Design and Simulation Analysis of an Energy Regenerative

Design and Simulation Analysis of an Energy

Regenerative Electromagnetic Shock

Absorber for Vehicles

Xiangyu Xiao2, Yanan Wang1,3,4*, Xin He1,3,4, Qingfeng Li1,3,4 and Hua Li1,3,4

1School of Mechanical Engineering, Shandong University, Jinan 250061, P.R. China2Department of Automotive Engineering, School of Transportation Science and Engineering, Beihang University,

Beijing 100191, P.R. China3Key Laboratory of High-Efficiency and Clean Mechanical Manufacture of Ministry of Education, Shandong University,

Jinan 250061, P.R. China4National Demonstration Center for Experimental Mechanical Engineering Education, Shandong University,

Jinan 250061, P.R. China

Abstract

An energy-regenerative shock absorber with damping adjustment function based on the

electromagnetic induction principle is proposed for the problem of energy dissipation in the vibration

of vehicle suspension systems. The structure of the shock absorber, the control system and the

electrical system are designed, and the dynamic model of the suspension system with the energy-

regenerative electromagnetic shock absorber is built. The vibration response of the vehicle body, the

frequency characteristic of the suspension system, and the energy-regenerative power of the

electromagnetic shock absorber are analyzed. The results show that this electromagnetic shock

absorber has good energy-regenerative effect on roads of different levels. Compared with the original

hydraulic telescopic shock absorber, the vibration displacement, speed and acceleration of the vehicle

body can be lowered significantly when the electromagnetic shock absorber is used with appropriate

damping. The electromagnetic shock absorber has a compact structure, adjustable damping and

energy-regenerative function, which can be used as a design reference for the electrification of the

suspension systems in new energy vehicles in the future.

Key Words: Electromagnetic Shock Absorber, Energy-regenerative, Suspension System, Linear

Generator, Damping, Vehicle

1. Introduction

With the continuous increase of fuel consumption,

the energy shortage and environmental pollution prob-

lems have become important factors restricting the de-

velopments of the society and the economy. Various en-

ergy-conservation and emission-reduction measures are

used in automotive industry and other fields. Experiments

show that only 10% to 16% of the energy generated by

the engine is effectively utilized, while most of the other

is dissipated in the form of heat [1]. Among which, the

energy dissipated by the suspension system accounts for

over 17.2% [2], which causes energy loss and mecha-

nical wear of the relevant components. As the main en-

ergy-consumption component in the suspension system,

the traditional hydraulic telescopic shock absorber as-

similates the vibration energy of the suspension and con-

verts it into heat energy, and then disperses it in the atmo-

sphere. In contrast, the energy-regenerative shock ab-

sorber can recycle the vibration energy generated during

vehicle running and reduce energy consumption. When

it is applied to new energy vehicles such as hybrid vehi-

Journal of Applied Science and Engineering, Vol. 22, No. 4, pp. 625�636 (2019) DOI: 10.6180/jase.201912_22(4).0004

*Corresponding author. E-mail: [email protected]

cles and electric vehicles, the recycled energy could fur-

ther be stored and lengthen the endurance mileage [3,4].

So the energy-regenerative shock absorber has important

theoretical research significance and practical applica-

tion value.

Research on the energy-regenerative shock absorber

began in the 1990s. As a new type of vibration-reduction

device, it can mainly be divided into electrohydraulic

type, electromagnetic type and mechanical type, etc. In

2009, the research team of MIT invented a hydraulic en-

ergy-regenerative shock absorber to recycle the vibra-

tion energy of a vehicle suspension system, and tests

showed that the shock absorber has good energy-regen-

erative effect [5]. Zou et al. proposed a new type of hy-

draulic energy-regenerative shock absorber based on a

traditional hydraulic shock absorber. It could convert the

bidirectional vibration into back-and-forth movement of

the piston and generate oil pressure to drive the hydraulic

motor to rotate, which generated electricity [6]. Yu et al.

