Small-scale MR damper: design, fabrication and evaluation

The results of an experimental investigation on a developed small-scale MR damper for seismic response reduction in buildings are presented in this article. The damper is intended to have a target capacity of 2 kN. The damper was designed and built using the flow mode principle. The MTS servo-hydraulic UTM was used for testing, and the results were obtained as force–velocity and force displacement plots based on real-time data collected by the MTS suite. From the force–displacement curve, energy dissipated by the MR damper for corresponding frequencies has also been determined. To compare the percentage increase in damping force, the force corresponding to all excitation frequencies is obtained and plotted as force velocity. The maximum force was 252.77 N at 1 Hz, and the minimum force was 175.55 N at 0.1 Hz, with the corresponding velocity of 31.22 mm/s at 1 Hz and 3.56 mm/s at 0.2 Hz. The experiment showed that the MR damper’s velocity varies with displacement control and variable excitation frequency. As the excitation frequency/velocity increases, so does the damping force. Furthermore, the energy dissipated by the MR damper increases significantly as the excitation frequency/velocity increases, ranging from 1.72 to 2.43 J, demonstrating that the developed small-scale MR damper is suitable for use as a vibration-control device in structures.


Introduction
Vibration is excessive in civil infrastructure, automotive systems, and industrial equipment. Vibration-control technologies have advanced in recent years. Magneto-rheological dampers and an improved hydraulic damper are used to stop excessive vibrations. Magneto-rheological fluid has replaced damper oil (MR fluid). This MR fluid contains carrier liquid and freely movable magnetic particles. MR fluid operates like damper oil without magnetic fields, and iron particles in a magnetic field generate a chain pattern. This structure dampens extrinsic vibrations in the electromagnetic field created by an electromagnet on the damper piston. Electromagnets have many copper coils, and electrifying the coils creates an electromagnetic field. The MR damper is popular with researchers because it is controllable and uses little electricity. Magneto-rheology is based on how a magnetic field affects fluid rheology. Magnetic fields abruptly modify viscosity (in a few milliseconds) (Chen et al., 2010).
Magneto-rheological fluid combines a carrier liquid with ferromagnetic particles and additives. Ferromagnetic particles float freely in the absence of a magnetic field. Ferromagnetic particles account for 20-40% of total volume (25-80 percent by weight). The absence of a magnetic field is OFF mode, whereas the presence is ON mode. In the ON mode, ferromagnetic particles form a chain due to the magnetic field. MR fluid has a robust damping force with a low magnetic field. The research needs to consider the damper's dynamic performance due to the various loading situations, stroke length, current input, and other factors (Ferdaus et al., 2015).
The MR damper is most commonly used in the suspension of motor vehicles; however, its application has recently been expanded to include other critically essential structures, such as buildings, turbines, wind bridges, washing machines, prosthetic limbs, landing gear, and so on. (Kasprzyk et al., 2014;Gudmundsson et al., 2010;Powell et al., 2013; 1 3 Nguyen et al.,;Motra et al., 2011;Oh J-S et al., 2016;Martynowicz et al., 2013). (Seid et al., 2017) studied many different magneto-rheological (MR) damper valve designs and analyzed their performance indices. These performance parameters included inductive time constant, valve ratio, dynamic range, and pressure drop. To reduce the risk of earthquakes, (C. Daniel et al., 2019) concentrate on the issue of adjusting the damping force of a shear mode magneto-rheological (MR) damper. Consequently, the semi-active MR damper capable of controlling vibration is studied using experimental and computational methods. (Seid et al., 2019) designed and analyzed an above-knee prosthesis using a magneto-rheological (MR) damper. A dynamic system model for the prosthetic leg swing phase with a single-axis knee and optimal MR damper was created. The researcher (Hou and Zeng Ning, 2010) investigated the performance of an MR damper after it had been mounted on a material testing machine (MTS) and put through a series of tests with varied excitation frequencies. The reaction time parameters, energy dissipation, and responsive force were analyzed in this research. Wu and Cai, (2006) discovered in their research that MR dampers are utilized to regulate the vibrations of cable-stayed bridges under various excitation frequencies, one of which is the resonant frequency. When constructing twin-tube MR dampers that are outfitted with a single coil, it is expected to practice using magnetic and sandwiched magnetic shields. This research was conducted by Ganesha et al., (2020) and concluded that the experiment was successful, as evidenced by improvements in suspension control, ride comfort, and deflection of tires.
This paper presents experiments with fixed 5 mm displacement, varying frequencies and fixed current inputs. This work examined the efficiency of small-scale MR dampers under varied loading situations. The reaction force for subjected excitations is plotted and evaluated for nonlinear behavior, especially the hysteresis loop and energy dissipation capacity. The damping force corresponding to various frequencies and energy dissipated is presented in this paper to use as vibration-control device in structure.

