Performance analysis of a magnetorheological damper with energy harvesting ability

A magnetorheological (MR) damper with energy harvesting ability was proposed based on electromagnetic induction (EMI) principle. The energy harvesting part was composed of a permanent magnet array and inducing coils which move vertically. This device could act as a linear power generator when the external excitation was applied, and the kinetic energy could be converted into electrical energy due to the relative linear motion between the magnets array and the inducing coils. Finite element models of both the MR damper part and the linear power generator part were built up separately to address the magnetic flux distributions, the magnetic flux densities, and the power generating efficiency using ANSYS software. The experimental tests were carried out to evaluate the damping performance and power generating efficiency. The results show that the proposed MR damper can produce approximately 750 N damping forces at the current of 0.6 A, and the energy harvesting device can generate about 1.0 V DC voltage at 0.06 m·s−1 excitation.


Introduction
Over the past couple of decades, magnetorheological (MR) fluid has undergone significant development due to its unique rheological properties under exerted magnetic fields [1]. These features have led to the development of many MRFbased devices such as the MR damper, MR valve, MR brake, and MR clutch. The most popular MRF-based devices are MR dampers due to their long range controllable damping force, fast adjustable response, and low energy consumption [2].
Till now, the MR dampers have wide applications in automotive industry including off-road vehicles [3,4], and they are also used in naval gun controlling [5], field of landing gear [6], prosthetic knees [7], washing machines [8], high speed train suspension [9,10], seismic vibration control of different civil structures [11,12], and so forth. However, a significant drawback of traditional MR damper is witnessed; that is, the kinetic energy from the vibration is wasted in heating rather than harvested as a reusable power resource due to lack of energy harvesting device.
Recently, energy harvesting MR dampers have received a great deal of attention due to their capability of recovering kinetic energy that normally dissipated by traditional MR dampers. Many researchers explored different principles and designs of energy harvesting MR dampers, which can be classified into two main categories. The first category is to convert the linear damper vibration into oscillatory rotation and use rotational permanent magnetic DC or AC generators to harvest kinetic energy. These mechanical mechanisms include rack and pinion, ball screw, and hydraulic transmission. Avadhany et al. [13] patented one type of rotary regenerative shock absorber based on hydraulic transmission. Choi et al. [14] proposed an electrorheological (ER) shock absorber integrated with a generator by employing a rack and pinion gear mechanism, which converted a linear motion of the piston to a rotary motion, thus activating a generator to produce electrical energy to self-power the excitation coil in the piston head. Li and Zuo [15,16] proposed an energy harvesting shock absorber with a mechanical motion rectifier (MMR), the roller clutches were embedded in two bevel  gears, and the function of "motion rectifier" was achieved with three bevel gears in the MMR. Yu et al. [17] proposed a new type of energy harvesting device system for the wireless sensing of inner-state conditions in the operation of MR dampers, where an impeller mechanism was used as the amplitude convert device, and an AC generator was applied as the energy converting part to convert the linear shock into electrical energy. Zhang et al. [18] developed and prototyped a regenerative shock absorber based on a ball screw mechanism and validated it with full vehicle experiments in the lab. Guan et al. [19] proposed a novel MR damper with a self-powered capability; the vibration energy harvesting mechanisms were adopted based on ball screw mechanisms and a rotary permanent magnet DC generator, which converted the external vibration energy into electrical energy to power the MR damping unit.
In addition to the energy harvesting with mechanical transmission mechanism in the MR damper, the second category is based on the design of an electromagnetic induction (EMI) device, which generates power from the relative linear motion between magnets and coils. Cho et al. [20] proposed a special structure of an EMI device to be used with an MR damper. Choi et al. [21] investigated experimentally a smart passive control system comprising an MR damper and an EMI device to generate electrical power. Choi and Wereley [22] studied the feasibility and effectiveness of a self-powered MR damper using a springmass EMI device. Sapiński established a permanent magnet power generator for MR damper, the designed vibration generator consisted of a special arrangement and a foil wound coil, and the numerical analysis and experiment were carried out to investigate the magnetic field distribution and efficiency of the generator [23,24]. Then, Sapiński proposed a multipole magnetic generator, the design of permanent magnets array was optimized, and both numerical method and finite element simulation were carried out to investigate the performance of the whole energy harvesting MR damper [25]. However, the large cogging force generated in the interaction between ferromagnetic components and permanent magnets array led to a negative impact on the control of MR damper. Chen and Liao also proposed a selfsensing MR damper with power generation; the design of the power generator significantly minimized the cogging force and improved the dynamic damping performance [26]. The guild layer and shield layer were adopted to minimize magnetic interaction effect between permanent generator and MR damper. However, the extra shield and guild layer increased the complex of the whole structure while the component itself provided litter contribution to the dynamic control or improvement of generating effect.
In this paper, a new MR damper with energy harvesting ability was proposed based on the EMI principle. The sharing component between the damper part and the linear power generator part could minimize the magnetic field interference without extra guild layer and shell layer; also the component itself provided necessary function in both generating process and damping capability. This new design is expected to simplify the structure of linear power generator and also provided a low cogging force. The inducing coils in the linear power generator had two representative electric circuits. In this study, finite element method was utilized to address the magnetic field distribution and magnetic flux density for the damper part and linear power generator part, respectively, and cogging force conducted from linear power generator was also identified. The properties of proposed MR damper were experimentally investigated, and power regenerative characteristics were also discussed. volume change when the piston rod moves vertically along the vibration direction. A compression spring is stalled in the accumulator to support the movement of floating piston. When the piston rod moves, the MR fluid in the cylinder flows through the annular gap between piton head and cylinder. The excitation coil wound around the piston head is electrically insulated. When a direct current was applied on the excitation coil, a magnetic field is generated around the excitation coil and piston head. Then the annular gap would become an activated area and the viscosity of MR fluid in the gap would be changed. Finally, the changeable damping force is achieved.

