Design,modeling,and controlling of a large-scale magnetorheological shock absorber under high impact load

Abstract

In this article, an MRD50 type of large-scale magnetorheological shock absorber was designed and manufactured in Smart Materials and Structures Laboratory of Nanjing University of Science and Technology. Upon providing a brief background on magnetorheological dampers, the detailed structure of this developed large-scale magnetorheological shock absorber was depicted. A suit of hardware-in-the-loop simulation platform under high impact load excitation was introduced for a weapon system. A series of tests were conducted to establish the dynamic behaviors of magnetorheological shock absorber under impact loads. The test results show that the inertia damping force should not be ignored like a common magnetorheological damper because of the large acceleration from the impact load. Based on the theory model and the experimental data, index parameters of magnetorheological fluid and other structural parameters in Herschel–Bulkley-Inertia model were identified by using the least square algorithm. In order to evaluate the controllability of large-scale magnetorheological shock absorber applied into high impact loads, three control algorithms, including on–off control, proportional–integral–derivative control, and fuzzy control algorithm, were used in tests to control the dynamic behavior of magnetorheological shock absorber, and some results of the controllability tests were exhibited in this article. In conclusion, the results indicated that the developed large-scale magnetorheological shock absorber was indeed able to effectively control the recoil dynamics.

Keywords

magnetorheological shock absorber impact load dynamic modeling controllability

Introduction

In recent years, magnetorheological fluid (MRF), which has the ability to reversibly change its rheological properties (elasticity, plasticity, and viscosity) with the application of a magnetic field, has been widely used in the area of vibration control, such as automobiles, civil engineering (Carlson, 2005; Duan et al., 2003; Yang et al., 2002), and so on. MR damper using MRF instead of conventional oil as working liquids becomes to be one of the most promising devices for vibration control. Other systems that could benefit from the application of MR damper are those involving shock loading, such as the force applied on military protective equipments (Ahmadian and Gravatt, 2004), the vibration load caused by helicopter rotor, the impulsive force applied on the suspension system of military vehicles (Facey et al., 2005; Wang and Li, 2006), the dynamics that occur upon firing a gun (Ahmadian et al., 2003; Ahmadian and Gravatt, 2004), and so on.

When the gun is fired and the projectile starts forward, the propellant gas pressure accelerates the recoiling parts rearward. The recoil velocity could be extremely large, sometimes more than several feet per second, and it will have a great effect on its firing accuracy and stability of the gun. Although most weapon systems already have a passive recoil mechanism, the desire for building lighter weapons with increased firing power and more mission flexibility has placed the new demands on the recoil mechanisms, which could not be met using the traditional systems. In contrast to the traditional recoil devices, an MR recoil device, using the MR shock absorber instead of the commonly used hydraulic damper, will be a promising method to achieve the above goals because the MR shock absorber is capable of sensing the recoil force and stroke of the gun and providing the optimal damping force for mitigating the recoil energy.

Virginia Tech has done some initiative experimental researches on the application of MR damper for controlling recoil dynamics, and their test results show that the MR damper was able to effectively control the recoil dynamics and provide a different force–stroke curve for different amounts of current supplied to the damper (Ahmadian and Gravatt, 2004; Goncalves, 2005). More importantly, researching results of Virginia Tech has showed that it is possible to design and use MR dampers for recoil application. Since 2002, the Smart Materials and Structures Laboratory of Nanjing University of Science and Technology (NUST) have focused on the application of large-scale MR shock absorber to control impact load and developed a series of MR shock absorbers (Wang and Li, 2006). However, a systematic architecture for an MR shock absorber subjected to impact load, including structural design, dynamic response model, and control method, has still not been formed for many years (Browne et al., 2009). So the primary purpose of this study is to provide a comprehensive research on the structural design, dynamic modeling, and control methods of a large-scale MR shock absorber under high impact load.

