Development of a new magnetorheological fluid–based brake with multiple coils placed on the side housings

Abstract

In this research, a new configuration of magnetorheological fluid–based brake with multiple coils placed on each side of the brake housing (multiple side-coil magnetorheological fluid–based brake) is proposed, optimally designed, and evaluated. With this configuration, the multiple side-coil magnetorheological fluid–based brake is expected to provide higher braking torque and more compact size than the traditional magnetorheological fluid–based brake. After a brief introduction about the development of magnetorheological fluid–based brake, the configuration of multiple side-coil magnetorheological fluid–based brake is proposed. Braking torque of the proposed magnetorheological fluid–based brake is then analyzed based on the Bingham plastic rheological model of magnetorheological fluid. The optimization of the proposed multiple side-coil magnetorheological fluid–based brake, the magnetorheological fluid–based brake with one coil placed on each side of the brake housing (single side-coil magnetorheological fluid–based brake), and the conventional magnetorheological fluid–based brake is then performed considering maximum braking torque and mass of the brakes. Based on the optimal results, advanced performance characteristics of the proposed magnetorheological fluid–based brake are figured out. In addition, experimental works are conducted to validate the performance of the proposed multiple side-coil magnetorheological fluid–based brake.

Keywords

Magnetorheological fluid (MRF)multiple-coil MR brake side-coil MR brake

Introduction

In the past two decades, research works on the development and application of brake featuring magnetorheological fluid (MRF) have interested many researchers. There has been numerous research works on improving the performance of MRF-based brake (MRB) with different configurations, such as disk-type MRB (An and Kwon, 2003; Liu et al., 2006; Park et al., 2006), drum-type MRB (Huang et al., 2002; Smith et al., 2007), and hybrid-type MRB with T-shaped rotor (Nguyen and Choi, 2010, 2012). To compare the performance of those mentioned above, Nguyen and Choi (2011) investigated the optimal design of different types of MRBs considering their maximum braking torque and specific volume. Later, Nguyen et al. (2014a) evaluated the effect of different shapes of envelop such as the rectangular, the polygonal, and the spline on the performance and the mass of MRBs. Recently, Nguyen et al. (2014b, 2015) proposed a new configuration of MRB in which a magnetic coil is wound on each side of the housing of the MRB (in this research, it is named as single side-coil MRB). The results showed that with this configuration, some disadvantages of the traditional ones such as the “bottle-neck” problem of magnetic flux, the requirement of nonmagnetic bobbin, and the difficulties in manufacturing and maintenance can be eliminated or minimized. In addition, the optimal solutions showed that the mass of the single side-coil MRB was significantly improved in producing the same braking torque as the conventional ones. From the abovementioned, it can be clearly realized that the side-coil configurations have many advantages compared with the conventional one; however, only the single side-coil with one coil on each side of the housing has just been considered. The properties of the side-coil MRBs which have more than one coil on each side of the envelope have not yet been figured out. The main contributions of this research are to investigate the performance of the side-coil MRB with multiple coils on each side of the housing and compare it with the single side-coil MRB and the conventional one. In addition, a comparison of the overall length and radius of the MRBs at different values of required braking torque is obtained and presented. Another contribution is that the optimization of the side-coil MRBs in which power consumption is constrained to be equal to the conventional one and the optimization of the multiple side-coil MRBs in which power consumption is constrained to be equal to the single side-coil one are investigated.

The remainder of the article is structured as follows. Section “MR brake with multiple coils placed on the side housings” shows the proposed configurations of MRBs with multiple coils placed on the side housings and the formulations for calculating their braking torque. Section “Optimization of MRBs based on finite element analysis” presents the optimal design problem and the optimization procedure for the proposed MRBs. Results and discussions are presented in section “Optimal results and discussions.” Finally, some conclusions are drawn in section “Conclusion.”

MR brake with multiple coils placed on the side housings

In this study, a configuration of a disk-type MRB with multi-coils placed on the side housing is proposed. Then, its braking torque is estimated based on the Bingham plastic rheological model of MRF. Figure 1(a) shows a typical conventional MRB and Figure 1(b) presents the single side-coil MRB. In these configurations, a disk (rotor) made of magnetic steel is fastened to the flange of the MRB shaft made of nonmagnetic steel. The disk is embedded inside a stationary envelop (housing) made of magnetic steel. In Figure 1(a), a wire coil is wound on a nonmagnetic bobbin which is fixed to the brake envelop, while in Figure 1(b) the coil is placed on each side of the brake housing (Nguyen et al., 2015). By using the side-coil configuration, it is observed that the coils can be placed directly on the housing. In addition, multiple coils can be implemented, especially for high braking torque MRBs. In this research, multiple side-coil MRBs shown in Figure 2 are considered. In Figure 2(a), the double side-coil MRB with two coils placed on each side of the housing is shown. It is noted that countercurrents are applied to the coils to generate a mutual magnetic field as shown in this figure. In the same way, configuration of the triple side-coil MRB with three coils placed on each side of the housing is shown in Figure 2(b). From the above, configuration of side-coil MRBs with more than three coils placed on each side housing can be also obtained.

