Zi-xuan Li,Guo-lai Yang,Yu-meng Fan,Jia-hao Li

School of Mechanical Engineering,Nanjing University of Science and Technology,Nanjing,PR China

Keywords:EMB Irreversibly demagnetization Magnetic Reynolds number Correction coefficient

ABSTRACT The permanent magnets will be irreversibly demagnetized under high temperature and high velocity during the electromagnetic buffering.In this study,the magnetic field induced by eddy currents and the self-demagnetizing field of permanent magnet are taken into consideration together for demagnetization analyse.The magnetic Reynolds number is used to express the eddy currents demagnetization.The correction coefficient being expressed as the index of the air-gap width,the inner cylinder thickness,iron pole axial length and the permanent magnet demagnetization coefficient is introduced by magnetic path analysis to represent the self-demagnetization effect and the demagnetization extent.The electromagnetic buffer(EMB)prototype is tested under intensive impact loads of different strengths at room temperature.The accuracy of the nonlinear irreversible demagnetization finite element model is verified by demagnetization on damping force,velocity and displacement.Finally,high-velocity demagnetization and high-temperature demagnetization are analysed in order to obtain the distribution law of irreversible demagnetization.

1.Introduction

The NdFeB permanent magnet was introduced and patented independently by Sumitomo Special Metals and General Motors(later Magnequench)in 1983[1].A distinct advantage of such permanent magnet is the high maximum magnetic energy product[2].However,the problem of poor thermal stability and weak resistance to demagnetization under high temperature still exists[1].In the past 3 decades,the magnetic strength and thermal stability of NdFeB permanent magnets have been significantly improved[3-9].The development of NdFeB permanent magnets provides a powerful air gap field for electromagnetic devices such as permanent magnet motors and electromagnetic buffers(EMBs).Due to the induced eddy currents and coil currents,the working permanent magnets will be inevitably demagnetized,changing the damping characteristics and even causing accidents.

The demagnetization effect of permanent magnet motor has been studied in detail.For example,Guo et al.[10]determined the minimum operation point by analyzing the irreversible demagnetization process of a novel flux reversal linear-rotary permanent magnet actuator.Kim and Hur[11,12]developed an irreversible demagnetization dynamics analysis algorithm to analyse the irreversible demagnetization dynamic characteristics of the permanent magnet brushless DC motor,and brought out the maximum current limit of the motor design.Faiz and Mazaheri[13]proposed a robust time-series feature extraction method for permanent magnet defect classification.

There is less research on demagnetization of EMBs since there is no high velocity during the electromagnetic buffering process except for the rotating ones.To describe the braking torque more reasonably at high velocity,Kapjin and Kyihwan[14-16]introduced the magnetic Reynolds number assumed as an exponential in a disc eddy current braking system.Sharif et al.[17]developed the magnetic Reynolds number by adding an exponentnobtained by the limit of power loss.Zhou et al.[18]introduced the concept of anti-magneto-motive force to develop the eddy current brake model,in which the eddy current demagnetization and the temperature effect were presented.The damping mechanism and cushioning performance of linear EMBs have also been studied intensively[19-21].

Tubular permanent magnets have high power density,low magnetic flux leakage,and the net attraction force between stator and rotor(moving parts)is zero[22-24].Therefore,the cylindrical linear EMB can avoids the lateral end effect and provides a stronger energy density with the application of the tubular permanent magnets.This made it possible to increase the damping force by merely changing the length dimension,in other words,increasing the number of magnetic groups,instead of increasing the size as a whole.Ebrahimi et al.[19-21]introduced a new cylindrical linear EMB for a vehicle suspension system.In his subsequent works,the analytical model considering the skin effect was obtained,and the accuracy of the theoretical model was verified by low-velocity experiments.However,the armature response has not been fully considered in low-velocity environments limited to suspension applications.