Principle of MR shock absorber

An MR shock absorber is an intelligent device whose damping force could be changed by altering the magnetic density in the magnetic coils, leading to the continuous change of viscosity in the piston gap. In this article, MR shock absorbers, functioning as the gun recoil damper, are mainly used to dissipate energy of the impact load caused by gun’s firing. Under the normal operating conditions, the impact load over very short duration that occurs upon firing a gun will transform to relatively calmer damping force over longer duration, which is ultimately acted on the ground. The problem, which is often existed in recoil mechanical’s structure design, is that there are two resistance peak values in the course of gun recoil, which will reduce the stability of gun. Figure 1 shows the standardized adjusted curve between the shock force and stroke of the gun recoil. In order to obtain an ideal recoil curve shown in Figure 1, the structure of traditional gun recoil device should be more complex and the dimension of the liquid-flow hole also needs to be repeatedly adjusted by tests.

Figure 1.

The adjusted curve between F_R and X.

Compared with the traditional passive buffering device of the gun, the structure of an MR shock absorber is simple, and the outputting damping force could be controlled in real time by adjusting the applied current in the piston coil of the absorber. Furthermore, based on the MR shock absorber, a closed-loop control system can be designed to obtain an ideal rule of recoil force and achieve a better control of the gun recoil.

A contain caliber gun equipped with an MR shock absorber is shown in Figure 2. According to Figure 2, the movement equation of the MR shock absorber equipped for a gun can be described as follows

Figure 2.

A sketch of a certain caliber gun equipped with an MR shock absorber. (1) clamp fixture, (2) spring, (3) MR shock absorber, (4) recoil slideway, (5) Axle sleeve and recoil counter and (6) benches

m_{h} \frac{d^{2} X}{d t^{2}} = m_{h} \frac{d v_{0}}{dt} = F_{pt} - F_{R}

(1)

where, $F_{pt}$ is the impact load, $m_{h}$ is the movement mass, $X$ is the recoil movement displacement, v is the movement velocity, and $F_{R}$ is the damping force, where $F_{R} = F_{Φ h} + F_{T}$ , $F_{Φ h}$ is the hydraulic damping force produced by the traditional recoil mechanism or MR dampers, and $F_{T}$ is the frictions between the contact surfaces.

Figure 3 shows the dynamic simulation results for a gun equipped with an MR shock absorber. Compared to Figure 1, it is easy to find that the fluctuation of recoil force becomes smaller when the gun is fired, and the saddle phenomenon disappears. The difference between $F_{R max}$ and $F_{R min}$ becomes smaller, and the amplitude of $F_{R max}$ is obviously reduced. Figure 3 also shows that the damping curve under different applied current is not in the same shape, and the shape under 2.0-A applied current is more like the ideal curve of $F_{R}$ −X, as shown in Figure 1. Therefore, the dynamic simulation also indicates that the damping force of an MR shock absorber can be controlled by the applied current.

Figure 3.

Force versus displacement for MR shock absorber.

Development of MR shock absorber

MRF allows one to control the damping force of a damper by replacing mechanical valves commonly used in adjustable dampers. This offers the potential for a more reliable damper. Typically, the structures of a large-scale MR shock absorber are divided into double-ended and single-ended or twin tube and monotube. The accumulator is the difference between the double-ended MR shock absorber and single-ended ones, and it provides a barrier between the MRF and a compressed gas (usually nitrogen) that is used to accommodate the necessary volume changes. The accumulator works only before the accumulator piston reaches the stops until the pressure exerted by the MRF on the accumulator is reduced to a value below maximum pressure. However, in the case of high flow velocity under impact load, the accumulator cannot accommodate the necessary volume changes within few milliseconds, so there is equally no accumulator in the MR shock absorber.

In this article, a novel large-scale single-ended MR shock absorber was designed and manufactured in Smart Materials and Structures Laboratory of NUST. The details of this developed MR shock absorber are shown in Figure 4.

Figure 4.

The details of the developed MR shock absorber.

The large-scale MR shock absorber uses a simple geometry in which the outer cylindrical housing is part of the magnetic circuit. This MR shock absorber includes a double-ended piston that is attached to a guide made of red copper. The magnet coil is winded on the notching of the piston to produce the electromagnetic field. The piston can move in the cylinder, guided by the guide and a seal that is incorporated into the front cap attached at the front end of the shock absorber. A small clearance (gap) between the piston and the cylinder’s inner diameter provides the means for the MRF to pass through as the piston moves within the cylinder. As the MRF is activated by a different magnetic flux density, it offers a different amount of resistance to the motion of the piston, therefore providing different damping force. The larger the magnetic flux density, the higher the fluid resistance to the piston and larger the damping force. The magnetic flux density is controlled by the amount of electrical current supplied to the piston coil.

