Design and simulation of a novel magnetorheological energy absorber with stroke-related damping control for artillery

Abstract

In shock mitigation, the magnetorheological energy absorber (MREA) should be avoided to be over excited because the viscous force generated with the motion is too high. A novel MREA with stroke-related magnetic circuits is proposed in this paper, which is designed to employ a dynamic stroke-related magnetic field distribution to absorb more energy while protecting the damper from being damaged by excessive stress. By simultaneously examining the motions of mechanical parts and the control circuit of the adaptive flow and magnetic design, an ideal variable magnetic distribution with four solenoid coils is obtained through magneto-flow coupled simulation. Through the coupled excitation method of stroke and circuit, the damping force output at a low speed in the later stage of the impact is significantly increased. As a result, more resistance is provided during the stroke, and more energy is absorbed. The output damping force of MREA reaches its maximum of 5.5 kN, which decreases by 15% compared with the traditional method, and the absorbing energy increases by 37%. With this design, the penetrating force peak can be smoothed to decrease the demand of the structural strength, and this paper provides a theoretical support for the experimental validation of a high-performance MREA.

Keywords

Magnetorheological energy absorber (MREA)stroke-related progressive current excitation (PCE)

1. Introduction

Shock absorbing is a critical aspect in various applications, including automotive (Kasprzyk et al., 2014), aerospace (Praveen and Jagadeesha, 2020), and industrial systems (Hua et al., 2020; Milecki and Hauke, 2012), where the resistant response of excessive vibrations and impacts is of utmost importance for safety (Singh and Srilatha, 2018), performance, and durability. MREAs have gained significant attention as active damping devices due to their ability to adjust damping characteristics in real-time by exploiting the rheological properties of magnetorheological (MR) fluids, which is named magnetorheological effect (Jolly et al., 1996). The application of MREA in the field of artillery recoil has become quite common (Hu et al., 2012). However, because the peak impact of the external incentives is fierce, the maximum allowable impact force of such dampers is generally rather small (Xi et al., 2021). Meanwhile, due to the positive correlation between impact velocity and output damping force, there are also certain issues with the sustainability of MREA output damping force (Wang et al., 2025). Nevertheless, in certain scenarios, it is generally recommended to avoid fiercely exciting the MREA due to the excessive damping forces generated during wild external motivation, which can lead to damage of the shock absorber system (Han et al., 2018; Yoon et al., 2020).

To overcome the challenge of excessive response amplitudes and potential structural damage under intense shocks, researchers naturally turned to the idea of constructing large-scale magnetorheological dampers (Bajkowski et al., 2012; Hu et al., 2012; Yang et al., 2002). The expanded stroke-scale of MR dampers is primarily achieved through methods such as increasing the size of the damper, optimizing the damper materials, and designing specialized structures. However, fundamentally, the composition materials and dimensions of the damper predominantly determine its stroke-scale, and improvement of the former often incur significant costs. This also implies that achieving a large scale in MR dampers often accompanies larger dimensions (Abdul Aziz et al., 2022). As a result, they are primarily utilized in large-scale installations such as buildings and bridges, where there are no specific constraints on the structural dimensions. However, in application scenarios such as UAV blocking nets and artillery recoil (Ahmadian and Poynor, 2001; Li and Wang, 2012), it is crucial for the MREA to generate significant damping forces within the small size and in an extremely short duration. This undoubtedly poses significant challenges for the construction of magnetorheological dampers with large stroke capacities (Huang et al., 2023).

In fact, the absorption behaviors of external excitation by MREA primarily stems from energy conversion, where the energy of the external excitation is absorbed by the work did by MREA (Cai et al., 2022). Therefore, in addition to expanding the scale of the MREA, increasing the damper stroke (Boelter and Janocha, 1998; Zemp et al., 2016) is also a possible way to resist excessive external excitation. However, this simultaneously results in an increase in the length of the MREA, thereby enlarging the overall dimensions. Consequently, this imposes limitations on the usability and applicability of MREAs in various scenarios. Upon close observation of the force-displacement curve of MREA under a single shock, it is evident that the area enclosed by the curve and the abscissa represents the work done by the MREA in response to external excitation. The trend of this curve (Kasprzyk et al., 2014) demonstrates an initial sharp increase during the early stage of the shock, followed by a gradual decrease until it eventually returns to zero. The damping force maintained for a very short duration within a relatively large range, leading to insufficient energy absorption by the MREA. If we can continuously sustain the output force of the MREA at a higher level, it undoubtedly has the potential to increase the upper limit of energy absorption.