From Figures 1 and 2, it is obviously observed that the braking torque of the proposed MR brake comes from two sources: the friction of MRF acting on the two end-faces and on the outer annular face of the disk. First, the friction between MRF and the end-faces of the disk is analyzed. The induced torque from MRF in radial duct acting on one end-face of a disk can be expressed as follows (Nguyen and Choi, 2012)

T_{e} = \int_{A} τ_{e} rdA = 2 π \int_{R_{1}}^{R_{2}} τ_{e} r^{2} dr

(1)

where A is the area of the end-face of the disk, r is the radius of an infinitesimal area of the disk, R₁ and R₂ are the inner and outer radius of the duct. $τ_{e}$ is the shear stress of the MRF at the interface, which can be predicted from the Bingham plastic model of the MRF as follows

τ_{e} = τ_{ye} + μ_{e} {\overset{\cdot}{γ}}_{e}

(2)

where τ_ye and µ_e are, respectively, the yield stress and post-yield viscosity of the MRF. ${\overset{\cdot}{γ}}_{e}$ is the shear rate of MR fluid at the interface. Because the gap size of the duct is very small, the shear rate of MRF in the gap is assumed to be linearly distributed, which can be approximately determined as follows

{\overset{\cdot}{γ}}_{e} = \frac{r Ω}{d}

(3)

where d is the gap size and Ω is the angular velocity of the drum.

Plugging equations (2) and (3) into equation (1), the following equation can be obtained

T_{e} = 2 π \int_{R_{1}}^{R_{2}} r^{2} μ_{e} (\frac{r Ω}{d}) dr + 2 π \int_{R_{1}}^{R_{2}} r^{2} τ_{ye} dr

(4)

Generally, the magnetic density in the MRF gap is a function of radius r; thus, the values of τ_ye and µ_e of the MRF in the gap are also functions of r. Equation (4) then has to be calculated by numerical integration. In order to facilitate the calculation, it is assumed that the magnetic density in the MRF gap is constant, and an average value of the magnetic density obtained from numerical integration is used. In this case, equation (4) can be analytically integrated to yield

T_{e} = \frac{π μ_{e} R_{2}^{4}}{2 d} [1 - {(\frac{R_{1}}{R_{2}})}^{4}] Ω + \frac{2 π τ_{ye}}{3} (R_{2}^{3} - R_{1}^{3})

(5)

The friction torque due to MRF in annular gap acting on the outer circular face of the disk can be determined by

T_{a} = \int_{A_{a}} R_{a} τ_{a} dA = \int_{0}^{L_{a}} R_{a} τ_{a} 2 π R_{a} dl = 2 π R_{a}^{2} \int_{0}^{L_{a}} (τ_{ya} + μ_{a} \overset{\cdot}{γ}) dl

(6)

where A_a is the area of the outer annular face of the disk, L_a and R_a are radius and length of annular duct, τ_a is the shear stress at the annular face of the disk, and τ_ya and µ_a are the yield stress and post-yield viscosity of the MRF in the annular duct. Similar to MRF in the end-face gap, by using average magnetic density obtained from numerical integration and assuming a linear distribution of shear rate in the MRF gap, the following can be obtained

T_{a} = 2 π R_{a}^{2} L_{a} (τ_{ya} + μ_{a} \frac{R_{a} Ω}{d})

(7)

From equations (5) and (7), the induced braking torque of the conventional disk-type MRB and the side-coil ones can be correspondingly obtained (Nguyen and Choi, 2010, 2011; Nguyen et al., 2014, 2015)

\begin{matrix} T_{c} = 2 T_{e} + T_{a} + 2 T_{sf} = \frac{π μ_{e} R_{d}^{4}}{d} [1 - {(\frac{R_{i}}{R_{d}})}^{4}] Ω \\ + \frac{4 π τ_{ye}}{3} (R_{d}^{3} - R_{i}^{3}) + 2 π R_{d}^{2} t_{d} (τ_{y 0} + μ_{0} \frac{Ω R_{d}}{d_{o}}) + 2 T_{sf} \end{matrix}

(8)

\begin{matrix} T_{s 1} = 2 (T_{e 1} + T_{e 2}) + T_{a} + 2 T_{sf} \\ = \frac{π μ_{1} R_{ci}^{4}}{d} [1 - {(\frac{R_{i}}{R_{ci}})}^{4}] Ω + \frac{4 π τ_{y 1}}{3} (R_{ci}^{3} - R_{i}^{3}) \\ + \frac{π μ_{2} R_{d}^{4}}{d} [1 - {(\frac{R_{co}}{R_{d}})}^{4}] Ω + \frac{4 π τ_{y 2}}{3} (R_{d}^{3} - R_{co}^{3}) \\ + 2 π R_{d}^{2} t_{d} (τ_{ya} + μ_{a} \frac{Ω R_{d}}{d_{o}}) + 2 T_{sf} \end{matrix}