used Carsim software to calculate and analyze the en-

ergy-regenerative potential of a mechanical rack-and-

pinion shock absorber [7]. Sabzehgar et al. designed a

mechanical energy-regenerative shock absorber, which

could recycle energy by using a spatial six-bar linkage to

convert vertical motion into rotational motion of the mo-

tor [8]. Zhang et al. converted the bidirectional vibration

to a unidirectional rotation of a generator module based

on a dual-gear rack mechanism. Compared to the me-

chanical rack-and-pinion shock absorber, the efficiency

was improved by up to 40% in simulation and bench

tests [9]. Zheng et al. used a brushless direct current

(DC) motor as the main body, a ball-screw mechanism

and other accessories as fittings, designed and manufac-

tured a mechanical energy-regenerative shock absorber

[10]. Li P et al. tested the energy-regenerative power of a

mechanical motion-rectifier-based shock absorber th-

rough bench and vehicle tests. By controlling the resis-

tance between the generator terminals, the semi-active

suspension function could be achieved [11]. Currently,

the research on the energy-regenerative shock absorbers

is still in a rapid development stage.

In this paper, an energy-regenerative shock absorber

with damping adjustment function based on the principle

of electromagnetic induction is proposed. The linear ge-

nerator without mechanical transmission loss is applied,

which theoretically could obtain higher energy-regenera-

tive power. The structure, the control system and the elec-

trical system are designed, and the vibration response of

the vehicle body, the frequency characteristic of the sus-

pension system and the energy-regenerative powers of the

shock absorber on roads of different levels are obtained by

the dynamic model and simulation of the suspension sys-

tem. The comparison with the suspension system with the

original hydraulic telescopic shock absorber shows that

the electromagnetic shock absorber has good vibration-re-

duction and energy-regenerative performance.

2. Theory and Method

2.1 Fundamental Theory

Vehicle is a multi-DOF vibration system with inertia,

elasticity and damping. Since the natural frequencies of

its various subsystems are different, strong vibration in

part of or even the entire vehicle could be caused by vari-

ous internal and external excitations, such as road rough-

ness, changes of speed and direction, imbalances in the

engine, transmission system and wheels, and shock gen-

erated by gears. The suspension system can isolate the

vibration through the shock absorber and the elastic me-

chanism, and absorb the vibration energy of the wheels

in the vertical direction, so that the frame and the body

can maintain stability while the wheels bump.

As shown in Figure 1, the research object of the ve-

hicle vibration problem is the “vehicle-road” system. The

“input” of the system is formed by road roughness, vehi-

cle speed and engine excitation. This “input” is transmit-

ted through the vibration system to obtain the “output” –

the relationship between the vibration displacement and

time, and the amplitude-frequency characteristic of the

vehicle body [12,13]. The vibration system consists of

elastic elements, damping elements, sprung and unsprung

mass, such as tires, suspensions and powertrain systems.

2.2 Research Method

The research methods of the vehicle vibration char-

626 Xiangyu Xiao et al.

Figure 1. “Vehicle-road” system.

acteristics mainly include experimental method and the-

oretical method. Experimental method usually uses ac-

tual road test, field test, indoor simulation test, etc., and

position and acceleration sensors are used to collect the

real-time test data. The theoretical method usually builds

the dynamic model consisting with the actual situation,

calculates the eigenvalues of the vibration system and

solves the vibration response, then processes the data

and obtains the vibration characteristics in time domain

or frequency domain. This paper mainly uses theoretical

method in the design and analysis research of the en-

ergy-regenerative electromagnetic shock absorber. The

advantages of this method are as follows,

(1) Manpower and material resources are reduced. Test

field and vehicles are not necessarily needed,

(2) The results won’t be affected by random errors caused

by natural environment,

(3) Compared with the experimental method, the input

values of theoretical analysis can be easily changed,

which could simulate different working conditions,

and multiple sets of experimental data can be ob-

tained quickly,

(4) The results of the theoretical analysis can provide

guidance for the optimal design of the product and

predict its performance before manufacture.

3. Vibration Characteristics of the

Suspension System

3.1 Models of the Suspension System

Although modern vehicle suspension system has a

variety of structural forms, it is usually composed of

three parts: an elastic component, a shock absorber and a

guide mechanism, as shown in Figure 2. They act as buf-

fer, damper and guidance, respectively. When the move-

ment in the vertical direction of the vehicle is only con-

sidered, the two-DOF model of the suspension can be

used for analysis, as shown in Figure 3.

