Development and Evaluation of a MR Damper With Enhanced Effective Gap Lengths

Traditional magnetorheological (MR) damper featuring fixed gaps has the shortcomings of small damping force, single dynamic performance, and low adaptability. To overcome these shortcomings, a new MR damper with enhanced effective gap lengths is developed in this work, which achieves a double extension of the effective gap lengths via compactly integrating the conical fluid channels into the annular fluid channels. On the other hand, by altering the axial position of the valve spool controlled by a locking nut, the relative distance between the valve spool and piston of the MR damper is flexibly regulated; thus, the width of this adjustable gap in the conical fluid channels can be continuously adjusted. The magnetic circuit of the proposed MR damper is developed and its mechanical model is established as well to evaluate the dynamic performance. Sequentially, the finite element analysis (FEA) methodology is applied by using ANSYS/Emag software to investigate the changes of magnetic flux densities in these adjustable gaps. Moreover, a prototype is manufactured and experimental tests are conducted to verify its dynamic performance. The experimental results, under a fixed applied current, indicate that the damping force decreases with the increase of the adjustable gaps, and the maximum damping force reaches 7.2 kN at the adjustable gap of 0.6 mm. Besides, the dynamic range increases with the increase of the adjustable gap, and the dynamic range appears with a peak of 13.6. In addition, the damping force varies from 0.2 kN to 7.2 kN while the dynamic range attains 33 correspondingly by regulating the applied current and adjustable gap from 1.6 mm to 0.6 mm. From an experimental results perspective, the damping force and dynamic range can be not only effectively controlled by excitation current but also flexibly altered by regulating the width of the adjustable gaps simultaneously. Therefore, the dynamic performance of the proposed MR damper is also enhanced.


I. INTRODUCTION
MR fluid is a smart material that mainly comprises carbonyl iron particles, carrier liquid, and some additives in a specific proportion [1]. The MR fluid can be transferred from ordinary newton-liquid state to solid state continuously and reversibly in milliseconds with or without magnetic fields, and its shear stress is related to the exerted magnetic field intensity [2], [3]. Due to its unique rheological properties, the MR fluid is widely employed in a variety of fields, such as bridges, buildings, vehicle suspensions, assistance orthoses, and robots [4], [5].
As a sort of typical semi-active actuating device, MR damper is successfully applied to various control systems The associate editor coordinating the review of this manuscript and approving it for publication was Shunfeng Cheng. owing to the utilization of MR fluid as a transmission medium. In general, MR dampers consist of the piston rod, piston head, excitation coil, and cylinder [6], [7]. With a magnetic field generated by the excitation coil, the MR fluid in the effective gap is rapidly energized to exhibit MR effect; thus, a damping force is promptly produced in the gap to weaken the vibration. Successive damping forces can be achieved by controlling the applied currents in the excitation coil [8], [9]. Therefore, MR damper possesses the merits of continuously controllable damping, fast response, low power consumption, and inexpensive cost [5], [10], [11].
To improve the dynamic performance of MR dampers, various significant researches have been studied on the structural design of MR dampers. By improving traditional MR fluid flow channels, Kim et al. [12] proposed an improved MR damper with a bifold flow mode, which is characterized by VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ connecting the inner and outer MR fluid flow channels with a feedback aperture on the magnetic core. It has been verified that this MR damper achieves a greater controllable damping force and equivalent damping. Liao et al. [13] designed a bypass MR damper featuring multi-stage radial channels. The multi-stage radial channels effectively extend the lengths of the gap and improve the utilization of the magnetic field. The experimental results manifest that the proposed MR damper possesses a better dynamic performance. Zemp et al. [14] presented a long-stroke MR damper by effectively prolonging the MR fluid channel and applied it to a 21-story building.
