Performance evaluation of an improved radial magnetorheological valve and its application in the valve controlled cylinder system

The structure of the improved radial MR valve is shown in figure 1. The magnetic disk, non-magnetic disk and non-magnetic ring are introduced to make the magnetic flux lines not only perpendicularly pass through the radial resistance gap, but also perpendicular to the annular resistance gap. Therefore, the improved radial MR valve can achieve the effects of conventional radial MR valve and the annular MR valve together.

Zoom In Zoom Out Reset image size

As shown in figure 1, the fluid flow paths of the proposed radial MR valve are comprised of two annular flow paths, two radial flow paths and two orifice flow paths. In detail, the radial resistance gap is formed between the positioning disk and the damping disk as the effective gap, in which the flow direction of MR fluid is perpendicular to the direction of magnetic fluxes. The annular resistance gaps are looped between the damping disk and the bobbin. The magnetic fluxes in a conventional radial MR valve do not go through the annular resistance gap, which causes the annular gap out of the magnetic field. To make full use of the annular resistance gap, the conventional radial MR valve is modified with a non-magnetic disk and two non-magnetic rings, and the magnetic material of the bobbin is also replaced. It is noted that the non-magnetic is arranged to divide damping disk. In addition, two non-magnetic rings are arranged at both ends of the bobbin respectively such that the magnetic fluxes can be uniformly distributed in the annular resistance gap. The material properties of each part in figure 1 are shown in table 1.

Since the non-magnetic disk and the non-magnetic rings are non-permeable materials, the magnetic fluxes are bent to form a serpentine flux path. Consequently, it can be guided to the annular flow path in the valve as much as possible, which adds two effective annular resistance gaps. The circular through holes in the middle of the locating plate forms the orifice flow paths, and they are not intensively exposed to the magnetic field. Therefore, the influence of the magnetic field on the yield stress of the MR fluid in these areas can be neglected. By arranging different materials inside the valve to twist the magnetic flux paths under the applied currents, the improved radial MR valve can achieve the effects of both the radial and annular MR valve without expand the valve sizes. When a constant direct is applied to the excitation coil, the serpentine closed-loop circuits will be generated in the valve body, the magnetic disk, the radial flow resistance gap, the damping disk, the annular resistance gap, and the bobbin. Then, the intense magnetic fields will generate in both the radial and annular resistance gaps. Finally, a pressure drop between the inlet and outlet ports of the valve will be produced because of the yield stress in both the resistance gaps. Therefore, this pressure drop can be controlled by adjusting the applied current.

Figure 2 shows the simplified magnetic circuit of the improved radial MR valve. According to the continuity principle of the magnetic flux, the magnetic flux density throughout its conduit is determined. It can be expressed as

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{\mathrm{MR},r}={{\rm{\Phi }}}_{\mathrm{MR},a}={{\rm{\Phi }}}_{{\rm{steel}}}={\rm{\Phi }},\end{eqnarray} \tag{ 1 }$$

where ${\rm{\Phi }}$ is the magnetic flux density of the circuit, ${{\rm{\Phi }}}_{\mathrm{MR},a}$ and ${{\rm{\Phi }}}_{\mathrm{MR},r}$ are the magnetic flux density of the MR fluid in the annular gap and radial gap, respectively; and ${{\rm{\Phi }}}_{{\rm{steel}}}$ is the magnetic flux density of the valve body, magnetic disks, positioning plates, bobbin and damping disk in the primary magnetic circuit.

Zoom In Zoom Out Reset image size

The magnetic circuit is deduced by applying the magnetic Kirchhoff's law, it is regarded as

$$\begin{eqnarray}&&{N}_{{\rm{c}}}I=\displaystyle \sum _{{i}=1}^{n}{H}_{{i}}{l}_{{i}},\end{eqnarray} \tag{ 2 }$$

where N_c is the number of turns of the excitation coil and I is the current applied to the excitation coil, H_i and l_i are the magnetic field intensity and the overall effective length in the ith link of the circuit, respectively.

On the other hand, the magnetic flux conservation rule based on Gauss's law can be givened as

$$\begin{eqnarray}&&{\rm{\Phi }}={B}_{{i}}{S}_{{i}},\end{eqnarray} \tag{ 3 }$$

where B_i is the magnetic flux density of the ith link, and S_i is the cross sectional area of that link.