The intensive impact load exists widely in the shooting processes of weapons and non-contact impact of submarines.A cylindrical linear EMB with tubular NdFeB permanent magnets can provide powerful energy density so that it is possible to complete the impact buffering.More importantly,these applications require adaptation to extreme environments.In this paper,the irreversible demagnetization process of the EMB under intensive impact load is studied,including high-velocity demagnetization induced by eddy currents, high-temperature demagnetization and selfdemagnetization.The self-demagnetization field strength of the permanent magnets affected by the rate permeance of the outer magnetic path is considered into the critical velocity.The local irreversible demagnetization distribution is analysed under multiple permanent magnet temperature and the test intensive impact load.

2.Electromagnetic damping

2.1.EMB

Without the demand of excitation currents,the permanent magnet EMB has higher reliability and lower economy for high power consumption under intensive impact load.Fig.1 illustrates the partial three-dimensional structural schematic of the studied cylindrical linear EMB,which mainly consists of two parts:(1)the primary part,which consists of a moving rod combined with a sequence of ring-shaped,axially magnetized permanent magnets separated by pure iron poles,and(2)the secondary part,which consists of an outer tube and an inner tube.High-velocity relative movement between the primary and secondary will occur under the intensive impact load.Due to the electromagnetic induction,circumferential eddy currents are generated in the secondary.They are sequentially arranged along the iron pole interval,and is opposite to the adjacent eddy currents.At the same time,the circumferential eddy currents induce a new magnetic field interacting with the primary magnetic flux to generate damping force,which hinders the relative motion of the primary and secondary according to Lenz’s law.

Fig.1.Partial schema of the studied EMB.

Fig.2 exhibits the layout of the permanent magnets which are oriented with magnetic poles of the same polarity facing each other.The iron pole is located between the two permanent magnets to increase the amount of magnetic flux entering the secondary.Therefore,the decrease of the quiescent operation point caused by the flux leakage in the cylinder hole of permanent magnet and excessive air-gap reluctance is reduced.The thick bold arrows show the direction of field line.

As shown in Fig.2,τm,τ,ri,ro,rd,Ri,Roare the thickness of the permanent magnet;the pole pitch;the internal radius of the inner cylinder;the external radius of the inner cylinder(the internal radius of the outer cylinder),the external radius of the EMB,the internal radius of the permanent magnet,the external radius of the permanent magnet,respectively.

2.2.Electromagnetic damping considering eddy current demagnetization and self-demagnetization

The eddy current magnetic field raised obviously along with the increasing of velocity.The operation point of the permanent magnet is forced by its resulting eddy current demagnetization forces to decline along the demagnetization curve.It may even locally falls below the knee point with occurring local irreversible demagnetization.The exponential model[25]can effectively simulate the entire demagnetization curve compared to the limit model or the linear model:

whereE,μrare the constants required for unit conversion,the permanent magnet relative permeability,respectively.K1,K2are the fitting constants.A larger value ofK1results in a sharper knee of the demagnetization curve.K2can be calculated by the following equation:

Fig.2.Configuration of the primary and secondary.

Since the axial length of the permanent magnet is shorter than the diameter,the equivalent magnetic volume current density and equivalent surface current density can be used to replace a cylindrical magnet[20,21].Therefore,the radial component of the net flux density at(r，z)is obtained in a cylindrical magnet,given by whereRm,K(k),andE(k)are the radius of the permanent magnet and complete elliptic integrals of the first and second kind,respectively.It is assumed that the permanent magnet is uniformly demagnetized along the demagnetization curve.Therefore,the net flux density radial component of the ring permanent magnetB02and the radial component of the air-gap flux densityB0at(r，z)can be expressed as

The eddy current density generated by the primary field in the inner and outer cylinders can be expressed by the following equation:

whereσ1andσ2are the inner and outer cylinders conductivity,respectively.