Zhu et al. [15] developed a MR damper characterizing multiple fluid flow channels, by combining the annular and radial MR fluid flow channels, and the results reveal that the MR damper can provide a large damping force of 3.5 kN, which exhibits a good damping performance. Yazid et al. [16] constructed a hybrid-mode MR damper excited by five groups of excitation coil, which combines the shear mode with the extrusion mode of MR fluid. The experimental results demonstrate this MR damper yields a greater damping force than conventional MR dampers with a single-mode of MR fluid. Solomon et al. [17] designed a valve-mode MR damper for a six-axis MR prosthetic knee within a constrained length and radius. The finite element design via the response surface method was carried out to geometrically optimize this MR damper. Both the theoretical and experimental results show that the mass of this MR damper is reduced by 71% compared with a traditional MR damper; thus, it can be applied in those applications with small installation volume and short strokes. Cheng et al. [18] designed an MR damper with a magnetic winding and the damping force attained 3.4 kN under the sinusoidal velocity excitation with amplitude of 0.0628 m/s. To extend the effective gap length of the MR fluid channels, Hu et al. [19] proposed an improved MR damper on the premise of a restrained structural dimension, utilizing three non-conducting magnetic sleeves and four conducting magnetic sleeves to divide a single MR fluid flow channel into a serial-type MR fluid flow channel. The experimental results illustrate the peak damping force equals 6.8 kN and the equivalent damping coefficient reaches 290 kN/sm −1 .
The above methods to improve the dynamic performance of MR dampers primarily include: extending the MR fluid channels, changing the piston structures, optimizing magnetic circuits, and increasing the number of coils. From the structural principle point of view, these methods mentioned above only extended the effective gap lengths without regulating the width of effective gaps [20], [21]. Although the dynamic performance of these MR dampers has improved to some extent, some problems inevitably occur such as large structures, simple dynamic performance, and poor adaptability [22], [23]. As a highlight, the gap is one of the key parameters in designing MR dampers, and an appropriate gap can make MR dampers not only generate a greater damping force but also possess a larger dynamic range simultaneously [24], [25]. Zheng et al. [26] designed a novel multi-coil MR damper with a variable resistance gap (VRG-MMD), which enables four electromagnetic coils with individual exciting currents. To obtain the optimal geometry of the proposed VRG-MMD, a multi-physics optimization including electromagnetics and fluid dynamics was conducted using Bound Optimization BY Quadratic Approximation (BOBYQA) technique. Though the multi coils achieve the extension of effective length that magnetic flux lines pass through, the axial dimension of VRG-MMD is inevitably increased and the variable resistance gap is only changed by the motion of piston rod but not flexibly adjusted according to the damping force requirement. Song et al. [27] investigated the effect of different MR fluid gaps on the braking performance of the MR brake. Verified by the theoretical analyses and experimental results, the braking torque increases with increasing the input current, and the difference for the impact of the gap exerts a huge effect on the braking torque under various input current. Phu et al. [28] proposed a new type of MR fluid mount featured by changeable gaps using a moved-plate valve structure, which is based on the flow mode and shear model of MR fluid. The main innovation of this MR fluid mount is the block-up behavior no longer occurs that may happen in conventional fixed plate mounts. However, due to only one excitation coil winding on the bobbin and simple magnetic circuit, the dynamic performance of the proposed MR fluid mount is not obviously enhanced compared with the conventional mount with the fixed gap. Kim et al. [29] presented a novel type of a tunable MR damper featured by permanent magnets, the damping force of which depends on the shape of the housing cylinder. The location of the permanent magnets that are connected to the moving piston varies with the magnetization area. The benefits of the proposed MR damper include no external power required to drive this damper, compact structures, higher cost-effectiveness, etc. Nevertheless, the damping force only controlled by the position of the piston is unable to meet the demand of practical damping force. To improve the dynamic performance of MR valves, Hu et al. [30] designed a new MR valve with a continuously tunable gap ranging from 1 mm to 2 mm. The adjustable range of the pressure drop varies from 470 kPa to 1150 kPa by tuning the resistance gap and applied current, which can replace a variety of MR valves featuring fixed gaps. Nonetheless, the main drawback of this MR valve lies in that the controllable pressure drop is still not sufficient for a great deal of application owing to the short effective gap length. It is also noted that moving parts frequently exist in those applications equipped with MR devices [31], [13]. Hence, the gap should be continuously adjustable while extending the effective length simultaneously, aiming to further boost the dynamic performance of MR dampers.
In terms of the aforementioned facts, the technical originality of this work is to propose a MR damper that extends the effective gap lengths and the gap of which can be flexibly adjusted simultaneously without restricted to the position of the piston rod, aiming to further boost the traditional MR damper with a single method to elevate its dynamic performance. This paper presents a new MR damper with enhanced effective gap lengths, which achieves a double extension of the effective gap lengths via compactly integrating the conical fluid channels into the annular fluid channels. By altering the axial position of the valve spool controlled by the locking nut, the relative distance of the valve spool and the piston is flexibly regulated; thus, the adjustable gaps in the conical MR fluid channel can be continuously adjusted. The magnetic circuit is studied and its mechanical model is established as well. The FEA methodology is applied by using ANSYS/Emag software to validate the damping performance, and a series of experimental tests are also carried out to study the dynamic performance of the proposed MR damper.

