 1.5 mm to 0.5 mm. The maximum pressure drop is approximately 2 650 kPa at the applied current of 1.2 A when the radial resistance gap is 0.5 mm.

Fig.13 Pressure drop under applied currents with four different radial resistance gaps

Fig.14 shows the comparison of experimental pressure drop and simulated pressure drop under applied currents with radial gap sizes of 0.5 mm, 0.8 mm, 1.0 mm and 1.5 mm, respectively. As shown in the figure, the simulated pressure drop is lower than the experimental pressure drop at first. The possible reason may be that the pressure drop from the viscous properties of the fluid makes dominated contributions when the current is small. At the same time, the thickening effect is not considered in the magnetic field simulation based on the Bingham model, which causes the simulated viscosity to be less than the experimental viscosity. As the applied current increases, the pressure drop from the field dependent yield stress of the fluid plays a leading role; the simulated pressure drop is bigger than that of experimental pressure drop. The possible reason may be that the enhanced yield stress phenomenon occurs when several single chain structures of magnetic particles join together and form a thick column, which makes the saturated yield stress value in the simulation bigger than the experimental conditions.

Fig.14 Pressure drop comparsion of simulation result and experimental result

The range changes under four different radial resistance gaps can be obtained by Eq.(16) and the experimental results. It can be deduced that the range changesare 7.31, 5.21, 5.03 and 4.20 when the radial gap size was changed from 0.5 mm to 1.5 mm. The smaller the radial gap size is, the bigger the range changes are. Moreover, the range changes increase sharply when the radial gap size changes from 0.8 mm to the 0.5 mm, which shows a good pressure regulating ability.

3.4 Effect of different load cases on the pressure drop of the MR valve

The relief valve (b) was applied in the experimental test rig to simulate the loading conditions in the hydraulic system, and two typical load cases were selected by adjusting the outside valve knob in this study. The load case 1 was denoted by adjusting the outside valve knob clockwise once at the initial state, and the load case 2 was denoted by adjusting the outside valve knob clockwise twice at the initial state. Fig.15 shows the variation of pressure drop and load cases under different applied currents for the four radial resistance gaps. Here the pressure drop remained at a stable value when the current was increased from 0 A to 1.8 A under the two different load cases, which means the load cases did not influence the pressure drop. It is also seen that the pressure drop increased as the applied current increased, specifically.

Fig.15 Variation of pressure drop under two typical load cases

The pressure drop is not affected by load cases; this is an advantage because it makes the proposed MR valve useful as an active control element, For example, it can be used as a bypass valve for controlling the damper, which constitutes a bypass type MR valve controlled damper. It can also effectively expand the adjustable range of the damping force so that the MR damper can be used in the vibration damping and seismic application under different damping conditions.

4 Conclusions

A compact annular-radial-orifice flow MR valve was developed and prototyped. The fluid flow paths of the proposed MR valve consisted of a single annular flow channel, a single radial flow channel and an orifice flow channel through structural design. In order to investigate the change of the magnetic flux density and yield stress along the fluid flow paths under the four different radial resistance gaps, magnetic circuit design and finite element analysis were carried out. The simulation results show that this proposed MR valve can provide a larger pressure drop of 3 342 kPa at a 0.5 mm width of the radial resistance gap and a 1.0 mm width of annular resistance gap. Meanwhile, the volume space of MR valve has an outer diameter of 62 mm and overall length of 80 mm.

The experimental pressure drop under the four different radial resistance gap was also carried out on the test rig. The results show that the pressure drop increases as the applied current increases, and the pressure drop also increases as the radial resistance gap decreases from 1.5 mm to 0.5 mm. The maximum pressure drop is approximately 2 650 kPa at the applied current of 1.2 A when the radial resistance gap is 0.5 mm, which is well accorded with the simulation results.

This proposed MR valve has significantly improved its efficiency through compact design and changeable radial resistance gap. This is beneficial to control the MR damper as a bypass control valve for its good pressure regulating capability.