Modeling and Analysis of a Hydraulic Energy-Harvesting ...downloads.hindawi.com/journals/mpe/2020/1580297.pdfthe eﬀect of these shock absorbers on vehicle dynamics. Abdelkareem et

Research ArticleModeling and Analysis of a Hydraulic Energy-HarvestingShock Absorber

Zhifei Wu and Guangzhao Xu

School of Mechanical and Vehicle Engineering Taiyuan University of Technology Taiyuan 030024 China

Correspondence should be addressed to Zhifei Wu wuzhifeityuteducn

Received 5 November 2019 Revised 30 December 2019 Accepted 16 January 2020 Published 8 February 2020

Academic Editor Fausto Arpino

Copyright copy 2020 Zhifei Wu and Guangzhao Xu is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

is paper proposes a hydraulic energy-harvesting shock absorber prototype which realizes energy harvesting of the vibrationenergy dissipated by the automobile suspension system e structural design of the proposed shock absorber ensures that theunidirectional flow of oil drives the hydraulic motor to generate electricity while obtaining an asymmetrical extensioncom-pression damping force A mathematical model of the energy-harvesting shock absorber is established and the simulation resultsindicate that the damping force can be controlled by varying the load resistance of the feed module thus adjusting the requireddamping force ratio of the compression and recovery strokes By adjusting the external load the target indicator performance ofthe shock absorber is achieved while obtaining the required energy recovery power A series of experiments are conducted on theprototype to verify the validity of the damping characteristics and the energy recovery efficiency as well as to analyze the effect ofexternal load and excitation speed on these characteristics

1 Introduction

Recovery of energy dissipated during driving of automobileshas been extensively researched [1 2] In addition to brakeenergy recovery suspension energy recovery technology hasbeen gradually implemented in vehicles A hydraulic energy-harvesting shock absorber can convert vibration energydissipated by the suspension system into electric energy forrecycling thereby realizing energy conservation and en-suring a stable working performance of the shock absorbererefore it has received considerable research attention

Many types of energy-harvesting shock absorbers havebeen developed Salman presented a regenerative absorberbased on helical gears and dual tapered roller clutches forelectric vehicles [3] Zhang presented an energy-harvestingshock absorber that uses an arm-teeth mechanism to convertlinear motion to rotational motion and to amplify thegenerator input speed [4] Energy-harvesting dampers are oftwo main forms electromagnetic and electrohydraulic Zuoet al designed and established a 1 2 prototype based on alinear motor-type feed-through suspension [5] Zheng et al

researched the structure of feed suspension with a DCmotorand a ball screw mechanism and improved the performanceof the suspension system of the vehicle by the active controlof vibration energy [6 7] Li et al proposed a novel energy-harvesting variableconstant damping suspension systemwith a motor-based electromagnetic damper which cansimultaneously achieve energy recovery and storage as wellas adjust the damping force according to different roadconditions [8] Similarly various hydraulic-electric energy-harvesting suspension systems have been used in the oilcircuit system design to convert the reciprocating vibrationenergy of the piston into the hydraulic energy of thedamping oil thus facilitating the rotation of the hydraulicmotor in the driving system and driving the generator togenerate electricity [9ndash11] However the damping fluid in anoil circuit system frequently switches the flow direction dueto the nonuniform excitation caused by uneven road sur-faces which dramatically reduces the feed efficiency of thegenerator Fang conducted considerable research on hy-draulic-electric energy-feeding suspension and proposedseveral implementation schemes by establishing dynamic

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 1580297 11 pageshttpsdoiorg10115520201580297

models and simulation analysis A bench test of the pro-totype was conducted for more systematic research [12ndash14]Fang et al also studied the effect of road excitation fre-quency external load and damping coefficient on energyrecovery efficiency [15] Many research studies on energy-harvesting shock absorbers mainly focused on road tests andthe effect of these shock absorbers on vehicle dynamicsAbdelkareem et al summarized the current situation ofenergy-harvesting dampers mainly from four aspectsnamely the principle simulation a bench test and a roadtest and summarized the advantages and limitations ofenergy-harvesting dampers [16] Zou et al proposed a hy-draulic interconnected suspension system based on a hy-draulic energy-regenerative shock absorber and investigatedthe dynamic characteristics of the system based on a 4-degrees-of-freedom (DOF) longitudinal half-vehicle model[17] Zou et al also investigated different working modesincluding bounce pitch and roll of the damper andcompared the damper with conventional shock absorbers interms of suspension dynamics and energy recovery [18]Abdelkareem et al established a comprehensive simulationmodel to analyze the potential harvested power of vehicles ofdifferent models and for different standard driving cycles[19] ey also used the HAVAL H8 SUV model to conductreal-vehicle road tests to analyze and verify the potentialharvested power [20] Abdelkareem et al analyzed thepotential energy recovery of suspension systems in differentdriving environments for six types of heavy trucks [21] Wuet al studied the effect of parameters of the accumulator on ahydraulic system and provided useful guidelines for theselection of system component parameters [22] eaforementioned studies mainly aimed at conducting roadtests to determine the corresponding efficiency of recoverypower and lack a detailed analysis of the recovery power ofthe damper and the factors affecting the recovery efficiency

e main objectives of the present study are as follows(1) To design a hydraulic energy-harvesting shock absorberprototype that can achieve unidirectional oil flow that drivesthe hydraulic motor to generate electricity (2) To propose amethod for adjusting the damping ratio and to obtain anasymmetric damping ratio through the design structure (3)To construct a model of the energy-harvesting shock ab-sorber and to analyze and refine the factors affecting theenergy recovery power and efficiency as well as determinethe extent to which the different factors affect them

2 Working Principle of the Energy-HarvestingShock Absorber

e principle of the hydraulic energy-harvesting shock ab-sorber is depicted in Figure 1 It consists of a double-actinghydraulic cylinder a hydraulic rectifier comprising two checkvalves an accumulator a hydraulic motor a permanentmagnetic generator and hydraulic lines In this study theupward and downward motions of the piston are described ascompression and extension respectively In the compressionstroke the oil directly flows through check valve 1 to sup-plement the rod-end chamber the oil flow rate through thehydraulic motor is obtained by multiplying the rod area and

piston speed In the extension stroke the oil flow rate throughthe hydraulic motor is obtained by multiplying the annulararea of the piston and piston speed e fuel flow drives thegenerator to generate electricity By this design principle thedamping force of the compression stroke is mainly generatedfrom check valve 1 while the damping force of the extensionstroke is primarily generated from the hydraulic motor andcheck valve 2 is allows adjustment of the relevant com-ponent parameters separately to achieve the required com-pression and extension damping forces

As shown in Figure 1 in the compression stroke becausecheck valve 2 is in the closed state the oil directly flowsthrough check valve 1 to supplement the rod-end chamberBecause the volume of the rod-end chamber is lower than thatof the cap-end chamber the oil will flow through the hy-draulic motor and lead to generation of electricity When thehydraulicmotor reaches node A owing to the high pressure atthe left end of check valve 2 which is in the closed state somepart of the oil is stored in the accumulator In the extensionstroke the downwardmovement of the piston drives the oil inthe rod-end chamber to be completely discharged Becausecheck valve 1 is in the closed state the oil can only passthrough the hydraulic motor After the oil-driven hydraulicmotor generates electricity the oil flows back to the cap-endchamber together with the oil stored in the accumulatorduring the compression stroke According to this workingprinciple the overall damping force of the energy-harvestingdamper can be divided into inherent damping force andcontrollable damping force Inherent damping is caused bythe no-load rotational damping force of the energy-feedingmodule and the passive damping of the accumulator oil lineand check valve in the actuator e controllable dampingforce refers to the hydraulic motor damping force caused bythe generatorrsquos counter electromotive force