In order to accomplish the thought, this paper presents a novel MREA design with variable multiple magnetic circuits that enables enhanced control of the damping forces throughout the stroke. The proposed MREA design aims to overcome the inherent challenges associated with conventional MREAs by utilizing an innovative approach that incorporates adaptive flow control and magnetic design strategies. By simultaneously considering the motion of mechanical components and the control circuitry, an appropriate variable magnetic distribution is achieved through magneto-flow coupled simulation, employing four solenoid coils. The unique characteristic provides the MREA with the ability to deliver consistent and sustainable output damping force at the end of the stroke, just before the reversal of motion. Furthermore, a theoretical model is developed by integrating the Navier-Stokes equation and magnetic circuit analysis. This model enables the evaluation and understanding of the factors influencing the output damping force of the MREA.

The proposed design offers several advantages. Firstly, it facilitates the smoothing of the penetrating force peak, thereby reducing the structural strength requirements. This feature is particularly beneficial in applications where weight reduction and structural optimization are critical considerations. Secondly, it extends the duration of output force, leading to more energy absorbed by MREA. This research provides a theoretical foundation to support the experimental validation of a high-performance MREA. The theoretical model and simulation results serve as a guide for the design and optimization of MREAs, enhancing their overall effectiveness and applicability.

2. Theoretical and simulation analysisof the novel stroke-related MREA

2.1. Theoretical model of the novel stroke-related MREA

2.1.1. Modeling

The novel MREA primarily consists of an outer cylinder, inner cylinder, damping outer channel, damping inner channel, excitation coils, piston rod, floating piston, and micro through-hole, as shown in Figure 1(a). Its internal structure comprises two main channels: the inner (damping) channel and the outer channel, where the MR fluid flows through driven by the piston. A piston is positioned within the inner channel, while four equally spaced coil regions are arranged along the damping (outer) channel. These four coils are individually connected to four circuits of the excitation power supply, enabling the control of the number of activated circuits to achieve the desired variation in the magnetic field within the damping channel. The length of MREA is 654 mm and the maximum stroke is 30 mm. When the damper is impacted, the piston rod is pulled out, and the excitation current gradually activates, thereby generating a gradual damping force. The spring gradually compresses with the increase of stroke. Finally, when the external force is exhausted, the damping rod and piston are pulled back by the restoring force of the spring, and at the same time, the one-way valve on the piston head opens, and the piston head eventually returns to its initial position.

The magnetic circuit distribution of the MREA is illustrated in Figure 1(b). In the figure, the red dashed arrows outside each coil group represent the ideal magnetic flux path. From the path, it can be observed that the induced magnetic field generated by the excitation coils travels successively through the upper damping gap channel, outer cylinder, lower damping gap channel, and finally returns to the magnetic yoke, forming a complete closed loop.

Since each magnetic circuit is identical, we isolate a single magnetic circuit for analysis, as shown in Figure 1(c). The magnetic circuit passes through the magnetic yoke, upper damping channel, outer cylinder, and lower damping channel during its progression. It’s assumed that the magnetic reluctance of the materials within each component is as depicted in Figure 1(d) and (e). By the definition of magnetic reluctance, its magnitude is directly proportional to the length of the magnetic circuit and inversely proportional to the cross-sectional area of the circuit. Therefore, the expression for calculating magnetic reluctance is:

R_{i} = \frac{l_{i}}{μ_{0} μ_{i} A_{i}}

(1.1)

Where $l_{i}$ represents the axial length of the magnetic flux lines passing through the magnetic field region of the coil, and $A_{i}$ represents the radial cross-sectional area of the magnetic material.

