# Parameter Optimisation of Power Regeneration on the Hydraulic Electric Regenerative Shock Absorber System

Authors: Peng Zheng; Ruichen Wang; Jingwei Gao; Xiang Zhang
Journal: Shock and Vibration
 (2019)

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## Abstract

With the increasingly prominent energy issues, regenerative shock absorber has attracted intensive attention in last two decades for the development of structure design. However, the researchers sometimes concentrate on conceptual designs without considering optimal parameter refinements. This paper proposes a regenerative shock absorber called the “hydraulic electric regenerative shock absorber (HERSA)” which includes an analytical regeneration performance parameters optimisation approach to promote the regeneration efficiency and regenerated power. The developed HERSA model is able to convert oscillatory motion into unidirectional rotary motion through the alteration of hydraulic flow while recovering power by a generator. The proposed model is also capable of obtaining the optimal parameters at certain condition, as well as providing the flexibility of different component combinations to match specific system need. The results demonstrate that the proposed model can effectively decide the optimal parameters in the system, and also the recoverable power can achieve average power of 331 W at 1 Hz-25 mm sinusoidal excitation in the system, which is approximately 65% efficiency. This study can be further used to guide prototype design in future study.


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## Body

## 1. Introduction

With the rapid development of the global economy, vehicles have been popularised by millions of households. However, the explosion of vehicles has also led to huge energy consumption and serious environmental pollution. For commercial vehicles, only 10% to 16% of the fuel energy has been utilised to provide proportion on driving. Most of the energy is wasted on road roughness and thermal exhaust. Among them, the kinetic energy loss by shock absorber/damper is the main energy dissipation [1]. In the past two decades, many researchers have done plenty studies on regenerative shock absorber to achieve the goal of energy recovery and the reduction of dissipation.According to the discovery of the enormous potential for vibration energy recovery in automotive vehicles [2–5], researchers have been more interested in the study of vehicular regenerative shock absorbers. In 1996, Okada et al. [6, 7] proposed a regenerative suspension system. It is mainly used for active dampers to reduce energy dissipation. The shock absorber uses an electric actuator that can generate power at high driving speeds. In 2003, Nakano et al. [8, 9] proposed an electromagnetic damper which is composed of a DC motor, a planetary gear, and a ball screw mechanism. The DC motor can rotate in both directions to supply power and recover energy. The results show that the damper system can recover a certain amount of energy under the low-frequency and large-amplitude excitation conditions. However, under the conditions of high-frequency excitation, the suspension system has poor damping effect and less energy can be recovered. In 2005, Bose Corporation [10] developed an electromagnetic active suspension system. The system is equipped with a linear electromagnetic motor for each wheel. It can not only achieve the reduction of vibration but also recover a small amount of energy for reuse. It has a simple structure with a low cost but may be damaged for the small magnetic pole gap. In 2007, Zhang et al. [11] combined the ball screw system and DC motor to model a kind of power regeneration system. Under the excitation of sine wave input, this system can output the maximum voltage of 17.5 V. In 2012, Li et al. [12] designed a built-in motion rectifier device for automotive suspension system. It converts the uncertain movement into the steady rotation of generator. The simulation shows that the regeneration efficiency is up to 60% and the power output is nearly 15 W when the vehicle travelled at a speed of 24 km/h. In 2013, Fang et al. [13] proposed a kind of hydraulic suspension system, which can achieve the active control by using a pump to adjust the pressure in hydraulic cylinder. In this system, the check valves are used to control the direction of oil flow to ensure the steady power output. In 2014, Fang et al. [14–16] developed a hydraulic electromagnetic shock absorber, which can regulate the fluid flow by applying a built-in hydraulic rectifier and internal accumulator in which the regeneration efficiency of the developed model is 16.6% at 10 Hz/3 mm harmonic excitation. Li et al. [17] designed and fabricated a hydraulic shock absorber prototype with a hydraulic rectifier to characterise and identify the several key mechanical and electrical parameters of an electromechanical model. According to lack of model accuracy, the parameter assumptions in the electromechanical model cannot be always identified.In general, the hydraulic electric regeneration shock absorber (HERSA) has attracted wide attention due to its stable work and compact structure [18], which is mainly integrated of hydraulic cylinder, check valves (rectifier modules), accumulators (stabilization modules), hydraulic motors (power conversion modules), and generators (power regeneration modules) [13–17, 19–22]. Some corresponding research studies have also been conducted based on the HERSA system. In 2015, Xu and Guo [19] applied the genetic algorithm in the power regenerating system to optimise the parameters of hydraulic pump. The results reveal that it can recover power of 33.4 W, the excitation of sinusoidal wave is 1.67 Hz-50 mm, and the regeneration efficiency is around 70%. In 2016, Wang et al. [20] designed a novel regenerative hydraulic shock absorber system. A model which takes into account the impacts of the dynamics of hydraulic flow, rotational motion, and power regeneration is developed. It can be found that this system achieves recoverable power of 260 W with an efficiency of around 40% under sinusoidal excitation of 1 Hz and 25 mm amplitude when the accumulator capacity is set 0.32 L with the load resistance 20 Ω. In order to obtain a better damper performance in the hydraulic regenerative system, Ahmad and Alam [21] analysed the influences of applied components used in the system such as hydraulic cylinder, hydraulic motor, and hydraulic accumulator. In 2017, Zhang et al. [22] proposed a semiactive regenerative suspension system. This model takes into account the hydraulic losses in hydraulic system such as throttle resistance of valves, frictional resistance of pipelines, and resistance of motor.In previous studies, it can be found that most research points on the HERSA mainly focus on the improvement of the modelling and experimental techniques but lack detailed research on parameter optimisation or optimal component combinations. A HERSA system is therefore proposed and studied in the following sections. This paper mainly focuses on the optimisation of power regeneration performance parameters and studies key parameters such as the hydraulic cylinder size, the check valve size, the accumulator capacity, the motor displacement, and the electrical load. Based on the principle of orthogonal test, the aim of the proposed HERSA is to find the optimal system parameters through modelling analysis to provide a reliable basis for the prototype design on variable applications, which can be universally used for general HERSA system.As shown in Figure1, this paper firstly introduces the vibration recovery potential and the modelling investigation of regeneration system. Secondly, the conceptual design of HERSA system is introduced, and then the model is created for optimising the parameters of key elements. Finally, the results of optimal component combinations are pointed out and then the dynamic behaviours of the HERSA are discussed and validated. Based on the orthogonal test method, a power regeneration optimisation method for general HERSA system is also proposed in this paper.Figure 1
The study procedures of the HERSA.