Because the MR shock absorber is expected to work at large velocities caused by the recoil dynamics, the gap between the piston and the cylinder had to be designed such that it is large enough that it does not unduly chock the fluid at high velocities, and yet it is small enough that sufficient magnetic flux density can be created across it for activating the fluid. After experimenting with different gap sizes, we determined that a radial gap of 2 mm worked the best for our design.

The developed MR shock absorber is used in the situation in which the piston rod is pulled out of the cylinder and not suppressed by the MRF. It is well known that liquid cannot be suppressed. However, if the piston rod is pulled out of the cylinder, there will be a vacuum space in the cylinder due to the volume change. Because the working time of the large-scale MR shock absorber is very short, the piston rod under well-sealed condition will be drawn back to the original position by the action of vacuum space pressure.

Test rig

The experimental platform for an MR shock absorber subjected to impact load is designed and exhibited in Figure 5. This test rig consists of four parts, which are closed bump, moving mass, slide way, and buffer. According to Figure 5, MR shock absorber is mounted to the slider block, which can move on the guide rail. The elastomeric bumper is designed to avoid the damper bumping into the test rig, and the allowed stroke of the test rig is 600 mm. The closed bump in the Figure 5 is used to stimulate the gun firing. During the test, several grams of powder are placed into the closed bump. Once the powder is ignited, an extremely large impact load up to 8000 N would be produced within 10 ms, and this shock force will press the MR shock absorber movement at the slide way. The moving mass that is about 258.8 kg is used to simulate the recoil mass. According to Newton’s second law, displacement law, and the action of the uncontrollable viscous damping of the MR shock absorber, before hitting the buffer, the time of the moving mass sliding on the guide way is about 500 ms.

Figure 5.

MR shock absorber and transducers.

The whole hardware-in-the-loop simulation platform for weapon system under high impact load excitation has several test devices, such as industry computer, dSPACE simulation system in real time, current controller, and rig testing, as shown in Figure 6. The industry computer is employed to demonstrate the signals transmitted from the dSPACE system and to control the current in the controller. dSPACE system is used as a data acquisition device to record all the signal of the sensors; moreover, it also works as a hardware-in-loop system to decode the MATLAB\Simulink frame into executive code and plant the executive code into the control devices. The controller is developed by Smart Materials and Structures Laboratory of NUST and has a current output capacity of 0–3 A.

Figure 6.

Developed hardware-in-the-loop simulation platform for weapon system.

In testing, five kinds of signal such as force, displacement, velocity, acceleration, and pressure were chosen to describe the dynamic behaviors of the MR shock absorber. Force sensor was installed at junction between piston rod and the fixed supports. Pressure sensor installed in working chamber of absorber was used to measure the cavity pressure of MR shock absorber. Displacement and speed sensor was used to monitor the stroke and speed of MR shock absorber. Considering that the impact time is very short, the sampling frequency is sated at 20 KHz to ensure that all dynamics signals can be captured.

The basic testing steps can be expressed as follows:

Put the powder into the chamber and use the electronic lighter device to light the powder.

With the impact force produced by the explosion of powder in close chamber, the MR shock absorber will slide on the guide rail.

The changed signal will be collected by sensors and transmitted to the industry computer.

Dynamic modeling and parameter identification

At the present time, a lot of dynamic models have been developed to describe the dynamic characteristics of MR damper when the load is random and smooth. While, when the loads are impulsive, little dynamic model could be used to describe the dynamic behavior of MR shock absorber (Lee et al., 2002, Goncalves, 2005). Because of its simplicity, the Bingham plastic model has been widely used to depict behavior of MRF under magnetic field; however, it is not valid to depict MRF, which experiences postyield thinning or shear thickening that often occurs upon firing a gun (Browne et al., 2009). In order to accurately model an MR shock absorber under impact load, the Herschel–Bulkley model, which allows for a nonlinear, postyield behavior, is often used to analyze the flow of the MRF in damping passage.

MRF would exhibit a non-Newtonian fluid behavior with the applied magnetic field. Because an MRF exhibits thinning effect under shock load, Herschel–Bulkley viscoplastcity model could be employed to accommodate this effect. In the model, the flow is governed by the Herschel–Bulkley model equation.