The differential equation of the motion of the two-

DOF model can be obtained according to Newton’s sec-

ond law,

m z C z z K z z

m z C z z K z

2 2 2 1 2 1

1 1 1 2 1

0�� ( � � ) ( )

�� ( � � ) (

� � � � �

� � � � � � �

�� z K z qt2 1 0) ( )

(1)

where m1 is the unsprung mass (i.e. mass of the wheel

assembly), m2 is the sprung mass (i.e. mass of the vehi-

cle body), K is the stiffness of the suspension, C is the

damping coefficient of the shock absorber, Kt is the

stiffness of the tire. q is the road roughness excitation,

z1, �z1, ��z1 are the displacement, velocity and acceleration

of the vehicle unsprung mass respectively, and z2, �z2, ��z2

are the displacement, velocity and acceleration of the

vehicle sprung mass respectively.

The performance of the suspension system could use

vehicle acceleration ab, dynamic tire load Ft and dyna-

mic suspension displacement Ss as the evaluation indexes

[14], where ab = ��z2, Ft = (q – z1)Kt, Ss = z2 – z1.

The average power consumption Pex of the shock

Design and Simulation Analysis of an Energy Regenerative Electromagnetic Shock Absorber for Vehicles 627

Figure 2. Vehicle suspension system.

Figure 3. Two-DOF model of the suspension system.

absorber in the suspension can be expressed by the work

done by the damping force per unit time

PT

F t d z t z t

TC

ex

T

� �

�

� �

� �

�

�

�1

1

2 10

( ) [ ( ) ( )]

[ �z t z t dtT

2 1

2

0( ) � ( )]��

(2)

where T is the sampling time, F(t) is the instantaneous

damping force of the shock absorber. Pex reflects the

amount of energy dissipated by the vibration during the

running of the vehicle, and also indicates the maximum

energy that can be recycled theoretically.

3.2 Excitation of the Road Roughness

In the ISO/TC108/SC2N67 document proposed by

the International Organization for Standardization, the

following equation is suggested as the fitting formula of

the road power spectral density Gq(n) [15].

G n G nn

nq q( ) ( )�

�

�

�

�

0

0

�

(3)

where n is the spatial frequency indicating the number

of cycles per meter, its unit is m-1, n0 is the referential

spatial frequency, n0 = 0.1 m-1, Gq(n0) is called road

roughness coefficient, which is the road spectrum under

the referential spatial frequency, and its unit is m3, � is

the frequency index reflecting the frequency structure

of the road spectrum, and the classified frequency index

of the road roughness is � = 2. The characteristic para-

meters of each road level are listed in Table 1.

3.3 Performance Indexes of the Suspension System

Table 2 shows the design parameters of one side of

the front axis of a car made in China. The input of ran-

dom road roughness excitation is fitted according to har-

monics, and the formula is q(t) = Rq sin(2�n0t). In which

Rq is the RMS deviation of the contour, seen in Table 1.

According to Rq of four road levels A, B, C and D in Ta-

ble 1, q(t) of each road level can be obtained. Substitut-

ing q(t) and the design parameters of the suspension sys-

tem in Table 2 into Eq. (1), z1, �z1, ��z1 and z2, �z2, ��z2 can be

obtained, and then vehicle acceleration ab, dynamic tire

load Ft, dynamic suspension displacement Ss and aver-

age power consumption Pex can be obtained.