It is assumed that:(1)the radial component of the induced field is uniformly distributed in the air-gap and the inner cylinder,and(2)the magnetic field strength(H)of the iron poles and the outer cylinder is zero.The magnetic induction of the eddy current field can be obtained from the integral path in Fig.2 by the Ampere circuital theorem:

whereδmS1,S2are the radial length of the air-gap,the crosssectional area of the inner and outer cylinders where the eddy currents are generated,respectively.ro-ri+δmis the radial length of the air gap and the inner cylinder with permeability close to the free space,which is indicated by the symbollm.

The magnetic Reynolds numberRmis introduced to characterize the eddy current demagnetization,which can be calculated by combining Eq.(5)and Eq.(6):

Therefore,the net gap flux density is defined as

Wherekm(T)is the undetermined coefficient.A larger value ofkm(T)will results in an intensive demagnetization.However,the eddy current demagnetization is considered by the introduced magnetic Reynolds number,which is the ratio of the eddy current field to the original field.Meaning that the self-demagnetization of the permanent magnet is not taken into account.Changing the value of the electromagnetic buffer parameters,such as the inner cylinder thickness and the air-gap width,will simultaneously cause alteration of the eddy current field and the self-demagnetization field.The self-demagnetization of the permanent magnet is affected by the rate permeance defined as the permeance ratio of the permanent magnetic path to external path.

As denoted in Fig.3,the magnetic flux generated by the permanent magnet forms three loops through the secondary,the moving rod and the air-gap.The black arrows indicate the direction of magnetic flux.

The equivalent magnetic path considering the flux leakage and the eddy current field is obtained by Fig.3,as illustrated in Fig.4(a).

The reluctance of the iron pole and outer cylinder is ignored due to the high magnetic permeability.Therefore,the simplified main magnetic path is given as illustrated in Fig.4(b).It can be seen that after the permanent magnet characteristic is selected,the quiescent operation point only moves with reluctance of the inner cylinder and air-gap.The conformal transformation can be used to obtain the accurate permeance between cylindrical equipotential surfaces of different magnetic potentials.Therefore,the reluctance of the inner cylinder and the air-gap is defined as

The outer cylinder of the EMB is a thin-walled structure,which can be unfolded into a plane when the reluctance is simplified.The reluctance of inner cylinder and the air-gap with permeability approximately close to the free space can is obtained by

It can be found from Eq.(10)that the inner cylinder and the airgap are equivalent in terms of the reluctance of the outer magnetic path and the resulting quiescent operation point.Therefore,the parameterkmcan be assumed as

Fig.3.Magnetic path and magnetic flux.

Fig.4.(a)The equivalent magnetic path.(b)The main magnetic path of a single permanent magnet.

wherekw(T)is the demagnetization coefficient of the permanent magnet considering the movement of the operation point,which is related to the parameters of structure,temperature and nonuniformity demagnetization.The parameterqis the undetermined index.

The parameterkw(T)can be regarded as a constant under room temperature.However,the EMB undergoing high-velocity and permanent magnets with elevated temperature can gradually bring down the dynamic operation point.Moreover,the dynamic operation point of the local permanent magnet will fall below the knee point to force the original field unevenly distributed.Under these situations makes parameterkw(T)a variable.The eddy currents in the secondary are induced by the primary field.Therefore,the fundamental frequency of the induced currents in the secondary is

The penetration depth is defined as the depth below the conductor surface at which the current density decreases to 1/eof the current density at the surface.The penetration depth of the secondary conductor is obtained from

whereμris the conductor permeability.The motional electromotive forces are generated in the inner cylinder and the outer cylinder.The eddy current damping force at the same pole of the two magnets resulting from the motional electromotive forces is obtained by

whereV,Γare volumes of the inner cylinder and outer cylinder,in which eddy currents are generated.

