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Development of a Novel Displacement-Sensitive Magnetorheological Damper for Vehicle Suspension with High-Speed Stability and Impact Resistance

Abstract

With the continuous improvement of people's requirements for ride comfort, variable damping coefficient dampers are more and more widely used in automobile suspensions, among which the most widely used are magnetorheological dampers that adjust the damping coefficient by adjusting the magnetic field strength and CDC dampers that adjust the damping coefficient by adjusting the size of the runner. However, because they have a delay of tens to hundreds of milliseconds in the adjustment of the damping coefficient, the suppression effect on high-frequency vibrations, especially shocks, is poor. In this paper, a new type of displacement-sensitive magnetorheological damper is proposed, which is controlled by the piston position and the current size, and the adjustment of the damping coefficient can achieve zero delay and ensure the adjustable range of the damping coefficient. The new displacement-sensitive magnetorheological damper is significantly better than the traditional variable damping coefficient damper for controlling the high-frequency vibration and impact of the vehicle. At the same time, this paper also verifies the obvious advantages of the displacement-sensitive magnetorheological damper in isolating high-frequency vibration and shock resistance compared with the traditional variable damping coefficient damper through comparative experiments.

1. Introduction

The shock absorber is an important part of the car, which directly affects the ride and driving safety of the car.

Introduction to magnetorheological dampers

The magnetorheological damper is composed of an outer cylinder, a piston, an excitation coil, a magnetorheological fluid, a piston rod, etc., of which the magnetorheological fluid is a new type of intelligent material composed of non-magnetic carrier base fluid (such as mineral oil, silicone oil, synthetic hydrocarbon oil, etc.), high permeability ferromagnetic tiny particles and anti-sedimentation surfactants. The viscosity, yield strength and other characteristics of the magnetorheological fluid can be changed by adjusting the magnetic field strength of the environment in which the magnetorheological fluid is located. Magnetorheological fluids have been studied by a large number of scholars because of their fast response time, reversible phase, low power consumption, and easy control of yield stress. The magnetorheological damper is to change the magnetic field intensity generated by the coil by changing the current of the excitation coil, so as to adjust the damping coefficient of the magnetorheological damper. From the perspective of application, magnetorheological fluids are mainly used in automobile main suspension systems [1-3], driver's seat suspension [4, 5], and shock protection [6]. 7], bridge cable vibration [89], flexible structure vibration control [10] and other components or systems of vibration control.

Among the many applications, one of the commercial products is magnetorheological dampers for semi-active suspension systems in vehicles [1, 1]. This directly indicates that the research on magnetorheological shock absorbers for automobiles is the most positive and will have a positive impact on improving the performance of automotive suspension systems. Many research teams have investigated semi-active control algorithms for quarter-car, half-car, or full-car models with MR dampers.

In terms of improving the dynamic range of magnetorheological dampers, some researchers have proposed to optimize the design of magnetorheological valves by finite element method without considering the response time of magnetorheological dampers to maximize the static range of the damper. Lee et al. [1, 2] proposed a method to optimize the dynamic range of the magnetorheological damper, but the response time of the proposed magnetorheological valve was between 28 ~ 125 [ms].

In order to effectively control the vehicle's suspension system, the response time of the magnetorheological damper should be less than about 1/5 to 1/10 of the highest frequency to be controlled [13]. There are two critical resonance frequencies in a vehicle's suspension system: the body mode and the wheel mode. In general, the frequency of the body mode is around 1.5-2.0 [Hz], and the resonance frequency of the wheel mode is around 15-20 [Hz]. Therefore, for higher ride comfort and road stability, the response time of the MR damper should be less than 10 ms if the criterion chosen is 1/5 of the maximum frequency to be controlled, 20 [Hz]. In response to shocks, the requirements for response time are higher.

If the response time is not fast enough for the state of the shock absorber to react to changes in the input in a timely manner, the control efficiency will be reduced [13, 14].

The MR damper response time is mainly composed of three parts, namely the current formation time, the magnetic field formation time, and the particle chain formation time. The time of magnetic field formation dominates the response time, which is mainly due to the influence of eddy currents. The conductor generates eddy currents in a changing magnetic field, and the magnetic field generated by the eddy currents is opposite to the desired magnetic field direction, forming a phenomenon that hinders the change of the magnetic field, and the magnitude of the eddy current is proportional to the rate of change of the generated magnetic field [15]. The higher the velocity controlled by the magnetic field, the more pronounced the eddy current effect will be.