Magneto-rheological (MR) fluid
Magneto-rheological fluids are non-colloidal dispersion of magnetizable particles with diameters ranging from 20 to 50 microns. MR devices have substantially greater yield strengths when triggered with a magnetic field. The size of the dipole particles distinguishes ferrofluids from MR fluids. These particles are an order of smaller magnitude in ferrofluids than in MR fluids, measuring upto maximum of 2 µm in MR fluids. MR fluid comprises mineral or siliconbased oil and variable percentages of ferrous particles coated with an anti-coagulant agent. Lord Corporation, revealed in engineering notes that MR fluid exhibits Newtonian-like behavior when subjected to a magnetic field, with ferrous particles scattered throughout the fluid forming magnetic dipoles when not activated. As seen in Fig. 1, these microsized magnetic particles arrange themselves along magnetic flux lines.
The commercially available 132DG-MRF developed by Lord's Corporation is used for this experiment. There are 3 types of MRF by Lord's corporation, i.e., high yield, medium yield and low yield. 132DG-MRF is chosen due to its non-settling, medium yield strength and efficient operating temperature characteristics. Figure 2 depicts the MR fluid used, and Table 1 depicts its properties. The MR fluid's properties are obtained from Lord's corporation profile to calculate the desired parameter, the yield strength.

Design of MR damper
The design of MR dampers is categorized into two primary parts (Phillips, 1969): (a) the design of the hydraulic system (Geometry) and (b) the design of the electromagnet. An iterative calculus is assumed throughout both steps.

Design of hydraulic system
The MR damper design chosen for this experiment operates entirely in shear mode. MR fluid flows in the annular space between the piston and the cylinder on excitation. Assuming certain aspects for the quasi-static analysis of MR damper, it is noted that (a) MR fluid behavior can be described using a simple Bingham plasticity model. (b) MR fluid flow is achieved without losses, and (c) the piston oscillates with continual velocity (Phillips, 1969).
Normal state (no field) and excited (with field) state are the two distinct ways that MR fluid acts. While Newtonian behavior is frequently seen in the normal state, when the fluid is excited, it behaves like a Bingham plastic model with diversified yield strength. Despite the fluid's  (Spencer et al., 1996).
The equation of the Bingham plastic model can determine the shear stress related to the flow of MR fluid (Wereley & Pang, 1998):
Furthermore, the MR fluid behaves as a visco-elastic material for fluid stresses below y in the Bingham plastic model. The governing equation can be written as where MR dampers typically use the shear flow mode of the fluid. According to Eq. (1), the pressure drop in a shear flow mode consists of pressure loss from (a) viscous component and (b) field-dependent yield stress.
Similar to Eq. 1, it is typically believed that the pressure drop created in a device based on shear flow mode is the consequence of the addition of a viscous component ∇P and a component ∇P that is field dependent and induces yield stress (Gavin HP et.al 1996a;Vibration & seat design, 2001). This pressure can be roughly calculated by where y = shear stress at yield point; . = shear strain rate; = plastic viscosityof fluid(newtonian viscosity).

∝
(2) = G ; < y = shear stress; = shearstress = shearstress y = shear stress at yield point; G = complex material modelus; = shear strain rate.  When the ratio, as mentioned above, is close to or equal to 1, the value for C is selected to be 2. The value for C is set to be 3 for ratios of roughly 100 or more (Gavin HP et al. 1996a). The volume of MR fluid exposed to the magnetic field is responsible for producing the required MR effect and is hence referred to as the minimum active volume V: where K = 12 ∕ c V is the minimum volume of fluid required to achieve the dynamic range of control ratio for the required power W n ;W n = Q. ▵ P .
Using the above parameter and further solving Eq. (4) gives Based on the parameters of the MR fluid, the required control ratio or dynamic range, and the flow or speed of the device, Eq. (5) provides the geometric limitations and the necessary aspect ratios for MR devices. In most cases, MR fluid devices' architecture is constructed so that MR fluid is saturated magnetically. The fluid creates its maximum yield stress ( y ) , under these conditions (Phillips, 1969). The variable y used in the preceding equations, however, should be taken from the MR fluid specifications (Table 1) to represent the expected operating situation. The effect of geometry on MR damper performance, controllable force, and dynamic range D can be determined using the operational model for shear flow.
The dynamic range is the ratio of the total damper output force, denoted by the letter F T to the uncontrolled force, denoted by the letter F un : = viscosity of MR fluid(normal state) y = Current dependent yield stress of MR fluid As viscous force and yielding force are developed due to the mechanical components and MR fluid in the damper, the geometry of the components plays a critical role in the design where as friction force is assumed to be negligible since the material used and mechanism opted is of little friction The force generated from the components and MR fluid is determined from Eqs. (7) and (8): Thus, the total force of the damper is given as F T in the following equation: The damper's resistive force is made up of two types of forces: one that can be controlled, denoted by F , and another that cannot be controlled, denoted by the letters F un . Both a viscous force, denoted by F and a friction force, denoted by F f are components of the force that cannot be controlled.
In Eq. 7, the parameter C is bounded (Vibration & seat design, 2001) between 2.07 and 3.07; hence, F can be written as This demonstrates a negative relationship between the controlled force range and the annular gap (g). Therefore, a small gap size is essential for efficiency but not less than 1 mm for regular MR fluid flow. A controlled force that is as lengthy as feasible is the best way to get the most out of an MR damper and ensure its maximum efficacy. On the contrary, a minimum annular gap (g) restricts the MR damper's dynamic range. Solving Eq. (6) using Eqs. (7) and (9) is derived as Finally, making use of the max. Dynamic range condition, the hydraulic system's annular gap (g) is procured.
The relations for the parameters in Eq. (9) are given as