3 Mathematical Model

31 Flow Rate Analysis According to the principle analysisthe extension stroke flow rate is

Qpi Qpu Acv(t) (1)

Qv1 0 (2)

Qv2 Agv(t) (3)

e compression stroke flow is

Checkvalve

CylinderAccumulator Interal

resistance

Interalinductance

Externalload

FlowdirectionSensor

Actuator

Motor

2

MA

Figure 1 Schematic diagram of the hydraulic energy-harvestingshock absorber

2 Mathematical Problems in Engineering

Qv1 Agv(t)11138681113868111386811138681113868

11138681113868111386811138681113868 (4)

Qpi Qpu Arv(t)1113868111386811138681113868

1113868111386811138681113868 (5)

Qv2 0 (6)

where Qpi and Qpu are the flow rates through the hydraulicline and the pump respectively Qv1 and Qv2 are the flowrates through check valves 1 and 2 respectively Ac is theannular area of the piston v(t) is the speed of the pistonmovement Ag is the full piston face area and Ar is thepiston rod area

e relationship between hydraulic motor speed andtorque is as follows

ωpu 2πQpu

qηv (7)

Tpu ΔPpuq

2πηm (8)

where ωpu is the rotating speed of the hydraulic motor Tpu isthe torque of the hydraulic motor Qpu is the flow ratethrough the hydraulic motor and q is the motor displace-ment ΔPpu is the pressure difference between the inlet andoutlet oil in the hydraulic motor ηv is the volumetric effi-ciency of the hydraulic motor and ηm is the mechanicalefficiency of the hydraulic motor

When the hydraulic motor drives the generator to rotatethrough the coupling the relationship of the generatoroutput voltage Uemf and the generator drive torque Tg is asfollows

Uemf keωg (9)

Tg Jg

dωdt

+ ktI (10)

where ωg is the generator rotating speed ke and kt are thegeneratorrsquos counter electromotive force constant and torqueconstant respectively Jg is the inertia of the generator rotorand I is the generator output current

According to Kirchhoffrsquos voltage law the following re-lationship can be obtained

Uemf minus LindI

dtminus I Rin + Rex( 1113857 0 (11)

where Lin is the generator internal inductance Rin is thegenerator internal resistance (usually the internal induc-tance of the generator is negligible) and Rex is the externalgenerator load

Since the hydraulic motor and the generator are con-nected by the coupling we have

ωpu ωg (12)

Tpu Tg (13)

Based on equations (7)ndash(13) the hydraulic pressuredifferenceΔPpu between the hydraulic motor inlet and outlet

in terms of the flow rate Qpu of the oil flowing through thehydraulic motor can be obtained as follows

ΔPpu 4π2Jgηv

q2ηm

_Qpu +4π2ktkeηv

q2ηm Rin + Rex( 1113857Qpu (14)

32 Controllable Damping Force Equation (14) indicatesthat when the external load Rex is infinite the hydraulicmotor works with inherent damping e second term onthe right side of the formula implies that the hydraulic motorcan be controlled by an external load e pressure decreasecan be expressed as follows

ΔPpc 4π2ktkeηv

q2ηm Rin + Rex( 1113857Qpu kpcQpu (15)

where kpc is the equivalent controllable impedance of thefeed module and is affected by the displacement of thehydraulic motor mechanical efficiency volumetric effi-ciency and power generation characteristics of thegenerator

In this part only the controllable pressure decrease isconsidered which is applied to the two ends of the ac-tuator piston and the equivalent controllable dampingforce of the energy-absorbing damper can be obtainede following relationship is satisfied in the extensionstroke

Pupc 0 (16)

Pdownc ΔPpc (17)

where pupc and Pdownc represent the controllable pressures ofthe rod-end and cap-end chambers respectively

e compression stroke satisfies the followingrelationship

Pupc ΔPpc (18)

Pdownc ΔPpc (19)

Combining equations (1)ndash(6) and (16)ndash(19) the totalequivalent controllable damping force of thehydraulic energy-absorbing damper can be expressed asfollows

Fsa AcPdownc minus AgPupc

π3ktkeηv D2 minus d2

rod1113872 11138732v(t)

q2ηm Rin + Rex( 1113857 v(t) ge 0

π3ktkeηvd4

rodv(t)

q2ηm Rin + Rex( 1113857 v(t) le 0

(20)

Furthermore based on equations (9)ndash(13) the expres-sion of the feed power is

Mathematical Problems in Engineering 3

Pr I2Rex

π4k2eη

2v D2 minus d2

rod1113872 11138732Rex

4q2 Rin + Rex( 11138572 v

2(t) v(t) ge 0

π4k2

eη2vd4

rodRex

4q2 Rin + Rex( 11138572v

2(t) v(t)le 0

(21)

e above equations indicate that in the case where themechanical structural parameters are determined themagnitude of feed power of the compression stroke and therecovery stroke depends mainly on the excitation speed andthe magnitude of the load resistance

33 Inherent Damping Force

(1) Calculation of the pressure decrease of the no-loadmotorAccording to the motor pressure decrease formulawhen the external resistor is infinite the relationshipof the hydraulic pressure decrease between the hy-draulic motor inlet and outlet with the flow rateunder the no-load conditions is given as follows

ΔPpup 4π2Jgηv

q2ηm

_Qpu cpp_Qpu (22)

where ΔPpup and Qpu represent the pressure dif-ference between the hydraulic motor inlet and outletoil and the hydraulic motor flow rate respectivelycpp is the equivalent inherent damping of the feedmodule

(2) Hydraulic line pressure decrease calculationHydraulic line pressure decrease ΔPpi can beexpressed as

Δppi 128ρLpiμπd4

piQpi kpiQpi (23)

where ρ represents the oil density kpi is the pipelinepressure decrease coefficient Qpi is the oil flow ratethrough the pipeline Lpi and dpi are the hydraulicpipe length and diameter respectively and μ is thedynamic viscosity of the oil

(3) Check valve pressure decrease calculationWhen the oil flows through the check valve thepressure at the check valve decreases which is ob-tained by the orifice formula

ΔPvi

ρ2

1113970Kvi

CdBviAviQvi1113888 1113889

23

(24)

where Qvi represents the flow rate through the checkvalve i i 1 2 ΔPvi is the check valve inlet and

outlet pressure difference Cd is the flow coefficientBvi Avi and Kvi are the valve blade perimeter areaand stiffness respectively of the check valve i

(4) AccumulatorBecause of the fixed mass of gas in the accumulatoraccording to the properties of an ideal gas the re-lationship between the volume and pressure of thegas is given by

P0Vn0 PtV

nt (25)

where P0 and V0 represent the gas pressure and volumein the accumulator in the initial state respectively Pt

and Vt are the gas pressure and volume in the accu-mulator at t time respectively and n is the variableindex e relationship between the gas volume at t

time Vt and the initial gas volume V0 is

Vt minus V0 Ar 1113946 v(t)dt (26)

Based on equations (25) and (26) the gas pressure inthe accumulator at time t is given by

Pt P0V

n0

Vnt

P0V

n0

Ar 1113938 v(t)dt + V01113872 1113873n (27)

where Pdownp and Pupp are the hydraulic oil pressure of therod-end and cap-end chambers respectively under a no-load condition e extension stroke satisfies the followingrelationship

Pupp Pt minus ΔPv2 (28)

Pdownp ΔPpup + Pt + ΔPpi (29)


Pupp ΔPpup + Pt + ΔPpi + ΔPv1 (30)