Because the response of most of the existing magnetorheological dampers has a delay of tens of milliseconds, the suppression effect of the existing magnetorheological dampers on high-frequency vibration and impact is average.

Many scholars have adopted the method of eddy current suppression to obtain a magnetorheological damper with faster response speed in reducing the response delay of magnetorheological damper. Yoon et al. [16] reduced the influence of eddy currents on the formation of magnetic fields by using soft magnetic materials (SMCs) and processing the inner surface of the piston housing with many grooves, and achieved a magnetorheological damper with a response time of less than 7 ms.

The excitation current formation time is mainly caused by the inductance. Yang et al. [17] demonstrated the possibility of using a current controller to reduce the time response of the excitation current. This controller maintains an input voltage higher than the corresponding voltage calculated according to Ohm's law until the required current is reached in the circuit. The initial input voltage of Yang's experimental current driver is approximately 5 times higher than the corresponding voltage calculated according to Ohm's law. The time response is 300 ms when voltage control is employed, while when the proposed current controller is employed, the time response is reduced to 60 ms. Strecker et al. [18] used a current controller to reduce the delay of the inductor on the formation time of the current, and the piston used a ferrite material to reduce the effect of eddy currents on the formation of the magnetic field. Although the response time can be significantly reduced by using a ferrite material, the adjustable range of the damper output force is much reduced due to the low permeability of the ferrite.

Give an example

These studies reduced the response delay of the damper from tens of milliseconds to about ten milliseconds by using SMC material, and although the effect was obvious, the range of damping coefficients that can be adjusted by coil current was reduced due to the low relative permeability of SMC material.

High-performance magnetorheological dampers not only need to have a low response time, but also a large damping coefficient dynamic range and a low input power.

In order to reduce the response time of magnetorheological dampers and to maintain an adjustable range with a large damping factor, we took inspiration from displacement-sensitive dampers. Its damping coefficient is passively changed and can achieve zero delay.

Introduction to displacement-sensitive dampers

Displacement-sensitive shock absorbers (DSSAs), also known as stroke-dependent shock absorbers, are similar in structure to conventional passive shock absorbers.

However, DSSA has additional flow channels, such as displacement sensitive holes in the cylinder wall. Depending on the piston stroke, the DSSA can implement different damping factor modes. When the piston stroke is within the range of the displacement sensitive hole, the leakage occurs through the displacement sensitive hole. In this range, the damping force is lower than that of passive shock absorbers. On the other hand, when the piston stroke is outside the range of the displacement-sensitive bore, leakage through the bore is stopped. In this range, the damping force becomes greater due to leakage blockage. Due to the small piston stroke and small damping force, the ride comfort under paved road driving conditions is improved. Due to the large piston stroke, high vibration amplitude and large damping force, the driving safety of the vehicle is improved when driving on rough roads or bumpy roads. As a result, DSSA can maintain ride comfort and driving safety.

But the damping coefficient of the existing displacement-sensitive damper can only be switched between two gears, although the vibration isolation effect is better on the paved road surface, but when the rough road surface is driving and the piston stroke is large, the transition of the damping coefficient from low to high is not smooth, and the ride comfort is affected. The damping coefficient only switches between two gears, and the energy dissipation efficiency is also low.

In this paper, a new displacement-sensitive damper structure is proposed, which is combined with magnetorheological technology, and the damping coefficient of the displacement-sensitive magnetorheological damper is controlled by the position and the current magnitude, which realizes the adjustment of the damping coefficient with zero delay and ensures the adjustable range of the damping coefficient with a large size. The high-speed stability and impact resistance of the vehicle are greatly improved.

2. Structure and working mechanism of the Novel Displacement-Sensitive Magnetorheological Damper

Structural schematic diagram of Fig1

Fuji2 structure diagram

For traditional automotive magnetorheological shock absorbers, the damping force is proportional to the square of the velocity under the condition of a certain current.