According to Kirchhoff’s second law for magnetic circuits, the magnetic flux linkage of the excitation coil can be expressed as:

F_{m} = N_{c} I = \sum_{i = 1}^{n} H_{i} l_{i}

(1.2)

Where $N_{c} I$ represents the total magnetic flux linkage in the magnetic circuit, expressed as $F_{m}$ , $N_{c}$ is the number of turns of the excitation coil, and $I$ is the external current. $H_{i}$ represent the magnetic field intensity in i part of the magnetic circuit, $l_{i}$ represents the length of i part in the magnetic circuit, and $H_{i} l_{i}$ represents the magnetic potential drop across i part in the magnetic circuit.

According to the relationship between magnetic induction intensity B and magnetic field intensity H. We can express the magnetic flux density $F_{m}$ and magnetic flux $ϕ$ as follows

\begin{matrix} F_{m} = \sum_{i = 1}^{n} \frac{B_{i}}{μ_{0} μ_{i}} l_{i} = \sum_{i = 1}^{n} \frac{ϕ_{i}}{μ_{0} μ_{i} A_{i}} l_{i} = ϕ R_{m} \\ ϕ = \frac{N_{c} I}{R_{m}} \end{matrix}

(1.3)

Finally, the magnetic flux density B inside the damping channel is obtained as follow

B = \frac{ϕ}{A_{i}} = \frac{N_{c} I}{R_{m} A_{i}}

(1.4)

Then, combining the Herschel-Bulkley model and Navier-Stokes equation, the output force of the MREA is obtained

\begin{matrix} Q = \frac{ω}{(n + 1) (n + 2)} \cdot \\ {(\frac{η L_{a}}{Δ P_{a}})}^{2} [{(\frac{Δ P_{a}}{η L_{a}} - \frac{τ_{y}}{η})}^{n + 2} - {(\frac{τ_{y}}{η})}^{n + 2}] \\ = \frac{Δ P_{a} ω b^{3}}{6 η L_{c}} = A_{p} v_{p} \\ F = Δ P \cdot A_{p} = (Δ P_{a} + Δ P_{c}) A_{p} \end{matrix}

(1.5)

Where $L_{a}$ represents the length of the excitation coil section subjected to the magnetic field, $A_{p}$ represents the cross-sectional area of the piston, $b$ represents the width of the damping channel, $L_{c}$ represents the length of the excitation coil section without the magnetic field, $η_{0}$ represents the viscosity of the magnetorheological fluid at zero-field intensity, $v_{p}$ represents the velocity of the piston, n represents is the index of liquidity behavior, $ω$ is the circumference of the intermediate layer in the damping channel, and $η$ is the viscosity of the magnetorheological fluid under the influence of the magnetic field, which depends on the magnetic induction intensity. Due to the chain formation phenomenon as shown in Figure 1(f) and (g), MR fluid was hard to flow in damping channel, which leads to the generation of output force. MREA outputs corresponding damping forces at different stages under the same impact by regulating the number of activation coils to achieve the purpose of absorbing more impact energy, which is realized in the mechanical model by regulating the value of $L_{a}$ and $L_{c}$ .

2.1.2. results and discussions

Through the theoretical model, the variation trend of the damping force with the stroke of piston is calculated and obtained. Figure 2(a) illustrates six scenarios: (I = 1 A, v = 3 m/s), (I = 1 A, v = 2 m/s), (I = 1 A, v = 1 m/s), (I = 2 A, v = 3 m/s), (I = 2 A, v = 2 m/s), and (I = 2 A, v = 1 m/s).

The force-displacement curve for the first scenario (I = 1 A, v = 3 m/s) is be analyzed as a typical situation. From the graph, it can be observed that the damping force within the damping channel exhibits a stepwise increasing trend with the stroke of piston. The theoretical values undergo four-step changes, starting from 0.154 kN, then reaching 2.04, 3.69, 5.49 kN, and eventually peaking at approximately 7.26 kN. Analyzing the variation pattern reveals that the damping force increases rapidly within one stroke of the piston and undergoes four-step changes.