Combining equations (1)ndash(6) and (28)ndash(31) the total in-herent damping force of the hydraulic energy-harvesting shockabsorber Fp can be expressed as

Fp AcPdownp minus AgPupp Ac ΔPpup + Pt + ΔPpi1113872 1113873

minus Ag Pt minus ΔPv2( 1113857 v(t)ge 0

Ac ΔPpup + Pt + ΔPpi1113872 1113873

minus Ag ΔPpup + Pt + ΔPpi + ΔPv11113872 1113873 v(t) le 0

(32)

which is


Fp minusπP0V

n0d2

rod

4 V0 + π4d2rod 1113938 v(t)dt1113872 1113873

n +32ρLpiμ

d4pi

D2

minus d2rod1113872 1113873

2v(t)

+π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)ge 0

minusπP0V

n0d2

rod

4 V0 + π4d2rod 1113938 v(t)dt1113872 1113873

n minus32ρLpiμ

d4pi

d4rodv(t) minus

π8ρ13

middotKv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)le 0

(33)

34 Overall Damping Force Combining equations (16)ndash(19)and (28)ndash(31) the hydraulic oil pressure can be expressed as

Pdown Pdownp + Pdownc (34)

Pup Pupp + Pupc (35)

where Pup and Pdown are the hydraulic oil pressures of therod-end and cap-end chambers

According to the above analysis the extension strokesatisfies the following relationship

Pdown ΔPpu + Pt + ΔPpi (36)

Pup Pt minus ΔPv2 (37)



Pup ΔPpu + Pt + ΔPpi + ΔPv1 (39)

According to equations (1)ndash(6) and (36)ndash(39) the overalldamping force F is as follows

F AcPdown minus AgPup minusπP0V

n0d

2rod

4 V0 +(π4)d2rod 1113938 v(t)dt1113872 1113873

n +32ρLpiμ

d4pi

+π3ktkeηv

q2ηm Rin + Rex( 1113857⎛⎝ ⎞⎠ D

2minus d

2rod1113872 1113873

2v(t)

+π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)ge 0

minusπP0V

n0d

2rod

4 V0 +(π4)d2rod 1113938 v(t)dt1113872 1113873

n minus32ρLpiμ

d4pi

+π3ktkeηv

q2ηm Rin + Rex( 1113857⎛⎝ ⎞⎠d

4rodv(t) minus

π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)le 0

(40)

4 Simulation and Analysis of the DampingForce and Feed Power

41 Damping Controllable Characteristics of the Energy-HarvestingDamper According to the theoretical analysis ofthe hydraulic energy-harvesting damper the damping forceof the damper is affected by the excitation frequency andexternal load erefore this section presents a simulationstudy on the controllable range of the damping force underthe same excitation amplitude (50mm) different excitationfrequencies and different external loads We established amathematical model and set simulation parameters for anexcitation amplitude of 50mm e external load resistancewas set to 10Ω 30Ω 50Ω and 100Ω e damper char-acteristics under different excitation frequencies and ex-ternal load resistance are shown in Figure 2

Figure 2 shows that the damping force of the extensionstroke is larger than that of the compression stroke which isconsistent with the requirement of asymmetric dampingcharacteristics for conventional dampers As the load in-creases both extension and compression stroke damping

forces increase and the extension stroke is relatively obvi-ous At the same frequency and under the same change inload resistance the extension stroke damping force can beadjusted from minus 583N to minus 1023N in multiples of 175 at023Hze extension stroke damping force can be adjustedfrom minus 2210N to minus 3393N in multiples of 154 at 062HzNote that as the frequency increases the adjustable range ofthe damping force widens and the adjustable multiple de-creases e accumulator parameters greatly affect thedamping force in both compression and extension strokesIn the first half of the compression stroke the damping forceincreases gradually due to the accumulator energy storageIn the second half of the extension stroke the impact andmagnitude of the force caused by the accumulator pressurerelease are related to the frequencye damping force in thesecond half of the extension stroke at 023Hz is larger thanthat in the first half

42 Simulation Analysis of the Effect of the Hydraulic Energy-Harvesting Shock Absorber on Vehicle Suspension Dynamics


To analyze the effect of the damping characteristics of theshock absorber on the vehicle suspension dynamics weestablished a 2-DOF quarter car model in MATLABSimulinken the results of the comparison and analysis ofsprung mass acceleration in Figure 3 suspension deflectionresponse and tire load response indicate that the effect of thehydraulic energy-harvesting shock absorber is less on thevehicle dynamic performance during energy recovery

43 Effect of External Load on the Energy RecoveryCharacteristics of the Hydraulic Energy-Harvesting ShockAbsorber According to the theoretical analysis of the en-ergy-absorbing damper the feed energy of the damper isaffected by the excitation frequency and the external loade simulation settings for this analysis are the same as thosefor the analysis in the previous section We discuss the

factors that affect the energy recovery power and efficiencyunder the same excitation amplitude (50mm) differentexcitation speeds and different external loads

From equations (21) and (40) the energy recovery ef-ficiency ηh is obtained as

ηh Pr

Fv(t) (41)

Because the recovery power of the compression stroke isextremely small we mainly focus on the extension strokeConsider Pr as the peak recovery power of the extensionstroke F is the peak damping force of the extension strokeand v(t) is the peak excitation speed at the excitation fre-quency to obtain the corresponding energy recovery effi-ciency Figures 4 and 5 indicate that as the excitationfrequency increases and the external load resistance

10Ω30Ω

50Ω100Ω

ndash3500

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000D

ampi

ng fo

rce (

N)

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50Displacement (mm)

(a)

10Ω30Ω

50Ω100Ω

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


(b)

10Ω30Ω

50Ω100Ω

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


(c)

10Ω30Ω

50Ω100Ω

ndash1200

ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

400

600

800D

ampi

ng fo

rce (

N)


(d)

Figure 2 Load resistance characteristics at an excitation frequency of 062Hz (a) 045Hz (b) 035Hz (c) and 023Hz (d)


-15ndash1

ndash050

051

152

25

Spru

ng m

ass a

ccel

erat

ion

(ms

lowast s)

1 2 3 4 5 6 7 8 9 100Time (s)

Passive suspensionHydraulic energy-harvesting absorber

Figure 3 Sprung mass acceleration of the hydraulic energy-harvesting absorber and passive suspension

10Ω30Ω

50Ω100Ω

0

50

100

150

200

250

300

Pow

er (W

)

1 2 3 4 5 60Time (s)

(a)

023Hz035Hz

045Hz062Hz

0

20

40

60

80

100

120

Pow

er (W

)

1 2 3 4 5 60Time (s)

(b)

Figure 4 Feed power (a) under different loads at an excitation frequency of 062Hz and (b) at different frequencies for a load of 30Ω

10Ω30Ω

50Ω100Ω

005

01

015

02

025

03

035

04

Effic

ienc

y

008 01 012 014 016 018 02006Speed (ms)

(a)

10 20 30 40 50 60 70 80 90 100Load resistance (Ω)

007ms011ms

014ms019ms

005

01

015

02

025

03

035

04

Effic

ienc

y

(b)

Figure 5 Feed efficiency (a) under different load resistance and (b) different excitation speeds


decreases the feed power increases greatly In the first half ofthe compression stroke the feed power is extremely smalldue to the energy storage of the accumulator and there is asudden change in power during the extension stroke eexcitation frequency has little effect on the energy efficiencyAs the speed increases the feed efficiency basically remainsunchanged As the load resistance decreases the feed effi-ciency increases considerably