Principle and Structure of the Proposed MR Damper with Energy Harvesting Ability
The linear power generator is radially arranged inside the MR damper. Each two permanent magnets are separated by a spacer; also a magnet and a spacer are grouped to a pole pair. There are totally eight pairs of magnet-spacer assembling together, and they are screwed on the shaft. The inducing coil was arranged on the winding base. The phase of the generated voltage depends on the magnetic field distribution, the phase angle is 90 ∘ between each nearby coil, and each two different phases of coil are connected together to increase power generating efficiency. In this design, the 0 ∘ and 180 ∘ phase coils are connected together, which is called coil A; also the 90 ∘ and 270 ∘ are connected together, which is called coil B. Thus, the 14 phase coils are wound in the winding base and combined into two inducing coils, that is, coil A and coil B. When the interaction between permanent magnets and inducing coils occurred, the vibration energy would be converted into electrics into coil A and coil B.
The magnetic circuit of the linear power generator is shown in Figure 2. The rotor of the linear power generator consists of a winding base and two inducing coils A and B, and the stator is assembled by a shaft, permanent magnets, and spacers. Each pole pair includes a permanent magnet and a pole spacer, and 8 pairs of magnet arrays are installed on the shaft; and the shaft is fixed by the cylinder through the screw, and this structure is also called multipole. As shown in Figure 2, the magnetic flux radially passes through the half-length of the spacer and then through air gap and the inducing coil, reaching the piston rod, and then returns to the winding base, air gap, and half-length of spacer, finally reaching the opposite of permanent magnet.

Finite Element Analysis of the Proposed MR Damper with Energy Harvesting Ability
In order to address the magnetic field distribution and magnetic flux density on the piston head and the generating property of the linear power generator, the finite element models were built up using ANSYS software, and the issues of cogging force and magnetic interference were also discussed in this section.