This behavior is a result of employing a stroke-related variable magnetic field design for the MREA, where the time of magnetic field effects generation for the four coils is related to the piston’s stroke. As the piston stroke changes, the four coils in the damping channel sequentially generate magnetic field effects, leading to the observed stepwise increase in damping force, as shown in Figure 2(b). Therefore, the analysis of the damping force variation validates the feasibility of the variable magnetic field design, and it is foreseeable that the function of variable magnetic field will play a role in delaying the decline of damping force when the piston velocity decreases rapidly after the damping stroke.

2.2. Simulated model of the novel stroke-related MREA

2.2.1. Modeling of simulation

A two-dimensional axisymmetric model of the MREA was established, as shown in the Figure 3. COMSOL’s magnetic module, fluid flow module and moving mesh module were employed to calculate the output force of MREA. The designed MREA, considering only the upward motion of the piston and without volume compensation, is shown in Figure 3(a). The 2D model of the MREA mainly consists of the piston, damping gap channel, magnetic coils, and magnetorheological fluid filled between the cylinder and the piston. Four sets of excitation coils are placed at the damping channel, forming the magnetic circuit which is shown in Figure 3(b). The entire model simulates the process of the piston moving upward at a certain velocity through the use of a dynamic mesh shown in Figure 3(c), driving the MR fluid in the main channel of the damper to flow through small holes into the other channel, and passing through the magnetic control coil region to generate damping force. The flow passageway is shown in Figure 3(d) in detail. The materials used in the model are selected from COMSOL’s material library. The regions of coil gaps, outer cylinders, coils, and damping channels are assigned as magnetic yoke, stainless steel, 10# steel and MR fluid, respectively. The magnetization model of each material adopts the permeability model, which is set by the corresponding B-H curve.

2.2.2. Results and discussions

Figure 4(a) shows the magnetic field distribution in the induction region at different time points. From the four different time points’ magnetic field distribution represented in the graph, we can observe the magnetic circuit trend within the damper. It is evident that the variations in the magnetic circuit are concentrated in the effective damping channel region of the main magnetic circuit. The locations with higher magnetic induction intensity exhibit denser magnetic field lines. Additionally, in this region, the direction of magnetic field lines is perpendicular to the direction of fluid motion, resulting in the most intense magnetic field effects, with a maximum magnetic induction intensity value of approximately 0.3 T. In contrast, within the ineffective damping channel region, the direction of magnetic field lines tends to be more parallel to the fluid motion direction within the damping channel, leading to weaker magnetic field effects, and consequently, the magnetic induction intensity value in this region tends to approach zero. By observing the changes in magnetic induction intensity and magnetic field line distribution, we can confirm that the arrangement of excitation coils and the magnetic circuit setup in the simulation model can indeed achieve the variable magnetic field effect, thereby fulfilling the design intentions.

Point calculations were performed on the model with excitation currents of 0.5, 1.0, 1.5, and 2.0 A, resulting in the magnetic induction intensity variation trends shown in Figure 4(b). From the graph, it can be observed that the magnetic induction intensity variation trends are consistent under different current conditions. As the fluid flows through points a, b, c, d, and e, their magnetic induction intensity shows the following trend over time: near point a, the magnetic induction intensity rapidly increases from 0 ms and reaches its maximum at 1 ms. After 1 ms, the magnetic induction intensity slowly decreases and gradually stabilizes. Near point b, the magnetic induction intensity rapidly increases from 3 ms and reaches its maximum at 5 ms. After 5 ms, the magnetic induction intensity slowly decreases and stabilizes. Near point c, the magnetic induction intensity rapidly increases from 5 ms and reaches its maximum at 7 ms. After 7 ms, the magnetic induction intensity slowly decreases and stabilizes. Near point d, the magnetic induction intensity rapidly increases from 7 ms and reaches its maximum at 9 ms. After 9 ms, the magnetic induction intensity slowly decreases and stabilizes. As the magnetic induction intensity is directly proportional to the current, from the variations in magnetic induction intensity values shown in the graph, it can be observed that with an increase in current, the magnetic induction intensity values gradually increase, from approximately 0.08 T at 0.5 A to around 0.25 T at 2 A.