44 External Load and Feed Efficiency Corresponding toTarget Indicator Characteristics rough simulation ahydraulic cylinder diameter of 50mm was selected such thatthe standard specifications under the conventional excita-tion (input frequency 1655Hz and amplitude 50mm) aremet e maximum extension and compression dampingforce that the damper needs to provide are minus 7000N and2800N respectively During the simulation process the loadvalue was changed several times and the load resistancevalue and the corresponding feed power value under thetarget indicator characteristic were obtained

Figure 6 shows that when the external load was 53Ω themaximum extension and compression damping forcereached minus 6972N and 2768N respectively which basicallymeets the target damping requirement At the same time thepeak power can be recovered at 50552W and the feedefficiency is 145

5 Experimental Methodologies

51 Experimental Setup To evaluate the effects of differentexcitation speeds and external loads on feed energy dampersa test bench was built and an existing hydraulic excitationplatform was used to simulate road excitation As shown inFigure 7 the test bench is mainly composed of a double-acting hydraulic cylinder check valves an accumulator ahydraulic motor a generator a high-power sliding rheostatand a compression and tension load sensor

e theory analysis and simulation described in previoussections show that the damping force of the shock absorberis affected by the excitation frequency and external loaderefore the damping force at a constant excitation dis-placement different excitation velocities and different ex-ternal loads was experimentally studied Because theexcitation platform used in the experiment cannot providesinusoidal excitation the experiment adopted uniform ex-citation and themaximum speed of the sinusoidal excitationis the same as the experimental excitation speed under thesimulation condition e experimental parameter setting isshown in Table 1

52 Experimental Procedure e hydraulic excitationplatform was adjusted to vary the excitation speed and thesliding rheostat was adjusted to vary the external load for theorthogonal test e value of the compression and tensionload from the sensor and the voltage value across the slidingrheostat were collected using a data acquisition instrumentwhich will be detailed as follows

53 Data Acquisition In this study an INV3060A 16-channel data acquisition instrument was used for collectingdata e DYLY-103 load cell was used as the compressionand tension load sensor During the experiment a DASP

Dam

ping

forc

e (N

)

ndash7000

ndash6000

ndash5000

ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

3000


Figure 6 Damping force diagram under target indicatorcharacteristics

Figure 7 Key components of the energy-harvesting shock ab-sorber system (1) hydraulic cylinder (2 4) check valves (3) hose(5) hydraulic excitation platform (6) accumulator (7) hydraulicmotor (8) coupling (9) three-phase alternator (10) rectifier (11)sliding rheostat (A) force transductor (B) pressure transductorand (C) voltage transductor

Table 1 Main component parameters of the hydraulic excitationsystem

Parameters Value UnitExternal load 10 30 50 100 ΩDisplacement plusmn50 mmSpeed 019 014 011 007 msFrequency 062 045 035 023 Hz


system was used to collect and display the values from thecompression and tension load sensor and the sliding varistorvoltage

6 Results and Discussion

61 Damping Controllable Feature Verification is sectiondiscusses the results of the experimental study on thecontrollable range of the damping force under the sameexcitation amplitude (50mm) different excitation speedsand different external loads

Figure 8 indicates that in the test data the damping forceof the extension stroke was larger than that of the com-pression stroke which is consistent with the requirement ofasymmetric damping characteristics for conventional shockabsorbers us the established model is verified by bothexperimental and simulation results However the experi-mental data were higher than the simulation data is isbecause the simulation is based on ideal conditions whereasin actual conditions due to the low oil temperature a certainenergy loss occurred in pipe joints and the flow meter Wecan observe that as the excitation speed increased under thesame load change condition the adjustable range of thedamping force increased with decreasing adjustable

multiplee accumulator significantly affected the dampingforce in both compression and extension strokes In the firsthalf of the compression stroke the damping force increasedgradually due to the accumulator energy storage In thesecond half of the extension stroke the impact and mag-nitude of the force caused by the accumulator pressurerelease were dependent on frequency It can be seen that thedamping force in the second half of the extension stroke at0073ms was greater than that in the first half In additionbecause there were a large number of pipe joints and otherfactors affecting the line pressure decrease during the actualtest the response speed of the extension stroke accumulatorunder the test conditions was much slower than that in thesimulation conditions

62 Verification of the Effect of External Load on FeedCharacteristics To calculate the energy recovery power andefficiency the average values of the damping force andgeneration voltage near the midpoint of the displacement ofthe extension stroke were taken as the effective values of thedamping force and voltage

From Figures 9 and 10 the following observations can beinferred (1) e test and simulation results are consistent

ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

Dam

ping

forc

e (N

)

ndash50 ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50Displacement (mm)

10Ω30Ω

50Ω100Ω

(a)

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(b)

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(c)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(d)

Figure 8 Damping characteristics with different loads at an excitation speed of 019ms (a) 014ms (b) 011ms (c) and 007ms (d)


thus the rationality of the simulation model is verified (2)Actual test load power and efficiency differ from those in thesimulation at the same speed and same load resistanceconditions is is because the simulation is performedbased on ideal conditions whereas in the actual situationthe low oil temperature the effect of the pipeline layout andthe actual power generation characteristics of the generatoraffect the recovery power and efficiency (3) With increasingexcitation speed and decreasing external load resistance theextension stroke feed power increases significantly (4)Because the excitation speed affects both inherent dampingforce and overall damping force the feed efficiency is notaffected by the excitation speed but greatly affected by theexternal load resistance at is as the load resistance de-creases the feed efficiency increases drastically (5) egenerator selected for the prototype has a rated power of100W which has low power-generation efficiency underlarge load and large speed and stable power generation at therated power is causes a significant inflection point in theefficiency plots

7 Conclusions

In this study a hydraulic shock absorber was proposed andthe design principle andmathematical model were describedin detail e principle prototype was built to verify thedamping characteristics and energy recovery characteristicse main conclusions are as follows

(1) e controllable range of the damping force dependson the external load and excitation frequency Toobtain an asymmetrical extensioncompressiondamping force the controllable range of the ex-tension stroke is large At an excitation frequency of062Hz the external load ranged from 10 to 100Ωand the peak damping force ranged from minus 3393 tominus 2210N

(2) e simulation results indicate that under the targetdamper characteristics the peak recovery power ofthe energy-absorbing damper was 50552W and therecovery efficiency was 145


007ms011ms

014ms019ms

008

01

012

014

016

018

02

Effici

ency

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 02

008

01

012

014

016

018

02Effi

cien

cy

(b)

Figure 10 Variation of efficiency with (a) speed and (b) load resistance


007ms011ms

014ms019ms

0

20

40

60

80

100

120

Pow

er (W

)

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 020

20

40

60

80

100

120

Pow

er (W

)

(b)

Figure 9 Variation of power with (a) speed and (b) load resistance


(3) Energy recovery power depends on the excitationspeed and external load At an excitation speed of019ms and external load of 10Ω the recoveredpower was 1037W e energy recovery efficiencymainly depends on the external load At varyingexternal load the recovery efficiency ranged from 8to 18 whereas at varying excitation speed theefficiency fluctuated by only 2

Data Availability

e authors declare that all data sources are original

Conflicts of Interest

e authors declare no conflicts of interest

Authorsrsquo Contributions

Zhifei Wu contributed to methodology and Guangzhao Xuwas responsible for validation All authors have read andapproved the final manuscript

Acknowledgments

is research was funded by e Shanxi Province Scienceand Technology Major Project grant number 20181102006e authors are grateful for the support by the VehicleDepartment of Taiyuan University of Technology

References

[1] J Ruan P Walker and N Zhang ldquoA comparative studyenergy consumption and costs of battery electric vehicletransmissionsrdquo Applied Energy vol 165 pp 119ndash134 2016