{_{\frac{du}{dy} = 0 (τ \leq τ_{Y})}^{τ = τ_{Y} sgn (\frac{du}{dy}) + k {(\frac{du}{dy})}^{n} τ > τ_{Y})}

(2)

In equation (2), $| τ |$ must be greater than yield stress $| τ_{Y} |$ to begin flow, $n$ is flow behavior index, $k$ is plastic flow index, and $du / du dy dy$ is shear strain rate. Depending on the choice of flow behavior $n$ , the Herschel–Bulkley model can be used to depict postyield shear thinning behavior or thickening: $n > 1$ stands for shear thickening behavior, $n = 1$ stands for Bingham behavior, and $n < 1$ stands for shear thinning behavior.

Depending on the Herschel–Bulkley model, the damping force that the MR damper produced could be concluded and expressed as

F_{HB} = \frac{KL}{n^{n}} \frac{A_{p}^{n + 1}}{A_{d}^{n}} \frac{1}{d^{n + 1}} {(\frac{2}{1 - δ^{-}})}^{n + 1} {[\frac{(2 n + 1) (n + 1)}{n (1 + δ^{-}) + 1}]}^{n} v_{0}^{n}

(3)

In equation (3), $L$ is the length of polar plate, $A_{d}$ is the sectional area of damping channel, $A_{p}$ is the active area of cylinder, $v_{0}$ is the flow rate of the MRF in damping channel, $δ^{-}$ is the shear thickness of the MRF and is equal to $\frac{2 L τ_{y}}{Δ Pd}$ , and $d$ is the gap between different polar plate. $Δ P$ is the pressure difference between the two terminals of the cylinder, and it has a relationship with the structure of the damper, flux of the MRF, and the fluid self-quality.

Based on equation (3), the damping force in the Herschel–Bulkley model would have a good correlation with the flow coefficient of the MRF. The variable of flow coefficient determines the order of magnitude for damping force. When the MRF flows through the damping channel, it will bear an inertia force produced by the fluid mass and its acceleration. This inertia force could produce a resisting force for the MRF, and it is directly proportional to the MRF’s acceleration.

The fluid inertia is caused by the flow acceleration. If the flow velocity is relative low, the fluid inertia can be neglected. For example, the inertia force is often ignored in some semiactive vibration control engineering applications like buildings and vehicle suppression. However, if an MR shock absorber was applied into the high impact load’s engineering environment, the impulsive force would be very large and would lead to an extremely large acceleration. Because of the effect of a large acceleration, the inertia force could not be ignored in the model of an MR shock absorber. Therefore, this derived Herschel–Bulkley model should be amended. When the inertia force the impact load produces is considered, an amended Herschel–Bulkley model could be obtained to describe MRF’s mechanical character. Equation (4) shows the inertia force of an MR shock absorber under impact load. This amended Herschel–Bulkley model could be expressed as equation (5).

F_{I} = ρ L \frac{A_{p}^{2} (A_{p} - A_{d})}{A_{d}} \overset{\cdot}{v}

(4)

F_{HBI} = F_{HB} + F_{I} + F_{friction}

(5)

where $ρ$ is the density of the MRF and $F_{friction}$ is the friction force between cylinder of MR damper and its cylinder tube.

Because the inertia force is included in the damping force, equation (5) is called Herschel–Bulkley-Inertia model. There commonly exits a certain model error between the actual model and the theory model. When the error is introduced into equation (5), the model can be described as equation (6).

\begin{matrix} F_{HBI}^{*} = C_{H 1}^{*} \frac{12 η L A_{p}}{d^{3} w} A_{p} v + C_{H 3}^{*} ρ L \frac{A_{p}^{2} (A_{p} - A_{0})}{A_{0}^{2}} v + F_{friction} \\ + C_{H 2}^{*} \frac{{KLA}_{p}^{n + 1}}{n^{n} A_{d}^{n} d^{n + 1}} {(\frac{2}{1 - \bar{δ}})}^{n + 1} [\frac{(2 n + 1) (n + 1)}{n (1 + \bar{δ}) + 1}] v^{n} \end{matrix}

(6)

In equation (6), $C_{H 1}^{*}$ , $C_{H 2}^{*}$ , and $C_{H 3}^{*}$ represent viscosity damping force, Coulomb damping force, and the amending coefficient of inertia force, respectively. And $C_{H 1}^{*}$ , $C_{H 2}^{*}$ , and $C_{H 3}^{*}$ can be amended by the experimental data.