As shown in figure 2, the magnetic circuit is divided into nine sections. The effective length of each section of the path is expressed as follows:

$$\begin{eqnarray}&&\begin{array}{l}{l}_{1}=0.5H-0.5t,\,{l}_{2}=R-{r}_{0},\,{l}_{3}={{h}}_{1}-0.5t,\,{l}_{4}={g}_{{\rm{r}}},\\ {l}_{5}={{h}}_{2},\,{l}_{6}={r}_{1},\,{l}_{7}={g}_{{a}},\,{l}_{8}=0.5\left(R-{t}_{{h}}-w-{r}_{1}-{g}_{{a}}\right),\\ {l}_{9}={{h}}_{2}+0.5{{h}}_{3}.\end{array}\end{eqnarray} \tag{ 4 }$$

On the other hand, the cross-sectional area of the ith link in the magnetic flux path can be deduced by

$$\begin{eqnarray}&&\begin{array}{l}{S}_{1}=\pi \left[{R}^{2}-{\left(R-{t}_{{h}}\right)}^{2}\right]\\ {S}_{2}=\pi \left(R+{{r}}_{0}\right)t\\ {S}_{3}=\pi \left({{r}}_{1}^{2}-{{r}}_{0}^{2}\right)\\ {S}_{4}={S}_{{\rm{MR}},{r}}=\pi \left({{{r}}_{1}}^{2}-{{{r}}_{0}}^{2}\right)\\ {S}_{5}=\pi {{r}}_{1}^{2}\\ {S}_{6}=\pi \left({{r}}_{1}-0.5{{r}}_{0}\right){{h}}_{2}\\ {S}_{7}={S}_{{\rm{MR}},{a}}=2\pi \left({{r}}_{1}+0.5{g}_{{a}}\right){{h}}_{2}\\ {S}_{8}=\pi \left(R-w-{t}_{{h}}\right){{h}}_{2}\\ {S}_{9}=\pi \left[{\left(R-w-{t}_{{h}}\right)}^{2}-{\left({{r}}_{1}+{g}_{{a}}\right)}^{2}\right].\end{array}\end{eqnarray} \tag{ 5 }$$

Based on the electromagnetic theory, the magnetic flux density B in terms of the magnetic field intensity H can be approximately expressed as

$$\begin{eqnarray}&&{B}_{{i}}={\mu }_{0}{\mu }_{{i}}{H}_{{i}},\end{eqnarray} \tag{ 6 }$$

where μ₀ = 4π×10^–7 T mA⁻¹ is the magnetic permeability of free space, and μ_i is the relative magnetic permeability of magnetic materials.

R_i represents the magnetic resistance of the ith link in the magnetic flux path, the equation of R_i is deduced as

$$\begin{eqnarray}&&{R}_{{i}}=\displaystyle \frac{{l}_{{i}}}{{\mu }_{0}{\mu }_{{i}}{S}_{{i}}}.\end{eqnarray} \tag{ 7 }$$

Therefore, the equation of magnetic Kirchhoff's law can be converted to

$$\begin{eqnarray}&&{N}_{{\rm{c}}}I\,=\,\displaystyle \sum _{i=1}^{n}{H}_{i}{l}_{i}\,=\,\displaystyle \sum _{i=1}^{n}\displaystyle \frac{{B}_{i}}{{\mu }_{0}{\mu }_{i}}{l}_{i}\,=\,\displaystyle \sum _{i=1}^{n}\displaystyle \frac{{l}_{i}}{{\mu }_{0}{\mu }_{i}{S}_{i}}{\rm{\Phi }}\,=\,\displaystyle \sum _{i=1}^{n}{R}_{i}{\rm{\Phi }}.\end{eqnarray} \tag{ 8 }$$

The magnetic flux density of each part of the magnetic circuit can be calculated by the following formula and respectively limited to the magnetization property of the used magnetic materials

$$\begin{eqnarray}&&{B}_{{j}}=\displaystyle \frac{{\rm{\Phi }}}{{S}_{{j}}}=\displaystyle \frac{{N}_{{\rm{c}}}I}{{S}_{{j}}\displaystyle \sum _{{i}=1}^{n}{R}_{{i}}}\leqslant {B}_{{j}{\rm{s}}{\rm{a}}{\rm{t}}},\end{eqnarray} \tag{ 9 }$$

where B_jsat is the saturated magnetic flux density of the corresponding material in the jth link.