[2] C Fiori K Ahn and H A Rakha ldquoPower-based electricvehicle energy consumption model model development andvalidationrdquo Applied Energy vol 168 pp 257ndash268 2016

[3] W Salman L Qi X Zhu et al ldquoA high-efficiency energyregenerative shock absorber using helical gears for poweringlow-wattage electrical device of electric vehiclesrdquo Energyvol 159 pp 361ndash372 2018

[4] R Zhang and X Wang ldquoParameter study and optimization ofa half-vehicle suspension system model integrated with anarm-teeth regenerative shock absorber using Taguchimethodrdquo Mechanical Systems and Signal Processing vol 126pp 65ndash81 2019

[5] L Zuo B Scully J Shestani and Y Zhou ldquoDesign andcharacterization of an electromagnetic energy harvester forvehicle suspensionsrdquo Smart Materials and Structures vol 19no 4 p 45003 2010

[6] X-c Zheng F Yu and Y-c Zhang ldquoA novel energy-re-generative active suspension for vehiclesrdquo Journal of ShanghaiJiaotong University (Science) vol 13 no 2 pp 184ndash188 2008

[7] G Zhang J Cao and F Yu ldquoDesign of active and energy-regenerative controllers for DC-motor-based suspensionrdquoMechatronics vol 22 no 8 pp 1124ndash1134 2012

[8] S Li J Xu X Pu T Tao H Gao and X Mei ldquoEnergy-harvesting variableconstant damping suspension system withmotor based electromagnetic damperrdquo Energy vol 189p 116199 2019

[9] J A Stansbury III ldquoRegenerative suspension with accumu-lator systems and methodsrdquo US Patent 7938217 2011

[10] A Okamoto ldquoEnergy regeneration device for either hybridvehicle or electric automobilerdquo US Patent 8479859 2013

[11] S Carabelli A Tonoli A Festini et al ldquoSuspension system fora wheeled vehicle and a wheeled vehicle equipped with such asuspension systemrdquo US Patent 7942225 2011

[12] Z G Fang X X Guo and L Zuo ldquoPotential study andsensitivity analysis of energy regenerative suspensionrdquoJournal of Jiangsu University vol 34 pp 373ndash377 2013

[13] L Xu ldquoStructure designs and evaluation of performancesimulation of hydraulic transmission electromagnetic energy-regenerative active suspensionrdquo in SAE Technical Paper SeriesSAE International Warrendale PA USA 2011

[14] Z Fang X Guo L Xu and H Zhang ldquoExperimental study ofdamping and energy regeneration characteristics of a hy-draulic electromagnetic shock absorberrdquo Advances in Me-chanical Engineering vol 5 Article ID 943528 2013

[15] Z Fang X Guo L Xu and H Zhang ldquoAn optimal algorithmfor energy recovery of hydraulic electromagnetic energy-re-generative shock absorberrdquo Applied Mathematics and Infor-mation Sciences vol 7 no 6 pp 2207ndash2214 2013

[16] M A A Abdelkareem L Xu M K A Ali et al ldquoVibrationenergy harvesting in automotive suspension system a detailedreviewrdquo Applied Energy vol 229 pp 672ndash699 2018

[17] J Zou X Guo L Xu et al ldquoSimulation research of a hydraulicinterconnected suspension based on a hydraulic energy re-generative shock absorberrdquo in SAE Technical Paper SeriesSAE International Warrendale PA USA 2018

[18] J Zou X Guo M A A Abdelkareem L Xu and J ZhangldquoModelling and ride analysis of a hydraulic interconnectedsuspension based on the hydraulic energy regenerative shockabsorbersrdquo Mechanical Systems and Signal Processingvol 127 pp 345ndash369 2019

[19] M A A Abdelkareem L Xu X Guo et al ldquoEnergy har-vesting sensitivity analysis and assessment of the potentialpower and full car dynamics for different road modesrdquoMechanical Systems and Signal Processing vol 110 pp 307ndash332 2018

[20] M A A Abdelkareem L Xu M K A Ali et al ldquoOn-fieldmeasurements of the dissipated vibrational power of an SUVcar traditional viscous shock absorberrdquo in Proceedings of theASME 2018 International Design Engineering TechnicalConferences and Computers and Information in EngineeringConference American Society of Mechanical Engineers(ASME) Quebec City Canada August 2018

[21] M A A Abdelkareem L Xu M K A Ali et al ldquoAnalysis ofthe prospective vibrational energy harvesting of heavy-dutytruck suspensions a simulation approachrdquo Energy vol 173pp 332ndash351 2019

[22] Z Wu Y Xiang M Li M Y Iqbal and G Xu ldquoInvestigationof accumulator main parameters of hydraulic excitationsystemrdquo Journal of Coastal Research vol 93 no sp1pp 613ndash622 2019


models and simulation analysis A bench test of the pro-totype was conducted for more systematic research [12ndash14]Fang et al also studied the effect of road excitation fre-quency external load and damping coefficient on energyrecovery efficiency [15] Many research studies on energy-harvesting shock absorbers mainly focused on road tests andthe effect of these shock absorbers on vehicle dynamicsAbdelkareem et al summarized the current situation ofenergy-harvesting dampers mainly from four aspectsnamely the principle simulation a bench test and a roadtest and summarized the advantages and limitations ofenergy-harvesting dampers [16] Zou et al proposed a hy-draulic interconnected suspension system based on a hy-draulic energy-regenerative shock absorber and investigatedthe dynamic characteristics of the system based on a 4-degrees-of-freedom (DOF) longitudinal half-vehicle model[17] Zou et al also investigated different working modesincluding bounce pitch and roll of the damper andcompared the damper with conventional shock absorbers interms of suspension dynamics and energy recovery [18]Abdelkareem et al established a comprehensive simulationmodel to analyze the potential harvested power of vehicles ofdifferent models and for different standard driving cycles[19] ey also used the HAVAL H8 SUV model to conductreal-vehicle road tests to analyze and verify the potentialharvested power [20] Abdelkareem et al analyzed thepotential energy recovery of suspension systems in differentdriving environments for six types of heavy trucks [21] Wuet al studied the effect of parameters of the accumulator on ahydraulic system and provided useful guidelines for theselection of system component parameters [22] eaforementioned studies mainly aimed at conducting roadtests to determine the corresponding efficiency of recoverypower and lack a detailed analysis of the recovery power ofthe damper and the factors affecting the recovery efficiency

e main objectives of the present study are as follows(1) To design a hydraulic energy-harvesting shock absorberprototype that can achieve unidirectional oil flow that drivesthe hydraulic motor to generate electricity (2) To propose amethod for adjusting the damping ratio and to obtain anasymmetric damping ratio through the design structure (3)To construct a model of the energy-harvesting shock ab-sorber and to analyze and refine the factors affecting theenergy recovery power and efficiency as well as determinethe extent to which the different factors affect them

2 Working Principle of the Energy-HarvestingShock Absorber

e principle of the hydraulic energy-harvesting shock ab-sorber is depicted in Figure 1 It consists of a double-actinghydraulic cylinder a hydraulic rectifier comprising two checkvalves an accumulator a hydraulic motor a permanentmagnetic generator and hydraulic lines In this study theupward and downward motions of the piston are described ascompression and extension respectively In the compressionstroke the oil directly flows through check valve 1 to sup-plement the rod-end chamber the oil flow rate through thehydraulic motor is obtained by multiplying the rod area and

piston speed In the extension stroke the oil flow rate throughthe hydraulic motor is obtained by multiplying the annulararea of the piston and piston speed e fuel flow drives thegenerator to generate electricity By this design principle thedamping force of the compression stroke is mainly generatedfrom check valve 1 while the damping force of the extensionstroke is primarily generated from the hydraulic motor andcheck valve 2 is allows adjustment of the relevant com-ponent parameters separately to achieve the required com-pression and extension damping forces