## 2. System Modelling of HERSA

### 2.1. Design Concept

To understand the mechanism of a regenerative shock absorber system, a mathematical model is designed on the basis of a typical configuration of the shock absorber.As shown in Figure2, a schematic design of the HERSA is proposed which consists of a hydraulic cylinder, four check valves, a hydraulic accumulator, a hydraulic motor, a permanent magnetic generator, pipelines, battery, and an oil tank. The key component of the system is the hydraulic cylinder that represents a conventional shock absorber or damper.Figure 2
Diagram view of the design concept for HERSA.When the piston of hydraulic cylinder moves up and down due to the excitation, the shock oil in cylinder can be forced to flow through one-way valve and hydraulic accumulator and drive the hydraulic motor. By the regulating effect of check valves, the fluid flow will pass through the motor in one direction. Meanwhile, the accumulator’s smoothing effect delivers a stable fluid flow to provide hydraulic motor a more reliable and stable working condition. Driven by the pressurised flow, the hydraulic motor converts linear motion into rotary motion as a motion converter, which will also drive the DC generator for the purpose of power regeneration. Finally, the power regenerated will be stored in battery or charged vehicle-mounted equipment.


### 2.2. Hydraulic Flows

The road excitation is normally consisted by numerous sinusoidal waves [23]. In order to simplify the model, the excitation is considered as the sinusoidal wave, which is defined as the fundamental element of road irregularity. Therefore, the movement of piston is expressed by(1)Xat=Xsin2πft,where f is the excitation frequency and X is the maximum amplitude. When the shaft moves up and down, the volume change of cap-end chamber VA and rod-end chamber VB can be calculated by(2)VA=AAX0∓Xa+Vcyd,VB=ABX0±Xa+Vcyd,up and down,Vcyd is dead volume which refers to the fluid volume in the cylinder chambers at zero position. It is considered as the necessary part of volume change. In addition, AA and AB are the areas of cap-end and rod-end on both sides of piston. X0 refers to the starting level of the piston.The processes of fluid flows in designed hydraulic system are shown in Figure3. According to Bernoulli’s principle,(3)P+ρvf22+ρgh=constant,where P is the pressure, ρ is the fluid density, vf is the flow speed, and h is the elevation of the point above a reference plane. The flow in cylinder and check valves can be expressed by(a)
Outflow of cylinder:(4)QAout=CCAC2PA−PMρ,PA>PM,QBout=CCAC2PB−PMρ,PB>PM.(b)
Inflow of cylinder:(5)QAin=CCAC2PM−PAρ,PM>PA,QBin=CCAC2PM−PBρ,PM>PB,CC and AC are the flow coefficient and the area of inline check valve port. PA, PB, and PM represent the pressures at the cap-end chamber, the rod-end chamber, and the motor inlet, respectively.Figure 3
Schematic view of fluid flows in hydraulic system.According to the influence of fluid compressibility in hydraulic elements, the pressure out of the cylinder during the piston motion can be simultaneously expressed:(a)
Up stroke:(6)P˙A=βAAAvt−QAout+QAinVA,(b)
Down stroke:(7)P˙B=βBAB−vt−QBout+QBinVB,βA and βB are the effective bulk modulus in cap-end chamber and rod-end chamber.In general, there are many empirical formulas for the effective bulk modulus. Given the relatively low pressure in the HERSA system (under 100 bar), Boes’s model [24] is applied to determine the bulk modulus of the fluid in the cylinder and motor:(8)β=βref⋅log99P/Pref+12.According to the variations of the cylinder chambers (cap-end and rod-end chambers), the fluid flow rate and pressure in those two chambers can also oscillated significantly. An accumulator is therefore used at the inlet of motor, and the flow volumeVacf in accumulator can be written as(9)Vacf=Vac1−PacPf1/k,Pf>Pac,where Vac is the volume of accumulator, Pac is precharged pressure to accumulator, Pf is the fluid pressure of the accumulator, and k is the gas specific heat ratio of gas-charged accumulator, and the fluid flow of accumulator can be written as(10)Qac=CacAacsgnPM−Pf2PM−Pfρ,where Cac is the accumulator flow coefficient and Aac is the area of the accumulator inlet port. The volume variation of accumulator fluid Vp is(11)Vp=−kPfQacP˙f.Considering the smoothing effect of hydraulic accumulator, a more accurate model of hydraulic motor can be determined including the variations of accumulator fluid flow and volume. Therefore, the pressure and fluid flow of hydraulic motor can be represented:(12)P˙M=βMQAout+QBout−Qac−QMVT,QM=DMωM2π,where βM is the effective bulk modulus of the motor chamber, DM is the displacement of the hydraulic motor, and ωM is the shaft speed of the hydraulic motor and generator, respectively.