According to equations (7) and (9), the magnetic flux density of MR fluid in the annular gap and radial gap can be obtained as follows

$$\begin{eqnarray}&&{B}_{\mathrm{MR},a}=\displaystyle \frac{{N}_{{\rm{c}}}I}{{S}_{7}\displaystyle \sum _{{i}=1}^{9}{R}_{{i}}}=\displaystyle \frac{{\mu }_{0}{N}_{{\rm{c}}}I}{{S}_{7}\displaystyle \sum _{{i}=1}^{9}\displaystyle \frac{{l}_{{i}}}{{\mu }_{{i}}{S}_{{i}}}},\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&{B}_{\mathrm{MR},r}=\displaystyle \frac{{N}_{{\rm{c}}}I}{{S}_{4}\displaystyle \sum _{{i}=1}^{9}{R}_{{i}}}=\displaystyle \frac{{\mu }_{0}{N}_{{\rm{c}}}I}{{S}_{4}\displaystyle \sum _{{i}=1}^{9}\displaystyle \frac{{l}_{{i}}}{{\mu }_{{i}}{S}_{{i}}}}.\end{eqnarray} \tag{ 11 }$$

To improve the utilization of magnetic field and reduce the energy loss, the yield stress in the radial and annular resistance gaps of the improved radial MR valve should reach saturation at the same time. Therefore, it is necessary to ensure the magnetic flux density of the radial gap equal to that of the annular gap. From equation (3), it can be deduced that

$$\begin{eqnarray}&&{B}_{\mathrm{MR},r}{S}_{\mathrm{MR},r}={B}_{\mathrm{MR},a}{S}_{\mathrm{MR},a}.\end{eqnarray} \tag{ 12 }$$

As mentioned above, B_MR,r is roughly equal to B_MR,a, and S_MR,r is also roughly equal to S_MR,a. So the relationship of r₁ and h₂ can be determined according to equation (5).

Since the relative permeability of the MR fluid is much smaller than the relative permeability of the magnetic material, the magnetic resistance of the fluid at the effective flow path is much greater than that of other structures of MR valve. As shown in equations (4) and (7), the gap size is proportionally related to the magnetic resistance, so the gap size is a significant factor influencing the performance of MR valve. A larger change in the gap thickness will significantly increase the magnetic resistance and decrease the magnetic flux density, which decreases the pressure drop. However, The MR fluid will be difficult to pass through the resistance gap if the gap thickness is too small. In general, the reasonable gap thickness ranges from 0.5 and 1.0 mm [23]. Therefore, the thickness of radial and annular resistance gaps is set as 1.0 mm, and the radius r₀ of orifice gap is assigned as 2 mm.

Finally, the size is determined by the comparison between theoretical calculation and simulation analysis. Table 2 summarizes the primary parameters of the proposed radial MR valve.

As show in figure 3, there are two orifice gaps, two radial gaps and two annular gaps together in the improved radial MR valve. Hence, the pressure drop Δp can be represented as

$$\begin{eqnarray}&&{\rm{\Delta }}p=2\left({\rm{\Delta }}{p}_{o}+{\rm{\Delta }}{p}_{r}+{\rm{\Delta }}{p}_{a}\right),\end{eqnarray} \tag{ 13 }$$

where Δp_o, Δp_r, Δp_a are the pressure drop through the orifice flow path, the radial flow path and the annular flow path, respectively.

Zoom In Zoom Out Reset image size

The pressure drop Δp_o in the orifice resistance gap can be expressed as [22]

$$\begin{eqnarray}&&{\rm{\Delta }}{p}_{{\rm{o}}}=\displaystyle \frac{8\eta {h}_{1}}{\pi {r}_{{\rm{0}}}^{{\rm{4}}}}q,\end{eqnarray} \tag{ 14 }$$

where q is system flow rate, and η is viscosity without magnetic field.

The pressure drop Δp_r in the radial resistance gap can be defined as [23]

$$\begin{eqnarray}&&{\rm{\Delta }}{p}_{{r}}={\rm{\Delta }}{p}_{{r}\mbox{--}{\eta }}+{\rm{\Delta }}{p}_{{r}\mbox{--}{\tau }}=\displaystyle \frac{6\eta q}{\pi {g}_{{r}}^{3}}\,\mathrm{ln}\,\displaystyle \frac{{{r}}_{1}}{{{r}}_{0}}+\displaystyle \frac{c\left({{r}}_{1}-{{r}}_{0}\right)}{{g}_{{r}}}{\tau }_{y,{r}},\end{eqnarray} \tag{ 15 }$$

where Δp_r−η is the pressure drop from the viscous properties of the fluid in the radial resistance gap, Δp_r−τ is the pressure drop from the field dependent yield stress of the fluid in the radial resistance gap, τ_y1 is the variation of yield stress in the radial resistance gap with respect to an applied magnetic field, and c is the flow velocity profile coefficient whose value range is 1–3.