Design of electromagnetic system
This section provides a condensed version of the explanation of the magnetic circuit design that can be found in the Lord Corporation Engineering Note (Vibration & seat design, 2001) (Design with MR fluids, 1999). As a rule, an MR damper's magnetic circuit uses low carbon steel, which possesses both a high magnetic permeability and saturation, as a magnetic flux conduit to direct and concentrate magnetic flux within the fluid gap. Determining the necessary coil turn numbers (NI) for the magnetic circuit is one of the tasks involved in the design of a magnetic circuit.
The design procedure is a five-step process that interrelates to each other. 3. Determine the magnetic field intensity H steel In the steel using Fig. 5, for experimental purposes, NI is procured as 590.5, and correspondingly by taking the maximum current input of 2 A, the number of copper coil turns N is procured as 300.

By using Kirchhoff's Law of magnetic circuits, the necessary number of amp-turns (NI) is
Using the maximum current output from the available DC power supply as 2 A, the number of coil turns required is determined from Eq. 17: Referring to the hydraulic and electromagnetic design, the geometric description of the developed MR damper is depicted in Fig. 6. The desired parameters and dimensions of the small-scale MR damper presented in Tables 2 and 3 are used to develop and fabricate for experimental investigation.

Experimental work
The damper cylinder, piston rod with copper wire winding and fully assembled small-scale MR damper are illustrated in Fig. 7. The fabricated damper is evaluated to see how well it performed compared to the intended behavior. The test setup utilized for this is illustrated in Fig. 8.     Fig. 9. The MR damper was evaluated using a servo-hydraulic UTM under computer control (MTS-suite). The actuator is connected to the top head of the damper, allowing the piston to move up and down. This enables the damper's damping force to be measured accurately. The excitation signal is transmitted from the computer to the hydraulic actuator through the MTS suit software. The UTM has sensors built-in that can monitor the force and displacement. The current controller is wired to the damper so that it may deliver a variety of current inputs that can be used to measure the responses of different forces. The displacement amplitude was held constant at 5 mm, and the current input was maintained at 2 A throughout the experiments. These tests were run under a variety of different frequencies. The value of 5 mm is the testing input for the displacement amplitudes and frequencies, respectively (0.1-1 Hz with an increment of 0.1 Hz). All experimental data, including time, displacement, and force, have been recorded to analyze the MR damper.

Results and discussion
The force-displacement parameters at the complete cycle are depicted in Fig. 10 for a range of frequencies and a displacement of 5 mm correspondingly. It has been found