(9)

\begin{matrix} T_{s 2} = 2 (T_{e 1} + T_{e 2} + T_{e 3}) + T_{a} + 2 T_{sf} \\ = \frac{π μ_{1} R_{c 1 i}^{4}}{d} [1 - {(\frac{R_{i}}{R_{c 1 i}})}^{4}] Ω + \frac{4 π τ_{y 1}}{3} (R_{c 1 i}^{3} - R_{i}^{3}) \\ + \frac{π μ_{2} R_{c 2 i}^{4}}{d} [1 - {(\frac{R_{c 1 o}}{R_{c 2 i}})}^{4}] Ω \\ + \frac{4 π τ_{y 2}}{3} (R_{c 2 i}^{3} - R_{c 1 o}^{3}) + \frac{π μ_{3} R_{d}^{4}}{d} [1 - {(\frac{R_{c 2 o}}{R_{d}})}^{4}] Ω \\ + \frac{4 π τ_{y 3}}{3} (R_{d}^{3} - R_{c 2 o}^{3}) + 2 π R_{d}^{2} t_{d} (τ_{ya} + μ_{a} \frac{Ω R_{d}}{d_{o}}) + 2 T_{sf} \end{matrix}

(10)

\begin{matrix} T_{s 3} = 2 (T_{e 1} + T_{e 2} + T_{e 3} + T_{e 4}) + T_{a} + 2 T_{sf} \\ = \frac{π μ_{1} R_{c 1 i}^{4}}{d} [1 - {(\frac{R_{i}}{R_{c 1 i}})}^{4}] Ω + \frac{4 π τ_{y 1}}{3} (R_{c 1 i}^{3} - R_{i}^{3}) \\ + \frac{π μ_{2} R_{c 2 i}^{4}}{d} [1 - {(\frac{R_{c 1 o}}{R_{c 2 i}})}^{4}] Ω + \frac{4 π τ_{y 2}}{3} (R_{c 2 i}^{3} - R_{c 1 o}^{3}) \\ + \frac{π μ_{3} R_{c 3 i}^{4}}{d} [1 - {(\frac{R_{c 2 o}}{R_{c 3 i}})}^{4}] Ω + \frac{4 π τ_{y 3}}{3} (R_{c 3 i}^{3} - R_{c 2 o}^{3}) \\ + \frac{π μ_{4} R_{d}^{4}}{d} [1 - {(\frac{R_{c 3 o}}{R_{d}})}^{4}] Ω + \frac{4 π τ_{y 4}}{3} (R_{d}^{3} - R_{c 3 o}^{3}) \\ + 2 π R_{d}^{2} t_{d} (τ_{ya} + μ_{a} \frac{Ω R_{d}}{d_{o}}) + 2 T_{sf} \end{matrix}

(11)

\begin{matrix} T_{sN} = \frac{π μ_{1} R_{c 1 i}^{4}}{d} [1 - {(\frac{R_{i}}{R_{c 1 i}})}^{4}] Ω + \frac{4 π τ_{y 1}}{3} (R_{c 1 i}^{3} - R_{i}^{3}) \\ + \sum_{j = 2}^{N} {\frac{π μ_{j} R_{cji}^{4}}{d} [1 - {(\frac{R_{c (j - 1) o}}{R_{cji}})}^{4}] Ω + \frac{4 π τ_{yj}}{3} (R_{cji}^{3} - R_{c (j - 1) o}^{3})} \\ + \frac{π μ_{(N + 1)} R_{d}^{4}}{d} [1 - {(\frac{R_{c (N + 1) o}}{R_{d}})}^{4}] Ω \\ + \frac{4 π τ_{y (N + 1)}}{3} (R_{d}^{3} - R_{cNo}^{3}) + 2 π R_{d}^{2} t_{d} (τ_{ya} + μ_{a} \frac{Ω R_{d}}{d_{o}}) + 2 T_{sf} \end{matrix}

(12)

The off-state force (the torque of the MRB when no magnetic field is applied to MRF) of all considered MRBs can be expressed as (Nguyen et al., 2015)

\begin{matrix} T_{0} = \frac{π μ_{0} R_{d}^{4}}{d} [1 - {(\frac{R_{s}}{R_{d}})}^{4}] Ω + \frac{4 π τ_{y 0}}{3} (R_{d}^{3} - R_{s}^{3}) \\ + 2 π R_{d}^{2} t_{d} (τ_{y 0} + μ_{0} \frac{Ω R_{d}}{d_{o}}) + 2 T_{sf} \end{matrix}

(13)

where T_c is the braking torque of the conventional MRB, T_sN is the braking torque of the side-coil MRB with N coils placed on each side of the housing, T₀ is the off-state torque of MRBs, T_sf is the friction torque between the shaft of the brake and the sealing, R_d is the outer radius of the disk, R_i is the inner radius of the active MRF volume in the end-face duct, R_s is the shaft diameter at the sealing, d is the gap size of the end-face MRF ducts between the disk and the housing, d_o is the gap size of the annular MRF duct at the outer cylindrical face of the disk, t_d is the thickness of the disk, R_ci and R_co are the inner and outer radius of the coil in case of the single side-coil MRB, R_cji and R_cjo are the inner and outer radius of the jth coil, Ω is the angular velocity of the rotor, µ_e and τ_ye are, respectively, the average post-yield viscosity and yield stress of MRF in the end-face duct of the conventional MRB, µ_j is the average post-yield viscosity of the jth active MRF volume (denoted by MRFj in Figures 1 and 2) in the end-face duct of the side-coil MRBs while τ_yj is the corresponding yield stress, µ_a and τ_ya are, respectively, the average post-yield viscosity and yield stress of MRF in the annular duct of the side-coil MRBs, and τ_y₀ and µ₀ are the zero-field yield stress and viscosity of the MRF. The rheological properties of MRF such as the induced yield stress τ_ye, τ_yj, τ_ya and the corresponding average post-yield viscosity µ_e, µ_j, µ_a depend on the exerted magnetic flux density across the active MRF volumes and can be approximated by (Zubieta et al., 2009)