The pressure drop Δp_a in the annular resistance gap can be calculated as [23]

$$\begin{eqnarray}&&{\rm{\Delta }}{p}_{{a}}={\rm{\Delta }}{p}_{{a}\mbox{--}{\eta }}+{\rm{\Delta }}{p}_{{a}\mbox{--}{\tau }}=\displaystyle \frac{6\eta \left({h}_{2}+{h}_{3}/2\right)}{\pi {r}_{1}{g}_{{a}}^{3}}q+\displaystyle \frac{c{h}_{2}}{{g}_{{a}}}{\tau }_{y,{a}},\end{eqnarray} \tag{ 16 }$$

where Δp_a−η is the pressure drop from the viscous properties of the fluid in the annular resistance gap, Δp_a−τ is the pressure drop from the field dependent yield stress of the fluid in the annular resistance gap, τ_y2 is the dynamic yield stress in the annular resistance gap that responds to an applied magnetic field.

By substituting equations (14)–(16) into equation (13), the pressure drop Δp of the improved radial MR valve can be obtained

$$\begin{eqnarray}\begin{array}{lll}{\rm{\Delta }}p & = & \displaystyle \frac{16\eta {h}_{1}}{\pi {{r}}_{0}^{4}}q+\displaystyle \frac{12\eta q}{\pi {g}_{{r}}^{{\rm{3}}}}\,\mathrm{ln}\,\displaystyle \frac{{{r}}_{1}}{{{r}}_{0}}+\displaystyle \frac{12\eta \left({h}_{2}+{h}_{3}/2\right)}{\pi {{r}}_{1}{g}_{{a}}^{{\rm{3}}}}q\\ & & +\displaystyle \frac{2c\left({{r}}_{1}-{{r}}_{0}\right)}{{g}_{{r}}}{\tau }_{y,{r}}+\displaystyle \frac{2c{h}_{2}}{{g}_{{a}}}{\tau }_{y,{a}}.\end{array}\end{eqnarray} \tag{ 17 }$$

As shown in equation (17), the pressure drop Δp contains five items. The first three items are the pressure drops from the viscous properties of the fluid which related to the system flow rate, and the later two items are the pressure drops from the field dependent yield stress of the fluid which are related to the applied magnetic fields.

The MR fluid selected for the proposed MR valve is MRF-J01T which was provided by the Chongqing Instrument Material Research Institute in China, and its field dependent properties is depicted in figure 4 [34]. As shown in figure 4(a), the relation between the yield stress and magnetic flux density can be fitted using a polynomial equation in equation (18)

$$\begin{eqnarray}&&{\tau }_{y,a}={a}_{3}\times {B}_{\mathrm{MR},a}^{{\rm{3}}}+{a}_{2}\times {B}_{\mathrm{MR},a}^{{\rm{2}}}+{a}_{1}\times {B}_{\mathrm{MR},a}+{a}_{0},\end{eqnarray} \tag{ 18 }$$

$$\begin{eqnarray}&&{\tau }_{y,r}={a}_{3}\times {B}_{\mathrm{MR},r}^{{\rm{3}}}+{a}_{2}\times {B}_{\mathrm{MR},r}^{{\rm{2}}}+{a}_{1}\times {B}_{\mathrm{MR},r}+{a}_{0},\end{eqnarray} \tag{ 19 }$$

where a₀, a₁, a₂ and a₃ are polynomial coefficients that determined by the least-squares fitting of the changes of yield stress data as a function of magnetic flux density, here a₀ = 0.0182 kPa, a₁ = −48.4644 kPa T⁻¹, a₂ = 865.3901 kPa T⁻² and a₃ = −984.2742 kPa T⁻³.

Zoom In Zoom Out Reset image size

The steel material used in magnetic disk, valve body, bobbin, damping disk and positioning plate are NO.10 low cabon steel materials, and the relationship between the manegtic flux density and the magnetic field intensity of the used steel materal is shown in figure 5.

Zoom In Zoom Out Reset image size

In order to simplify the calculation, a 2D axis-symmetric finite element model of the improved radial MR valve is built by using ANSYS/Emag software, which is shown in figure 6. The improved radial MR valve is divided into four areas in terms of material properties, namely the non-magnetic material, the coil, the magnetic material and the MR fluid. The permeability of the magnetic material in the valve is assumed to the B–H curve of No. 10 steel shown in figure 5. The highest magnetic flux density is up to 2.4 T when the applied magnetic field intensity exceeds 320 kA m⁻¹, and the relative permeability of the non-magnetic material is assumed to be 1. The excitation coil is made from copper wire with a relative permeability of 1 and the number of turns is calculated as 743. The current density in the excitation coil is set 2.51 A mm⁻² when the applied current is 2.0 A.