2.2.2.1. The picture has been modified

An analysis and discussion were conducted on different conditions with MREA’s damping channel widths of 1, 1.5, and 2 mm. Various magnitudes of current excitations were applied to obtain the distribution of induced magnetic field intensity along the damping gap magnetic circuit path, as shown in Figure 4(c). From the graph, it can be observed that the internal magnetic induction intensity within the damping channel varies with the Y-coordinate under different damping gap widths. Since there are four magnetic induction coils in the Y-direction, the overall magnetic induction intensity variation trend exhibits five distinct oscillations. At the effective damping channel region, the magnetic induction intensity increases rapidly along the path. For a width of 1 mm, the maximum magnetic induction intensity reaches approximately 0.25 T; for a width of 1.5 mm, the maximum magnetic induction intensity inside the damping channel is approximately 0.18 T; and for a width of 2 mm, the maximum magnetic induction intensity reaches around 0.14 T. Summarizing the variation pattern, as the damping channel width increases, the generated magnetic induction intensity decreases, while as the damping channel width decreases, the generated magnetic induction intensity increases. This confirms that optimizing the damping gap size can enhance the performance of the damper.

2.2.2.2. The picture has been modified

Considering the Reynolds number of MR fluid within the MREA, it can be determined that the MR fluid is in a laminar flow state and behaves as an incompressible non-Newtonian fluid when subjected to the magnetic field. Therefore, in the simulation calculations, a laminar physics field is employed, and the no-slip fixed wall boundary condition is applied to the piston boundary and fluid domain. The fluid properties are defined as a Bingham-Papanastasiou fluid with viscosity varying with shear rate and magnetic induction intensity. This allows for the analysis of the distribution pattern of the internal flow field within the MREA under the influence of the magnetic field.

By setting boundary conditions to give the piston a velocity of 3 m/s in the upward direction, transient results of velocity and magnetic induction intensity over time are obtained, as shown in Figure 5(a). From the graph, it can be observed that as the piston moves upward, the fluid within the main channel of the damper is gradually driven by the piston to flow through the micro-sized orifices between the flow paths and enter the outer damping gap channel until the piston reaches the orifice position. As the piston continues to move and the coils are energized, the magnetorheological fluid inside the damping channel gradually transitions from liquid to semi-solid state, leading to an increase in viscosity. The high fluid viscosity makes it difficult for the magnetorheological fluid to flow within the channel, resulting in an increased pressure difference at both ends of the piston, which generates damping force. As the stroke increases, the number of coils being energized also gradually increases, making the magnetorheological fluid even more difficult to flow, ultimately leading to an increase in output force, which is shown in Figure 5(b) and (c).

The output force is also calculated by the simulated model, which is shown in Figure 5(d) to (f). It can be seen that, with the displacement of the piston, the MR fluid inside the damping channel undergoes changes in magnetic induction intensity as it passes through each coil. These changes enable the superposition of magnetic fields, resulting in an increase in damping force with the increment of the stroke. Simultaneously, the output force is found to be proportional to both the piston velocity and the magnitude of the excitation current, which is consistent with the reality. It confirms the accuracy of the proposed model. In a word, the trend of output force of the novel MREA is completely identic with our previous expectations. The output force of MREA is related with the stroke of piston, and provide more resistance at the second half of displacement.

2.3. Fast response current source

Given the impacts are dynamic behaviors occurring in an extremely short time, the influence of response time is particularly crucial for constructing the energy-absorbing capacity of the MREA. The design requires that the MREA should complete the loading, launching, impact energy absorption, and resetting of a shell within 300 ms. Therefore, the impact energy absorption is required to be completed in as short a time as possible. Thus, this paper constructs a fast-response current source based on the synergistic effect of a supercapacitor and a Buck converter. Its control strategy is to achieve fast response through the supercapacitor during the voltage-rising stage. The supercapacitor, with its ultra-high energy density, enables rapid voltage increase. Subsequently, after reaching the target voltage, the Buck converter is used to continuously and stably output the target voltage. The circuit schematic diagram is shown as Figure 6(a).