### 2.3. Power Regeneration

Driven by the fluid flow, the hydraulic motor can produce rotary motion which is able to drive the DC generator to produce electricity. The working process of power regeneration is shown in Figure4.Figure 4
Schematic view of energy conversion (mechanical to electrical) and power circuit.Where the mechanical efficiency of motor isηM, the driving torque of motor TM is(13)TM=DMPMηM2π.According to Newton’s second law of motion, the rotary motionωm is(14)ω˙M=TM−TGJt,where Jt is the shaft moment of inertia. In addition, the electromagnetic torque of generator TG would change with the variation in the induced current, and it is considered as the resistance torque because it provides the rotation to the motor in an opposite direction. Therefore, it can be written as(15)TG=KTI.The electromotive force (EMF) can be expressed as(16)E=KEωM,where KT is torque constant coefficient and KE is the electromotive voltage constant coefficient.According to Kirchhoff’s voltage law [25], assuming that the susceptibility at any temperature and the flux that is established by the PM poles are constant, the variation in current can be calculated by(17)I˙=E−Rin+RBILG,where LG is the internal inductance, RB is the external electrical load of battery, and Rin is the internal resistance of generator. Then, the instantaneous voltage can be expressed as(18)U=IRB.Therefore, the output of regenerated power is(19)Pout=I2RB=U2RB.In addition, the effective input power of this system is considered as the sum of the piston damping force multiplied by the effective piston area. Given the areas of cap-end and rod-end are known, the piston damping force can be written as(20)FA=PAAA,FB=PBAB.Therefore, the input power of the HERSA system is(21)Pin=PAAAvt+PBABvt,up+down.Hence, the power regeneration efficiency can be calculated from the following equation:(22)ηreg=PoutPin.


## 2.1. Design Concept

To understand the mechanism of a regenerative shock absorber system, a mathematical model is designed on the basis of a typical configuration of the shock absorber.As shown in Figure2, a schematic design of the HERSA is proposed which consists of a hydraulic cylinder, four check valves, a hydraulic accumulator, a hydraulic motor, a permanent magnetic generator, pipelines, battery, and an oil tank. The key component of the system is the hydraulic cylinder that represents a conventional shock absorber or damper.Figure 2
Diagram view of the design concept for HERSA.When the piston of hydraulic cylinder moves up and down due to the excitation, the shock oil in cylinder can be forced to flow through one-way valve and hydraulic accumulator and drive the hydraulic motor. By the regulating effect of check valves, the fluid flow will pass through the motor in one direction. Meanwhile, the accumulator’s smoothing effect delivers a stable fluid flow to provide hydraulic motor a more reliable and stable working condition. Driven by the pressurised flow, the hydraulic motor converts linear motion into rotary motion as a motion converter, which will also drive the DC generator for the purpose of power regeneration. Finally, the power regenerated will be stored in battery or charged vehicle-mounted equipment.


## 2.2. Hydraulic Flows

The road excitation is normally consisted by numerous sinusoidal waves [23]. In order to simplify the model, the excitation is considered as the sinusoidal wave, which is defined as the fundamental element of road irregularity. Therefore, the movement of piston is expressed by(1)Xat=Xsin2πft,where f is the excitation frequency and X is the maximum amplitude. When the shaft moves up and down, the volume change of cap-end chamber VA and rod-end chamber VB can be calculated by(2)VA=AAX0∓Xa+Vcyd,VB=ABX0±Xa+Vcyd,up and down,Vcyd is dead volume which refers to the fluid volume in the cylinder chambers at zero position. It is considered as the necessary part of volume change. In addition, AA and AB are the areas of cap-end and rod-end on both sides of piston. X0 refers to the starting level of the piston.The processes of fluid flows in designed hydraulic system are shown in Figure3. According to Bernoulli’s principle,(3)P+ρvf22+ρgh=constant,where P is the pressure, ρ is the fluid density, vf is the flow speed, and h is the elevation of the point above a reference plane. The flow in cylinder and check valves can be expressed by(a)
Outflow of cylinder:(4)QAout=CCAC2PA−PMρ,PA>PM,QBout=CCAC2PB−PMρ,PB>PM.(b)
Inflow of cylinder:(5)QAin=CCAC2PM−PAρ,PM>PA,QBin=CCAC2PM−PBρ,PM>PB,CC and AC are the flow coefficient and the area of inline check valve port. PA, PB, and PM represent the pressures at the cap-end chamber, the rod-end chamber, and the motor inlet, respectively.Figure 3
Schematic view of fluid flows in hydraulic system.According to the influence of fluid compressibility in hydraulic elements, the pressure out of the cylinder during the piston motion can be simultaneously expressed:(a)
Up stroke:(6)P˙A=βAAAvt−QAout+QAinVA,(b)
Down stroke:(7)P˙B=βBAB−vt−QBout+QBinVB,βA and βB are the effective bulk modulus in cap-end chamber and rod-end chamber.In general, there are many empirical formulas for the effective bulk modulus. Given the relatively low pressure in the HERSA system (under 100 bar), Boes’s model [24] is applied to determine the bulk modulus of the fluid in the cylinder and motor:(8)β=βref⋅log99P/Pref+12.According to the variations of the cylinder chambers (cap-end and rod-end chambers), the fluid flow rate and pressure in those two chambers can also oscillated significantly. An accumulator is therefore used at the inlet of motor, and the flow volumeVacf in accumulator can be written as(9)Vacf=Vac1−PacPf1/k,Pf>Pac,where Vac is the volume of accumulator, Pac is precharged pressure to accumulator, Pf is the fluid pressure of the accumulator, and k is the gas specific heat ratio of gas-charged accumulator, and the fluid flow of accumulator can be written as(10)Qac=CacAacsgnPM−Pf2PM−Pfρ,where Cac is the accumulator flow coefficient and Aac is the area of the accumulator inlet port. The volume variation of accumulator fluid Vp is(11)Vp=−kPfQacP˙f.Considering the smoothing effect of hydraulic accumulator, a more accurate model of hydraulic motor can be determined including the variations of accumulator fluid flow and volume. Therefore, the pressure and fluid flow of hydraulic motor can be represented:(12)P˙M=βMQAout+QBout−Qac−QMVT,QM=DMωM2π,where βM is the effective bulk modulus of the motor chamber, DM is the displacement of the hydraulic motor, and ωM is the shaft speed of the hydraulic motor and generator, respectively.