By now, the least square algorithm was the most popular parameter identification method in engineering field. The parameters identification model is expressed as follows

min J (θ) = \sum_{i = 1}^{N} [F_{d} (t_{i}) - F_{HBI} (t_{i})]

(7)

In equation (7), θ is the identified parameter, $F_{d} (t_{i})$ is the testing force of the MR shock absorber at time $t_{i}$ , and $F_{HBI} (t_{i})$ is the numerical result using the Herschel–Bulkley-Inertia model. The identification steps include

Select experimental date of damping force versus velocity;

Use the linear regression method to determine the values of $C_{H 1}^{*}$ , $C_{H 2}^{*}$ , and $C_{H 3}^{*}$ ;

Step the identification step when the velocity of the established linear regression equation is equal to 0.

By using the linear regression method, the fitting Herschel–Bulkley-Inertia model is expressed as

\begin{matrix} F_{HBI} = 4.195 {(\frac{2}{1 - \bar{δ}})}^{1.8} {[\frac{4.68}{0.8 \times (1 + \bar{δ}) + 1}]}^{0.8} v^{0.8} \\ + 1.653 \overset{\cdot}{v} + \frac{1}{4.8 \times 10^{10}} e^{\overset{\cdot}{v}} \end{matrix}

(8)

In order to check the accuracy of this fitting Herschel–Bulkley-Inertia model in depicting the behavior of the MR shock absorber, a test was done to get the curve between the damping force and velocity of the piston rod under 1.0 A current input in coil. Figure 7 shows the comparison graph with the actual test curve, the simulated curves of the fitting Herschel–Bulkley-Inertia model and the fitting Herschel–Bulkley model. Refer to Figure 7, where it is shown that the fitting Herschel–Bulkley-Inertia model curve corresponds closely to the test results because of adding inertia force. But there is still a variant $\bar{δ}$ related with the damper’s velocity in Herschel–Bulkley-Inertia model, which would result in the computation time increasing in actual numerical calculation and engineering application. Therefore, in order to obtain a real-time control of the MR shock absorber, based on the existing Herschel–Bulkley-Inertia model, a simplified dynamic model of the MR shock absorber should be established in actual engineering application. This work has being done in Smart Materials and Structures Laboratory of NUST.

Figure 7.

Comparison among different models.

Controllability analysis

Using an MR shock absorber in the gun recoil mechanism is aimed at obtaining a more favorable compromise between recoil force and stroke, in other words, obtaining an ideal recoil curve, as shown in Figure 1. This control objective can be achieved by real-time change in the applied current in the coil of the MR shock absorber. At present, only little research has been done in the control technique of an MR shock absorber applied in the antishock engineering fields (Duan et al., 2004; Wang and Li, 2006). Therefore, there is an urgent need for designing an effective controlling strategy, including hardware and software element, so as to achieve an ideal controlling effect for an MR shock absorber.

Before starting the controllability analysis, it is necessary to measure the dynamic current response time of the MR shock absorber. In actual testing, 2.0-A step current was applied in the coil of the MR shock absorber in order to check the time dissipation in the process of the damping force changing from zero to a steady value. The test date was collected and processed by low-pass filtering, as shown in Figure 8. Figure 8(a) shows the step current that was applied for 0.2 s after the beginning of impact process. Figure 8(b) shows the relationship between the damping force and recoil time, and it could be seen that the damping force suddenly increases when the operating current is applied. The increasing time lasts about 100 ms, and it indicated that the response time of the MR shock absorber is 100 ms. It is easy to see that the response time of the MR shock absorber is less than the movement time, so it is feasible to do controllability test on this developed simulation platform.

Figure 8.

Response time under step current input.

It should be noted that all test results shown in this article were acquired on the condition that 2 g of powder was put and ignited in the closed bump. And the saturated exciting current of the developed MR shock absorber is 2.5 A.

Dynamic behaviors under fixed current

In order to study the controllability of the MR shock absorber under impact load, the dynamic behaviors of the MR shock absorber under fixed current should be tested first. In this test, four fixed currents, which are 0 A, 0.8 A, 1.8 A, and 2.0 A, were chosen to consider its characterization. Each test was repeated a minimum of three times to ensure the accuracy of the experimental date, which is represented in Figure 9.