II. STRUCTURAL DESIGN
A. STRUCTURAL PRINCIPLE Fig. 1 and Fig. 2 portray the schematic configuration and photograph of the proposed MR damper with enhanced effective gap lengths, respectively. It is noted that the excitation coil is uniformly wound onto the piston which comprises the magnetic yoke I, conical sleeve, and magnetic yoke II. The chambers I, II, III filled with MR fluids are accordingly formed by the piston, non-magnetic sleeves, cylinder, and piston rod, respectively. The channels in which MR fluid flows between chamber I and II are represented as the conical fluid channels, and the channels between chamber I and III are denoted as the annular fluid channels. (1) locking nut (2) end cover I (3) non-magnetic sleeve I (4) valve spool (5) magnetic yoke I (6) excitation coil (7) conical sleeve (8) magnetic yoke II (9) piston rod (10) non-magnetic sleeve II (11) cylinder (12) floating piston (13) end cover II. In this design, the conical fluid channels with adjustable gaps are integrated into the annular fluid channels with fixed gaps. As a result, the proposed MR damper not only doubly extends the effective gap lengths but also is capable of continuously regulating these adjustable gaps in the conical fluid channels, thus significantly enhancing the dynamic performance of the proposed MR damper.
The locking nut is installed to adjust the axial position of the valve spool which can flexibly alter the adjustable gaps in the conical fluid channels. Specifically, when the locking nut is tightened clockwise, the valve spool axially moves to the right side to reduce the relative distance between the valve spool and piston. On the contrary, the valve spool horizontally shifts to the left side when the locking nut is unscrewed counterclockwise, thus augmenting the relative distance between the valve spool and piston. In this manner, the gap in the conical fluid channels can be continuously adjusted by regulating the locking nut. Thus, the damping force of the proposed MR damper can be directly alerted by regulating the width of adjustable gaps. Fig. 3a and Fig. 3b respectively depict the distribution of the fluid channels under two particularly working modes, where the proposed MR damper operates with the maximum and minimum gap, respectively. When the extended length l of the valve spool comes up to l max , the gap between the valve spool and piston reaches the maximum value h 2max . On the contrary, the adjustable gap accordingly attains the minimum value h 2min when extended length l is equal to l min . The adjustable gap in the conical MR fluid channels can be expressed by where h 2 is the adjustable gap in the conical fluid channels, h 2max and h 2min are the maximum and minimum values of h 2 , respectively, l is the extended length of the valve spool, l max and l min are the maximum and minimum values of l, respectively, θ is the half cone angle of the conical fluid channels, it can be expressed as External vibration drives the piston rod of the MR damper persistently moving back and forth along the axial direction. Here, the process of the piston rod moving to the right side is represented the stretching stroke (shown in Fig. 3a) while moving to the left side is acknowledged as the compression stroke (shown in Fig. 3b). With a direct current applied to the excitation coil, magnetic flux lines immediately begin with the valve core, then perpendicularly passes through the conical fluid channels, magnetic yoke I, annular fluid channels, cylinder, and the magnetic yoke II, ultimately returns to the valve spool to form a closed circuit. It is noted that the MR effect occurs in the conical and annular fluid channels simultaneously, namely paths 1, 2, 3, and 4 that the magnetic flux lines vertically pass through. To compensate the change of pressures p c1 , p c2 , and p c3 in chambers I, II, and III (shown in Fig. 3), the field-dependent shear yield stress comprising p a in the annular fluid channels and p c in the conical fluid channels is accordingly produced in paths 1, 2, 3, and 4 so that the MR damper generates damping force to suppress the external vibration. Therefore, with the adjustable gaps fixed, the damping force can be continuously adjusted by controlling the applied current. The specifications of the proposed MR damper are listed in Table 1.  Fig. 4 illustrates the magnetic circuit diagram of the proposed MR damper. Supposing there is no leakage in the magnetic circuit, the magnetic circuit can be analyzed using the Ohm's law, and it is expressed as

B. MAGNETIC CIRCUIT ANALYSIS
where N represents the number of turns of the excitation coil, I is the control current applied in the excitation coil, H is the magnetic field intensity, l is the length passed through by the magnetic flux lines, R m is the total magnetic resistance of the magnetic circuit, and φ is the magnetic flux, which is deduced by where B denotes the magnetic flux density, and S represents the area passed through by the magnetic flux lines. The equivalent magnetic circuit of the proposed MR damper is depicted in Fig. 5. The total magnetic resistance can be expressed as The magnetic resistance of the cylinder is where W denotes the length of the valve spool, w 1 is the length of the magnetic yoke I, w 2 is the length of magnetic yoke II, r is the radius of the proposed MR damper, µ 1 is the relative magnetic permeability of #10 steel, and µ 3 is the magnetic permeability of free space, with a constant value of 4π×10 −7 H/m. The magnetic resistance of the MR fluid between the cylinder and magnetic yoke II can be represented as where h 1 is the fixed gap, D is the thickness of the cylinder, µ 2 is the relative magnetic permeability of MR fluid. The magnetic resistance of the magnetic yoke II and valve spool on the right side can be approximately added by The magnetic resistance of the MR fluid between the magnetic yoke II and valve spool can be expressed as where r 3 is the small-end radius of the conical MR fluid channel.