## 2.3. Power Regeneration

Driven by the fluid flow, the hydraulic motor can produce rotary motion which is able to drive the DC generator to produce electricity. The working process of power regeneration is shown in Figure4.Figure 4
Schematic view of energy conversion (mechanical to electrical) and power circuit.Where the mechanical efficiency of motor isηM, the driving torque of motor TM is(13)TM=DMPMηM2π.According to Newton’s second law of motion, the rotary motionωm is(14)ω˙M=TM−TGJt,where Jt is the shaft moment of inertia. In addition, the electromagnetic torque of generator TG would change with the variation in the induced current, and it is considered as the resistance torque because it provides the rotation to the motor in an opposite direction. Therefore, it can be written as(15)TG=KTI.The electromotive force (EMF) can be expressed as(16)E=KEωM,where KT is torque constant coefficient and KE is the electromotive voltage constant coefficient.According to Kirchhoff’s voltage law [25], assuming that the susceptibility at any temperature and the flux that is established by the PM poles are constant, the variation in current can be calculated by(17)I˙=E−Rin+RBILG,where LG is the internal inductance, RB is the external electrical load of battery, and Rin is the internal resistance of generator. Then, the instantaneous voltage can be expressed as(18)U=IRB.Therefore, the output of regenerated power is(19)Pout=I2RB=U2RB.In addition, the effective input power of this system is considered as the sum of the piston damping force multiplied by the effective piston area. Given the areas of cap-end and rod-end are known, the piston damping force can be written as(20)FA=PAAA,FB=PBAB.Therefore, the input power of the HERSA system is(21)Pin=PAAAvt+PBABvt,up+down.Hence, the power regeneration efficiency can be calculated from the following equation:(22)ηreg=PoutPin.


## 3. Simulation of HERSA

This study focuses on the effect of the key parameters which include the sizes of shock absorber body, the size of check valve port, hydraulic motor displacement, and hydraulic accumulator capacity. Hence, the investigation is performed on the proposed parameter optimisation method to study the HERSA’s behaviour and power level, as well as the desirable parameter solutions.


### 3.1. Parameters Setting and Study

In the modelling, a few assumptions made during this process were as follows:(a)
There are no additional electrical losses in generator configuration to be considered. It means the output power of hydraulic motor is equal to the input power of generator.(b)
The cylinder internal leakage between the chambers is not accounted for by the model.(c)
The external electrical load (battery/resistor) has no influence by the varying temperature.(d)
Fluid compressibility is defined as using Boes’s model in hydraulic system.In practical applications, there are various types of losses in HERSA system, such as hydraulic motor internal flow leakage, pressure loss in the pipeline, check valve pressure loss, and hydraulic cylinder piston friction.To simplify the model, the impact of these losses and influences in the system are not taken into account at this stage. Therefore, the model is ideally configured and the following main parameters are selected.


#### 3.1.1. Size of the Hydraulic Cylinder

In this system, the hydraulic cylinder is applied to replace the traditional shock absorber and absorb vibration energy. This paper takes 4x4 SUV “Beijing Jeep 2021” as the example and determines that the maximum stroke of cylinder is 200 mm. The sizes of the shock absorber body are determined according to the standard, ISO 3320-2013 [26]; it is well known that a conventional viscous shock absorber has asymmetrical damping characteristic due to its inherent design structure which can provide different damping forces during the compression and extension strokes. The piston diameter and rod diameter are therefore determined as Table 1.Table 1
Hydraulic cylinder specification.
FactorA
Level 1
Level 2
Level 3
Level 4
Piston diameter (mm)
50
40
32
25
Rod diameter (mm)
28
25
20
16


#### 3.1.2. Size of the Check Valve Port

The fluid pressurised by the oscillation flows through check valve arrangement to ensure fluid always flows through hydraulic motor in one direction and enable the chambers in the cylinder can be replenished as fast as possible for each run. In terms of the standard port size on double-acting cylinder, the common sizes of check valves are shown in Table2.Table 2
Check valves specification.
FactorB
Level 1
Level 2
Level 3
Level 4
Check valve diameter (mm)
6.35
9.525
12.7
19.05