Y = Y_{\infty} + (Y_{0} - Y_{\infty}) (2 e^{- B α_{SY}} - e^{- 2 B α_{SY}})

(14)

where Y represents the rheological parameters of MRF such as the yield stress and the post-yield viscosity; $Y_{0}$ and $Y_{\infty}$ , respectively, represent the value of Y in the absence of magnetic field and in saturated state of MRF; α_SY is the saturation moment index of the Y parameter; and B is the applied magnetic density. The sealing used in this study is the lip seal from Parker Corporation. From the manual book of Parker Corporation, the friction torque of the seal T_sf can be approximately estimated by (Nguyen et al., 2015)

T_{sf} = 0.65 {(2 R_{s})}^{2} Ω^{1 / 3}

(15)

In the above, T_sf is the friction torque of a lip seal in ounce-inches, Ω is the rotation speed of the brake shaft measured in rounds per minute, and R_s is the shaft diameter at the sealing measured in inches.

Optimization of MRBs based on finite element analysis

In this part, the optimal design problem of the conventional, the single side-coil, and the proposed multi-coil MRBs is investigated. In design of MRBs, maximizing braking torque and reducing mass are two opposite objectives. With a specific required braking torque, the mass of the MRBs should be as small as possible in order to decrease the MRB size and cost (Le-Duc et al., 2016; Nguyen et al., 2015). Therefore, in this article, the optimal objective is to find the lightest design of the MRBs which can achieve the required braking torque. Generally, the MRB mass can be approximately calculated by (Nguyen et al., 2015)

m_{b} = V_{d} ρ_{d} + V_{h} ρ_{h} + V_{s} ρ_{s} + V_{MR} ρ_{MR} + V_{bob} ρ_{bob} + V_{c} ρ_{c}

(16)

where V_d, V_h, V_s, V_MR, V_bob, and V_c are, respectively, the geometric volume of the disk, the housing, the shaft, the MRF, the bobbin, and the coil of the brake; ρ_d, ρ_h, ρ_s, ρ_MR, ρ_bob, and ρ_c are correspondingly density of the disks, the housing, the shaft, the MRF, the bobbin in case of conventional MRB (in case of the side-coil MRBs, this term is eliminated), and the coil material.

In order to determine the braking torque of the MRBs, first, finite element analysis (FEA) is used to evaluate the magnetic density across the ducts of MRF. In detail, the finite element models using two-dimensional (2D) axisymmetric couple element (PLANE 13) of commercial ANSYS software are applied to solve the magnetic circuits of the MRB. After that, the induced MRF rheological properties in the ducts such as the yield stress (τ_ye, τ_yj, τ_ya,) and the post-yield viscosity (µ_e, µ_ej, µ_a) are calculated by equation (6) via the average magnetic density and its initial rheological parameters. From the obtained values of all the abovementioned parameters, the on-state of each MRB can be then estimated by equations (8) to (12), and the off-state torque can be calculated by equation (13). The mass of the MRBs which is also the objective function of MRB optimal design problem is determined from the computer-aided design (CAD) model of the MRBs in ANSYS software and updated in each optimization loop. In this research, the optimization procedure is conducted using the first-order optimization method with the gradient decent algorithm. A detailed description of this algorithm integrated with ANSYS software is shown in previous research (Nguyen and Choi, 2009; Nguyen et al., 2007).

Optimal results and discussions

In this section, the optimal results of all considered MRBs are obtained and some necessary discussions are presented in detail. The commercial silicon steel is used in the magnetic components of the MRB, such as the housing and the disk. The commercial MRF which is used in this research is MRF132-DG made by Lord Corporation. From experimental results at different values of magnetic density, the relevant parameters to determine the rheological properties of the MRF132-DG such as yield stress and post-yield viscosity using equation (14) are determined using the least square curve fitting method. The results are as follows (Nguyen et al., 2015): $μ_{0} = 0.1 Pa s$ , $μ_{\infty} = 3.8 Pa s$ , $τ_{y 0} = 15 Pa$ , $τ_{y \infty} = 40, 000 Pa$ , $α_{s μ} = 4.5 T^{- 1}$ , and $α_{s t_{y}} = 2.9 T^{- 1}$ . The copper coil wires are sized as24-gauge (diameter = 0.511 mm) whose maximum working current is around 3 A, and during the optimization process, a current of 2.5 A is applied to the coil. The cross section of the coils is rectangular and its geometric dimensions are calculated by (Le-Duc et al., 2016)

\begin{matrix} w_{c} = \frac{n_{w} d_{c}}{ξ_{_{w}}} \\ h_{c} = \frac{n_{h} d_{c}}{ξ_{_{h}}} \end{matrix}

(17)

where w_c and h_c are, respectively, the height and the width of the coil; n_w and n_c are the corresponding number of wire layers; ξ_w and ξ_h are the corresponding filling ratio in the width and the height direction which is set to 0.9 in this study; and d_c is the diameter of the wire. In ANSYS software, an excitation current density is applied to the coils. Assuming that the coils are wound by layers aligned to each other, the applied current density is calculated as follows (Le-Duc et al., 2016)

j = \frac{NI}{S_{coil}} = \frac{n_{w} . n_{h} I}{w_{c} . h_{c}} = ξ_{w} ξ_{h} \frac{I}{d_{c}^{2}} = 0.81 \frac{I}{d_{c}^{2}}

(18)

where N and S_coil are correspondingly the number of turns in the winding and the cross-sectional area of the coil.