The magnetic resistance of the valve spool is where V is the effective volume of the valve spool, which can be calculated as where r 2 is the large-end radius of the conical MR fluid channel.
The magnetic resistance of the MR fluid between the magnetic yoke I and valve spool can be represented as The magnetic resistance of the magnetic yoke I and the valve spool on the left side is approximately added by The magnetic resistance of the MR fluid between the cylinder and magnetic yoke I is Hence, the magnetic flux densities of MR fluid in paths I, III, IV, and VI that shown in Fig. 6 can be obtained as follows Therefore, four segments of effective gap lengths accordingly occur under the applied current, and the field-dependent pressure drop p is activated in paths I, III, IV, and VI. The total pressure drop p consisting of the field-dependent and viscosity pressure drops can be represented as where p η and p τ are the total viscosity and fielddependent pressure drops, respectively; p a−η and p a−τ are the viscosity and field-dependent pressure drops in the annular fluid channels, respectively; p b−η and p b−τ are the viscosity and field-dependent pressure drops in the conical fluid channels, respectively; p i is the pressure drop in i-th section of MR fluid channels; p i−η and p i−τ are the viscosity and field-dependent pressure drop generated in the i-th section, respectively. Supposing no magnetic flux lines passing through the middle gaps in annular and conical MR fluid channels, i.e. II and V, there is According to the parallel plate model portrayed in Fig. 7, the shear rate u of MR fluid is given by [32] where η is the viscosity of MR fluid without a magnetic field, l is the parallel plate length, y is the longitudinal position VOLUME 8, 2020  of MR fluid, and h is the gap between the upper plate and lower one. The flow rate q is where b is the unfolded width of MR fluid.
Based on the Bingham model, the pressure drop p can be expressed as where τ y is the yield stress of MR fluid. Therefore, the viscosity pressure drop p a−η and fielddependent pressure drop p a−τ in the annular fluid channels can be expressed as where A is the piston area, v is the piston velocity, c is the correctional factor, and τ 3 denotes the yield stress of the MR fluid in paths I and III. Supposing the conical gap is similar to a parallel disk gap, the pressure drop in the conical fluid channels can be determined via the parallel disk model as depicted in Fig. 8. Based on the parallel disk model [30], the flow rate q can be calculated as where R means the parallel disk radius, dr is the unit radius of the parallel disk, and dp is the pressure drop in dr. In view of Equation (25), it can be obtained as follows Similarly, the pressure drop of the parallel disk model can be expressed as (27) where R 2 and R 3 represent the maximum and minimum radius of the parallel disk as shown in Fig. 8, respectively. By unfolding the conical fluid channels shown in Fig. 9, the half core angle α of the extended surface can be calculated as Accordingly, the viscosity pressure drop p c−η and field-dependent pressure drop p c−τ in the annular fluid channels can be deduced as where τ 1 and τ 2 denote the yield stress of the MR fluid in paths IV and VI, respectively. The total pressure drop p of the proposed MR damper can be obtained as Observing equation (31), the total pressure drop p includes four terms; the first two terms called viscosity pressure drop coming from the uncontrollable part which is related to the specific structure of the MR damper, and the latter two terms derived from the field-dependent part which is entirely relied on the applied magnetic field controlled by a direct current.