According to the circuit schematic, a circuit simulation model was established in the computer to simulate the boost results with expected voltages of 3, 6, and 9 A, as shown in Figure 6(b). In the boost phase, due to the positive correlation between the voltage rise rate and the initial voltage of the supercapacitor, we set the initial voltage of the supercapacitor to its maximum value of 44 V to achieve the fastest possible boost speed. As shown in the figure, the response time of the current increases with the expected value, with response times of 1.3, 2.7, and 4.5 ms for 3, 6, and 9 A, respectively. From this, it can be seen that the fast response current source under the synergistic effect of supercapacitors and Buck converters greatly shortens the response time of the current, which theoretically proves the outstanding advantages of this scheme.

In addition, the buffering force of the MREA is regulated by the magnetic field, which is generated by the excitation current. Therefore, in addition to paying attention to the response of the excitation current, we should also focus on the magnetic field response of the magnetorheological recoil device. Therefore, this article used simulation software to simulate the dynamic response of the magnetic field. In the simulation setting, the medium in the damping channel is air, and the current curve is used as the current excitation of the coil to obtain the response curve of the magnetic induction intensity in the damping gap over time, as shown in the Figure 6(c). Obviously, it can be seen that the magnetic induction intensity of each curve first rapidly increases to a “turning point” and then tends to stabilize. Mark each curve with the magnetic induction intensity at the turning point, and define the response time as the time it takes for the magnetic induction intensity to reach 95% of the turning point. It can be inferred that the expected magnetic induction strengths for currents 3, 6, and 9 A are 0.08, 0.16, and 0.26 T, respectively, with corresponding response times of 2.5, 5, and 8 ms, respectively. It can be seen that the magnetic induction intensity is positively correlated with the current, and the response time increases with the increase of magnetic induction intensity. In addition, by comparing the response time of magnetic field and current, it can be found that the current effect causes the response of magnetic induction intensity to lag behind the current, with a lag time of 1.2–3.5 ms.

According to the above analysis, even under high current excitation, the fast output current source can control the power response time within 15 ms, which can meet the power response time requirements of the MREA.

3. Experimental characterizations of the novel stroke-related MREA

3.1. Experimental method

Two experimental researches were conducted on the MREA, including single-impact experiments and recoil experiments. The former aimed to investigate the energy absorption performance of the MREA under progressive current excitation, while the latter aimed to assess the practical application effectiveness of this energy absorber. The system for the single-impact experiment is illustrated in Figure 6. The signal amplifier, signal acquisition instrument and two PCs are used to collect and output the signal of damping force. The platform supplies a suitable plate for experiments. Multi-power-supply provides progressive current excitation to MREA. DC power supply provides the power to electric devices. The impact hammer gives the MREA controllable stimulation incentives. The experiment conducted tests on the damping force of the MREA at different impact hammer heights of 50 mm with excitation currents set at 0, 0.5, 1.0, 1.5, and 2.0 A. By employing the progressive current excitation (PCE) approach, the study investigated the enhancement effect of this excitation method on the energy absorption performance of the MREA. Due to confidentiality agreements, the experimental setup and system for recoiling experiment are not extensively disclosed.

3.2. Results and discussions

The output force and displacement of the MREA under different current excitations were recorded through experiments, as illustrated in Figure 7.

Here, we compared the output force of the MREA under three different conditions: without current excitation, with a constant 2 A current excitation and with PCE, which is shown in Figure 7(a). The maximum output force of MREA under 0 A, 2 A (PCE), and 2 A are 3601 N, 5540 N, and 6489 N, respectively. It is observed that the peak of output force in the third condition falls between the first two, but its decreasing trend is much slower. This indicates that the output force of the MREA can remain at a higher level during the latter half of the impact, allowing it to absorb more external energy. Compared to the cases of non-magnetic field and fixed magnetic field, the MREA operates more steadily and the output force of it is more lasting and greater. As time goes by, the increasing displacement arouses the coils gradually and bring greater MR effect, resulting in it is more difficult for MREA to be compressed. Ultimately, the output force of MREA under 2 A (PCE) maintains in a higher level than other situations. And the displacements of MREA under 0, 0.5, 1.0, 1.5, and 2.0 A with PCE are shown in Figure 7(b). From the graph, it can be observed that as the current increases, the displacement of the piston rod gradually decreases. Specifically, without current applying, the displacement variation of the damper is 16.1 mm, under 0.5 A, the displacement variation of the damper is 14.5 mm, under 1 A it is 13.8 mm, under 1.5 A it is 13.3 mm, and under 2 A it is 12.4 mm. Furthermore, it is evident that during a single impact, the displacement rises rapidly at the initial stage. As the damping force of the MREA gradually increases to match the external impact, the upward trend of the displacement slows down, indicating that the output damping force of the MREA tends to stabilize.