In the optimization, the design variables are significant geometric dimensions of the MRBs such as the coil height (h_c, h_cj), the coil width (w_c, w_cj), the inner radius of the disk R_i, the outer radius of the disk R_d, and the disk thickness t_d. Outer radius of the brake R, the housing thickness t_h_, and the inner radius of the coils in case of the side-coil MRBs R_ci are considered as design variables. It is noted that in design of MRB, the gap size of the MRF ducts should be as small as possible considering the manufacturing availability and cost. Therefore, during the optimization process, the MRF gap size is not considered as a design variable and fixed at a certain value. In this research, two typical values of the gap size, which are 0.8 and 1.0 mm, are considered. The braking torque is constrained to be greater than 10 N m with 2% accuracy and the convergence rate is set to 0.1%. It is also noted that the shaft radius is set to R_s = 6 mm considering the strength of the shaft. In order to solve the magnetic circuit of the MRBs, the finite element model using 2D axisymmetric couple element (PLANE 13) of ANSYS software as shown in Figure 3 is used.

The optimal solutions of the MRBs are summarized in Table 1. In this table, it is seen that the mass of the side-coil MRBs is significantly smaller than the conventional one; however, its power consumption is significantly increased. It is also noted that the width of the coils in case of double side-coil MRB is almost similar. In case of triple side-coil MRB, the width of middle and outer coils is almost the same, while the width of the inner coil is smaller. However, the difference is not very much (around 0.3 mm), which is smaller than the diameter of the coil wire used (0.51 mm). Therefore, in practical, it is suggested that the width of the coils should be set equal to each other to facilitate the optimal design and manufacturing. Figure 4 shows optimal solutions of the MRBs with coils placed on the side housings. From Figure 4(a), it is seen that the mass of the optimized conventional MRB is 1.69 kg. As shown in Figure 4(b), for single side-coil MRB, the minimum mass is 1.67 kg which is a bit smaller than that of the conventional one. Figure 4(c) shows the optimal solution of the double side-coil MRB. It is observed that the minimum mass is 1.34 kg which is significantly smaller than that in case of single side-coil MRB. From Figure 4(d), it is found that the minimum mass is 1.26 kg, which is a bit smaller than that of the double side-coil one. Figure 5 shows the magnetic density distribution of the MRBs at their optimal solution. From Figure 5(a) and 5b, it is observed that the magnetic distribution in the housing of the side-coil MRBs is more uniform than that of the conventional one. This results in a more compact size of the side-coil MRB as mentioned above. From Figure 5(b) to (d), it is observed that if more coils are used, more uniform magnetic distribution density in the housing can be obtained.

Table 1.

Optimal solution of the MRBs when the required torque is 10 N m and the MRF duct gap is 0.8 mm.

MRB types	Design parameter (mm)	Characteristics
Conventional	Coil: Width w_c = 6.6; height h_c = 4.7; radius R_b = 54.2; no. of turns: 96 Housing: R_s = 6, R = 65.2, t_h = 7.2, L = 20 Disk: Radius R_i = 13, R_d = 53; thickness t_d = 4 MRF duct gap: 0.8	Maximum torque: 10 N m Mass: 1.69 kg Off-state Torque: 0.08 N m Power consumption: 15.1 W Coil resistance (Ω): R_c = 2.43
Single coil	Coil: Width w_c = 2.83; height h_c, = 9.67; radius R_ci = 40.57; no. of turns: 2 ×83 = 186 Housing: R_s = 6, R = 56.3, t_h = 6.84, L = 22.7 Disk: Radius R_i = 25.5, R_d = 54.0; thickness t_d = 7.95 MRF duct gap: 0.8	Maximum torque: 9.93 N m Mass: 1.67 kg Off-state torque: 0.09 N m Power consumption: 22.2 W Coil resistance (Ω): R_c = 1.78
Double coil	Coil: Width w_c₁ = 2.8, w_c₂ = 2.7; height h_c₁ = 6.7; h_c₂ = 7.3; radius R_c_1i = 28.8, R_c_2i = 47.5; no. of turns: 2 × (58 + 61) = 238 Housing: R_s = 6, R = 59.8, t_h = 5.0, L = 15.9 Disk: Radius R_i = 17.3, R_d = 57.5; thickness t_d = 4.3 MRF duct gap: 0.8	Maximum torque: 10.1 N m Mass: 1.34 kg Off-state torque: 0.1 N m Power consumption: 27.8 W Coil resistance (Ω): R_c₁ = 0.8, R_c₂ = 1.4
Three- coil	Coil: Width w_c₁ = 2.8, w_c₂ = 2.5, w_c₃ = 2.45; height h_c₁ = 6.6; h_c₂ = 7.2; h_c₃ = 7.4; radius R_c_1i = 15.6, R_c_2i = 31.7, R_c_3i = 48.2; no. of turns: 2 × (78 + 84 + 84) = 492 Housing: R_s = 6, R = 59.6, t_h = 4.9, L = 15.5 Disk: Radius R_i = 8.6, R_d = 58.1; thickness t_d = 4 MRF duct gap: 0.8	Maximum torque: 10 N m Mass: 1.28 kg Off-state torque: 0.08 N m Power consumption: 40.7 W Coil resistance (Ω): R_c₁ = 0.5, R_c₂ = 1.1, R_c₃ = 1.6