Figure 9.

Responses under fixed current.

Figure 9(a) shows the relationship between its displacement and time. From Figure 9(a), it could be seen that the cylinder displacement varies from each other. Slope of the stroke curves decreases with the increase in applied currents. When the applied currents increase, peak value of the displacement moves right and is cut down. It should be noted that when the applied currents are 0 and 0.8 A, the moving mass collides with the buffer and slides back to opposite direction, which makes an obvious turn in the curve. When the applied current is larger than 0.8 A, the damping force is big enough to keep the moving mass from a collision with the buffer. So we can see that the stroke of the MR shock absorber can be controlled from more than 600 mm to about 340 mm with a distinct slope change.

Figure 9(b) shows the damping force versus recoil time for different currents supplied to the MR shock absorber. As was mentioned earlier, the saturated current of the piston coil is 2.5 A. As is expected, Figure 9 shows that the peak of the damping force increases as the applied current increases; for example, it increases from 1400 to 2300 N as the applied current increases from 0 A to 2.0 A. The increase in the damping force appears to be nonlinearly dependent on the increase in applied current, with larger increases observed at lower current to the piston coil. Furthermore, by comparing Figure 9(a) with Figure 9(b), it can be seen that the damping force is inversely proportional to the recoil stroke with the increase of applied currents. For larger damping force, the recoil stork is shortened significantly, whereas for smaller damping force, the change in recoil stroke appears to be far smaller. When no current was supplied to the MR shock absorber, the moving mass exceeded the 600-mm allowable stroke designed into the test rig and hit the elastomeric bumper installed at the end of the travel, as shown in Figure 9(a).

This test indicated that it is indeed possible to use MR shock absorber for recoil application. But there is a “peak” shape in the curve of damping force, as shown in Figure 9(b). This peak force will cause the jittering of the test rig and seriously jeopardize the performance of artillery in realization. So it is necessary to design an effective control algorithm to eliminate the “peak” shape and achieve a better control effect on gun recoil.

Controllability under on–off controlling policy

An open-loop, on–off control strategy aimed at reducing the “peak” damping force was designed to control the applied current in piston coil. In this control policy, we switched the applied currents from 0 to 2.0 ampere at a certain time-point during the motion of the MR shock absorber. This certain time-point is called switch time (ST). This control policy can be written as

I = {\begin{matrix} \begin{matrix} 0 A & 0 < t < ST \end{matrix} \\ \begin{matrix} 2.0 & A t \geq ST \end{matrix} \end{matrix}

(9)

This control policy is an open-loop control algorithm and is excited by the displacement signal in the experiment. Six STs are chosen in this test, which are ST = 0 ms, ST = 20 ms, ST = 100 ms, ST = 150 ms, ST = 250 ms, and ST = 350 ms. In order to ensure the accuracy of the experimental date, each test was repeated a minimum of three times, which is represented in Figure 10.

Figure 10.

Dynamic response under on–off control policy.

Figure 10(a) shows the damping force versus recoil stroke under on–off control policy. From Figure 10(a), it can be seen that peak of the damping force decreases as the ST value increases, and the recoil stroke is inversely proportional to the damping force. For larger the ST value, the recoil stroke is lengthened significantly, but the damping force peak is decreased, and the curve becomes more flat.

Figure 10(b) shows the damping force versus recoil time under this on–off control policy. From this figure, it can be see that there is a distinct change on the shape of the damping force curve by putting the working time of applied current off. When the ST is 0, the peak of the damping force is very large and the curve is in the shape of a sharp peak. The peak of damping force decreases, and the shape of the curve becomes flat by putting the working time of applied current off.

The testing results with on–off control policy indicated that it is possible to decrease the peak of damping force by putting the working time of applied current into “off”, but it is at the cost of increasing the recoil stroke.

Controllability under proportional–integral–derivative controlling policy

The testing results with on–off control policy show that on–off control policy could be used to control the current applied in the piston coil and decrease the peak of the damping force. However, it would cause the recoil stroke to increase and finally complicate the recoil control system. So, another control algorithm is presented to deal with this problem. In this chapter, three kinds of proportional–integral–derivative (PID) control policy, such as PI control policy, P control policy, and PID control policy were designed to control the applied current in the piston coil. The parameter of those control algorithms is shown in Table 1, and the testing results are shown in Figure 11.