Each index of the suspension performance ab, Ft, Ss

is measured by its root mean square value [14], shown in

Table 3. It can be seen that ab, Ft and Ss rise as the road

level decreases, which indicates that the increase in the

road roughness reduces the ride comfort of the vehicle

and deteriorates the handling stability of the vehicle. The

average power consumption Pex rises as the road level


Table 1. Characteristic parameters of each road level [16]

Level

Geometric mean of the

power spectral density

Gq(n0)/10-6 m3

RMS deviation of the

contour Rq/10-3 m

A 0016.00 03.52

B 0064.00 07.05

C 0256.00 14.09

D 1024.00 28.19

E 4096.00 56.37

F 16384.000 112.740

G 65536.000 225.490

Table 2. Design parameters of a car

Parameters Symbols Units Valves

Total sprung mass M kg 0975.37

Unsprung mass m1 kg 0049.00

Equivalent sprung mass m2 kg 0243.84

Equivalent damping coefficient of telescopic shock absorber C N·s/m 1560.25

Equivalent vertical stiffness of the tire Kt N/m 302342.7000

Equivalent stiffness of the suspension system K N/m 26144.100

Table 3. Suspension characteristic indexes on roads of

different levels

Road surface

levelab/(m/s2) Ss/mm Ft/kN Pex/W

A 0.51 02.00 0302.34 022.80

B 1.02 05.30 0604.69 043.70

C 2.57 10.00 0907.03 132.76

D 3.69 15.00 1511.71 315.17

decreases, which indicates that the vibration energy caused

by the vehicle running and the road roughness is ab-

sorbed by the shock absorber and then dissipates [17].

4. Working Principle and Design of the

Electromagnetic Shock Absorber

4.1 Introduction of Cylindrical Halbach

Permanent-magnet Linear Generator

The cylindrical Halbach permanent-magnet linear

generator is an energy conversion device based on the

electromagnetic induction principle, which can convert

the kinetic energy of linear motion into electric potential

energy in the coil windings [18].

Figure 4 is a schematic diagram of a cylindrical lin-

ear generator, and it mainly consists of a stator, a mover

and coil windings. The moving part of a linear genera-

tor is called a mover, which is composed of a magnetic

yoke and a plurality of permanent magnet poles and is

mounted on a straight axis. As a good conductor, the

magnetic yoke covers the straight axis and constitutes

the magnetic path between magnetic poles. The annular

magnetic poles are installed on the outside of the mag-

netic yoke at the same interval, which is equal to the

tooth space of the stator, and the thickness of the annu-

lar magnetic pole is the same as the tooth space of the

stator.

Along the motion direction in Figure 4, during the

movement of the mover, the change of the magnetic flux

in the coil windings produces the electromotive poten-

tial, and the periodic movement will generate single-

phase alternating current (AC) to achieve power genera-

tion [19].

4.2 Structure Design of the Electromagnetic Shock

Absorber

As part of the vehicle suspension system, the struc-

ture of the electromagnetic shock absorber should have

good applicability to achieve the purpose of maximizing

energy recovery and facilitating installation. Therefore,

the similar appearance with the hydraulic telescopic shock

absorber is adopted in the structure design. According to

the working principle of the Halbach permanent-magnet

linear generator, the structure of the energy-regenerative

electromagnetic shock absorber is designed, which is

shown in Figure 5.

The shock absorber is mainly composed of coil wind-

ings, inner and outer cylinders, a piston rod, permanent

magnets, fasteners, seals and other components. There

are 18 pie-shaped coil windings between the inner and

outer cylinders of the stator, the number of coils in each

coil winding is 16 turns, and they are placed in two lay-

ers. The mover is composed of a piston rod and perma-

nent magnets. The piston rod uses non-magnetic mate-

rial with lighter weight, and the permanent magnets use

neodymium-iron-boron as the magnetic source of the

generator. There is a proper gap between the permanent

magnets and the inner cylinder, and the coil windings are


Figure 5. Structure of the energy-regenerative electromagnetic shock absorber.

Figure 4. Schematic diagram of a cylindrical linear generator.

fixed by windings cages. The main mechanical move-

ment is the translation of the piston rod (mover) relative

to the coil windings (stator). The main structural dimen-

sions of this shock absorber are shown in Table 4.

4.3 Control System Design of the Electromagnetic

Shock Absorber

As shown in Figure 6, the control system of the en-

ergy-regenerative electromagnetic shock absorber mainly

includes sensors, electronic control unit (ECU), battery,

energy recovery circuit and control circuit [20]. The two

ends of the electromagnetic shock absorber are respec-

tively mounted on the vehicle body and the suspension

through the shackles, and the coil windings are connected

with the control circuit through the connecting wires.