MRB: magnetorheological fluid–based brake; MRF: magnetorheological fluid.

In order to investigate the characteristics of the MRBs as a function of maximum achievable braking torque, optimal solutions of the MRBs at different values of required (constrained) braking torque are obtained in the same manner as that in case of 10 N m and are shown in Figure 6. From Figure 6(a), it is seen that at small values of required braking torque (≤5 N m), the mass of all MRBs is almost similar. In addition, the mass of single side-coil MRB is almost the same as that of the conventional one with the required braking torque being smaller than 50 N m. With some values of the braking torque being higher than 50 N m, the mass of the single side-coil MRB is a bit smaller than that of the conventional one. It is also observed that the mass of double side-coil and triple side-coil MRBs is significantly smaller than that of the single side-coil and the conventional ones in the case of the required braking torque being greater than approximately 5 N m. From Figure 6(b), it is observed that the off-state torque of the conventional MRB is generally smaller than that of the side-coil MRBs. In addition, the more coils are used in MRB systems, the greater the off-state torques are resulted. This is mainly due to a larger diameter of the disk being required for multi-side-coil MRBs, which is presented in Figure 6(c). In Figure 6(d), it can be realized that the width of the double and the triple side-coil MRBs is significantly smaller than that of the conventional and the single side-coil ones. This is the reason that the mass of the multiple side-coil MRBs is smaller than that of the rest. As aforementioned, the power consumption of the side-coils MRBs is significantly greater than that of the conventional one, especially the multiple side-coil MRBs. This is more clearly presented in Figure 6(e). Noteworthily, power consumption is also a critical issue. The high power consumption will result in a high temperature of the MRBs, which may degrade the braking performance (maximum working temperature of most of commercial MRFs is limited to 130°C). Therefore, the temperature issue should be taken into account for each specific application of the MRBs (Nguyen and Choi, 2010, 2012). In addition, in many applications, electric power is limited and should be as small as possible such as in haptic systems. In order to take power consumption of the MRBs into account, optimal solutions of the side-coil MRBs with power consumption constrained to be equal to that of the conventional one are obtained and presented in Figure 7. It is observed that in case of power consumption constraint, the mass of the double and triple MRBs is significantly increased while that of the single side-coil MRB is slightly increased compared to that in case of no power consumption constraint shown in Figure 6. In this case, the mass of the double MRB is almost equal to that of conventional one and a bit smaller than that of the single and triple MRBs. This correspondingly leads to a significant increase in the overall length. Besides, the overall radius of the side-coil MRBs is also increased in case of power consumption constraint. However, there is a slight increase in the overall radius.

In order to evaluate the effects of the MRF duct size on performance characteristics of all considered MRBs, the optimal design procedure is generated with the MRF duct size being 1.0 mm. The optimal solutions in this case are presented in Figure 8. In this figure, it can be seen that almost the conclusions in this case are equivalent to the one in the case having an MRF duct of 0.8 mm. Obviously, the mass, the outer radius, the width, and the power consumption of all optimal MRBs in this case are greater than those in the previous case. However, the off-state torque is somewhat smaller, which can reduce the heat friction generating in the MRF duct. As abovementioned, it is realized that the duct size of MRF has an important role in the performance of MRBs. Therefore, choosing suitable values for MRF duct size is a critical issue which should be determined carefully when considering the mass and the thermal effect simultaneously in the MRB optimal design problem. Similar to the case of 0.8 mm MRF duct, in this case optimal solutions of the side-coil MRBs with power consumption constrained to be equal to that of the conventional one are obtained and presented in Figure 9. From the results, similar conclusions can be achieved.

In order to have a better comparison between the single side-coil MRB and the multiple ones when power consumption is taken into account, optimal solutions of the multiple side-coil MRBs with power consumption constrained to be equal that of the single side-coil one are obtained and presented in Figure 10. In this case, it is observed that the mass of the double and triple MRB is significantly increased compared to that in case of no constraint on power consumption. However, the mass of the multiple side-coil MRBs is still smaller than that of the single one, especially when the braking torque is higher than 20 N m.