Zoom In Zoom Out Reset image size

Figure 7 shows the magnetic flux distribution of the improved radial MR valve at the applied current of 1.0 A. The magnetic flux line vertically pass through the two radial resistance gaps, it is also perpendicularly pass through the annular resistance gap with the effort of the non-magnetic disk and non-magnetic ring. To investigate the distribution of the magnetic flux density clearly, the path S₁, S₂, S₃ and S₄ along the fluid flow paths are defined separately, as shown in figure 7.

Zoom In Zoom Out Reset image size

Figure 8 shows the magnetic flux density vector of the presented valve, it can be observed that the magnetic flux lines have been twisted in the middle of the valve spool. Figure 9 shows the magnetic flux density contour. Different color distributions represent different values of the magnetic flux densities in different regions. The magnetic flux densities in the non-magnetic ring and non-magnetic disk are close to 0 T. The color distributions in the radial gap and the annular gap are very similar, the magnetic flux densities in both gaps are identical, and the average values are 0.44 T.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Figure 10 shows the magnetic flux density along with the defined fluid flow paths shown in figure 7. The region S₃ and S₄ can achieve higher magnetic flux density while that of the conventional radial MR valve is almost zero. Moreover, the magnetic flux density increases both in the radial and annular resistance gaps by the augmentation of current input to the excitation coil. The peak value of the magnetic flux density at the radial region S₁ and S₂ is slightly lower than at the annular region S₃ and S₄. However, the difference is not obvious. Therefore, the method of serpentine flux paths in the proposed valve can achieve a high utilization of the magnetic flux density. In addition, the magnetic flux densities in the radial and annular fluid flow paths were focused on the middle region, and they decrease gradually at the both end of the defined paths. Furthermore, the magnetic flux densities at the annular region S₃ and S₄ which are close to the non-magnetic disk decreases rapidly until zero, exhibiting that the magnetic properties of the valve are good. The change of magnetic flux density at radial fluid flow path S₁ is equal to the radial fluid flow path S₂. Meanwhile, the change of magnetic flux density at annular fluid flow path S₃ is equal to the annular fluid flow path S₄. As a consequence, the average magnetic flux density at the arbitrarily resistance gaps can be selected to analyze the MR rheological performance changes, such as S₁ and S₃.

Zoom In Zoom Out Reset image size

The yield stress value can be predicted by the magnetic flux density value shown in figure 11. The change of the yield stress variation is similar to the change of the flux density variation. The peak values of yield stress at the annular region S₃ and S₄ are slightly higher than those of the radial region S₁ and S₂. In addition, the yield stress at the radial and annular resistance gap are close, which remain almost 70 kPa at the current of 1.5 A. It indicates that the yield stress of MR fluid almost reaches the saturation under this applied current.

Zoom In Zoom Out Reset image size

Figure 12 shows the average magnetic flux density and the corresponding yield stress variations of the radial resistance gaps S₁ and the annular resistance gap S₃ under different applied currents. The average magnetic flux density increases as the applied current increases. In addition, the higher average magnetic flux density was observed in the radial gap S₁ than the annular gap S₃ under same applied current. The average magnetic flux density in the radial fluid flow path is 0.52 T and in the annular fluid flow path is 0.44 T when the current applied to the excitation coil is 1.6 A. However, the deviation of the magnetic flux density in the radial and annular resistance gap is small, which shows the high utilization of the magnetic flux density for the improved radial MR valve.

Zoom In Zoom Out Reset image size

Figure 12 also shows the yield stress for each corresponding current input. The yield stress has a consistent increase with the increment of current input to the excitation coil on the initial stage. When the current increases to 1.6 A, the yield stress almost reaches the saturation value of about 70 kPa. The corresponding average magnetic flux density is 0.53 T. Therefore, the yield stress value is kept constant at 70 kPa once the average magnetic flux density value in the effective gap exceeding 0.53 T. Though the yield stress in annular gap S₃ is not saturated when the applied current is 1.8 A, it is close to the saturation value of about 67 kPa.

Since there are variations of yield stress value in each gap, the pressure drops generated from each of the gaps will be different. The estimation results of the pressure drop with the variation of the current input are shown in figure 13. The rate of increment of pressure drops of the radial gap is faster than that of the annular gap with the increasing of applied current. It means that the radial gaps provide more dominant contribution to the pressure drop of the valve than that of the annular gaps. In addition, the pressure drop of radial gap reaches saturation at first and the value is 4630 kPa at the applied current of 1.6 A, while the pressure of annular gaps still not reach saturation at the applied of 1.8 A and the maximum pressure drop is approximately 1760 kPa. The pressure drop of orifice gap is always 35 kPa as the applied currents change. Therefore, the total pressure drop of the proposed valve at applied current of 1.8 A is about 6.425 MPa. By observing figure 13(b), the contribution of the annular gap, the radial gap and the orifice gap to the pressure drop of the valve are around 71.23%, 28.22% and 0.55%, respectively.