As shown in Figure 1 in the compression stroke becausecheck valve 2 is in the closed state the oil directly flowsthrough check valve 1 to supplement the rod-end chamberBecause the volume of the rod-end chamber is lower than thatof the cap-end chamber the oil will flow through the hy-draulic motor and lead to generation of electricity When thehydraulicmotor reaches node A owing to the high pressure atthe left end of check valve 2 which is in the closed state somepart of the oil is stored in the accumulator In the extensionstroke the downwardmovement of the piston drives the oil inthe rod-end chamber to be completely discharged Becausecheck valve 1 is in the closed state the oil can only passthrough the hydraulic motor After the oil-driven hydraulicmotor generates electricity the oil flows back to the cap-endchamber together with the oil stored in the accumulatorduring the compression stroke According to this workingprinciple the overall damping force of the energy-harvestingdamper can be divided into inherent damping force andcontrollable damping force Inherent damping is caused bythe no-load rotational damping force of the energy-feedingmodule and the passive damping of the accumulator oil lineand check valve in the actuator e controllable dampingforce refers to the hydraulic motor damping force caused bythe generatorrsquos counter electromotive force

3 Mathematical Model

31 Flow Rate Analysis According to the principle analysisthe extension stroke flow rate is

Qpi Qpu Acv(t) (1)

Qv1 0 (2)

Qv2 Agv(t) (3)

e compression stroke flow is

Checkvalve

CylinderAccumulator Interal

resistance

Interalinductance

Externalload

FlowdirectionSensor

Actuator

Motor

2

MA

Figure 1 Schematic diagram of the hydraulic energy-harvestingshock absorber


Qv1 Agv(t)11138681113868111386811138681113868

11138681113868111386811138681113868 (4)

Qpi Qpu Arv(t)1113868111386811138681113868

1113868111386811138681113868 (5)

Qv2 0 (6)



ωpu 2πQpu

qηv (7)

Tpu ΔPpuq

2πηm (8)



Uemf keωg (9)

Tg Jg

dωdt

+ ktI (10)



Uemf minus LindI




ωpu ωg (12)

Tpu Tg (13)



ΔPpu 4π2Jgηv

q2ηm

_Qpu +4π2ktkeηv

q2ηm Rin + Rex( 1113857Qpu (14)


ΔPpc 4π2ktkeηv




Pupc 0 (16)

Pdownc ΔPpc (17)



Pupc ΔPpc (18)

Pdownc ΔPpc (19)




rod1113872 11138732v(t)

q2ηm Rin + Rex( 1113857 v(t) ge 0

π3ktkeηvd4

rodv(t)

q2ηm Rin + Rex( 1113857 v(t) le 0

(20)



Pr I2Rex

π4k2eη

2v D2 minus d2

rod1113872 11138732Rex

4q2 Rin + Rex( 11138572 v

2(t) v(t) ge 0

π4k2

eη2vd4

rodRex

4q2 Rin + Rex( 11138572v

2(t) v(t)le 0

(21)




ΔPpup 4π2Jgηv

q2ηm

_Qpu cpp_Qpu (22)




piQpi kpiQpi (23)



ΔPvi

ρ2

1113970Kvi


23

(24)




P0Vn0 PtV

nt (25)






Pt P0V

n0

Vnt

P0V

n0

Ar 1113938 v(t)dt + V01113872 1113873n (27)










Ac ΔPpup + Pt + ΔPpi1113872 1113873


(32)

which is


Fp minusπP0V

n0d2

rod

4 V0 + π4d2rod 1113938 v(t)dt1113872 1113873

n +32ρLpiμ

d4pi

D2

minus d2rod1113872 1113873

2v(t)

+π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)ge 0

minusπP0V

n0d2

rod

4 V0 + π4d2rod 1113938 v(t)dt1113872 1113873

n minus32ρLpiμ

d4pi

d4rodv(t) minus

π8ρ13

middotKv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)le 0

(33)













n0d

2rod

4 V0 +(π4)d2rod 1113938 v(t)dt1113872 1113873

n +32ρLpiμ

d4pi

+π3ktkeηv

q2ηm Rin + Rex( 1113857⎛⎝ ⎞⎠ D

2minus d

2rod1113872 1113873

2v(t)

+π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)ge 0

minusπP0V

n0d

2rod

4 V0 +(π4)d2rod 1113938 v(t)dt1113872 1113873

n minus32ρLpiμ

d4pi

+π3ktkeηv

q2ηm Rin + Rex( 1113857⎛⎝ ⎞⎠d

4rodv(t) minus

π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)le 0

(40)











ηh Pr

Fv(t) (41)


10Ω30Ω

50Ω100Ω

ndash3500

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000D

ampi

ng fo

rce (

N)


(a)

10Ω30Ω

50Ω100Ω

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


(b)

10Ω30Ω

50Ω100Ω

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


(c)

10Ω30Ω

50Ω100Ω

ndash1200

ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

400

600

800D

ampi

ng fo

rce (

N)


(d)



-15ndash1

ndash050

051

152

25

Spru

ng m

ass a

ccel

erat

ion

(ms

lowast s)

1 2 3 4 5 6 7 8 9 100Time (s)



10Ω30Ω

50Ω100Ω

0

50

100

150

200

250

300

Pow

er (W

)

1 2 3 4 5 60Time (s)

(a)

023Hz035Hz

045Hz062Hz

0

20

40

60

80

100

120

Pow

er (W

)

1 2 3 4 5 60Time (s)

(b)


10Ω30Ω

50Ω100Ω

005

01

015

02

025

03

035

04

Effic

ienc

y

008 01 012 014 016 018 02006Speed (ms)

(a)


007ms011ms

014ms019ms

005

01

015

02

025

03

035

04

Effic

ienc

y

(b)











Dam

ping

forc

e (N

)

ndash7000

ndash6000

ndash5000

ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

3000














ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(a)

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(b)

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(c)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(d)




7 Conclusions





007ms011ms

014ms019ms

008

01

012

014

016

018

02

Effici

ency

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 02

008

01

012

014

016

018

02Effi

cien

cy

(b)



007ms011ms

014ms019ms

0

20

40

60

80

100

120

Pow

er (W

)

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 020

20

40

60

80

100

120

Pow

er (W

)

(b)




Data Availability






Acknowledgments


References
























Qv1 Agv(t)11138681113868111386811138681113868

11138681113868111386811138681113868 (4)

Qpi Qpu Arv(t)1113868111386811138681113868

1113868111386811138681113868 (5)

Qv2 0 (6)



ωpu 2πQpu

qηv (7)

Tpu ΔPpuq

2πηm (8)



Uemf keωg (9)

Tg Jg

dωdt

+ ktI (10)



Uemf minus LindI




ωpu ωg (12)

Tpu Tg (13)



ΔPpu 4π2Jgηv

q2ηm

_Qpu +4π2ktkeηv

q2ηm Rin + Rex( 1113857Qpu (14)


ΔPpc 4π2ktkeηv




Pupc 0 (16)

Pdownc ΔPpc (17)



Pupc ΔPpc (18)

Pdownc ΔPpc (19)




rod1113872 11138732v(t)

q2ηm Rin + Rex( 1113857 v(t) ge 0

π3ktkeηvd4

rodv(t)

q2ηm Rin + Rex( 1113857 v(t) le 0

(20)