Furthermore, we also measured the variation of the output damping force of the MREA over time under the influence of different control currents, as shown in Figure 7(c). It can be observed that the magnitude of the external excitation current mainly affects the peak value of the output damping force. At the same time, it also plays a role in maintaining the output damping force during the later declining stage, than the situation under 0 A. This indicates that the PCE does not vary with the magnitude of the current in its excitation effect on the MREA. The great impression on energy absorption under high current is attributed to the large current itself rather than the PCE measure. The reason why the output force with the current of 1.5 and 2.0 A was getting weaken in second half and the end of the route is that, as the current arising, the change of damping force become more wild and the DC power supply could not catch up with strict requirements in timeliness and stability.

Figure 7(d) exhibits the relationship between the displacement and output force of MREA under 0, 2.0, and 2.0 A with PCE. The projection of the relationship curve in the X-axis direction is the work did by MREA, symbolizing the energy absorbed by MREA. Obviously, with PCE, the maximum output force reduces from 6489 to 5540 N by 15%. Lower peak output force could provide safer environment for MREA to absorb energy and protect it from crushing and cracking. As the displacement increasing, the remain coils are activated, maintaining the output force at a higher level. By integrating the curve, the energy absorbed by MREA is calculated. The absorbing energy under 2 A and is 1.55e⁴ N·m, which is 201% of the energy under 0 A. The absorbing energy under 2 A (PCE) and is 1.83e⁴ N·m, which is 238% of the energy under 0 A. The latter increased by 37% than the former, implying that PCE endow MREA stronger energy absorbing capability. In other words, PCE reduces the maximum output force of MREA and absorbs more energy than direct excitation at the same time. It means the security and efficiency of MREA have been improved, proving the success of our design of a stroke-related MREA, which can absorb more external energy compared to traditional dampers.

In the recoil experiment, the displacement and output force of the MREA at different PCE of 0, 2, 4, and 6 A are shown in Figure 8. It should be noticed that the current is consist of two MREAs, and the output force is as the same. From the graph, it can be observed that the MREA can provide sufficient output force for recoiling, with a maximum value of approximately 12.18 kN, and maintains a good resistance level during the latter half of the impact cycle. Meanwhile, the piston displacement of the MREA does not show significant changes, indicating an increase in the absorbed energy. This novel MREA can effectively serve as the recoil energy absorber, providing adequate support.

When considering the distinction based on PCE, the output force of the MREA is shown in Figure 8(c). It can be observed that during the early stage of impact, there is not much difference between the two cases, and even at the first peak, there is no significant divergence. However, as the impact behavior continues, the MREA with PCE clearly outputs higher damping force, indicating greater energy absorption. This is attributed to the continuous excitation provided by the PCE, which increases the magnetic field strength as the piston velocity decreases in the latter half of the stroke. That’s leading to increasing the viscosity of the MR fluid inside the MREA to compensate for the deficiency in velocity. This demonstrates that the MREA can provide sustained high-level output force and stay a high-level in energy absorption, thereby offering substantial and consistent support for recoil. This experiment confirms the excellent energy absorption capacity of this novel MREA (Figure 9).

4. Conclusions

A magnetic and mechanical theoretical model for a stroke-related MREA is established and the output damping force of the MREA under PCE is calculated and experimented. It is found that the configuration with multiple coils can provide the MREA with more resistance capability in single impact scenarios at the theoretical level, enabling it to absorb more energy. A simulation model is developed to simulate the magnetic field variation and damping force changes of the MREA under PCE, confirming the correctness of the design and its theoretical model. Furthermore, the MREA is validated through impact hammer experiments and recoil experiments under PCE, demonstrating that it can provide higher output damping force than traditional MREAs during the latter half of the single impact cycle. This implies that the MREA can absorb more external energy, aiding in the more efficient operation of recoil systems.