The air-gap magnetic flux at the upper and lower ends of the EMB is generated by a single permanent magnet during the buffering process.It is assumed that the magnetic induction generated by the end permanent magnets is half ofB0,and the damping force during the buffering process is

wherenis the number of permanent magnets.The critical velocity is an extremely essential technical index,especially under intensive impact loads.The eddy current damping force increases with the velocity.When the buffer velocity exceeds a threshold,the critical velocity of the EMB,the damping force no longer increases.

The penetration depth of the inner cylinder is calculated as 5.8 mm at the theoretical maximum velocity of the EMB under impact load using Eq.(13).Since the penetration depth is much larger than the thickness of the inner cylinder designed to be 1 mm,the inner tube skin effect can be ignored in the approximate calculation.The conductivity of outer cylinder is lower than the inner cylinder and contributes less to the damping force.In addition,the outer cylinder is close to magnetic saturation at flux density of primary field,making the skin effect at the outer cylinder negligible.By the definition of critical velocity,its expression is obtained by deriving Eq.(15)as follows:

The values ofkwandqcan be obtained by subsequent impact experiments and theoretical analysis.

3.Irreversible demagnetization model

3.1.Considering irreversible demagnetization

In view of the fact that the EMB studied is of the plurality of rotating bodies,the cylindrical about z solution in the 2D module of the low-frequency electromagnetic field software Ansoft Maxwell is selected.The corresponding simplification is made for the finite element analysis model that the connection between the inner cylinder and the outer cylinder with less influence on magnetic field be ignored.The inner cylinder and the outer cylinder are fixedly connected.And between the moving rod and the iron pole,the iron pole and the magnet are rigid body contact connection.

There are two main causes of the irreversible demagnetization:intensive impact load and high temperature.Two kinds of impact loads with different intensities act on the primary of the EMB,which is calculated by the Lagrange quadratic interpolation,according to the pressure distribution in the container,as shown in Fig.5,to compare shock damping characteristics of reversible and irreversible demagnetization.Fig.6 shows the recuperator force applied to the EMB for the purpose of eventually stopping the movement of the primary and returning it to the initial position.The impact load and the recuperator force are introduced into the finite element analysis model by the pwl function.

The extent of local demagnetization is investigated,according to the demagnetization curve of permanent magnet at different temperatures,which is given in Fig.7.As the temperature increasing,the remanence and coercive force decrease correspondingly,and the knee point gradually increases.The reversible temperature coefficients of remanence and intrinsic coercivity of NdFeB permanent magnets at 20°C-60°C are-0.12%/°C and-0.75%/°C,respectively.They can be considered as constants at 20°C-60°C,but as variables at 60°C-120°C.The remanence and intrinsic coercivity at T1temperature can be represented by

When the impact load of the EMB being kept constant,if the temperature only increase marginly,the permanent magnet will recover along the demagnetization curve after the velocity reducing.There is a critical temperature that causes remanence of the permanent magnet to decrease along the recoil line,i.e.,the irreversible demagnetization occurs.The critical temperature depends on the above temperature coefficient of permanent magnet and the magnitude of the impact load.

Fig.5.Different test impact loads.

Fig.6.Recuperator force.

Fig.7.Demagnetization curve of NdFeB from room temperature to 120 °C.

3.2.Considering magnetization nonlinearity

The permeability of ferromagnetic material is a nonlinear function of magnetic field intensity.The magnetic saturation of the iron pole and the outer cylinder under the primary field and the induced field must be fully considered to obtain a reasonable damping force.The magnetization relationship of the iron pole and the outer cylinder is given in Fig.8.

Since the outer cylinder is a soft magnetic material with excellent permeability,there is substantially no magnetic leakage outside the EMB.Therefore,the magnetic vector potential with the angleθin the RZ coordinate system at the boundary can be set to zero.At the same time,the primary domain is set in the motion band as a moving part.Therefore,considering the irreversible demagnetization and magnetization nonlinearity,the irreversible demagnetization model is established in this paper,the partial details are shown in Fig.9.