Table 1.

The used parameters in PID control policy.

Control policy	K _P	K _I	K _D
PID control 1	4	8	0.4
PID control 2	3	6	0.4
PI control	5	1	0
P control	7	0	0

PID: proportional–integral–derivative.

Figure 11.

Dynamic response under different PID control policy.

Figure 11(a) shows the relationship between the stroke of the MR shock absorber and recoil time. From the figure, it can be seen that the stroke under the control of P control algorithm is just about 350 mm, which is smaller than the stroke value under fixed current and on–off control algorithms. The control effect of PID control 1 algorithm, on the converse, is worst, and the stroke is almost 600 mm. The P control algorithm also does a good job in reducing the peak of damping force, where the peak value is mere 2000 N, as is shown in Figure 11(b).

By comparing the effects of those control algorithms, it should be convinced that the P control algorithm can reduce the recoil stroke as well as the peak value of damping force. However, there is still a small sharp peak in the damping force curve under P control algorithm. So, for the purpose of minimizing peak value of the damping force, it is necessary to continue the control algorithm experimental study.

Controllability under fuzzy controlling policy

The mathematic model of the MR shock absorber shows the feature of highly nonlinear, time-delaying and time-varying characteristics. And, it would be very difficult to exactly measure and obtain some control parameters of MR shock absorber in engineering application. So, it is very difficult to make a real-time feedback control of the applied current. Compared to the classical control theory, fuzzy control algorithm has strong robustness in dealing with the nonlinear, time-varying, strong coupling, and large time-delay system. Therefore, this study aiming at the application of fuzzy control algorithm to control the dynamic behaviors of an MR shock absorber has a high engineering application value.

For the process of designing the fuzzy controller for an MR shock absorber, some particular factors should be considered

Because the response time of the experimental system is very short under impact loads, the selected input control variable should be very simple. And the acceleration response of the MR shock absorber under impact load contains intractable high-frequency noise, and the shake of the signal is very marked, so the cavity pressure of the MR shock absorber was chosen as the input control variable in fuzzy control algorithm.

The fuzzy control logic rules should be very simple in order to reduce its calculating time.

The detailed principle for the designed fuzzy policy includes the following:

At pressure signal–rising phase, when the pressure value is less than the given value, a small current will be applied into the MR shock absorber in order to make MRFs pass through the annular gap easily; when the pressure value is bigger than the given value, the input current will be set to zero in order to cut down the peak value of the damping force.

At pressure signal–descending phase, when the pressure value is bigger than the given value, the input current is also set to zero for the purpose of cutting down the peak value of the damping force; when the pressure value is smaller than the given value, a high current will be applied into the MR shock absorber in order to reduce the speed of the pressure attenuation.

A series of field test were conducted to evaluate the controlling effects of the designed fuzzy control algorithm. Each test was repeated a minimum of three times to ensure the accuracy of the date, which is represented in Figure 12.

Figure 12.

Responses under fuzzy controlling policy.

Figure 12(a) shows the recoil stroke versus recoil time under the designed fuzzy control algorithm. From this figure, it could be seen that the stroke of the MR shock absorber is about 340 mm. At the same time, the peak value of the damping force is just about 1700 N and the curve is more flat under fuzzy control policy, as is shown in Figure 12(b). A lot of experimental results have proved that the fuzzy control strategy could achieve a good harmonious effect between stroke and pressure control, and simultaneously reduce the stroke and pressure peak to a great extent. What is more, this controlling strategy could effectively extend its width of pressure platform and satisfy the MR shock absorber’s requirements of engineering applications under high impact load.

Comparison of control effect

In this section, application of several control algorithms for controlling the dynamic behaviors of MR shock absorber was examined. A simple comparison of control effect of those control policies is shown in Table 2.

Table 2.

Peak value under different control algorithms.

Control policy	Stroke (mm)	Damping force (N)
On–off control	450	1450
P control	350	2000
Fuzzy control	340	1700

P: proportional.