Modelling of the MR Damper Part.
As shown in Figure 1, the damper piston is radially outside of the linear power generator. The benefit of this structure is that the piston rod is utilized both as the shield and outer core of the linear power generator. This design can minimize the magnetic interaction between the linear power generator and the MR damper part while not adding extra structure in the damper.
As the producer of electromagnetic field, the excitation coil is considered as electromagnet. By varying the driving current through the excitation coil, the magnetic flux density can be varied too. The DC current is supplied to the excitation coil, and the current density is given by where is the number of turns of the excitation coil, is the DC current, and is the cross-sectional area of the coil.
In this simulation analysis, the physics environment is set as magnetic nodal option from preferences of ANSYS. The two-dimensional axisymmetric entity model of the MR damper part is built up as shown in Figure 3(a). The entity model includes the piston rod, the piston head, the excitation coil, the cylinder, and the resistance gap filled with MR fluid. Figure 3(b) presents the finite element model of the damper part. The element type is chosen as PLANE 13, and the 4-node quadrilateral meshing is used for the finite element model. This model is divided into 1237 elements and 3850 nodes. The leakage of magnetic flux is considered to acquire the reliable magnetic field distribution for the piston head. Figure 4 illustrates the finite element model and static electromagnetic field simulation of the MR damper part. Figure 4(a) shows the magnetic flux of the MR damper part; it can be seen that the magnetic flux vertically passes through the annular gap, which means the high efficiency of magnetic field. Figure 4(b) illustrates the magnetic flux density of the main area for the MR damper part; the magnetic flux density within the annular gap ranged from 0.55 T to 0.74 T when the excitation current was set as 1 A, which leads to generating a large damping force. Figure 5 shows the magnetic flux density of the annular resistance gap under the different applied current. As shown in the figure, the magnetic flux density is increased with  Figure 6 shows the relation between damping force and displacement under different applied current. The amplitude is set as 5 mm and the frequency is 1 Hz. Observing the figure, the damping force increased as the increasing of the excitation, and the change of damping force agreed well with the simulation result for the magnetic field.

Modelling of the Linear Power Generator
Part. The numerical analysis was carried out to address the magnetic property for only one pole pair. It can be assumed that the reluctance values of the pole spacer are neglected for their high magnetic permeability; thus the magnetic flux is given as [27] = rem 0 where is the magnetic flux of air gap without considering the leakage, 0 is the relative magnetic permeability and equals 4 × 10 −7 (N/A 2 ), is the magnetic field intensity of magnet, rem is the flux density of the magnet, is Shock and Vibration  the surface area of cylindrical air gap, is the cross-section area of magnet, and and can be obtained by where is the diameter of shaft, is the thickness of the permanent magnet, is the length of air gap between piston rod and permanent magnet array, and is the magnet thickness.
The induced voltage in the inducing coil is defined as where is number of turns of the inducing coil, is spacer thickness, is the displacement, / is the velocity, and is the initial phase angle of inducing coil. The number of turns of is defined as where is the cross-sectional area of electrical wire and is the diameter of the wire. Figure 7 shows the modelling of the linear power regenerator. As shown in Figure 7(a), the main components of the linear power generator include the air chamber (A1), the permanent magnet arrays (A2, A3, A4, and A5), the shaft (A6), the winding base and inducing coils (A7), the piston rod (A8), and the zone filled with MR fluid (A9). There are two arrangements for the permanent magnets: 0 ∘ phase and 180 ∘ phase. Each two opposite arranged magnets are represented by a spacer. Figure 7(b) shows the finite element model of the linear power generator. The element type is chosen as PLANE 13, and the finite element model consists of 1217 elements and 3816 nodes. The winding base is made of ABS material, which is a nonmagnetic material; the electrical wire is made of brass material. As a result, the permeability of the two materials in the air gap is identical. The shaft is made of aluminum. The spacer and piston rod are made of steel 1020 which provide a high permeability. Figure 8 illustrates the finite element analysis of the linear power regenerator. Figure 8(a) shows the magnetic flux distribution; the magnetic flux passes through the gap between the magnet arrays and the piston rod. As a result, the inducing coils installed in the winding base can generate induced voltage when the relative linear motion between the magnet arrays and inducing coil occurred. Figure 8 while the flux density in the spacer is 0.3 T on average. The winding base is made of ABS material, which is a nonmagnetic material; also the electrical wire is made of brass material. As a result, the magnetic flux density within the inducing coils and the flux leakage coefficient is small. Figure 9 shows the cogging force distribution of the linear power generator. As shown in the figure, a low cogging force is obtained due to the compact structural design, and the total cogging force is about 1 N.  Figure 10 shows the main components and assembly of the manufactured MR damper, and the parameters of the MR damper are shown in Table 1. The cylinder and the piston rod are made of high magnetic material steel 1020, the shaft of the linear power generator is made of aluminum which is a nonmagnetic material, and the material used in spacers is steel 1020. The permanent magnets that are used in the design are NdFeB magnets grade N52. The magnets are stacked in pairs as shown in Figure 1; the magnetic flux passes through the spacers under the driving of opposite magnetomotive forces. Figure 11 shows the damping properties under different coil currents, in the test, the frequency is set as 1 Hz and the amplitude is 5 mm, and the direct current is selected as 0 A, 0.2 A, 0.4 A, and 0.6 A, respectively. It can be seen that the damping force is about 200 N without the applied current; the reason is that the damping force at 0 A is generally from the stiffness of the accumulator and the MR fluid in the damper that works under Newtonian fluid model. The damping force increases from 200 N to about 750 N when 0.6 A current is applied. In this situation, the power consuming of the proposed damper is about 1.4 W. It can be seen that the damping force depends on the applied current, and the damping force will be changed by changing the current input. Thus, the proposed damper could generate large controllable damping force output, while under relatively low power consumption. Figure 12 illustrates the damping force and velocity response under different applied currents, and in the test, the frequency is set as 1 Hz and the amplitude is 5 mm. The maximum velocity is 17 mm/s when the MR damper operates under 0.6 A excitation. Figure 13 shows the comparison of damping force between the theoretical result and experimental result. The excitation current is set at 0.6 A. As shown in Figures 13(a) and 13(b), the theoretical results agree well with the experimental ones. It can be summarized that the feasibility of proposed analysis had been proved. Velocity v (mm/s)