Fig.8.Magnetization relationship of Iron pole and outer cylinder.

4.Impact test

Fig.10(a)shows a high-velocity photographic acquisition and storage equipment,which is used to collect the dynamic displacement and velocity information of the EMB.As demonstrated in Fig.10(b),a manufactured prototype EMB system has been tested under two different intensive impact load,which is consistent with the impact load of the finite element model shown in Fig.5,under room temperature.The displacement and velocity data of the movement are analysed by ProAnalyst software.The force data is obtained by measuring test-force-ring attached to the end of the moving rod.The output terminal of test-force-ring is connected to the data acquisition system via a charge amplifier.Then,the inertial force is removed from force data measured by the test-force-ring to obtain reliable eddy current damping force.

Fig.11 shows the comparison of experimental results in terms of motion displacement,motion velocity and damping force with finite element simulation under two different impact loads.It can be seen that the intensive impact experimental results are in good agreement with the nonlinear irreversible demagnetization finite element model.Moreover,the vibration of the experimental platform is caused by the high-intensity impact 2 causing the fluctuating damping force.However,the buffering nodes including the maximum velocity time and the buffering completion time are also highly consistent.Therefore,the established finite element model is acceptable.

The peak velocity appears at the same time as the peak damping force occurs with the impact 1 acting on the primary,indicating that the EMB does not reach the critical velocity.When the impact 2 acting,the time of the peak velocity is significantly later than that of the peak damping force,that is,the EMB has exceeded the critical velocity.

Fig.10.Experimental set-up for the prototype EMB.(a)High-velocity photographic acquisition and storage equipment.(b)Fabricated prototype for proof of concept.

Fig.11.Comparison of experimental(a)distance-time,(b)velocity-time,(c)force1-time,(d)force2-time characteristics with that calculated by simulation.

5.Irreversible demagnetization analysis

5.1.Demagnetization effect of high velocity

Fig.12.Operation point movement caused by increased air-gap width.

The operation point movement of the permanent magnet is illustrated in Fig.12.Without loss of generality,among many electromagnetic applications,the permanent magnet works in the open path,so the relative motion can be generated.Since the permanent magnet in the open path is subject to its own demagnetizing field,the magnetic induction intensity in EMB magnetic path is not at theBr0of the closed path,but theP1lower than theBr0.TheP1is the quiescent operation point of the permanent magnet,whose value depends on the rate permeance of the outer magnetic path.Once the structure and material parameters of the EMB are determined,the quiescent operation point of the permanent magnet is determined.The eddy currents magnetic field produced with buffering motion has a significant demagnetization effect on the magnetic field of permanent magnet.For this reason,the magnetic induction intensity of the permanent magnet decreases to the corresponding value at the dynamic operation point P2along the demagnetization curve.

When the air-gap width becomes larger,the rate permeance of the outer magnetic path increases,resulting in the quiescent operation point moving fromP1toP’1due to the increase of selfdemagnetization.However,the eddy currents magnetic field is reduced due to the decrease of the magnetic induction intensity,which causes the dynamic operation point to drop fromP2toP’2because of the increase of eddy current demagnetization.Therefore,the dynamic working point changes little under the above two demagnetization effects.The inner cylinder thickness can also cause the same phenomenon of the quiescent operation point.The difference is that the eddy current demagnetization will increase with the inner cylinder thickness.

The solid arrow and the dotted arrow indicates the demagnetization process with the marked initial parameters and the increased value of air-gap width under the eddy current demagnetization field and the self-demagnetization field,respectively.

Moreover,by analyzing the experimentally verified finite element model,the parameter analysis is performed to obtain the critical velocity as denoted in Fig.13.It can be seen that the critical velocity varies slightly with the air-gap width and the inner cylinder thickness,which is consistent with the theoretical analysis of the operation point.Therefore,the parameterqin Eq.(16)can be solved as one.Then the expression of the critical velocity can be

Eq.(18)shows that the critical velocity is independent of the parameters such as the remanence and coercive force when the temperature of the permanent magnet is constant.The critical velocity obtained eliminates the effect of the iron pole,and decreases as the increase of the product of the inner cylinder thickness and permeability,and of the outer cylinder thickness and permeability.This is consistent with the results obtained by the finite element in Fig.13.