#### 3.1.3. Hydraulic Accumulator Capacity

A common hydraulic accumulator is used to minimise the fluctuation of the pressurised flow. Initially, the gas chamber is precharged to pressure Pac and set to 20 bar.In equations (9)–(11), several assumptions have been made to simplify the hydraulic accumulator model:(a)
The accumulator is set as a diaphragm type accumulator without heat exchange during the process.(b)
There is a transient pressure balance inside the accumulator between fluid chamber and gas chamber.(c)
Frictions and thermal losses are neglected here.(d)
Only fully charged and fully discharged states are considered in the hydraulic model.(e)
The precharge pressure in the accumulator is set at 60% of the working pressure (20 bar) to provide pressure pulsation damping.According to the damping forces in a traditional shock absorber in a SUV, the accumulator capacity has been estimated with a peak of 100 bar, which is shown in Table3.Table 3
Hydraulic accumulator specification.
FactorC
Level 1
Level 2
Accumulator capacity (L)
0.63
1


#### 3.1.4. Hydraulic Motor Displacement

The hydraulic motor is defined as a transfer device which is able to convert the unidirectional hydraulic flow/pressure into rotational motion/torque. Its main parameters are shown in Table4.Table 4
Hydraulic motor displacement.
FactorD
Level 1
Level 2
Level 3
Level 4
Motor displacement (cc)
5.77
7.07
8.01
8.94


#### 3.1.5. External Electrical Load

For the regenerative shock absorber, the electrical load has significant effects on the capability of power regeneration and the dynamics of the system [1], and it can be considered as Table 5.Table 5
Battery/Resistor resistance.
FactorE
Level 1
Level 2
Level 3
Level 4
Electrical load (Ω)
10
20
30
40


#### 3.1.6. Other Key Parameters

As shown in Table6, the values of several other parameters are displayed.Table 6
Other key specifications of the HERSA.
Symbol
Value
Unit
f
1
Hz
X
a
25
mm
ρ
872
kg/m3
C
C
0.7
—
X
0
200
mm
l
1
m
β
ref
1.2 × 109
—
P
ref
20
bar
k
1.4
—
η
m
100
%
J
t
0.003
kg·m2
K
T
0.65
—
K
E
0.65
—
R
in
7.5
Ω
L
G
0.03
H
V
agd
0.1%V
L
D
ac
Dcv
mm
C
ac
0.7
—


### 3.2. Orthogonal Simulation Test Design

The orthogonal test design is an important approach of statistical evaluation, which can reduce the number of attempts and then effectively obtain desired results [27]. Large-scale engineering testing is a complex system engineering. There are many factors influencing the test results: some factors play an independent role, and some factors can interact with others to produce the comprehensive effect. The reason that affects the results during the test is called the test factor, and the state adopted under each factor is called the level. Starting from Section 3.1, five-factor and four-level conditions have been applied in this test, as shown in Table 7. The simplest method is to apply an exhaustive method to test all factors and levels at the same time.Table 7
Simulation test combinations.
Level
Factor
A (mm)
B (mm)
C (L)
D (cc)
E (Ω)
Level 1
50/28
6.35
0.63
5.77
10
Level 2
40/25
9.525
1
7.07
20
Level 3
32/20
12.7
—
8.01
30
Level 4
25/16
19.05
—
8.94
40As shown in Table7, the designed test has four 4-level factor and one 2-level factor. If all factors and their levels achieve their best performance for integration testing, then the total of 512 tests need to be performed. Obviously, a large number of tests definitely demand a lot of manpower and material resources as well as take a long time to reach the target. Therefore, this paper focuses on the problem that how to reasonably arrange the test and obtain the necessary indication through less number of tests. The orthogonal method is an effective mathematical method to solve the problem of multifactor test. It also applies the orthogonal table design scheme and the mathematical statistics method to analyse the test data. However, the L16 (44 × 2) orthogonal table (Table 8) is designed for the simulation test of HERSA [28], and only 16 tests need to be carried out. It is obvious that the proposed parameter optimisation method can effectively improve the efficiency of simulation and fastly obtain the required simulation results.Table 8
Orthogonal simulation test design listL16 (44 × 2).
No.
Factor
A (mm)
B (mm)
C (L)
D (cc)
E (Ω)
Test 1
50/28
6.35
0.63
5.77
10
Test 2
50/28
9.525
0.63
7.07
20
Test 3
50/28
12.7
1
8.01
30
Test 4
50/28
19.05
1
8.94
40
Test 5
40/25
6.35
1
7.07
30
Test 6
40/25
9.525
1
5.77
40
Test 7
40/25
12.7
0.63
8.94
10
Test 8
40/25
19.05
0.63
8.01
20
Test 9
32/20
6.35
0.63
8.01
40
Test 10
32/20
9.525
0.63
8.94
30
Test 11
32/20
12.7
1
5.77
20
Test 12
32/20
19.05
1
7.07
10
Test 13
25/16
6.35
1
8.94
20
Test 14
25/16
9.525
1
8.01
10
Test 15
25/16
12.7
0.63
7.07
40
Test 16
25/16
19.05
0.63
5.77
30According to the above test design table, numerical simulation is carried out in mathematical model. A sinusoidal excitation 1 Hz-25 mm is set as predefined input. All other parameters are kept the same as in Table6.