Zoom In Zoom Out Reset image size

To validate the dynamic performance of the improved radial MR valve, the prototype was fabricated as shown in figure 14, and the experimental test rig was also built up, which is shown in figure 15. A motor driven gear pump was applied as a power unit. Pressure sensor (a) and (b) were used to measure the inlet and 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 control system. The DC power (a) was used to supply power to the two pressure sensors, and the DC power (b) was applied to supply power for the excitation coil of the radial MR valve. A data acquisition board was used to capture the pressures value. A host computer was used to monitor the relevant test parameters of the hydraulic control system in real time [30].

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

4.2.1. Pressure drop performance analysis of improved radial MR Valve

In the tests, three typical load cases were selected by adjusting the outside valve knob of the relief valve (b). The load case 1 was defined by adjusting the outside valve knob one clockwise circle at the initial state, and the load case 2 was defined by adjusting the outside valve knob two clockwise circles at the initial state, and the load case 3 was defined by adjusting the outside valve knob three clockwise circles at the initial state.

Figure 16 shows the experimental pressure of the MR valve at load case 1 over the range of current input between 0 and 2.0 A with a 0.2 A interval. The inlet port pressure and the pressure drop increase steadily as the applied currents increase until saturation is reached at a maximum pressure drop of about 4.2 MPa pertaining to the current of 1.8 A. In addition, the outlet port pressure is basically kept constant at a value of 500 kPa due to the back pressure provided by the relief valve (b). However, the outlet port pressure shows a slight fluctuation because the gears in the gear pump were worn out due to the long operating time and the abrasive nature of the MR fluid. Little air mixed into the MR fluid when the fluid was back to cylinder may also cause this problem.

Zoom In Zoom Out Reset image size

Figure 17 shows the effect of the load cases on the pressure drop of the valve. The relationship between the pressure drop and the current input under the three load cases is almost coincident, indicating that the pressure drop is not affected by the load cases basically. It is only related to the applied currents, which show that the pressure drop of the improved radial MR valve is stable. Therefore, a bypass-type MR damper can be constituted by the radial MR valve installing in the hydraulic cylinder with a bypass duct, which control the movement of the piston by the generated pressure drop from the MR valve. The bypass-type MR damper has advantages of simplicity in structure design and assembly and convenience in maintenance. Besides, the design of the improved radial MR valve can generate larger pressure drop. These advantages further effectively expand the adjustable range of the damping force, so that the damper can be used in a narrow and compact volume under different load conditions.

Zoom In Zoom Out Reset image size

Figure 18 shows the comparison between the experimental pressure drop and the simulated pressure drop with various current inputs and the constant flow rate 4 l min⁻¹. The simulated pressure drop is slightly lower than that of experimental tests when the applied current is less than 0.5 A. The possible reason is that the viscous pressure drop provides more dominant contribution in the low current input condition, while the shear thickening effect of the MR fluid is not considered in the simulation based on the Bingham model. However, when the applied current is greater than 0.5 A, the experimental pressure drop is lower than the simulation value. The possible reason is that the pressure drop induced by the yield stress plays a dominated role with the increament of input current. The relationship between the yield stress and the magnetic flux density is obtained under the assumption that the magnetic particles in the MR fluid form a single-chain structure. However, the structure formed by the magnetic field is not a single-chain structure, but a column-like structure. Therefore, the saturated yield stress will be smaller in the actual experiment tests. On the other hand, the simulation results are obtained in ideal situations and only consider the proposed MR valve itself, but the experimental pressure drop values are measured in the whole test system, which consist of power unit, hydraulic pipe, MR valve, and so on. The abrasion of gear pump, the resistance of hydraulic pipe and the sedimentation of MR fluid will affect the experimental results, which are not considered in the simulation. Moreover, the leakages of the magnetic flux will reduce the magnetic flux density in the effective area to some extent, which also makes the experimental pressure drop smaller than the simulated pressure drop. Based on above possible reasons, the maximum pressure drop in experimental tests is lower than that in simulation when the applied current is bigger than the 0.5 A. Nevertheless, the change trend of pressure drop from experiment measurement is in accordance with the predicted one from FEM.