5.2.Demagnetization effect of temperature

After the impact load being applied to the EMB,if the temperature of the permanent magnets increase,the irreversible demagnetization will have a greater influence on the electromagnetic and damping characteristics.Considering the complexity of the EMB application environment,it is necessary to analyse the demagnetization mechanism of the EMB at extreme temperatures.The finite element model was corrected by the above impact test.The dynamic characteristics of the EMB at different temperatures are calculated,according to the demagnetization curve of NdFeB permanent magnets from room temperature to 120°C in Fig.7.

Fig.13.Critical velocity vs.structure parameters of the EMB.

The dynamic damping force as a function of time under the impact 1 and the impact 2 are shown in Fig.14.Fig.14(a)signifies that the permeabilityμrof permanent magnet is assumed to be a constant value of 1.02 with a small decrease in the damping force amplitude as the temperature rises.When the permeability of the simulation model conforms to the demagnetization curve of Fig.7,the damping force decreases significantly due to the local irreversible demagnetization under high temperature conditions.However,the damping force did not reach the critical value,that is,impact 1 did not cause the EMB to reach the damping force threshold.

Similarly,the damping force amplitude is weakened slightly with the temperature rising when the permeabilityμris assumed to be a constant value of 1.02,and the resulting critical velocity does not substantially change under the impact 2.When the permeability of the simulation model conforming to the demagnetization curve of Fig.7,the damping force decreases significantly with increasing temperature,as exhibited in Fig.14(d).However,the difference between the peak damping force and the valley damping force increases,resulting in decreasing critical velocity since the knee point position is continuously increased and the local demagnetization area of the permanent magnet is gradually enlarged,under such conditions.

The detailed change in the critical velocity is given in Fig.15.It can be seen that after the structure and material parameters are determined,the critical velocity becomes a variable with temperature.The high temperature leads to the decrease of remanence and coercive force.Different from the case of constant permeability,the knee position is also rising with the result of the critical velocity obviously decreasing when considering the irreversible demagnetization.

As illustrated in Fig.16,the magnetic induction distribution of the semi-sectional view of the annular permanent magnet under the impact loads is given.The permanent magnet of order 3 starting from the right side in Fig.1 is selected with the magnetization direction from bottom to top along the paper surface.Obviously,the permanent magnet only undergoes reversible demagnetization as the velocity is less than 9 m/s.

Two parts of irreversible demagnetization area appear in the permanent magnet with the velocity increasing.The first demagnetization portion is located on the upper side of the permanent magnet outer(if the magnetization direction is reversed,the demagnetization position is moved to the lower side),corresponding to the A portion in Fig.16.The induced magnetic field generated by the inner cylinder and the outer cylinder acts on the primary magnetic field,causing the dynamic operation point to fall along the demagnetization curve,and down to below the knee point with the velocity increasing.Therefore,the local demagnetized region A occurs at the position away from the relative motion direction.The second demagnetization portion is located on the upper and lower sides of the annular permanent magnet,corresponding to the B portion in Fig.16.Since the B portion is close to the inner side of the annular permanent magnet,the field lines do not pass through the magnetic path 1(iron pole-air gap-inner and outer cylinder-iron pole)and path 3(iron pole-air gap-iron pole)back to the other pole like the outer portion of the annular permanent magnet,but are closed along the magnetic path 2(iron pole-moving rod-iron pole),as illustrated in Fig.17.The permeability of the moving rod with great reluctance in the magnetic path 2 is close to the free space.Therefore,the B portion of the two permanent magnets demagnetize each other due to the respective fields.As the velocity increases,the demagnetization at the A portion causes the field lines originally passing through the magnetic path 1 to be squeezed into the magnetic path 2.The strengthened mutual demagnetization results in the occurrence of the demagnetized region B.