Thus, the output damping force of the proposed MR damper is represented as where F η and F τ represent the viscosity damping force and field-dependent damping force, respectively. The dynamic range K of the proposed MR damper is defined as the ratio of F to F η

IV. SIMULATION ANALYSIS USING THE FEA METHOD A. MODELING OF THE PROPOSED MR DAMPER
To validate the structural feasibility of the proposed MR damper with enhanced effective gap lengths, the FEA method was conducted by using ANSYS/Emag software (version 17.0). The FEA in which the magnetic field is produced by the excitation coil can be modeled via static electromagnet simulation without considering the effect of piston velocity on changing the distribution of magnetic field. In fact, the piston velocity exerts a little effect on the distribution of magnetic field in effective gaps. Firstly, a 2-D finite element model of the proposed MR damper was constructed as depicted in Fig. 10. It mainly consists of the valve spool, non-magnetic sleeves, magnetic yokes, excitation coil, conical sleeve, piston rod, and cylinder. Among them, valve spool, magnetic yokes, and cylinder are made from 10# steel with a high magnetic permeability, whose B-H property is depicted in Fig. 11. Here, the MR fluid adopts MRF-J01T provided by the Chongqing Instrument Material Research Institute in China; its magnetic properties are defined by τ -B curve and B-H curve, as shown in Fig. 12. Non-magnetic sleeves, conical sleeve, and piston rod are made from the stainless steel with a relative permeability of 1; the excitation coil is made of copper which possesses a relative permeability of 1 as well.
After meshing grid and assigning material areas, the input current was loaded and the boundary constraint of magnetic flux lines was specified. Finally, the solving procedure was processed. Observing Fig. 12a, the relationship between τ and B can be confirmed using the least square method to the cubic polynomial fitting of MRF-J01T, which is expressed as: where a 0 , a 1 , a 2 and a 3 respectively denote polynomial coefficients, here α 1 = −984.27 kPa/T 3 , α 2 = 865.39 kPa/T 2 , α 3 = −48.46 kPa/T, and α 4 = 0.018 kPa [32].  In general, the magnetic flux lines are intensively distributed in the primary magnetic circuits. However, there is a proportion of magnetic leakage which exists at the non-magnetic sleeves, owing to the permeability superiority of 10# steel over MR fluid. On the other hand, it is found that magnetic field lines are distributed centrally around the excitation coil, and magnetic flux lines in magnetic yokes are denser than that in other regions. Moreover, the magnetic flux lines nearly vertically pass through the effective gaps in the annular and conical fluid channels.   Fig. 14, the magnetic flux densities in effective gaps are relatively higher than that in other regions, which is consistent with the distribution of magnetic flux lines as portrayed in Fig. 13. In addition, the maximum magnetic flux density intensively located at path 1 is greater than that in path 3 and path 4, indicating that the conical fluid channels play an important role in the design of the proposed MR damper. Thereby, it can be preliminarily verified that the dynamic performance of the proposed MR damper can be obviously enhanced by compactly integrating the conical fluid channels into the annular MR channels. The magnetic flux density along path 3, i.e. B x , is essentially identical to that along path 4, due to the structural symmetry of the annular MR fluid channel as shown in Fig. 14. Nevertheless, the magnetic flux densities along path 1 and path 2 are not precisely coincident with the x-direction or y-direction. Thus, the coordinate transformation is implemented to convert them into the directions vertical parallel to path 1 and path 2, it can be expressed as: where B represents the magnetic flux density parallel to the path 1 and path 2, B ⊥ represents the magnetic flux density perpendicular to path 1 and path 2, and B x and B y are the magnetic flux density along x-direction and y-direction, respectively. Fig. 15a shows the distribution of magnetic flux density at the adjustable gaps along path 1. As portrayed in Fig. 15a, the magnetic flux density B ⊥ perpendicular to the effective gap is basically stable at −0.52 T, where the negative symbol represents that the magnetic flux density direction is opposite to the given direction. The magnetic flux density B parallel to the effective gap is slightly zero, which greatly attributes that the magnetic flux lines can almost vertically pass through the adjustable gaps. On the other hand, the magnetic flux density varies sharply at the position of 0 mm and 13 mm in path 1, this is because the magnetic flux lines did not vertically pass through the adjustable gaps.   