When the automobile shock absorber copes with the impact condition, due to the large instantaneous speed of the impact, the instantaneous peak force is easy to cause damage to the human body and the body structure, and the energy dissipation efficiency is low. Conventional magnetorheological dampers have a constant gap size, and the reduction of peak forces is ineffective in reducing the peak force by simply adjusting the damping coefficient by adjusting the current in response to shocks. The main reasons are as follows: first, according to the Bingham model, the total damping force of the magnetorheological damper is composed of viscous damping force (Fv) and magnetorheological damping force (FMR), At high speeds, viscous forces dominate the damping force, so changing the magnetic field to adjust the magnetorheological damping force has less effect. Second, because the response time of the existing magnetorheological dampers ismostly more than 1 0 ms, the magnetorheological dampers cannot respond to the impact in time.

And because it has a constant flow channel clearance, it is impossible to take into account the large damping requirements when the impact resistance on rough roads and the low damping requirements at high speeds, so the high-speed vibration isolation ability of the traditional magnetorheological damper also has room for improvement.

Therefore, this paper proposes a new displacement-sensitive damper structure, in which the damping coefficient of the displacement-sensitive magnetorheological damper is controlled by the position and the current magnitude, which realizes the adjustment of the damping coefficient with 0 delay and ensures the adjustable range of the damping coefficient with a large size. The high-speed stability and impact resistance of the vehicle are greatly improved.

As shown in Figure 1, the initial position of the piston is located in the cylindrical area, and there is the largest flow channel gap in the cylindrical area, which can achieve a small damping coefficient and better isolate the high-frequency and small-amplitude vibration of the vehicle under high-speed conditions. If the piston moves up or down beyond a certain range, it will reach the conical area, the flow channel gap is reduced, the damping coefficient is increased, and the energy to the impact can be efficiently dissipated, and the peak force is low. Because the impact velocity is greatest at the beginning of the impact, the piston is located in the cylindrical area and the damping coefficient is minimal, thus avoiding excessive impact forces (the damping force of the damper is proportional to the square of the velocity). After the piston reaches the cone zone, the speed decreases and the damping coefficient increases, which can maintain a large damping force and maintain a high energy dissipation efficiency throughout the impact stroke.

The new displacement sensitive damper is mainly composed of pistons, hollow piston rods, variable bore cylinders, guides, floating plugs and sealsas shown in Figure 2. According to hydrodynamics, the damping coefficient of the MR damper varies with the change in the damping gap. Therefore, the structure proposed in this paper can achieve different damping coefficients at different positions by changing the flow channel gap between the piston and the cylinder barrel at different positions.

3. Dynamic modeling of the New Displacement-Sensitive Damper

From the structure of the shear valve type damper, it can be seen that the gap h between the liquid flowing through the cylinder barrel and the piston is very small, only 1~2mm, which is very small compared with the circumference of the piston and the axial length L of the piston, so its structure can be simplified to a flat plate structure.

According to the structure and working principle of the shear valve damper, the movement form of the magnetorheological fluid in the damper can be divided into two situations to consider: on the one hand, the piston squeezes the magnetorheological fluid on one side of the cylinder block, so that the pressure increases, so that the pressure difference in the cavity on both sides of the damper is generated, and the pressure difference makes the magnetorheological fluid flow to the piston in the cylinder block through the gap

the other side, known as differential pressure flow or Poiseuille flow; On the other hand, due to the relative motion between the cylinder block and the piston, the magnetorheological fluid is dragged from one side to the other, known as shear flow, or Couette flow. Therefore, the total damping force of the shear valve magnetorheological damper will be combined by the damping forces Fp and Fs.

3.1 Calculation of damping force in the cylindrical area

For shear flow, the damping force is calculated as: $F_{} = LπDτ = LπD τ_{} + \frac{L πDμ}{h} v$

For differential pressure flow, the damping force is calculated as: $F_{} = Δ P ⋅ A_{} = \frac{12 η L A_{}}{π D h^{}} A_{} v + \frac{3L τ_{}}{h} A_{} sgn v$

From the superposition of the above formula, the calculation formula of the damping force of the shear valve type magnetorheological damper can be obtained:

$F = (\frac{12 ηL}{πD h^{3}} + \frac{L πDη}{h}) v + (\frac{3L A_{p}}{h} +L πD) τ_{y} sgnv$

v is the effective area of the piston under pressure; v is the relative speed of the piston and the cylinder; D is the diameter of the piston; d is the wall thickness of the cylinder block, and L is the total effective length; h is the runner gap; η is the dynamic viscosity of the fluid. 3.2 Calculation of damping force in the conical area