### 3.3. Simulation Results and Discussion

To use the model with orthogonal test approach developed in Sections3.1 and 3.2 for subsequent studies on the improvement of parameter optimisation, this section firstly presents studies on the investigation of key model parameters based on modelling analysis. Then, it shows the quantitative behaviours (pressure, shaft speed, regenerated power, and regeneration efficiency) of the system under designed test table, gaining a preliminary understanding of the system behaviours. However, the key results are summarised in Table 9. According to the principle of orthogonal test, the averages of outputs are calculated in the mean response analysis.Table 9
Summary of simulation tests.
Test no.
Shaft speed (rpm)
Hydraulic motor pressure (bar)
Input power (W)
Regenerated power (W)
Regeneration efficiency
Test 1
1651.3928
46.4087
781.801
417.5
0.53402
Test 2
1340.0569
19.8006
342.7223
223.9
0.65334
Test 3
1175.6696
11.384
204.1776
139.8
0.68482
Test 4
1055.314
7.317
137.1768
94.2
0.68667
Test 5
810.6328
8.8879
101.5277
66.43
0.65427
Test 6
988.5237
10.621
117.1773
82.61
0.70496
Test 7
665.2814
11.886
129.5599
66.65
0.50674
Test 8
727.5167
9.4879
65.9557
65.96
0.62528
Test 9
461.2982
3.5676
30.0727
17.98
0.59788
Test 10
410.7713
3.5638
29.6083
17.06
0.57626
Test 11
648.1021
11.7337
81.8903
52.31
0.63877
Test 12
531.5388
12.1918
84.7933
43.18
0.50923
Test 13
251.6925
2.9404
15.4995
7.888
0.5089
Test 14
284.2986
5.7556
26.3095
12.35
0.46945
Test 15
312.0371
2.7366
14.5937
8.228
0.56378
Test 16
388.8416
5.2267
24.2388
15.28
0.63042As shown in Figure5, the variation of the motor shaft speed, pressure, mechanical power, and regenerated power is dramatically levelled up at larger cylinder size with lower motor displacement, accumulator capacity, the size of check valve, and external load resistance. The averages of those results are shown in Table 9. It is also clear that the change of component combination can significantly affect the system dynamics and regenerated power level to meet the demands of various vehicle suspension systems. By changing the component combinations, the maximum regenerated power of 417.5 W with the regeneration efficiency of approximately 53.4% can be achieved on test 1. It is also obvious that the highest regeneration efficiency occurs at test 16 (approximately 63%) which is designed with small size of cylinder, motor displacement, accumulator capacity, and large check valve port. Additionally, the results of those 16 tests reveal that the change of motor displacement, external loads, and accumulator capacity is capable of smoothing the flow oscillations and allow effective minimisation to the instability of hydraulic circuit, thus altering the performance of the system and power capability.Figure 5
Hydraulic motor shaft speed, pressure, mechanical power, and regenerated power at different 16 tests.
(a)
(b)
(c)
(d)It can be summarised that the change of component combinations can not only affect the stability of system dynamics but also dramatically impact on the level of regenerated power.


## 3.1. Parameters Setting and Study

In the modelling, a few assumptions made during this process were as follows:(a)
There are no additional electrical losses in generator configuration to be considered. It means the output power of hydraulic motor is equal to the input power of generator.(b)
The cylinder internal leakage between the chambers is not accounted for by the model.(c)
The external electrical load (battery/resistor) has no influence by the varying temperature.(d)
Fluid compressibility is defined as using Boes’s model in hydraulic system.In practical applications, there are various types of losses in HERSA system, such as hydraulic motor internal flow leakage, pressure loss in the pipeline, check valve pressure loss, and hydraulic cylinder piston friction.To simplify the model, the impact of these losses and influences in the system are not taken into account at this stage. Therefore, the model is ideally configured and the following main parameters are selected.


### 3.1.1. Size of the Hydraulic Cylinder

In this system, the hydraulic cylinder is applied to replace the traditional shock absorber and absorb vibration energy. This paper takes 4x4 SUV “Beijing Jeep 2021” as the example and determines that the maximum stroke of cylinder is 200 mm. The sizes of the shock absorber body are determined according to the standard, ISO 3320-2013 [26]; it is well known that a conventional viscous shock absorber has asymmetrical damping characteristic due to its inherent design structure which can provide different damping forces during the compression and extension strokes. The piston diameter and rod diameter are therefore determined as Table 1.Table 1
Hydraulic cylinder specification.
FactorA
Level 1
Level 2
Level 3
Level 4
Piston diameter (mm)
50
40
32
25
Rod diameter (mm)
28
25
20
16


### 3.1.2. Size of the Check Valve Port

The fluid pressurised by the oscillation flows through check valve arrangement to ensure fluid always flows through hydraulic motor in one direction and enable the chambers in the cylinder can be replenished as fast as possible for each run. In terms of the standard port size on double-acting cylinder, the common sizes of check valves are shown in Table2.Table 2
Check valves specification.
FactorB
Level 1
Level 2
Level 3
Level 4
Check valve diameter (mm)
6.35
9.525
12.7
19.05


### 3.1.3. Hydraulic Accumulator Capacity

A common hydraulic accumulator is used to minimise the fluctuation of the pressurised flow. Initially, the gas chamber is precharged to pressure Pac and set to 20 bar.In equations (9)–(11), several assumptions have been made to simplify the hydraulic accumulator model:(a)
The accumulator is set as a diaphragm type accumulator without heat exchange during the process.(b)
There is a transient pressure balance inside the accumulator between fluid chamber and gas chamber.(c)
Frictions and thermal losses are neglected here.(d)
Only fully charged and fully discharged states are considered in the hydraulic model.(e)
The precharge pressure in the accumulator is set at 60% of the working pressure (20 bar) to provide pressure pulsation damping.According to the damping forces in a traditional shock absorber in a SUV, the accumulator capacity has been estimated with a peak of 100 bar, which is shown in Table3.Table 3
Hydraulic accumulator specification.
FactorC
Level 1
Level 2
Accumulator capacity (L)
0.63
1