When the vehicle is running on the road, the road rough-

ness is transmitted to the shock absorber through the

wheels, which drives the outer cylinder to reciprocate re-

lative to the piston rod and the permanent magnets. The

strong magnetic field produced by the high-density per-

manent magnets continuously cuts the coil windings of

the stator, and induces AC in the coil windings according

to the electromagnetic induction principle. The inductive

AC is converted into DC after being rectified and stabi-

lized by the energy recovery circuit, and then transferred

and stored in the on-board battery.

The number of the coil windings of the electromag-

netic shock absorber connected in the circuit can be ad-

justed according to the running conditions for the pur-

pose of wider damping adjustment range and stronger

adaptability. When the vehicle runs on the roads of dif-

ferent levels, ECU acquires the vibration level informa-

tion collected by the sensors, calculates the optimum

damping coefficient of the shock absorber under the cur-

rent condition and sends a signal to the control circuit to

change the number of coil windings connected in the en-

ergy recovery circuit. Consequently, the damping adjust-

ment function of the shock absorber is realized.

4.4 Electrical System Design of the Electromagnetic

Shock Absorber

The rectification module and voltage stabilization

module are introduced in the energy recovery circuit to

store the instantaneous single-phase AC produced by the

electromagnetic shock absorber. These two modules can

be realized through a single-phase bridge rectifying cir-

cuit and a diode voltage stabilizing circuit respectively in

the energy recovery circuit, as shown in Figure 7. The

battery is charged by the rectified low-pulse DC power,

and then the “production-rectification-storage” process

of the electric energy is completed.

4.5 Dynamic Model and Load Analysis of the


The motion and force state of the electromagnetic

shock absorber is shown in Figure 8, where m is the mass

of the mover, v is the instantaneous relative speed of the

reciprocating motion of the piston rod, and i is the instan-

taneous induced current generated in the coil windings.

The overall length of the coils can be obtained by the fol-

lowing equations,

l = �dxk (4)


Table 4. Main structural dimensions of the

electromagnetic shock absorber

Parameters Values/mm

Outer diameter of stator 62.00

Inner diameter of stator 46.00

Diameter of piston rod 22.00

Outer diameter of permanent magnet 38.00

Inner diameter of permanent magnet 22.00

Thickness of permanent magnet 08.00

Figure 6. Control system of the energy-regenerative electro-magnetic shock absorber. Figure 7. Energy recovery circuit of the control system.

where d = 0.06 m is the diameter of the coil windings, k

is the ratio of the number of the coil windings connected

in the circuit to the total number of the coil windings, x

is the total number of the coil windings, here x takes 288

according to the design parameters.

The total resistance of the coil windings R0 can be

obtained as following

Rl

s0 � � (5)

where � = 1.75 � 10-8 �·m is the resistivity of the cop-

per, S is the cross-sectional area of the wire and takes

1.08 � 10-6 m2.

The relationship between the instantaneous damping

force F generated by the shock absorber and the instanta-

neous speed v of the piston rod can be expressed by the

following equation,

FB l

Rv�

2 2

0

(6)

where B is the equivalent magnetic induction intensity.

According to the material properties, the magnetic in-

duction intensity of the surface remanence of the neo-

dymium-iron-boron magnet is about 0.8�1.4 T, here B

takes 1.2 T. The relative speed of the piston v = ( �z2 � �z1).

The average damping force F can be obtained by the

average speed v by equation (6), so the damping coeffi-

cient can be obtained by

CF

v1 � (7)

and C1 = 4823.02 k N�s/m according to the parameters

given above.

The electromotive potential generated in the coil

windings is

u = Blv (8)

The energy-regenerative power P of the electromag-

netic shock absorber is numerically equal to the product

of the electromotive potential induced in the coil wind-

ings and the current in the coil windings, which can be

expressed as

P uu

Rkv� �

0

2482302. (9)

The energy-regenerative power P calculated by Eq. (9)

can be used as an evaluation index of the energy-regen-

erative performance of the electromagnetic shock ab-

sorber.