Fig.14.Damping force at different temperatures.(a)Permeabilityμr=1.02 under impact 1.(b)Considering irreversible demagnetization under impact 1.(c)Permeabilityμr=1.02 under impact 2.(d)Considering irreversible demagnetization under impact 2.

Fig.15.Critical velocity vs.temperature.

The magnetic induction of the annular permanent magnet with temperature at the velocity of 9 m/s is given in Fig.18.Only the local demagnetized region A appears with the temperature between 20°C and 80°C.The decline of quiescent operation point caused by the increase in the temperature of the permanent magnets leads to small eddy current field and the resulting weakened demagnetization of region B.However,the demagnetization performance of adjacent permanent magnets is different as the temperature continues to increase,which is particularly noticeable at 120°C.Fig.18(a)and(b)signify the demagnetized region comparison at 120°C of the above permanent magnet and the adjacent permanent magnet.The air-gap magnetic induction of the end permanent magnet is half of that of the adjacent permanent magnet.So,its resulting eddy currents and induced eddy current fields are weaker.It causes a higher dynamic operation point to be obtained,which forces the demagnetized region B of adjacent permanent magnet to increase.Moreover,the high temperature causes the position of the permanent magnet knee point to rise,so that the adjacent permanent magnet demagnetized region expanded rapidly.

6.Conclusion

The irreversible demagnetization mechanism of NdFeB permanent magnets during electromagnetic buffering under the condition of impact load,high temperature and self-demagnetization field is analysed in detail.The following conclusions has been obtained:

Fig.16.The magnetic induction of the permanent magnet with velocity at the temperature of 20 °C considering irreversibly demagnetized.

Fig.17.The magnetic path and field lines at room temperature and the velocity of 9 m/s under impact 2.

Fig.18.The magnetic induction of the permanent magnet with temperature at the velocity of 9 m/s under impact 2 considering irreversibly demagnetized.

(1)The critical velocity determined by structural parameters of the EMB is related to the eddy current demagnetization,high-temperature demagnetization and selfdemagnetization.

(2)The parameterkmis expressed as the index of the air-gap width,the inner cylinder thickness,iron pole axial length and the permanent magnet demagnetization coefficient.The critical velocity considering self-demagnetization is obtained using the finite element and theoretical analysis results.The demagnetization coefficientkwis only related to permanent magnet structure,temperature,and demagnetization inhomogeneity.

(3)The permanent magnet does not undergo irreversible demagnetization during the electromagnetic buffering process under the action of the impact 1 at room temperature,but undergoes two parts of irreversible demagnetization under the impact 2.

(4)The irreversible demagnetized region A of the permanent magnet occurs first,and the demagnetization degree of adjacent permanent magnets is different at high temperatures.

For the convenience of research,the demagnetization effect of high-velocity,high-temperature and self-demagnetization field of permanent magnets during electromagnetic buffering is simplified.For example,the skin effect and boundary effect are neglected,which may cause a certain deviation of the eddy current and damping force.Subsequent study is mainly to establish a detailed analysis model.Then,introduce cushioning measures to reduce the vibration caused by strong impact loads on the test platform.And go through the impact test at different temperature to get the changing law of parameterkw.Magnetic path design and optimization considering irreversible demagnetization will be implemented to obtain reasonable impact parameters of the EMB.

Declaration of competing interest

No conflict of interest exits in the submission of this manuscript,and manuscript is approved by all authors for publication.I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously,and not under consideration for publication elsewhere,in whole or in part.All the authors listed have approved the manuscript that is enclosed.

Acknowledgement

The work was primarily supported by the National Natural Science Foundation of China(grant number 301070603).