### 3.1.4. Hydraulic Motor Displacement

The hydraulic motor is defined as a transfer device which is able to convert the unidirectional hydraulic flow/pressure into rotational motion/torque. Its main parameters are shown in Table4.Table 4
Hydraulic motor displacement.
FactorD
Level 1
Level 2
Level 3
Level 4
Motor displacement (cc)
5.77
7.07
8.01
8.94


### 3.1.5. External Electrical Load

For the regenerative shock absorber, the electrical load has significant effects on the capability of power regeneration and the dynamics of the system [1], and it can be considered as Table 5.Table 5
Battery/Resistor resistance.
FactorE
Level 1
Level 2
Level 3
Level 4
Electrical load (Ω)
10
20
30
40


### 3.1.6. Other Key Parameters

As shown in Table6, the values of several other parameters are displayed.Table 6
Other key specifications of the HERSA.
Symbol
Value
Unit
f
1
Hz
X
a
25
mm
ρ
872
kg/m3
C
C
0.7
—
X
0
200
mm
l
1
m
β
ref
1.2 × 109
—
P
ref
20
bar
k
1.4
—
η
m
100
%
J
t
0.003
kg·m2
K
T
0.65
—
K
E
0.65
—
R
in
7.5
Ω
L
G
0.03
H
V
agd
0.1%V
L
D
ac
Dcv
mm
C
ac
0.7
—


## 3.1.1. Size of the Hydraulic Cylinder

In this system, the hydraulic cylinder is applied to replace the traditional shock absorber and absorb vibration energy. This paper takes 4x4 SUV “Beijing Jeep 2021” as the example and determines that the maximum stroke of cylinder is 200 mm. The sizes of the shock absorber body are determined according to the standard, ISO 3320-2013 [26]; it is well known that a conventional viscous shock absorber has asymmetrical damping characteristic due to its inherent design structure which can provide different damping forces during the compression and extension strokes. The piston diameter and rod diameter are therefore determined as Table 1.Table 1
Hydraulic cylinder specification.
FactorA
Level 1
Level 2
Level 3
Level 4
Piston diameter (mm)
50
40
32
25
Rod diameter (mm)
28
25
20
16


## 3.1.2. Size of the Check Valve Port

The fluid pressurised by the oscillation flows through check valve arrangement to ensure fluid always flows through hydraulic motor in one direction and enable the chambers in the cylinder can be replenished as fast as possible for each run. In terms of the standard port size on double-acting cylinder, the common sizes of check valves are shown in Table2.Table 2
Check valves specification.
FactorB
Level 1
Level 2
Level 3
Level 4
Check valve diameter (mm)
6.35
9.525
12.7
19.05


## 3.1.3. Hydraulic Accumulator Capacity

A common hydraulic accumulator is used to minimise the fluctuation of the pressurised flow. Initially, the gas chamber is precharged to pressure Pac and set to 20 bar.In equations (9)–(11), several assumptions have been made to simplify the hydraulic accumulator model:(a)
The accumulator is set as a diaphragm type accumulator without heat exchange during the process.(b)
There is a transient pressure balance inside the accumulator between fluid chamber and gas chamber.(c)
Frictions and thermal losses are neglected here.(d)
Only fully charged and fully discharged states are considered in the hydraulic model.(e)
The precharge pressure in the accumulator is set at 60% of the working pressure (20 bar) to provide pressure pulsation damping.According to the damping forces in a traditional shock absorber in a SUV, the accumulator capacity has been estimated with a peak of 100 bar, which is shown in Table3.Table 3
Hydraulic accumulator specification.
FactorC
Level 1
Level 2
Accumulator capacity (L)
0.63
1


## 3.1.4. Hydraulic Motor Displacement

The hydraulic motor is defined as a transfer device which is able to convert the unidirectional hydraulic flow/pressure into rotational motion/torque. Its main parameters are shown in Table4.Table 4
Hydraulic motor displacement.
FactorD
Level 1
Level 2
Level 3
Level 4
Motor displacement (cc)
5.77
7.07
8.01
8.94


## 3.1.5. External Electrical Load

For the regenerative shock absorber, the electrical load has significant effects on the capability of power regeneration and the dynamics of the system [1], and it can be considered as Table 5.Table 5
Battery/Resistor resistance.
FactorE
Level 1
Level 2
Level 3
Level 4
Electrical load (Ω)
10
20
30
40


## 3.1.6. Other Key Parameters

As shown in Table6, the values of several other parameters are displayed.Table 6
Other key specifications of the HERSA.
Symbol
Value
Unit
f
1
Hz
X
a
25
mm
ρ
872
kg/m3
C
C
0.7
—
X
0
200
mm
l
1
m
β
ref
1.2 × 109
—
P
ref
20
bar
k
1.4
—
η
m
100
%
J
t
0.003
kg·m2
K
T
0.65
—
K
E
0.65
—
R
in
7.5
Ω
L
G
0.03
H
V
agd
0.1%V
L
D
ac
Dcv
mm
C
ac
0.7
—