By changing k, the ratio of the number of coil wind-

ings connected in the circuit to the total number of coil

windings, the relationship between the damping of the

electromagnetic shock absorber and the number of coil

windings connected in the circuit can be obtained. Tak-

ing k value as 1, 0.75, 0.5 and 0.25 respectively, the num-

ber of the coil windings and the overall length of the

coils connected in the circuit will change, as well as the

damping of the shock absorber, which are listed in Table

5. It can be seen that the damping coefficient of the shock

absorber rises with the number of the coil windings con-

nected in the circuit.

According to the data in Table 5, this shock absorber

can improve the vehicle ride comfort on roads of differ-

ent levels by adjusting the damping in multiple levels ac-

cording to the change of running conditions. When it is


Figure 8. Dynamic model of the electromagnetic shock ab-sorber.

Table 5. Damping coefficients of the shock absorber

kNumber of coil

windings x·k

Coil length

l (m)

Damping C1

(N·s/m)

1 288 54.29 4823.02

0.75 216 40.72 3617.27

0.5 144 27.15 2411.51

0.25 072 13.58 1205.76

installed in the active suspension system and works with

the elastic mechanism, the shock absorber can be further

used to regulate the roll motion during the steering pro-

cess and the pitching motion during the acceleration and

deceleration process, and eventually improve the ride

comfort and handling stability of vehicles.

5. Vibration-reduction Performance and

Energy-regenerative Performance Analysis

5.1 Vibration Response of the Vehicle Body

5.1.1 Mathematical Models

Eq. (1) is used for the basic mathematical model of

the suspension system, where relevant parameters refer

to Table 2, and the damping coefficient C1 of the de-

signed electromagnetic shock absorber is 4823.02k N�s/

m. The mathematical model of the suspension system

with the original hydraulic telescopic shock absorber in-

troduced in 3.1 is also built, and the damping coefficient

C is 1560.25 N�s/m.

The input takes road of C level as an example ac-

cording to the road roughness introduced in 3.2. The

white noise with finite bandwidth is used to simulate the

actual road excitation at the vehicle speed of 20 m/s, and

the emulational road surface is obtained by integration.

The power spectrum of the white noise with finite band-

width is

G f G n n uq q( ) ( )� 4 2

0 0

2

1� (10)

where Gq(n0) = 2.56 � 10-4 m3, u1 = 20 m/s is the vehicle

speed, and the result of Gq(f) is 0.002.

5.1.2 Vibration Response in Time Domain

As shown in Figure 9, the suspension system model is

built in the Simulink module of MATLAB according to


Figure 9. Model of the suspension system in Simulink.

Eq. (1). After calculation in the range of 0�60 s, the curves

of the displacement z2, speed �z2 and acceleration ��z2 of the

vehicle body on road of C level are obtained when k is

0.75 and 1, as shown in Figure 10 (a)�(c) and Figure

11(a)�(c) respectively. The results of the suspension sys-

tem with the original hydraulic telescopic shock absorber

are also calculated as comparisons. Meantime, the speed

of the piston rod of the electromagnetic shock absorber is

figured up for the purpose of obtaining the energy-regen-

erative power, as shown in Figure 10(d) and Figure 11(d).


Figure 10. Simulation results (k = 0.75, C level road). Figure 11. Simulation results (k = 1, C level road).

It can be seen from the results that under the given

conditions, the displacement, speed and acceleration of

the vehicle body in the time domain are lowered signifi-

cantly after the adoption of the electromagnetic shock

absorber. And the reduction magnitude is more signifi-

cant as k increases.

5.2 Frequency Characteristic of the Suspension

System

The differential equation of motion of the suspen-

sion system (1) can be Fourier transformed to obtain

(11)

and the frequency response function of the suspension

system is

(12)

By substituting the parameters of the suspension sys-

tem into Eq. (12) and taking the module, the ampli-

tude-frequency characteristic of the suspension system

can be obtained, as shown in Figure 12. As can be seen

from the figure, the amplitude-frequency characteristic

curves of the suspension system vary with k. At the

same time, there are two feature points of 2.1 Hz and

13.0 Hz. The amplitude-frequency characteristic curves

of different k-values all pass through these two feature

points.