Pr I2Rex

π4k2eη

2v D2 minus d2

rod1113872 11138732Rex

4q2 Rin + Rex( 11138572 v

2(t) v(t) ge 0

π4k2

eη2vd4

rodRex

4q2 Rin + Rex( 11138572v

2(t) v(t)le 0

(21)




ΔPpup 4π2Jgηv

q2ηm

_Qpu cpp_Qpu (22)




piQpi kpiQpi (23)



ΔPvi

ρ2

1113970Kvi


23

(24)




P0Vn0 PtV

nt (25)






Pt P0V

n0

Vnt

P0V

n0

Ar 1113938 v(t)dt + V01113872 1113873n (27)










Ac ΔPpup + Pt + ΔPpi1113872 1113873


(32)

which is


Fp minusπP0V

n0d2

rod

4 V0 + π4d2rod 1113938 v(t)dt1113872 1113873

n +32ρLpiμ

d4pi

D2

minus d2rod1113872 1113873

2v(t)

+π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)ge 0

minusπP0V

n0d2

rod

4 V0 + π4d2rod 1113938 v(t)dt1113872 1113873

n minus32ρLpiμ

d4pi

d4rodv(t) minus

π8ρ13

middotKv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)le 0

(33)













n0d

2rod

4 V0 +(π4)d2rod 1113938 v(t)dt1113872 1113873

n +32ρLpiμ

d4pi

+π3ktkeηv

q2ηm Rin + Rex( 1113857⎛⎝ ⎞⎠ D

2minus d

2rod1113872 1113873

2v(t)

+π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)ge 0

minusπP0V

n0d

2rod

4 V0 +(π4)d2rod 1113938 v(t)dt1113872 1113873

n minus32ρLpiμ

d4pi

+π3ktkeηv

q2ηm Rin + Rex( 1113857⎛⎝ ⎞⎠d

4rodv(t) minus

π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)le 0

(40)











ηh Pr

Fv(t) (41)


10Ω30Ω

50Ω100Ω

ndash3500

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000D

ampi

ng fo

rce (

N)


(a)

10Ω30Ω

50Ω100Ω

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


(b)

10Ω30Ω

50Ω100Ω

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


(c)

10Ω30Ω

50Ω100Ω

ndash1200

ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

400

600

800D

ampi

ng fo

rce (

N)


(d)



-15ndash1

ndash050

051

152

25

Spru

ng m

ass a

ccel

erat

ion

(ms

lowast s)

1 2 3 4 5 6 7 8 9 100Time (s)



10Ω30Ω

50Ω100Ω

0

50

100

150

200

250

300

Pow

er (W

)

1 2 3 4 5 60Time (s)

(a)

023Hz035Hz

045Hz062Hz

0

20

40

60

80

100

120

Pow

er (W

)

1 2 3 4 5 60Time (s)

(b)


10Ω30Ω

50Ω100Ω

005

01

015

02

025

03

035

04

Effic

ienc

y

008 01 012 014 016 018 02006Speed (ms)

(a)


007ms011ms

014ms019ms

005

01

015

02

025

03

035

04

Effic

ienc

y

(b)











Dam

ping

forc

e (N

)

ndash7000

ndash6000

ndash5000

ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

3000














ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(a)

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(b)

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(c)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(d)




7 Conclusions





007ms011ms

014ms019ms

008

01

012

014

016

018

02

Effici

ency

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 02

008

01

012

014

016

018

02Effi

cien

cy

(b)



007ms011ms

014ms019ms

0

20

40

60

80

100

120

Pow

er (W

)

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 020

20

40

60

80

100

120

Pow

er (W

)

(b)




Data Availability






Acknowledgments


References
























Pr I2Rex

π4k2eη

2v D2 minus d2

rod1113872 11138732Rex

4q2 Rin + Rex( 11138572 v

2(t) v(t) ge 0

π4k2

eη2vd4

rodRex

4q2 Rin + Rex( 11138572v

2(t) v(t)le 0

(21)




ΔPpup 4π2Jgηv

q2ηm

_Qpu cpp_Qpu (22)




piQpi kpiQpi (23)



ΔPvi

ρ2

1113970Kvi


23

(24)




P0Vn0 PtV

nt (25)






Pt P0V

n0

Vnt

P0V

n0

Ar 1113938 v(t)dt + V01113872 1113873n (27)










Ac ΔPpup + Pt + ΔPpi1113872 1113873


(32)

which is


Fp minusπP0V

n0d2

rod

4 V0 + π4d2rod 1113938 v(t)dt1113872 1113873

n +32ρLpiμ

d4pi

D2

minus d2rod1113872 1113873

2v(t)

+π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)ge 0

minusπP0V

n0d2

rod

4 V0 + π4d2rod 1113938 v(t)dt1113872 1113873

n minus32ρLpiμ

d4pi

d4rodv(t) minus

π8ρ13

middotKv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)le 0

(33)













n0d

2rod

4 V0 +(π4)d2rod 1113938 v(t)dt1113872 1113873

n +32ρLpiμ

d4pi

+π3ktkeηv

q2ηm Rin + Rex( 1113857⎛⎝ ⎞⎠ D

2minus d

2rod1113872 1113873

2v(t)

+π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)ge 0

minusπP0V

n0d

2rod

4 V0 +(π4)d2rod 1113938 v(t)dt1113872 1113873

n minus32ρLpiμ

d4pi

+π3ktkeηv

q2ηm Rin + Rex( 1113857⎛⎝ ⎞⎠d

4rodv(t) minus

π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)le 0

(40)











ηh Pr

Fv(t) (41)


10Ω30Ω

50Ω100Ω

ndash3500

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000D

ampi

ng fo

rce (

N)


(a)

10Ω30Ω

50Ω100Ω

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


(b)

10Ω30Ω

50Ω100Ω

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


(c)

10Ω30Ω

50Ω100Ω

ndash1200

ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

400

600

800D

ampi

ng fo

rce (

N)


(d)



-15ndash1

ndash050

051

152

25

Spru

ng m

ass a

ccel

erat

ion

(ms

lowast s)

1 2 3 4 5 6 7 8 9 100Time (s)



10Ω30Ω

50Ω100Ω

0

50

100

150

200

250

300

Pow

er (W

)

1 2 3 4 5 60Time (s)

(a)

023Hz035Hz

045Hz062Hz

0

20

40

60

80

100

120

Pow

er (W

)

1 2 3 4 5 60Time (s)

(b)


10Ω30Ω

50Ω100Ω

005

01

015

02

025

03

035

04

Effic

ienc

y

008 01 012 014 016 018 02006Speed (ms)

(a)


007ms011ms

014ms019ms

005

01

015

02

025

03

035

04

Effic

ienc

y

(b)











Dam

ping

forc

e (N

)

ndash7000

ndash6000

ndash5000

ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

3000














ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(a)

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(b)

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(c)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(d)




7 Conclusions





007ms011ms

014ms019ms

008

01

012

014

016

018

02

Effici

ency

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 02

008

01

012

014

016

018

02Effi

cien

cy

(b)



007ms011ms

014ms019ms

0

20

40

60

80

100

120

Pow

er (W

)

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 020

20

40

60

80

100

120

Pow

er (W

)

(b)




Data Availability






Acknowledgments


References
























Fp minusπP0V

n0d2

rod

4 V0 + π4d2rod 1113938 v(t)dt1113872 1113873

n +32ρLpiμ

d4pi

D2

minus d2rod1113872 1113873

2v(t)