Fig. 15a, the magnetic flux density B ⊥ that is perpendicular to the adjustable gaps primarily remains 0.51 T, the magnetic flux density B parallel to the effective gaps is nearly zero. Nevertheless, magnetic flux density B ⊥ in path 1 is slightly higher than that in path 2, owing to the denser magnetic flux lines distributed in path 1 than that in path 2. Fig. 16a and Fig. 16b reveal the relationship between magnetic flux densities and applied current in path 1 and path 2 with the adjustable gaps ranging from 0.6 mm to 1.6 mm, respectively. It can be found the magnetic flux density increases with the increase of the applied current, but decreases as the adjustable gaps increase in the longitudinal direction. This is because reducing the adjustable gaps decreases the resistance of the MR fluid in path 1 and path 2, which gives rise to the promotion of the magnetic flux density. Specifically, the magnetic flux density changes prominently around the adjustable gap of 1 mm. On the other hand, the magnetic flux density in path 1 is slightly greater than that in path 2 at the identical gap and applied current. Fig. 16c illustrates the relationship between the magnetic flux density and applied current in path 3 and path 4 at the adjustable gap of 1.0 mm. The magnetic flux density in path 3 and path 4 reaches about 0.43 T at the applied current of 1 A, which is slightly less than that in path 1 and path 2 at the adjustable gap fixed at 1 mm. Fig. 17 illustrates the variation of the damping force and Fig. 18 displays the distribution of damping force under different applied currents and adjustable gaps, where the piston velocity is fixed at 25.12 mm/s. The damping force increases by increasing the applied current and reducing the adjustable gaps. It is noted that the increasing tendency of the damping force emerges smoothly at the applied current larger than 0.8 A and the adjustable gaps greater than 1.2 mm, owing to the saturation phenomenon of the magnetic circuit. Specifically, the regulating scope of the damping force under different gaps and applied currents ranges from 0.2 kN to 9.6 kN, which manifests the proposed MR damper has better dynamic performance compared with conventional MR dampers.

V. DYNAMIC PERFORMANCE ANALYSIS A. PROTOTYPE AND DYNAMIC TEST RIG
The experimental test rig is set up shown in Fig. 19. In this experiment, the dynamic test rig mainly consists of the DC power supply (PS-305D), Fatigue machine (WPL-50), prototype of MR damper, data acquisition board, and PC (Intel i7-3.4 GHz processor and 8 GB of RAM). The MR damper was fixed on the Fatigue machine using a specific clamp. Fatigue machine was utilized to provide different kinds of displacement excitation, the DC power supply was applied to adjust the control current in the excitation coil, and the PC was adopted to collect experimental data via the data acquisition board. By setting the displacement excitation with amplitude of 4 mm and frequency of 0.4 Hz, the damping force-displacement and damping force-velocity curves at the adjustable gap of 1 mm were obtained, as detailed in Fig. 20 and Fig. 21, respectively. It can be obviously found from Figs. 20 and 21 that the simulated damping force fits quietly well with experimental damping force under different displacement and velocity, thus demonstrating the correctness of the design theory. Observing Fig. 20, the growing trend of damping force is slightly associated with the increase of the displacement, indicating that there is no apparent relationship between the damping force and displacement. As depicted in Fig. 21, the damping force augments with the increment of the applied current at an optionally fixed velocity. The increasing tendency of damping force is gradually smooth, suggesting that the magnetic circuit smoothly approaches saturation. Furthermore, when the applied current remains unchanged, the damping force almost monotonously raises with enhancing the velocity. Specifically, the experimental damping force appears a peak of 4.3 kN at applied current of 1.0 A Nevertheless, the minimum damping force, namely the viscosity damping force, achieves only 0.3 kN at applied current of 0 A.
The damping force-displacement curve at an adjustable gap of 1mm was acquired, under the displacement excitation with frequency of 0.4 Hz and amplitudes of 4 mm, 6 mm, and 8 mm, as depicted in Fig. 22. It is apparent that the damping force exhibits a mild enhancement with the augmentation of the amplitude. This phenomenon directly results from that   increasing the amplitude enlarges the velocity of the piston rod at a settled frequency. Therefore, the curve of the damping force manifests a slight increment. Additionally, the maximum damping force is identified with the values of 4.3 kN and 5.1 kN associated with the amplitudes of 4mm and 8mm, respectively.