In general, the peak of the damping force can be cut down to minimal value under on–off control algorithm; the peak of stroke is just about 340 mm under fuzzy control algorithm, which is the best value among those control algorithms. However, the stroke is very long under the control of on–off control algorithm. P control algorithm can reduce the recoil stroke as well as the peak value of the damping force, but there is still a small sharp peak in the damping force curve. Compared with on–off and P control algorithm, the fuzzy control algorithm does best in controlling the dynamic behaviors of the MR shock absorber. Under fuzzy control policy, both the peaks of stroke and damping force will reduce to a smaller value, and the working time of damping force extends to a larger value.

Conclusion

The application of an MR shock absorber for controlling recoil dynamics was examined, using a suit of hardware-in-the-loop recoil simulation platform. A novel large-stroke MR shock absorber was designed such that it could work effectively at the large velocities commonly occurring in a fired gun and could also be easily adjusted to reasonably optimize the damper performance for the recoil simulation test rig that was used for this study. The dynamic model of this MR shock absorber under impact load was developed. Inertia damping force, which is induced by abrupt acceleration of the MR shock absorber and could not be neglected in the dynamic model, was introduced.

A series of tests were done to evaluate the dynamic behaviors of the designed MR shock absorber under different applied current. The results of those tests reconfirm the expectation that as the applied current increases, the damping force increases significantly and the recoil stroke decreases by a large amount. Also, the test results show that it is indeed possible to design and use MR shock absorber for recoil application.

Furthermore, for the purpose of evaluating the controllability of MR shock absorber under impact loads, three kinds of control algorithms, including on–off control, PID control, and fuzzy control algorithm, were designed to control the applied current in the piston coil. It was seen from the test results that the fuzzy control strategy could achieve a good harmonious effect between stroke and pressure control and simultaneously reduce the stroke and pressure peak of the MR shock absorber to a great extent. Besides, their effectiveness was compared and shown from different aspects, including stroke control result, damping force control result, peak of pressure control result, and width of pressure platform control result. Especially, the control effect, the algorithm complex degree, and control policy feasibility were given a comprehensive consideration, when different control policies were compared, evaluated, and selected for the MR shock absorber.

Footnotes

The research work is supported by the national natural science foundation of China (50675106), China Postdoctoral Science Foundation (20080431099), the natural science foundation of Zhejiang Province (Y1110313), and NUST Research Funding (2010GJPY004).

References

Ahmadian

Gravatt

(2004) A comparative analysis of passive twin tube and skyhook MRF dampers for motorcycle front suspensions. In: Liu

S-C

(ed.) Smart Structures and Materials 2004: Damping and Isolation, vol. 5386. Bellingham, WA: SPIE, pp.238–248.

Ahmadian

Appleton

Norris

(2003) Designing magneto-rheological dampers in a fire out-of-battery recoil system. IEEE Transactions on Magnetics 39(1): 21–25.

Browne

Mccleary

Namuduri

. (2009) Impact performance of magnetorheological fluids. Journal of Intelligent Material Systems and Structures 20(6): 723–728.

Carlson

(2005) MR fluids and devices in the real world. International Journal of Modern Physics B 19(7–9): 1463–1470.

Duan

. (2003) Amplitude-dependent frequency and damping identification of bridge cables with MR shock absorbers in different setups. In: Liu

S-C

(ed.) Smart Structures and Materials 2003: Smart Systems and Nondestructive Evaluation for Civil Infrastructures, vol. 5057. Bellingham, WA: SPIE, pp.218–228.

Facey

Rosenfeld

Choi

Y-T

. (2005) Design and testing of a compact magnetorheological damper for high impulse loads. International Journal of Modern Physics B 19(7–9): 1549–1555.

Goncalves

(2005) Characterizing the behavior of magnetorheological fluids at high velocities and high shear rates (2005). PhD Thesis, Virginia Tech University, Blacksburg, VA.

Lee

D-Y

Choi

Y-T

Wereley

(2002) Performance analysis of ER/MR impact damper system using Herschel-Bulkley model. Journal of Intelligent Material Systems and Structures 13(7): 525–531.

Wang

(2006) Dynamic simulation and test verification of MR shock absorber under impact load. Journal of Intelligent Material Systems and Structures 17(4): 309–314.

10.

Yang

Spencer

Carlson

. (2002) Large-scale MR fluids dampers: modeling and dynamic performance consideration. Engineering Structures 24(3): 309–323.