Applying BPM model, total damping force can be expressed as:

F_{on} = F_{off} + F_{MR}

The damping force of MR with magnetic field is:

$F_{MR} = A_{p} \sum_{i=1}^{n_{1}} \frac{2 L_{ai} τ_{yi}}{h_{i}}$

The damping force of MR without magnetic field can be written as:

$F_{off} = A_{p} [Δ P_{off-1} + \frac{ρ}{2} (K_{entry} + K_{exit})]$

Where $i$ represents different microelements in the calculation area of the piston; $A_{p}$ is Cross-Section Area of piston; $L_{a}$ MR effective length; $τ_{y}$ Shear yield strength; $h$ Effective damping gap; $Δ P_{off}$ Passive pressure drops; $V_{h}$ Average fluid velocity in piston gap; $ρ$ Material density; $K_{entry}$ Inlet loss coefficient; $K_{exit}$ Outlet loss coefficient.

The equation of total pressure of fluid channel is:

$Δ P_{off} = \sum_{i=1}^{n_{1}} Δ P_{{off}_{i}}$

Where $Δ P_{{off}_{i}}$ Passive viscous pressure drops in the activation and coil area;

The pressure in the activation area, coil area and inlet and outlet can be expressed respectively as:

$Δ P_{{off}_{i}} = f_{ηi} \frac{ρ L_{i}}{4 h_{i}}$

Where $f_{η}$ Darcy-friction factors in the piston gap; $L$ is the piston length;

$V_{di} = \frac{A_{p} V_{p}}{A_{hi}}$

$A_{p}$ is Cross-Section Area of piston; $A_{h}$ is the Cross sectional area of the piston gap;

$A_{p} = \frac{π}{4} (-)$

$A_{hi} = \frac{π}{4} [-(D_{ini} -2 h_{i})^{2}]$

Darcy-friction factor is expressed as:

$f= {\begin{matrix} & \frac{96}{Re}, (if Re ≤2000) \\ & \\ &(1-α) \frac{96}{2000} +α \frac{1}{{1.8 {log}_{10} ⁡ [{(\frac{ε/ D_{0}}{3.7})}^{1.11} + \frac{6.9}{4000}]}^{2}}, \\ & \\ & (if 2000<Re ≤4000) \\ & \\ &1.8 {log}_{10} [{(\frac{ε/ D_{h}}{3.7})}^{1.11} + \frac{6.9}{Re}], (if Re >4000) \end{matrix}$

Which

$α= \frac{Re -2000}{4000-2000}$

$Re = \frac{ρ V_{d} D_{h}}{η}$

$D_{hi} =2 h_{i}$

3.2 Magnetic field analysis

According to the calculation method of the magnetic flux continuity theorem, the key parameters of NDS-MRD and the equivalent magnetic circuit model are shown in Fig. The magnetic flux is expressed as

$ϕ_{MRF} = ϕ_{steel} =ϕ$

According to Ohm's law:

$\begin{matrix} NI &=ϕ (R_{c} + R_{c1} + R_{c2} + R_{LMRF} + R_{RMRF} + R_{p1}) \\ &+ R_{p2} + R_{p}) \end{matrix}$

Where $R_{c}$ Magnetic resistance of cylinder; $R_{p}$ Magnetic resistance of piston; $R_{RMRF}$ Magnetic resistance of MRF; $ϕ$ Magnetic flux; $N$ Number of turns of the exciting coil; $I$ Excitation current;

Magnetoresistance in different parts:

$R_{c} = \frac{L_{c} +0.5 (L_{a_{1}} + L_{a_{2}})}{\frac{V}{L_{c} +0.5 (L_{a_{1}} + L_{a_{2}})} μ_{3}}$

$R_{p1} = \frac{r_{p} - r_{g}}{2π r_{p} L_{a_{1}} μ_{1}}, R_{p2} = \frac{r_{p} - r_{g}}{2π r_{p} L_{a_{2}} μ_{1}}$

$\begin{matrix} R_{C1} = \frac{0.5 L_{a_{1}} tan ⁡θ}{2π(r_{1} -0.5 L_{a_{1}} tan ⁡θ) L_{a_{1}} μ_{3}}, \\ R_{C2} = \frac{r_{1} - r_{2} -0.5 L_{a_{2}} tan ⁡θ}{2π(r_{2} +0.5 L_{a_{2}} tan ⁡θ) L_{a_{2}} μ_{3}} \end{matrix}$

