**2. General description of M.R. devices**

The magnetorheology (M.R.) device is a device that implements intelligent materials as a working medium such as magnetorheological fluids (MRFs) and magnetorheological elastomers (M.R.E.s). M.R. devices are types of the controllable (semi-active) category. During its development, this device has been developed into a working medium such as M.R. damper, brake, and mounting for various applications. On the commercialization side, this device is not popular enough because of several things such as higher costs, more difficult production levels, and still under development. However, compared to other types of devices in its application (active and passive), M.R. devices have more advantages. MRFs and M.R.E.s are materials that are often used for research and development of M.R. devices.

As new technologies are developed, these materials have been discovered and developed in several applications. This material is unique because external stimuli can alter it. In this case, magnetorheological fluids are materials with properties that can be controlled by magnetic fields [16]. The MR fluids condition can be altered by using a varying magnitude of the magnetic field. This fluid is composed of magnetic particles that are pressed into a viscosity fluid. The absence of a magnetic field in this fluid causes its lower viscosity. These particles have a tiny size, ranging from 3 to 10 microns [17]. The magnetic particles of M.R. fluids are equipped with a special coating to weaken their magnetism and reduce the tendency to bond with each other between the particles. One of the weaknesses in M.R. fluid is the deposition, which occurs due to differences in density and gravitational force so that the fluid only focuses on the point where it is treated. Another disadvantage is the possibility of leakage into unwanted areas in the mechanism and thickening after long-term use, so component replacement is required. However, the application of M.R. fluid is extensive due to its precise control capabilities and dynamic response [17, 18]. The resulting output is relatively faster and more accurate because it uses an electric current as a conductor when compared to conventional mechanical mechanisms [19].

The structure and properties of the M.R. fluid outside or under the influence of the magnetic field are shown in **Figure 1**. The changes that occur when the M.R. fluid is under the influence of a magnetic field occurs in less than ten milliseconds. M.R. fluids regain their properties in the temperature range − 40 to 150 C, while the yield points of M.R. fluids range from 50 to 100 kPa [20].

The particle chain blocks the flow and converts the liquid to a semi-solid state in milliseconds. This phenomenon develops yield stress which increases with the magnitude of the applied magnetic field [21]. M.R. devices typically consist of hydraulic cylinders containing micron-sized magnetically polarized particles suspended in the fluid [17, 18].

#### **Figure 1.**

*Structures of M.R. fluid, ferromagnetic particles in silicon oil suspension: (a) without magnetic field effect, and (b) with magnetic field effect [17].*

M.R. fluids work in several modes, including shear mode, valve mode, and squeeze mode [22]. MRF has been widely applied through shear mode and valve mode. Meanwhile, the application of MRFs which work with the new squeeze mode, has recently been developed. Also, MRFs can be operated in a combination of common MRFs working modes.

The shear mode is an operating mode in which the MRFs are influenced by a magnetic field between two parallel surfaces. One of the surfaces will move, and the other will be in a fixed condition. The shear mode is mostly applied to brakes and clutches. However, some dampers use a shear mode. The second is flow mode or valve mode; this mode is an operating mode in which the MRFs flow between two parallel surfaces that are at rest and simultaneously subjected to a magnetic field perpendicular to the direction of flow. Many applications of valve mode are found in dampers. Squeeze mode is an operational mode in which the MRFs flow-through two parallel surfaces and are subjected to a magnetic field that is perpendicular to the direction of flow. Squeeze mode is different from shear mode, the force exerted by one of the surfaces is the compression force, while in the shear mode it provides the shear force. **Figure 2** shows an illustration of the working principle of each MRFs working mode.

The commercialization of the use of MRFs technology was first used in 1995 for braking on stationary bicycles. MRFs technology tends to be cheaper and easier to use when compared to previous eddy-current-based braking technologies [24]. The world is full of potential applications for MRFs. Systems that require fluid motion control by changing viscosity, solutions based on MRFs technology may be applied to save functionality as well as costs. Simple and smart technology that can produce better products is the crucial factor of MRFs technology. Superior features such as fast response, simple application of electrical power input and mechanical power output, and controllability make MRFs technology the choice of many engineering

**Figure 2.** *MRFs working mode; (a) shear mode; (b) flow mode; (c) squeeze mode [23].*

*Finite Element Magnetic Method for Magnetorheological Based Actuators DOI: http://dx.doi.org/10.5772/intechopen.94223*

technologies. The sliding mode (used in brake and clutch) and valve mode (used in shock breakers) have been thoroughly studied, and several products are already on the market [25].