Footnotes

Declaration of conflicting interests

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

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research is supported by National Natural Science Foundation of China (No. 62073050)

ORCID iDs

Minghui Zhu

Shiwei Chen

Honghui Zhang

Data availability statement

The data generated and analyzed in this study are available from the corresponding author upon reasonable request. The corresponding author will respond promptly, providing data in suitable formats. If there are data - use restrictions, like for sensitive info, they’ll be clearly communicated.

References

Abdul Aziz

Mohtasim

Ahammed

(2022) State-of-the-art recent developments of large magnetorheological (MR) dampers: a review. Korea-Aust Rheol J34: 105–136.

Ahmadian

Poynor

(2001) An evaluation of magneto rheological dampers for controlling gun recoil dynamics. Shock and Vibration 8: 147–155.

Bajkowski

Jasiński

Mączak

, et al. (2012) The active magnetorheological support as an element of damping of vibrations transferred from the ground to large-scale structure supports. Key Engineering Materials 518: 350–357.

Boelter

Janocha

(1998) Performance of long-stroke and low-stroke MR fluid dampers. In: Smart structures and materials 1998: passive damping and isolation, pp. 303–313. San Diego, CA: SPIE.

Cai

Zhu

SJR

Reviews

(2022) The nexus between vibration-based energy harvesting and structural vibration control: a comprehensive review. Renew Sustain Energy Rev155: 111920.

Han

Kim

Choi

(2018) Design of a new magnetorheological damper based on passive oleo-pneumatic landing gear. J Aircr55: 2510–2520.

Hua

Liu

Sun

, et al. (2020) A magnetorheological fluid-filled soft crawling robot with magnetic actuation. IEEE/ASME Transactions on Mechatronics 25: 2700–2710.

Huang

Yang

Processing

(2023) Towards novel energy shunt inspired vibration suppression techniques: principles, designs and applications. Mechanical Systems and Signal Processing 182: 109496.

Jiang

Wang

, et al. (2012) Design, modeling, and controlling of a large-scale magnetorheological shock absorber under high impact load. Journal of Intelligent Material Systems and Structures 23: 635–645.

10.

Jolly

Carlson

Munoz

(1996) A model of the behaviour of magnetorheological materials. Smart Materials and Structures 5: 607.

11.

Kasprzyk

Wyrwał

Krauze

(2014) Automotive MR damper modeling for semi-active vibration control. In: 2014 IEEE/ASME international conference on advanced intelligent mechatronics, pp. 500–505. Besancon, France: IEEE.

12.

Wang

(2012) A gun recoil system employing a magnetorheological fluid damper. Smart Materials and Structures 21: 105003.

13.

Milecki

Hauke (2012) Application of magnetorheological fluid in industrial shock absorbers. Mechanical Systems and Signal Processing 28: 528–541.

14.

Praveen

Jagadeesha

(2020) Synthesis and characterization of cost effective and eco-friendly magneto rheological fluid for aerospace applications. In: IOP conference series: materials science and engineering. Chennai, India: SRM Inst Sci & Technol, 022027.

15.

Singh

Srilatha

(2018) Design and analysis of shock absorber: a review. Materials Today Proceedings 5: 4832–4837.

16.

Wang

Cai

, et al. (2025) Design and experiment study on a novel magnetorheological impact damper coupled with multiple parallel relief orifices for reducing higher impact peaks. Journal of Intelligent Material Systems and Structures 36: 242–258.

17.

Dong

, et al. (2021) A novel passive adaptive magnetorheological energy absorber. Smart Materials and Structures 30: 014001.

18.

Yang

Spencer

Carlson

, et al. (2002) Large-scale MR fluid dampers: modeling and dynamic performance considerations. Engineering Structures 24: 309–323.

19.

Yoon

Kang

Kim

, et al. (2020) New control logic based on mechanical energy conservation for aircraft landing gear system with magnetorheological dampers. Smart Materials and Structures 29: 084003.

20.

Zemp

De La Llera

Saldias

, et al. (2016) Development of a long-stroke MR damper for a building with tuned masses. Smart Materials and Structures 25: 105006.