Zoom In Zoom Out Reset image size

Figure 19 shows the comparison of the pressure drops of the improved radial MR valve at flow rates of 4 l min⁻¹ and 10 l min⁻¹, respectively. In the test, two fixed gear pumps were used to investigate the change of pressure drop separately. The flow rate of the first fixed gear pump is 4 l min⁻¹, and the other is 10 l min⁻¹. Observing figure 19, it can be seen that the measured pressure drop at the 10 l min⁻¹ flow rate is slightly bigger than that at the 4 l min⁻¹ flow rate. In addition, the pressure drop increases gradually when the current increases from 0 to 1.8 A.

Zoom In Zoom Out Reset image size

4.2.2. Pressure drop comparison of improved and conventional radial MR valve

To confirm that the improved radial MR valve can achieve better pressure drop performance, a conventional radial MR valve with same geometry conditions and electromagnetic parameters was fabricated, as shown in the figure 20, and its pressure drop has been measured on the test rig too. Figure 21 shows the experimental pressure of the conventional MR valve at load case 1 when the current input was applied from 0 to 2.0 A with a 0.2 A interval. The inlet port pressure and the pressure drop increase steadily as the applied currents increase. When the current was applied at 1.4 A, the pressure was saturated and the maximum pressure drop reached 3.2 MPa.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Figure 22 shows the comparison of pressure drop between the improved and conventional radial MR valve under different applied currents. The pressure drop of the improved valve is lower than the conventional valve at first. When the applied current is greater than 0.9 A, the pressure drop of the conventional valve is increase at a slower rate, while the pressure drop of improved valve continue to increase rapidly. At the same time, the pressure drop of the improved valve is greater than the conventional valve. Moreover, the pressure drop of conventional valve reaches saturation at the applied current of 1.2 A, and the maximum pressure drop is approximately 3.2 MPa. The pressure drop of improved valve reaches saturation at the applied current of 1.8 A, and the maximum pressure drop is 4.2 MPa. It can be seen that the pressure drop of the improved radial MR valve is higher than that of the conventional radial MR valve with a value of 1 MPa when they all reach the saturation value. The test results show that the pressure drop of the improved radial MR valve can increase by 31.25% than that of conventional valve, which show a better control performance.

Zoom In Zoom Out Reset image size

4.2.3. Response time analysis of the improved radial MR valve

Although the performance of MR valve is mainly determined by the pressure drop, the response time is also an important factor affecting its dynamic performance [35]. Therefore, the response time of the pressure drop was experimentally investigated too. In order to collect test data facilitately, the response time of the hydraulic test system is regarded as that of MR valve. Due to the influence of the hydraulic pipe and the response time of motor driven pump, the measured value will be slightly larger than the actual response time of MR valve, but it still can reflect the response characteristics of MR valve to some extent. In the system, the response performance consists of the rising response time and falling response time. The rising response time is defined as the time required for the pressure drop of the system to rise from its initial state to two thirds of its saturated value after the current is applied. Conversely, the falling response time is defined as the time required for the pressure drop of the system to fall from its initial saturated state to one third of its saturated value after the current is applied [35].

Figure 23 shows the response performance of the improved radial MR valve under different applied currents. The rising pressure response time is 98 ms at the applied current of 0.4 A while the rising pressure response time is up to 204 ms at 1.6 A. It can be concluded that the rising response time increases with increasing applied current since the greater the current is applied, the greater the pressure drop that needs to be established. Additionally, the falling response time of pressure drop under different currents is close to about 107 ms, which shows that the falling response time is almost independent of the applied currents. According to reference [35], it is shown that the rising response time of pressure for the annular and radial MR valve at the 3 mm resistance gap is 110 ms and 68 ms, and the falling response time of pressure for the annular and radial MR valve at the 3 mm resistance gap is 160 ms and 60 ms, respectively. In our works, the proposed MR valve consists of radial and annular resistance gaps simultaneously, and both of the thicknesses are 1 mm. The rising and falling response time of the proposed MR valve are between 98 and 204 ms, which also shows a good response characteristic to some extent compared with the study in [35].

Zoom In Zoom Out Reset image size

Figure 24 shows the response performance of the improved radial MR valve under different flow rates with respect to the applied currents of 0.4 A, 0.8 A and 1.2 A, respectively. From the figure, no matter how much current is applied, the rising response time of the flow rate of 4 and 10 l min⁻¹ is basically equal, as well as the falling time. However, the response time at various flow rates is slightly different, both within 2 ms, which indicates the response time is nearly independent of the flow rate.