Besides MRFs, magnetorheological elastomers (M.R.E.s) are also intelligent materials that are currently a topic of development. In the last 20 years, the number of publications related to the creation, characterization, and application of M.R.E. has increased significantly. This significant increase occurred after 1995 regarding the viscoelasticity properties of M.R.E. initiated by Rigby and Jilken in their 1983 publication [26] when it is compared with the number of publications in the field of MRF and MRF applications.

The development of intelligent components based on M.R.E.s must pay attention to the composition of M.R.E.s because it can be formed with a variety of fill materials. The characteristics of the pre-blended matrix greatly influence the physical properties of M.R.E.s, which can make M.R.E.s solid or hollow. However, in general, M.R.E.s use a non-hollow matrix. To obtain a non-hollow matrix, the degassing method can be used to remove air bubbles or voids in the matrix. The magnetizable particles have an essential role in the magnetic induction properties of M.R.E.s. Much research has focused on these magnetized particles to achieve better rheological properties. Particles that are generally used are iron particles because they have a high permeability value and can be magnetized well [27]. M.R. effect is greatest due to the relationship between iron particles, this property can be achieved with high permeability and particle saturation. However, high saturation is also followed by an increase in the residual magnetic field that appears [28]. Therefore, the use of alloy particles in M.R.E.s, such as iron and cobalt or nickel alloys, is not as widely used as the use of C.I.P. The residual magnetic field in the particles will remain after the magnetic field has been lost so that the M.R. properties cannot return to their original state [29]. The size of the particles must be considered because it affects the properties of M.R.E. in receiving several magnetic domains.

#### **3. Reluctance circuit for M.R. devices**

Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is defined as the ratio of magnetomotive force (mmf) to magnetic flux. It represents the opposition to magnetic flux and depends on the geometry and composition of an object.

Magnetic reluctance in a magnetic circuit is analogous to electrical resistance in an electrical circuit in that resistance is a measure of the opposition to the electric current. The definition of magnetic reluctance is analogous to Ohm law in this respect. However, the magnetic flux passing through a reluctance does not give rise to the dissipation of heat as it does for current through a resistance. Thus, the analogy cannot be used for modeling energy flow in systems where energy crosses between the magnetic and electrical domains. An alternative analogy to the reluctance model, which correctly represents energy flows is the gyrator– capacitor model. The magnetic circuit is derived using Kirchoff law, as illustrated in **Figure 3** [30, 31].

The symbols 1 dan Mrfluid are used to illustrate the reluctance of the design. So that it can be obtained as in the Eq. (1):

$$\Re = \frac{L}{\mu A} \tag{1}$$

**Figure 3.** *Illustration of reluctance circuit on M.R. device.*

where *L* is the effective distance that magnetic flux passes in each slice, μ is the magnetization property, and *A* is the effective area of the magnetic flux. Eq. 2 shows the total magnetomotive force generated from the sum of the magnetomotive force on all parts contained in one loop. So that we get the direct magnetomotive force for magnetic flux and reluctance as illustrated below,

$$
\left(\Phi\_1 + \Phi\_2 - \left(2\Re\_1\right) - \left(2\Re\_{surfluid}\right)\right) = \mathbf{0} \tag{2}
$$

Magnetic flux depends on a large number of copper coils and the current flowing in the coil so that Eq. (2) can be rewritten as Eq. (3),

$$NI - \left(\mathfrak{R}\mathfrak{R}\_1\right) - \left(\mathfrak{R}\mathfrak{R}\_{mfldid}\right) = \mathbf{0} \tag{3}$$

where *N* and *I* are the numbers of copper turns on the coil and the current flowing in the coil.