Fig. 10
Force vs displacement plot for various frequency that the force produced by a given specific displacement of the piston rises in proportion to the velocity of that piston's displacement. When the frequency is high, there is a discernible rise in the magnitude of the force-displacement loop in the region just before yielding. The smooth curve of the force-displacement plot depicted in Fig. 10 is due to the absence of air bubbles inside the MR damper. Similar smooth curves were observed by (Dixon JC, 2007). The velocity of the piston is estimated using real-time data from a DAQ system linked to a computer via MTS Suite and plotted as shown in Fig. 10 for frequencies of 0.1 Hz, 0.2 Hz, 0.3 Hz, 0.4 Hz, 0.5 Hz, 0.6 Hz, 0.7 Hz, 0.8 Hz, 0.9 Hz, and 1 Hz. Figure 11 depicts the force change as the piston velocity changes. Figure 11 shows that increasing velocity causes an increase in force. The frequency-velocity relationship for the experiment is compiled for better understanding and presented in Fig. 12 for clarity. It has also been observed that the percentage increase in velocity concerning 0.1 Hz ranges from 47.14 to 88.77%. According to the graph, the velocity of the piston increases as the frequency increases.
The reaction forces due to exciting frequency developed in two different cycles, i.e., a negative cycle when the piston is moving downwards and a positive cycle when the piston is moving upwards. Forces developed due to different frequencies are plotted in Fig. 11 concerning their respective velocities. Maximum and minimum forces for the negative cycle are recorded as 135.89 N at 25.3 mm/s (0.8 Hz) and 60.84 N at 6.7 mm/s (0.2 Hz), respectively. Similarly, for the positive cycle, 135.11 N at 12.9 mm/s (0.4 Hz) and 91.25 N at 25.3 mm/s (0.8 Hz) as maximum and minimum forces, respectively. It is also inferred from Fig. 12 that the velocity increase is linear. The test run is performed as displacement control with variation in excitation frequency; hence, the relation between frequency excitation and velocity is obtained manually from the real-time data recorded from the DAQ system. The data recorded for all the negative and positive cycles is combined and plotted with their respective velocities, as shown in Fig. 13. It is observed that variation in forces occurs, respectively, to the increase in frequencies, and the reason is due to the effect of shear thinning and shear thickening effect, which occurs inside the MR damper. A similar phenomenon has also been observed by (Sapiński & Horak, 2013;Rendos et al., 2020 andDimock, 2000).
The sum of the forces in the negative and positive cycles throughout the cycle is used to express the total damping force produced by the small-scale MR damper (Liu et al., 2022;Dimock et al., 2000;Jacob et al., 2022;Londono et al., 2015;Weber et al., 2008). Figure 14 depicts the overall damping force produced by the small-scale MR damper for a 5 mm displacement at various excitation frequencies.  Table 4 shows the forces obtained in the positive and negative cycles for various frequencies. Figure 14, the plot of total damping forces for all frequencies, also demonstrates how damping forces increase with frequency. The damping force of the designed small-scale MR damper increases noticeably as the frequency excitation increases. Installing additional dampening devices is a simple way to reduce structural vibration (Dyke et al., 1998)  . Using the natural motion of the structure, this concept generates displacements within the MR damper's portion. These devices should respond by applying intense local dampening pressures, distributing energy evenly (London et al. 2015). The energy dissipation by the developed small-scale MR damper is studied experimentally using a constant magnetic field/induced current of 2 A, sinusoidal excitation with constant displacements, and sinusoidal excitation. To calculate the effectiveness of the small-scale MR damper, the total energy absorbed by the MR damper devices during a typical vibration cycle with the MR damper running in a constant magnetic field is used (Hgsberg et al., 2008). The MR damper dissipates its cyclic energy at each frequency by forming a hysteresis closed-loop force-displacement curve (Ha et al., 2018;Li et al., 2000). The energy dissipation of the designed small-scale MR Damper in a single cycle is calculated using the area enclosed by a hysteresis closed loop (Dixon, 2007) based on an average of ten complete cycles with a frequency range of 0.1-1 Hz and a displacement of 5 mm. Figure 15 depicts the energy lost for the highest cycle of the 10 cycles for 5 mm, which correspond to different frequencies. Figure 15 shows that as the excitation frequency increases, so does the energy dissipated, which is critical for using the developed small-scale MR damper as a vibration-control device in the structure.
For a displacement of 5 mm, the energy dissipation ranged from 1.7 to 2.4 J, corresponding to an excitation frequency of 0.1 Hz to 1 Hz. Energy dissipation is proportional to excitation frequency, with a maximum rise observed when the frequency is increased while displacement remains constant at 5 mm. The experimental data for the designed, developed, and manufactured small-scale MR damper is shown above. Furthermore, the data have been compiled for clarity and is presented in Table 4.

Conclusion
Magneto-rheological (MR) fluid dampers have enabled effective semi-active control in various practical applications. Because of their ease of use, low input power, scalability, and inherent resilience, such MR fluid dampers appear extremely promising for civil engineering applications. Experiments were carried out to investigate the force-velocity, force-displacement and energy dissipation capacity of a fabricated small-scale MR damper. The total damping force varies between 175.55 and 252.77 N, while the velocity varies between 3.5 and 31.5 mm/s. The manufactured MR damper demonstrated an excellent range of force-velocity, force-displacement and energy dissipation characteristics with a constant 2 A current input and a maximum excitation frequency of 1 Hz. The force-velocity characteristics of the MR damper range were determined at various excitation frequencies. The force increases as velocity/excitation frequency increases. The energy dissipated by the developed MR damper increases significantly as velocity/excitation frequencies increase. MR dampers are widely used in various engineering applications, and the performance requirements vary depending on the domain. In this case, the small-scale MR damper is self-designed and developed to be installed in a structure to reduce vibration. The energy dissipated in this current study has revealed the performance of the smallscale MR damper, and it concludes that the self-styled MR damper is efficient for being used as a semi-active vibrationcontrol device.