Zoom In Zoom Out Reset image size

In order to broaden the industrial applications of MR valve, a MR valve controlled cylinder system which used the improved radial MR valve as its control unit was established. This arrangement solves the problem of difficulties in maintenance and disassembly of traditional MR damper. Moreover, the improved radial MR valve controlled cylinder system can increase the damping force without enlarge the dimension of the MR damper, and the system can achieve different performance by replacing different MR valves.

Figure 25 shows the prototype of improved radial MR valve controlled single rod cylinder system, which consists of an improved radial MR valve, a single rod hydraulic cylinder, an accumulator and hydraulic pipes. The improved radial MR valve, hydraulic cylinder and hydraulic pipes are filled with MR fluids. The piston rod is moving to and fro in the single rod hydraulic cylinder, which makes the MR fluid flows through the improved radial MR valve. Hence, the controllable pressure drop produces in the inlet and outlet of the MR valve when the current applies to the excitation coil, then the system can output controllable damping force. Since effective working area of the stretching chamber and the compression chamber is not equal in the single rod hydraulic cylinder, an accumulator is used to compensate the volume change.

Zoom In Zoom Out Reset image size

As shown in figure 26, an experimental test rig was established to validate the dynamic performance of the improved radial MR valve controlled cylinder system. An INSTRON fatigue test machine provides vibration excitation with different frequencies and displacements for valve controlled cylinder system. The lower end of the hydraulic cylinder is fixed on the fixture of fatigue test machine, and the upper end is connected with the power rod and force transducer. A DC power supply is used to supply power to the excitation coil of the valve. A host computer was used to monitor the relevant test parameters of the experiment system in real time.

Zoom In Zoom Out Reset image size

Figure 27 shows the relationship between the damping force of the presented system and piston displacement of the hydraulic cylinder under different currents. The upper half of the curve represent damping force of the stretching stroke, while the lower half of the curve represents damping force of the compression stroke. Observing figure 27, the damping forces of both the stretching stroke and the compression stroke increase by increasing applied current, the reason is that the pressure drop of the MR valve increases as the current increases. The compression damping force is always greater than the stretching damping force as the effective area of the compression chamber in the single rod cylinder is larger than that of the stretching chamber. The maximum compression damping force is up to 5.8 kN and the maximum stretching damping force is up to 4.2 kN when the applied current is 1.25 A. The increase trend of the damping force is first rapidly and then slowly, which is coincide with the trend of pressure drop of the improved radial MR valve shown in figure 16. The curve of damping force is not full, of which both the stretch and compression stroke have a slight missing. It is explained that a small amount of air was mixed in when the MR fluid is injected into the system.

Zoom In Zoom Out Reset image size

Figure 28 shows the variation of the damping force of the proposed valve controlled cylinder system pertaining to the piston displacement of the hydraulic cylinder under different amplitudes. This damping force increases as the amplitudes increases, and the increase is small. Figure 29 shows the variation of the damping force of proposed valve controlled cylinder system pertaining to the piston displacement of the hydraulic cylinder under different frequencies. The damping force also increased slightly with frequency. The possible reason is that the pressure drop of MR valve consists of viscous pressure drop related to the system flow rate and yield pressure drop related to the applied current in terms of equation (17). The increases of amplitudes and frequencies of piston rod increase the flow rate of MR fluid in the system, leading to the enlargement of the viscous pressure drop. The effects of piston velocity on the damping force are little, and the system can output stable damping forces in a variety of operating conditions.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In order to further explore the application of the improved radial MR valve in different structural hydraulic cylinders, an improved radial MR valve controlled double rod cylinder system was proposed and established as shown in figure 30. It consists of an improved radial MR valve and a double rod hydraulic cylinder. Unlike the improved radial MR valve controlled single rod cylinder system, there is no accumulator in the MR valve controlled double rod cylinder system since the effective working area of the compression chamber is equal to that of the stretching chamber.

Zoom In Zoom Out Reset image size

Figure 31 shows the variation of the damping force of the MR valve controlled double rod cylinder system pertaining to the piston displacement of the hydraulic cylinder at different currents. The damping forces both the stretching stroke and the compression stroke increase with the increasing of applied current, which coincides with figure 27. Conversely, the compression damping force is always equal to the stretching damping force because the effective working area of the compression chamber of the double hydraulic cylinder is equal to that of the stretching chamber. The maximum damping force is close to 3.9 kN. The curve of damping force is not full as well.

Zoom In Zoom Out Reset image size

Figures 32 and 33 show the variation of the damping force of the MR valve controlled double rod cylinder system pertaining to the piston displacement of the hydraulic cylinder under different amplitudes and different frequencies, respectively. The damping force increases slightly with the increasing of frequencies or amplitudes, which agrees with the trend of the valve controlled single rod cylinder system.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size