In order to validate the above optimal results, the prototypes of the optimized MRB are manufactured and some relative results are also presented here. In this study, the experiments are performed for a prototype of single side-coil MRB, a prototype of double side-coil MRB, and a prototype of triple side-coil MRB. For the single and double side-coil MRBs, optimal results of the MRBs with a required braking torque of 10 N m shown in Table 1 are implemented. In order to investigate the actual performance of MRBs at higher braking torque, the prototype of triple side-coil MRB with a required braking torque of 70 N m is considered, and its optimal design parameters are shown in Table 3. Figure 11 shows some major parts of the prototype MRBs. It is reminded that, in the prototypes, first the coils are wound using outside bobbins and then they are taken off the bobbins and placed directly on the side housings of the MRBs. For convenience in manufacturing, some actual parameters of the prototypes are a bit different from the optimal ones. The actual parameters of the manufactured prototypes of single and double MRBs are shown in Table 2, while those of the triple MRBs are shown in Table 3. Figure 12 shows the experimental setup for testing the performance of the abovementioned prototypes. In this experimental system, a gear-box DC motor controlled by a computer revolves the shaft of the MRB rotor at a constant angular speed of 4π rad/s. A torque sensor is used to measure the torque generated by the MRB. Through the A/D converter, the analog output signal which is produced by the torque sensor is then sent to the computer for evaluation. When the experiment process is stated, a step current signal generated from the computer is provided to the current amplifier and the amplified step current from the amplifier is then applied to the coils of the MRBs.

Table 2.

Parameters of the manufactured single and double side-coil MRB prototypes.

MRB types	Design parameter (mm)	Characteristics
Single coil	Coil: Width w_c = 2.8; height h_c, = 9.6; radius R_ci = 40.5; no. of turns: 2 × 80 = 160 Housing: R_s = 6, R = 55.6, t_h = 6.9, L = 23 Disk: Radius R_i = 21.5, R_d = 53.1; thickness t_d = 8.05 MRF duct gap: 0.8	Maximum torque: 9.85 N m Mass: 1.71 kg Off-state Torque: 0.39 N m Coil resistance (Ω): R_c = 1.7
Double coil	Coil: Width w_c₁ = 2.8, w_c₂ = 2.8; height h_c₁ = 6.7; h_c₂ = 7.3; radius R_c_1i = 28.8, R_c_2i = 47.5; no. of turns: 2 ×(56 + 62) = 236 Housing: R_s = 6, R = 59.8, t_h = 5.0, L = 15.9 Disk: Radius R_i = 17.3, R_d = 57.5; thickness t_d = 4.3 MRF duct gap: 0.8	Maximum torque: 10.1 N m Mass: 1.45 kg Off-state Torque: 0.41 N m Coil resistance (Ω): R_c₁ = 0.75, R_c₂ = 1.3

MRB: magnetorheological fluid–based brake; MRF: magnetorheological fluid.

Table 3.

Parameters of the triple side-coil MRB prototype.

MRB types	Design parameter (mm)	Characteristics
Optimal design results	Coil: Width w_c₁ = 3.1, w_c₂ = 2.9, w_c₃ = 2.54; height h_c1 = 8.2; h_c₂ = 9.1; h_c₃ = 9.7; radius R_c_1i = 56.4, R_c_2i = 79.6, R_c_3i = 101.1; no. of turns: 2 × (60 + 66 + 70) = 392 Housing: R_s = 10, R = 116, t_h = 4.85, L = 15.7 Disk: Radius R_i = 32.1, R_d = 113.4; thickness t_d = 4.4 MRF duct gap: 0.8	Maximum torque: 70.1 N m Mass: 4.98 kg Off-state Torque: 0.98 N m Power Cons.: 110 W Coil resistance (Ω): R_c₁ = 1.9, R_c₂ = 2.95, R_c₃ = 3.94
Actual parameters	Coil: Width w_c₁ = w_c₂ = w_c₃ = 2.9; height h_c₁ = 8.2; h_c₂ = 9.1; h_c₃ = 9.7; radius R_c_1i = 56.4, R_c_2i = 79.6, R_c_3i = 101; no. of turns:2 × (60 + 65 + 70) = 390 Housing: R_s = 10, R = 116, t_h = 4.9, L = 15.8 Disk: Radius R_i = 32, R_d = 113.2; thickness t_d = 4.4 MRF duct gap: 0.8	Maximum torque: 68.5 N m Mass: 5.16 kg Off-state torque: 1.1 N m Coil resistance (Ω): R_c₁ = 1.95, R_c₂ = 3.0, R_c₃ = 3.9

Figure 13 shows step response of the single side-coil MRB prototype at the time of 0.5 s. Eight step currents are investigated, which are 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, and 2.5 A. In Figure 13(a), the measured current applied to the coil is presented. It is observed from the figure that at steady state, the average measured currents are almost equal to the desired ones which are, respectively, 0.49, 0.746, 0.99, 1.24, 1.49, 1.756, 2.01, and 2.492 A. It is also observed that the steady values of the measured current are almost achieved at the time of 0.7 s for all cases; thus, the current response time is around 0.2 s. From Figure 13(b), it is observed that the maximum braking torque of the prototype MRB at the applied current of 2.5 A is around 9.5 N m which is a bit smaller than that from the simulation (9.9 N m). The error is around 4% in this case. The main reason may come from inaccurate estimation of the friction torque, braking torque, and loss of magnetic field to the ambient and at the contact between the magnetic parts of the MRBs. In addition, a slight difference between the design and the manufactured prototype is also a potential reason. At different values of the applied current, a good agreement between the manufactured and the simulated one is also achieved. The average braking torques at the applied currents of 0.5, 0.75, 1.0, 1.25, 1.5A, 1.75, and 2.0 A are, respectively, 1.56, 2.64, 3.75, 5.21, 6.65, 8.1, and 8.7 N m, while those from the simulation as shown in Figure 13(c) are 1.5, 2.6, 3.9, 5.3, 6.7, 7.9, and 8.9 N m, respectively. The corresponding errors are 4%, 1.54%, 3.85%, 1.7%, 0.75%, 2.53%, and 2.25%. From Figure 13(b), it is also found that the steady values of the measured torque are almost achieved at the time of 0.82 s for all cases; thus, the torque response time is around 0.32 s. The larger response time of the measured torque compared to that of the measured current comes from the time response of the MRF, the hysteresis of mechanical system, and the torque measurement.