$R_{RMRF} = \frac{d_{2} +0.5 L_{a_{2}} tan ⁡θ}{2π (r_{2} +0.5 d_{2} +0.5 L_{a_{2}} × tan ⁡θ) L_{a_{2}} μ_{2}}$

$R_{LMRF} = \frac{d_{1} -0.5 L_{a_{1}} tan ⁡θ}{2π (r_{1} -0.5 d_{1} -0.5 L_{a_{1}} × tan ⁡θ) L_{a_{1}} μ_{2}}$

$R_{p} = \frac{L_{c} +0.5(L_{a_{1}} + L_{a_{2}})}{π[{(r_{p} -wc)}^{2} -] μ_{1}}$

Where $V$ Effective volume of the cylinder; $μ_{1}$ Relative permeability of piston material; $μ_{2}$ Relative permeability of MRF; $μ_{3}$ Relative permeability of cylinder material

As the piston moves axially from the intermediate position, the damping gap gradually decreases. At the same time, the magnetic induction intensity in the damping gap also increases

3.3 Magnetic field simulation

According to the dimensional parameters of the design, the model was built in COMSOL, and the magnetic field of the floating plug at different positions in the cylinder barrel was simulated. Among them, the damper cylinder barrel and piston material are selected magnetic permeability material 20# steel, and the following figure shows that the piston is located in the middle of the cylinder barrel, 3/4Simulation results at the stroke and at the bottom three positions of the stroke. It can be seen that as the piston moves from the middle position to one end, the magnetic field strength in the flow channel gradually increases and reaches its highest at the very bottom. This will make that when the piston constant speed moves from the middle of the cylinder barrel to both ends, not only the reduction of the runner gap will increase the damping force, but also the increase of the magnetic field strength of the runner gap will also increase the shear yield strength of the magnetorheological fluid, thereby increasing the damping force. That is, the increase of damping force, the decrease of the channel gap and the increase of the magnetic field strength are superimposed, which is also the reason why the new position-sensitive magnetorheological damper can achieve a large adjustable range.

In the middle position of the piston runner gap, a point probe for measuring the magnetic field is placed to measure the change of the magnetic field strength at the runner during the piston movement, and the position and result of the point probe are shown in the figure below. The figure shows the change trend of the magnetic flux density at point A at the piston coil with the piston moving from the bottom of the stroke to the middle of the cylindrical area with the piston moving from the bottom of the stroke to the middle of the cylindrical area, it can be seen that when the piston is located at the bottom of the conical area, the magnetic flux density at point A of the flow channel is the largest, which is 1.48T, and when the piston moves to the cylindrical area, the magnetic flux density at point A reaches the minimum of 0.84T, a decrease of 34.78%.

4. Experimental and simulation verification

4.1 MTS Force Displacement Test

In order to verify the performance of the proposed NDS-MRD, a prototype of the damper was manufactured according to the design parameters, and the force-displacement test was done, and the test equipment was MTS, The tensile and compression cycles of the damper were tested at a speed of 0.016m/s and an amplitude of ±60mm using a constant velocity triangular wave excitation signal. The test results are shown in the figure below, and the change of damping force under different currents is shown in the table, the force increases by 36.8% at 0A and increases at 1A104.3%, an increase of 94.3% at 2A and an increase of 87.1% at 3A. At 3 A, the maximum resistance in the conical zone is 1437N, compared to 0 AThe minimum force in the cylindrical region 76N increases by 1791 times.