Energy Harvesting Capability of the Linear Power Generator without AC-DC Rectifier.
In this experiment, the measured inducing voltage from the two inducing coils A and B illustrated the properties of the linear power regenerator. The calculation data was obtained by the numerical analysis mentioned in Section 3.2. The comparison of inducing voltage between numerical analysis and experiment measurement is shown in Figure 14. Observing Figures 14(a) and 14(b), the experiment data from coil A and coil B agreed well with the numerical results, and the measured peak inducing voltage is 1.22 V. However, the wave of the inducing voltage is not the typical sinusoidal wave when the amplitude increases; the reason is the effect of frequency multiplication [26].

Energy Harvesting Capability of the Linear Power Generator with AC-DC Rectifier.
Because the inducing coils installed in the piston are equivalent as an electrical inductance, the value of generated DC voltage is better to evaluate the performance effect of proposed linear power generator compared with AC voltage. Thus, a bridge rectifier is developed, and the relevant experiment was carried out to evaluate performance of the linear power generator. The principle of the bridge rectifier is shown in Figure 15, two inducing coils A and B were applied in the linear power generator, and six diodes and one capacitor were needed in the bridge rectifier. In the experiment, the vibration excitation was constant, and the output of the proposed rectifier was connected to DAQ board. The MR damper was installed in the MTS which provided the amplitude and frequency excitation. The inducing coils from the generator were connected with the rectifier which adhered with the outer cylinder of the MR damper. In order to prevent the noise signal from DC power source, the DC power source state was set as off. However, there are still large numbers of noises in the experimental data. Figure 16 shows the inducing voltage of the linear power generator after the rectifier processing. The rectified DC voltage from the two inducing coils is approximately 1.0 V Shock and Vibration at 0.06 m⋅s −1 excitation. However, there are still some noises existing in the initial data denoted as black line due to lack of filtering. There are two ways to minimize the signal noises: the first is a commercial rectifier or DAQ board should be adopted as the signal processing unit to minimize the noises from electro circuit. The second is a shield or a filter should be applied to isolate the interference from environment.

Conclusions
In this study, an MR damper with energy harvesting ability was designed, fabricated, and tested. The proposed MR damper used the piston rod as the sharing component between the linear power regenerator and the MR damper part, and this shared component could isolate the magnetic field between two function areas. As a result, the magnetic field interference was minimized without extra designed shield and guild layer.
The finite element method was developed to address the magnetic field and magnetic flux distribution of the MR damper part. The simulation result proved the efficiency and feasibility of the proposed MR damper. Then the numerical method was utilized to evaluate the generating performance of the linear power generator, and the finite element model was utilized to investigate the magnetic field distribution. The issue of cogging force and minimization of the magnetic interaction had been solved.
Experimental tests were carried out to address the performances of the proposed MR damper. The results show that the damping force ranges from 200 N at the current of 0 A to 750 N at the current of 0.6 A. The dynamic range equals about 3.75. The AC-DC rectifier was applied on the power generating, and the results show that 1.0 V DC voltage output was harvested after the AC-DC processing.