When the MR damper was loaded under the displacement excitation with amplitude of 4 mm and frequencies of 0.4 Hz, 0.6 Hz, and 0.8 Hz, the damping force-displacement plot illustrated in Fig. 23 was obtained. Observing Fig. 23, the damping force grows up slowly as the frequency of excitation uniformly augments as well. This is the enhancement of frequency increases the damper velocity at an invariable amplitude; thus, the damping force increases mildly, which is similar to the occurrence of the damping force displayed in Fig. 22. Moreover, the maximum damping force gently reaches 4.3 kN at the frequency of 0.4 Hz, and the maximum damping force is up to 4.9 kN at the amplitude of 0.8 Hz, indicating that the frequency of the excitation signal plays a less crucial role in enlarging damping force. From discussed above, it is obviously seen that both the frequency and amplitude of the excitation signal exert a little influence on controlling the damping force. Nevertheless, the applied current is one of the determining factors which greatly affect the damping force until the magnetic circuit ascends to saturation, verifying the effectiveness of controlling the current to achieve the continuous adjustment of damping force. As a highlight, the proposed MR damper with the adjustable gap of 1mm displays an expected damping performance, which achieves the damping force varying from 0.4 kN to 4.3 kN with applied currents of 0 A and 1.0 A, respectively. Hence, this MR damper with the adjustable gap of 1 mm can be served as a conventional MR damper featuring enhanced effective length, which obviously shares a better damping force compared with the most common used MR damper.
C. DYNAMIC PERFORMANCE WITH ADJUSTABLE GAPS RANGING FROM 0.6 mm TO 1. 6 mm In this part, a series of experiments of the proposed MR damper with different gaps were conducted to acquire a more promising dynamic performance compared with the fixed gap of 1mm. By applying the displacement excitation with amplitude of 4 mm and frequency of 0.4 Hz, the damping force-gap curve was obtained as depicted in Fig. 24. It is noticeably revealed that both the experimental and simulated damping force uniformly decreases with the increase of the gap at a specified velocity. Concretely, the obvious tendency appears as the experimental gap rises from 0.6 mm to 1.2 mm, while the decreasing trend is relatively slow at the gap large than 1.2 mm. Specifically, the experimental damping force varies significantly at the gap of around 1 mm.  It can be observed that both the experimental and simulated damping forces positively associate with the applied current while negatively correlate to the adjustable gap, whereas a little difference between the experimental and simulated damping forces occurs primarily due to the weakening rheological properties of the long-unused MR fluid and regulation precision of the adjustable gaps when conducted experiment. Specifically, the maximum experimental damping force appears with the applied current of 1.2 A and adjustable gap of 0.6 mm, while the minimum one occurs at applied current of 0 A and adjustable gap of 1.6 mm.
The relationship between the damping force and the adjustable gap was obtained as presented in Fig. 26 under sequentially applied currents from 0 A to 1.2 A with an interval of 0.2 A. According to Fig. 26, there exists a positive correlation between the damping force and current but the increasing tendency becomes slowly owing to the saturation phenomenon of the magnetic circuit. On the other hand, the damping force linearly associates the adjustable gap when the applied current basically remains unchanged. Figure 27 displays the distribution of damping force under different gaps and currents. The peak damping force appears at applied current of 1.2 A and adjustable gap of 0.6 mm while the minimum one occurs at applied current of 0 A   and adjustable gap of 1.6 mm. Nevertheless, the damping force undergoes a relatively mild augmentation as the applied current is larger than 0.8 A, which implies that the magnetic circuit approaches saturation slowly. Fig. 28 shows the regulating scope of the damping force at different currents and adjustable gaps. Note that the viscous damping force appears with the applied current of 0 A. Likewise, both the viscous damping force and field-dependent damping force decrease with the increase of the adjustable gap, while the field-dependent damping force increase as increasing the applied current. Moreover, the damping forces at applied current of 0 A, namely the viscous damping forces, respectively reach 0.2 kN and 1.3 kN. The maximum damping forces achieve 2.9 kN and 7.2 kN at an applied current of 1 A, respectively. Compared with the adjustable gap of 1 mm, the damping force with the adjustable gaps ranging from 0.6 mm to 1.6 mm exhibits an enhanced dynamic performance, whose damping force is approximately 1.4 times larger than that at the adjustable gap of 1 mm. The dynamic variation of dynamic range under different currents and adjustable gaps is displayed in Fig. 29. It can be noticed that the dynamic range positively associates with the adjustable gap while negatively correlate to the applied current. Moreover, the experimental dynamic range corresponds well with the simulated one. The maximum dynamic range significantly reaches 33, appearing with the applied current of 0 A and adjustable gap of 1.6 mm, while the minimum one occurs at applied current of 1.2 A and adjustable gap of 0.6 mm.  The regulating scope of the dynamic range depicted in Fig. 30 was experimentally and theoretically obtained. It can be noticed in Fig. 30a that the experimental dynamic range uniformly decreases as the applied current increases and this tendency is a little different compared with the simulated damping force depicted in Fig. 20a. Furthermore, the experimental dynamic range varies from 2.6 to 5.7 at the applied currents of 1.2 A and 0 A, respectively. Observing Fig. 30b, the dynamic range non-linearly increases with the enlargement of the gap. Specifically, the experimental dynamic range attains 13.6 at the adjustable gap of 1.6 mm while the minimum one equal to 5.9 at the adjustable gap of 0.6 mm.