+π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)ge 0

minusπP0V

n0d2

rod

4 V0 + π4d2rod 1113938 v(t)dt1113872 1113873

n minus32ρLpiμ

d4pi

d4rodv(t) minus

π8ρ13

middotKv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)le 0

(33)













n0d

2rod

4 V0 +(π4)d2rod 1113938 v(t)dt1113872 1113873

n +32ρLpiμ

d4pi

+π3ktkeηv

q2ηm Rin + Rex( 1113857⎛⎝ ⎞⎠ D

2minus d

2rod1113872 1113873

2v(t)

+π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)ge 0

minusπP0V

n0d

2rod

4 V0 +(π4)d2rod 1113938 v(t)dt1113872 1113873

n minus32ρLpiμ

d4pi

+π3ktkeηv

q2ηm Rin + Rex( 1113857⎛⎝ ⎞⎠d

4rodv(t) minus

π8ρ13

Kv2

Cddv2Av21113888 1113889

23

D113

v(t)23

v(t)le 0

(40)











ηh Pr

Fv(t) (41)


10Ω30Ω

50Ω100Ω

ndash3500

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000D

ampi

ng fo

rce (

N)


(a)

10Ω30Ω

50Ω100Ω

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


(b)

10Ω30Ω

50Ω100Ω

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


(c)

10Ω30Ω

50Ω100Ω

ndash1200

ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

400

600

800D

ampi

ng fo

rce (

N)


(d)



-15ndash1

ndash050

051

152

25

Spru

ng m

ass a

ccel

erat

ion

(ms

lowast s)

1 2 3 4 5 6 7 8 9 100Time (s)



10Ω30Ω

50Ω100Ω

0

50

100

150

200

250

300

Pow

er (W

)

1 2 3 4 5 60Time (s)

(a)

023Hz035Hz

045Hz062Hz

0

20

40

60

80

100

120

Pow

er (W

)

1 2 3 4 5 60Time (s)

(b)


10Ω30Ω

50Ω100Ω

005

01

015

02

025

03

035

04

Effic

ienc

y

008 01 012 014 016 018 02006Speed (ms)

(a)


007ms011ms

014ms019ms

005

01

015

02

025

03

035

04

Effic

ienc

y

(b)











Dam

ping

forc

e (N

)

ndash7000

ndash6000

ndash5000

ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

3000














ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(a)

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(b)

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(c)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(d)




7 Conclusions





007ms011ms

014ms019ms

008

01

012

014

016

018

02

Effici

ency

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 02

008

01

012

014

016

018

02Effi

cien

cy

(b)



007ms011ms

014ms019ms

0

20

40

60

80

100

120

Pow

er (W

)

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 020

20

40

60

80

100

120

Pow

er (W

)

(b)




Data Availability






Acknowledgments


References




























ηh Pr

Fv(t) (41)


10Ω30Ω

50Ω100Ω

ndash3500

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000D

ampi

ng fo

rce (

N)


(a)

10Ω30Ω

50Ω100Ω

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


(b)

10Ω30Ω

50Ω100Ω

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


(c)

10Ω30Ω

50Ω100Ω

ndash1200

ndash1000

ndash800

ndash600

ndash400

ndash200

0

200

400

600

800D

ampi

ng fo

rce (

N)


(d)



-15ndash1

ndash050

051

152

25

Spru

ng m

ass a

ccel

erat

ion

(ms

lowast s)

1 2 3 4 5 6 7 8 9 100Time (s)



10Ω30Ω

50Ω100Ω

0

50

100

150

200

250

300

Pow

er (W

)

1 2 3 4 5 60Time (s)

(a)

023Hz035Hz

045Hz062Hz

0

20

40

60

80

100

120

Pow

er (W

)

1 2 3 4 5 60Time (s)

(b)


10Ω30Ω

50Ω100Ω

005

01

015

02

025

03

035

04

Effic

ienc

y

008 01 012 014 016 018 02006Speed (ms)

(a)


007ms011ms

014ms019ms

005

01

015

02

025

03

035

04

Effic

ienc

y

(b)











Dam

ping

forc

e (N

)

ndash7000

ndash6000

ndash5000

ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

3000














ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(a)

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(b)

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(c)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(d)




7 Conclusions





007ms011ms

014ms019ms

008

01

012

014

016

018

02

Effici

ency

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 02

008

01

012

014

016

018

02Effi

cien

cy

(b)



007ms011ms

014ms019ms

0

20

40

60

80

100

120

Pow

er (W

)

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 020

20

40

60

80

100

120

Pow

er (W

)

(b)




Data Availability






Acknowledgments


References
























-15ndash1

ndash050

051

152

25

Spru

ng m

ass a

ccel

erat

ion

(ms

lowast s)

1 2 3 4 5 6 7 8 9 100Time (s)



10Ω30Ω

50Ω100Ω

0

50

100

150

200

250

300

Pow

er (W

)

1 2 3 4 5 60Time (s)

(a)

023Hz035Hz

045Hz062Hz

0

20

40

60

80

100

120

Pow

er (W

)

1 2 3 4 5 60Time (s)

(b)


10Ω30Ω

50Ω100Ω

005

01

015

02

025

03

035

04

Effic

ienc

y

008 01 012 014 016 018 02006Speed (ms)

(a)


007ms011ms

014ms019ms

005

01

015

02

025

03

035

04

Effic

ienc

y

(b)











Dam

ping

forc

e (N

)

ndash7000

ndash6000

ndash5000

ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

3000














ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(a)

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(b)

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(c)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(d)




7 Conclusions





007ms011ms

014ms019ms

008

01

012

014

016

018

02

Effici

ency

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 02

008

01

012

014

016

018

02Effi

cien

cy

(b)



007ms011ms

014ms019ms

0

20

40

60

80

100

120

Pow

er (W

)

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 020

20

40

60

80

100

120

Pow

er (W

)

(b)




Data Availability






Acknowledgments


References
































Dam

ping

forc

e (N

)

ndash7000

ndash6000

ndash5000

ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

3000














ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(a)

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(b)

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(c)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(d)




7 Conclusions





007ms011ms

014ms019ms

008

01

012

014

016

018

02

Effici

ency

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 02

008

01

012

014

016

018

02Effi

cien

cy

(b)



007ms011ms

014ms019ms

0

20

40

60

80

100

120

Pow

er (W

)

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 020

20

40

60

80

100

120

Pow

er (W

)

(b)




Data Availability






Acknowledgments


References































ndash4000

ndash3000

ndash2000

ndash1000

0

1000

2000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(a)

ndash3000

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(b)

ndash2500

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(c)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

Dam

ping

forc

e (N

)


10Ω30Ω

50Ω100Ω

(d)




7 Conclusions





007ms011ms

014ms019ms

008

01

012

014

016

018

02

Effici

ency

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 02

008

01

012

014

016

018

02Effi

cien

cy

(b)



007ms011ms

014ms019ms

0

20

40

60

80

100

120

Pow

er (W

)

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 020

20

40

60

80

100

120

Pow

er (W

)

(b)




Data Availability






Acknowledgments


References

























7 Conclusions





007ms011ms

014ms019ms

008

01

012

014

016

018

02

Effici

ency

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 02

008

01

012

014

016

018

02Effi

cien

cy

(b)



007ms011ms

014ms019ms

0

20

40

60

80

100

120

Pow

er (W

)

(a)

10Ω30Ω

50Ω100Ω

Speed (ms)006 008 01 012 014 016 018 020

20

40

60

80

100

120

Pow

er (W

)

(b)




Data Availability






Acknowledgments


References

























Data Availability






Acknowledgments


References
























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Modeling and Analysis of a Hydraulic Energy-Harvesting ...downloads.hindawi.com/journals/mpe/2020/1580297.pdfthe eﬀect of these shock absorbers on vehicle dynamics. Abdelkareem et