4.2 Dynamic simulation

In order to verify the effect of the new displacement-sensitive magnetorheological damper in terms of vehicle shock absorption and impact resistance, a quarter vehicle dynamics model was built in MATLABsimulink, as shown in the figure, which consists of the unsprung mass Ms, and the unsprung massMu, suspension spring Ks, passive damper C0, semi-active damper Cs and elastic tire Kt, This model ignores the damping of the tires.

where X0 is the pavement excitation, Xu is the vertical displacement of the non-suspended mass, and Xs is the vertical displacement of the suspended mass. Then the differential equation of motion for a quarter of a vehicle model with two degrees of freedom of suspension is:

$\begin{matrix} & M_{s}_{s} + (c_{0} + c_{s})_{s} + k_{s} x_{s} = (c_{0} + c_{s})_{u} + k_{s} x_{u} \\ & M_{u}_{u} + b_{s}_{u} +(k_{s} + k_{t}) x_{u} = b_{s}_{s} + k_{s} x_{s} + k_{t} x_{0} \end{matrix}$

< $_{}$ pan data-immer $_{}$ ive-translate-walked="23c3b060-8ca8-4483-83c9-566016b8a9b1" style="font-family: &q $_{}$ ot; Times New Roman&q $_{}$ ot;; "> where s and u are the vertical acceleration of the suspended mass and the unsuspended mass, respectively; s and u are the vertical velocity of the suspended mass and the unsuspended mass, respectively. According to the above differential equations, a simulation model of quarter vehicle dynamics was built in MATLABsimulink. $c_{}$ Among them is the damping coefficient provided by the new position-sensitive magnetorheological damper, which can be obtained from the above-mentioned MTS force-displacement test experiment。 In MATLABsimulink, the relationship between the damping coefficient and the relative displacement and the magnitude of the current is established using the 2-DLookupTable, where the magnitude of the current is controlled by the ceiling control algorithm. It is obtained by judging the relationship and magnitude of the velocity on the spring and the relative velocity. At the same time, the 2-DLookupTable is used to establish the damping coefficient model of the traditional magnetorheological damper, that is, the damping coefficient is only controlled by the current magnitude.

Therefore, the damping coefficient model of the quarter-car model and the damping coefficient model of the new position-sensitive magnetorheological damper and the damping coefficient model of the traditional magnetorheological damper are constructed, and the new damper is evaluated compared with the traditional magnetorheological damper under different road conditions by applying different road surface excitationsand the effect of passive dampers.

4.2.1 sweep

To evaluate the effect of the proposed new position-sensitive magnetorheological damper at different frequency ranges, a pavement excitation was applied with an amplitude of 20mm and frequencies from 0 Hz to 10Hz, a sine sweep signal with a time of 60s, as shown in the figure below. The on-spring acceleration response of the three suspensions, passive dampers, conventional magnetorheological dampers and new position-sensitive magnetorheological dampers, is shown in the figure.

4.2.2 Shock

4.2.3 Random pavement excitation

5. Results and discussion

In this study, a new type of displacement-sensitive magnetorheological damper is proposed, and the theoretical calculation formula of damping force and magnetic field is given. At the same time, finite element simulations of the magnetic field are also carried out to verify the process of the piston movement from the cylindrical region to the conical region of the new NDS-MRD, and the magnetic flux density in the runner gap gradually increases, which proves that the position-sensitive characteristics of the NDS-MRD damping force are affected by the flow channel gap and the magnetic flux density, so the damping force of the NDS-MRD has a large adjustable range (1). 7.91 times). In order to further verify the displacement sensitivity characteristics of NDS-MRD, a sample was fabricated and the force displacement test was carried out, and the results showed that under the same speed and the same current, the increase of the damper force caused by position change could reach 104.3%, which had excellent position sensing performance.

The vehicle dynamics of the NDS-MRD were analyzed using a quarter-car model. The simulation results of the vertical acceleration response on the NDS-MRD spring were compared with the results of the traditional magnetorheological damper and the passive shock absorber, respectively, by applying the swept frequency signal, the shock signal and the random vibration signal, respectively. The results show that NDS-MRD has a significant effect on the on-spring acceleration compared with the traditional magnetorheological damper and passive shock absorber, which can significantly improve the ride comfort of the vehicle.

The control algorithm in the vehicle dynamics simulation in this paper uses an improved ceiling control algorithm, and the later development of the control algorithm for displacement-sensitive dampers should be able to achieve better control results.

Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant No. 52005474, 52105081), the Anhui’s Key R&D Program of China (Grant Nos. 202104a05020009, and 202104b11020004), USTC start-up funding (KY2090000067) and the Fundamental Research Funds for the Central Universities (WK2480000009), and the USTC-IAT-Xiaoxian Intelligent Manufacturing Innovation Center, and Students' Innovation and Entrepreneurship Foundation of USTC(CY2023G017). These financial supports are gratefully acknowledged.

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