When the frequency of the road excitation is less

than 2.1 Hz, the greater the k, the smaller the vibration

displacement of the vehicle body. When the frequency of

the road excitation is between 2.1 Hz and 13.0 Hz, the

greater the k, the greater the vibration displacement of

the vehicle body. When the frequency of the road excita-

tion is greater than 13.0 Hz, the effect of k on the ampli-

tude-frequency characteristic of the suspension system is

not obvious. The damping of the energy-regenerative

electromagnetic shock absorber can be controlled ac-

cording to the above law. Therefore, by monitoring the

road excitation frequency and changing k constantly, the

ride comfort can be effectively improved.

5.3 Energy-regenerative Power of the


Taking road of C level and k = 0.75 as an example,

the energy-regenerative power of this electromagnetic

shock absorber can be calculated by Eq. (9). The average

speed of the piston rod in Eq. (9) can be obtained by us-

ing Figure 10(d) to calculate the mean square value in the

range of 0�60 s. After calculation, the average speed v is

0.16 m/s, and the average energy-regenerative power P is

69.56W. When k takes 1, 0.75, 0.5, 0.25, the same

method can be used to calculate the average energy-re-

generative power on road of different levels, and the re-

sults are shown in Table 6. It can be seen that with the de-

creasing of the road level and the increasing of k, the av-

erage energy-regenerative power rises, and the shock

absorber can recycle more energy.


Figure 12. Amplitude-frequency characteristic of the suspension system.

6. Conclusions

The design and simulation research on an energy-re-

generative electromagnetic shock absorber is conducted

in this paper. The structure, control system, and electrical

system of the shock absorber are designed based on the

electromagnetic induction principle and the structure of

the Halbach permanent-magnet linear generator. On the

foundation of the two-DOF model of the suspension sys-

tem, the dynamics simulation and performance analysis

of the electromagnetic shock absorber are carried out

and compared with the suspension system with the origi-

nal hydraulic telescopic shock absorber.

The results show that the designed shock absorber

can effectively attenuate the vibration of the vehicle

body caused by the road roughness and has good en-

ergy-regenerative performance. This shock absorber has

a compact structure with clear working principle, and its

damping can be adjusted within a certain range, which

make it have good practical application prospect. The

design idea and research method of the energy-regenera-

tive electromagnetic shock absorber can provide refer-

ence for the recovery and utilization of the suspension

vibration energy, and can be applied in the design and

analysis process of the electrical suspension system in

new energy vehicles in the future.

Acknowledgements

This research is supported by National Natural Sci-

ence Foundation of China (Grant No. 51405269) and

Foundation of State Key Laboratory of Automotive Sim-

ulation and Control (Grant No. 20181102).

References

[1] Guntur, H. L., W. Hendrowati, and R. R. Lubis (2013)

Development and analysis of a regenerative shock ab-

sorber for vehicle suspension, Journal of System De-

sign and Dynamics 7(3), 304�315. doi: 10.1299/jsdd.

7.304

[2] Zuo, L., B. Scully, and J. Shestani (2010) Design and

characterization of an electromagnetic energy harvester

for vehicle suspensions, Smart Materials and Struc-

tures 19(4), 1007�1016. doi: 10.1088/0964-1726/19/

4/045003

[3] Huang, K., F. Yu, and Y. Zhang (2011) Active control-

ler design for an electromagnetic energy-regenerative

suspension, International Journal of Automotive Te-

chnology 12(6), 877�885. doi: 10.1007/s12239-011-

0100-2

[4] Li, Z., L. Zuo, and J. Kuang (2012) Energy-harvesting

shock absorber with a mechanical motion rectifier,

Smart Materials and Structures 22(2), 1�10.

[5] Avadhany, S. N. (2009) Analysis of hydraulic power

transduction in regenerative rotary shock absorbers

as function of working fluid kinematic viscosity, Ph. D

Thesis, Massachusetts Institute of Technology.

[6] Zou, J., X. Guo, L. Xu, G. Tan, C. Zhang, and J. Zhang

(2017) Design, modeling, and analysis of a novel hy-

draulic energy-regenerative shock absorber for vehicle

suspension, Shock and Vibration 1�12. doi: 10.1155/

2017/3186584

[7] Yu, C. M., W. H. Wang and Q. N. Wang (2009) Analy-

sis of energy-saving potential of energy regenerative

suspension system on hybrid vehicle, Journal of Jilin

University (Engineering and Technology Edition) 39(4),

841�845.