According to the damping force and dynamic range with the adjustable gaps, it can be found that the dynamic range decreases with the increment of the gap; nevertheless, the dynamic range increases with the increase of the adjustable gap. This phenomenon markedly reflects the enhancement of dynamic range decreases the damping force, which, in a large degree, inevitably appears for conventional MR dampers featuring fixed gaps, resulting in a lot of tedious and repetitive MR damper design for different conditions.
In order to verify the designed damping force under different applied currents and gaps, by adopting the current as sinusoidal excitation and velocity of 15.7 mm/s, the damping force control result is represented as Fig. 31. It can be observed that the damping force follows the control current at a fixed gap and the controlling damping force increases with the decrease of the adjustable gaps; meanwhile, from the damping force profile, it can be calculated by equation (33) that the proposed MR damper possesses a wider dynamic range, indicating that this MR damper can be well controlled by applied currents and the adjustable gaps. The response time of the electromagnetic field is also one of the significant factors to assess the dynamic performance of the proposed MR damper. Herein, the response time experiment of the electromagnetic field under different adjustable gap was conducted, and the result is depicted in Fig. 32. It is noted that the time when the voltage attains 90% of steady voltage U 0 is defined as the response time of the electromagnetic field. It is noted that the structure size significantly influences the dynamic performance of MR dampers. Hence, the comparison between the proposed MR damper and other classic MR dampers is meaningless because the structure sizes of the VOLUME 8, 2020 above MR dampers are not designed with the same structure size. Nevertheless, when the adjustable gap is fixed as 1 mm, the proposed MR damper can be served as a classic MR damper which has been successfully proposed and designed in literature. Therefore, the comparison between the proposed MR damper with adjustable gaps of 1 mm and conventional one is conducted, which is listed in Table 2. It can be noticed that the proposed MR damper with enhanced effective gap lengths achieves satisfactory goals. From a structural configuration perspective, the proposed MR damper achieves a double extension of the effective gap lengths via compactly integrating the conical fluid channels into the annular fluid channels. On the other hand, from the control strategy point of view, the damping force can be not only controlled by excitation current but also simultaneously altered by regulating the width of the adjustable gaps in the conical fluid channels. Hence, the MR damper designed in this paper can promisingly replace a variety of conventional MR dampers featuring fixed gaps, which vastly improve the dynamic performance of conventional MR dampers and further expand the application domains applied with MR dampers.

VI. CONCLUSION
The proposed MR damper with enhanced effective gap lengths can alter the relative position between the valve spool and piston by adjusting the locking nut; therefore, the gap in the conical fluid channels can be continuously adjusted. Meanwhile, the proposed MR damper can achieve a double extension of effective gap lengths via compactly integrating the conical fluid channels into the annular fluid channels.
The experimental results show that the damping force decrease with the increment of the adjustable gap under a fixed applied current, and the maximum damping force comes up to 7.2 kN at the adjustable gap of 0.6 mm. Moreover, the dynamic range increases with increasing the width of adjustable gaps, and the dynamic range appears with a peak of 13.6.
The damping force and dynamic range can be not only effectively controlled by excitation current but also flexibly altered by regulating the width of the adjustable gap simultaneously. Compared with the dynamic performance of the conventional MR damper featuring fixed gap (the damping force and dynamic range only reach 5.7 kN and 9.6, respectively), the damping force of the proposed MR damper varies from 0.2 kN to 7.2 kN and the dynamic range attains 33 correspondingly. Thus, the dynamic performance of the proposed MR damper is significantly enhanced.