Figure 14 shows the step response of the double side-coil MRB prototype. From Figure 14(a), it is observed that at steady state, the average measured currents are almost equal to the desired ones, which are, respectively, 0.482, 0.745, 0.984, 1.234, 1.48, 1.75, 2.02, and 2.484 A. The current response time is around 0.24 s which is a bit greater than that of the single side-coil MRB. This comes from larger time constant of the resistor–inductor (R-L) circuit of the double side-coil MRB. (It is noted that in this research, the two coils at each side of the brake are connected in series.) From Figure 14(b), a good agreement between the manufactured and the simulated one is observed. The average braking torques at the applied currents of 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, and 2.5 A are, respectively, 1.26, 2.4, 3.6, 4.74, 6.14, 7.1, 8.13, and 10.04 N m, while those from the simulation as shown in Figure 14(c) are 1.2, 2.3, 3.5, 4.7, 6.0, 7.2, 8.25 and 10.1 N m, respectively. The corresponding errors are 5%, 4.34%, 2.85%, 0.85%, 2.33%, 1.39%, 1.45%, and 0.6%. From Figure 14(b), it is also found that the steady values of the measured torque are almost achieved at the time of 0.84 s for all cases; thus, the torque response time is around 0.34 s.

Figure 15 shows the step response of the triple side-coil MRB prototype. The average measured currents observed from Figure 15(a) are, respectively, 0.488, 0.748, 0.994, 1.24, 1.49, 1.754, 2.01, and 2.486 A. The current response time is around 0.25 s which is a bit greater than that of the single and the double side-coil MRBs. From Figure 15(b), a good agreement between the manufactured and the simulated one is observed. The average braking torques at the applied currents of 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, and 2.5 A are, respectively, 11.7, 18.9, 29.08, 40.0, 50.8, 57.73, 63.0, and 67.93 N m, while those from the simulation as shown in Figure 14(c) are 11.5, 18.9, 29.3, 39.8, 49.8, 57.9, 63.5, and 70.1 N m, respectively. The corresponding errors are 1.74%, 0.53%, 0.75%, 0.5%, 2.0%, 0.3%, 0.8%, and 3.09%. In this case, the error is smaller than that in the previous cases. It is obvious that at high braking torque, the percentage error due to inaccurate estimation of friction torque and the measured data processing are reduced. From Figure 15(b), it is also found that the steady values of the measured torque are almost achieved at the time of 0.88 s for all cases; thus, the torque response time is around 0.38 s.

Conclusion

In this research work, MR brake with multiple coils placed on each side of housing, which was referred to as side-coil MRB, was proposed and investigated. After the introduction of MRB development, configuration of the proposed side-coil MRB with multiple coils was presented. Based on the Bingham rheological model of the MR fluid, braking torque of the single side-coil MRB, double side-coil MRB, and the side-coil MRB with three or more coils placed on each side of the housing was derived. The optimization of the MRBs was then conducted based on magnetic finite element solution using ANSYS software. The optimal results showed that with a required braking torque greater than 5 N m, the mass of multiple side-coil MRBs is significantly smaller than that of the single side-coil MRB and the conventional MRB. It was also shown if more coils are used, then more mass reduction of the MRBs can be achieved, especially at high value of required braking torque. However, more coils result in more power consumption, which should be taken into account in reality. Simulation with power constraint showed that at the same power consumption, the mass of the double MRB is almost equal to that of conventional one and a bit smaller than that of the single and triple MRB. In addition, simulation with power constraint only for side-coil MRBs showed that the mass of the multiple side-coil MRBs is still smaller than that of the single one, especially when the braking torque is higher than 20 N m.

Experiment results on single side-coil and double side-coil MRB prototypes of 10 N m maximum torque and triple side-coil MRB prototype of 70 N m maximum torque showed that the braking torque of the prototype MRBs well agreed with calculated ones. For all cases, the errors were smaller than 5%. It was also observed that the error from inaccurate estimation of friction torque was very significant, especially as small braking torque. In addition, it was observed that the time response due to R-L circuit of the coils played an important role in time response of the MRBs. Therefore, in order to improve time response of the MRBs, the coils should be powered in parallel. However, the parallel circuit required a power system with high output current.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant no. 107.01.2015.32

ORCID iD

Ngoc Diep Nguyen

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