[8] Sabzehgar, R., A. Maravandi and M. Moallem (2014)

Energy regenerative suspension using an algebraic

screw linkage mechanism, IEEE/ASME Transactions

on Mechatronics 19(4), 1251�1259. doi: 10.1109/

TMECH.2013.2277854

[9] Zhang, Z., X. Zhang, and W. Chen (2016) A high-effi-

ciency energy regenerative shock absorber using su-

percapacitors for renewable energy applications in

range extended electric vehicle, Applied Energy 178,

177�188. doi: 10.1016/j.apenergy.2016.06.054

[10] Zheng, X. C., F. Yu, and Y. C. Zhang (2008) A novel

energy-regenerative active suspension for vehicles,

Journal of Shanghai Jiaotong University (Science)

13(2), 184�188. doi: 10.1007/s12204-008-0184-7


Table 6. Energy-regenerative power on roads of different

levels

Road level A B C D

k = 1 4.96 19.31 77.23 304.69

k = 0.75 4.35 17.39 69.56 278.24

k = 0.5 3.83 14.67 58.69 234.76P(W)

k = 0.25 3.20 12.77 51.10 204.39

[11] Li, P., L. Zuo, J. Lu, et al. (2014) Electromagnetic re-

generative suspension system for ground vehicles,

IEEE International Conference on Systems, IEEE. doi:

10.1109/SMC.2014.6974304

[12] Hyniova, K., J. Honcu, and A. Stríbrsky (2005) Vibra-

tion control in automotive systems, IFAC Proceedings

Volumes 38(1), 317�321. doi: 10.3182/20050703-6-

CZ-1902.01263

[13] Peng, M., X. Guo, and J. Zou (2016) Simulation study

on vehicle road performance with hydraulic electro-

magnetic energy-regenerative shock absorber, SAE Te-

chnical Paper 2016-01-1550. doi: 10.4271/2016-01-

1550

[14] Kawamoto, Y., Y. Suda, H. Inoue, et al. (2008) Elec-

tro-mechanical suspension system considering energy

consumption and vehicle manoeuvre, Vehicle System

Dynamics 46(sup1), 1053�1063. doi: 10.1080/0042

3110802056263

[15] Yanping, Z., H. Zhengang, and X. Xiaomei (2013) A

design method of automotive driving axle casing un-

der the random load, Journal of Applied Sciences

13(19), 4028�4033. doi: 10.3923/jas.2013.4028.4033

[16] Cantisani, G., and G. Loprencipe (2010) Road rough-

ness and whole body vibration, evaluation tools and

comfort limits, Journal of Transportation Engineering

136(9), 818�826. doi: 10.1061/(ASCE)TE.1943-5436.

0000143

[17] Mú�ka, P. (2016) Energy-harvesting potential of auto-

mobile suspension, Vehicle System Dynamics 54(12),

1651�1670. doi: 10.1080/00423114.2016.1227077

[18] Ibrahim, T., J. Wang, and D. Howe (2008) Analysis

and experimental verification of a single-phase, quasi-

Halbach magnetized tubular permanent magnet motor

with non-ferromagnetic support tube, IEEE Transac-

tions on Magnetics 44(11), 4361�4364. doi: 10.1109/

TMAG.2008.2001510

[19] Arof, H., and H. W. Ping (2010) Analysis of magnetic

field distribution of a cylindrical discrete Halbach per-

manent magnet linear generator, IET Electric Power

Applications 4(8), 629�636. doi: 10.1049/iet-epa.2009.

0267

[20] Zhang, H., X. X. Guo, and Z. G. Fang (2015) Potential

energy harvesting analysis and test on energy-regener-

ative suspension system, Journal of Vibration, Mea-

surement & Diagnosis 35(2), 225�230.

Manuscript Received: Apr. 16, 2019

Accepted: Sep. 4, 2019


Documents

Design and Simulation Analysis of an Energy Regenerative