## 3.2. Orthogonal Simulation Test Design

The orthogonal test design is an important approach of statistical evaluation, which can reduce the number of attempts and then effectively obtain desired results [27]. Large-scale engineering testing is a complex system engineering. There are many factors influencing the test results: some factors play an independent role, and some factors can interact with others to produce the comprehensive effect. The reason that affects the results during the test is called the test factor, and the state adopted under each factor is called the level. Starting from Section 3.1, five-factor and four-level conditions have been applied in this test, as shown in Table 7. The simplest method is to apply an exhaustive method to test all factors and levels at the same time.Table 7
Simulation test combinations.
Level
Factor
A (mm)
B (mm)
C (L)
D (cc)
E (Ω)
Level 1
50/28
6.35
0.63
5.77
10
Level 2
40/25
9.525
1
7.07
20
Level 3
32/20
12.7
—
8.01
30
Level 4
25/16
19.05
—
8.94
40As shown in Table7, the designed test has four 4-level factor and one 2-level factor. If all factors and their levels achieve their best performance for integration testing, then the total of 512 tests need to be performed. Obviously, a large number of tests definitely demand a lot of manpower and material resources as well as take a long time to reach the target. Therefore, this paper focuses on the problem that how to reasonably arrange the test and obtain the necessary indication through less number of tests. The orthogonal method is an effective mathematical method to solve the problem of multifactor test. It also applies the orthogonal table design scheme and the mathematical statistics method to analyse the test data. However, the L16 (44 × 2) orthogonal table (Table 8) is designed for the simulation test of HERSA [28], and only 16 tests need to be carried out. It is obvious that the proposed parameter optimisation method can effectively improve the efficiency of simulation and fastly obtain the required simulation results.Table 8
Orthogonal simulation test design listL16 (44 × 2).
No.
Factor
A (mm)
B (mm)
C (L)
D (cc)
E (Ω)
Test 1
50/28
6.35
0.63
5.77
10
Test 2
50/28
9.525
0.63
7.07
20
Test 3
50/28
12.7
1
8.01
30
Test 4
50/28
19.05
1
8.94
40
Test 5
40/25
6.35
1
7.07
30
Test 6
40/25
9.525
1
5.77
40
Test 7
40/25
12.7
0.63
8.94
10
Test 8
40/25
19.05
0.63
8.01
20
Test 9
32/20
6.35
0.63
8.01
40
Test 10
32/20
9.525
0.63
8.94
30
Test 11
32/20
12.7
1
5.77
20
Test 12
32/20
19.05
1
7.07
10
Test 13
25/16
6.35
1
8.94
20
Test 14
25/16
9.525
1
8.01
10
Test 15
25/16
12.7
0.63
7.07
40
Test 16
25/16
19.05
0.63
5.77
30According to the above test design table, numerical simulation is carried out in mathematical model. A sinusoidal excitation 1 Hz-25 mm is set as predefined input. All other parameters are kept the same as in Table6.


## 3.3. Simulation Results and Discussion

To use the model with orthogonal test approach developed in Sections3.1 and 3.2 for subsequent studies on the improvement of parameter optimisation, this section firstly presents studies on the investigation of key model parameters based on modelling analysis. Then, it shows the quantitative behaviours (pressure, shaft speed, regenerated power, and regeneration efficiency) of the system under designed test table, gaining a preliminary understanding of the system behaviours. However, the key results are summarised in Table 9. According to the principle of orthogonal test, the averages of outputs are calculated in the mean response analysis.Table 9
Summary of simulation tests.
Test no.
Shaft speed (rpm)
Hydraulic motor pressure (bar)
Input power (W)
Regenerated power (W)
Regeneration efficiency
Test 1
1651.3928
46.4087
781.801
417.5
0.53402
Test 2
1340.0569
19.8006
342.7223
223.9
0.65334
Test 3
1175.6696
11.384
204.1776
139.8
0.68482
Test 4
1055.314
7.317
137.1768
94.2
0.68667
Test 5
810.6328
8.8879
101.5277
66.43
0.65427
Test 6
988.5237
10.621
117.1773
82.61
0.70496
Test 7
665.2814
11.886
129.5599
66.65
0.50674
Test 8
727.5167
9.4879
65.9557
65.96
0.62528
Test 9
461.2982
3.5676
30.0727
17.98
0.59788
Test 10
410.7713
3.5638
29.6083
17.06
0.57626
Test 11
648.1021
11.7337
81.8903
52.31
0.63877
Test 12
531.5388
12.1918
84.7933
43.18
0.50923
Test 13
251.6925
2.9404
15.4995
7.888
0.5089
Test 14
284.2986
5.7556
26.3095
12.35
0.46945
Test 15
312.0371
2.7366
14.5937
8.228
0.56378
Test 16
388.8416
5.2267
24.2388
15.28
0.63042As shown in Figure5, the variation of the motor shaft speed, pressure, mechanical power, and regenerated power is dramatically levelled up at larger cylinder size with lower motor displacement, accumulator capacity, the size of check valve, and external load resistance. The averages of those results are shown in Table 9. It is also clear that the change of component combination can significantly affect the system dynamics and regenerated power level to meet the demands of various vehicle suspension systems. By changing the component combinations, the maximum regenerated power of 417.5 W with the regeneration efficiency of approximately 53.4% can be achieved on test 1. It is also obvious that the highest regeneration efficiency occurs at test 16 (approximately 63%) which is designed with small size of cylinder, motor displacement, accumulator capacity, and large check valve port. Additionally, the results of those 16 tests reveal that the change of motor displacement, external loads, and accumulator capacity is capable of smoothing the flow oscillations and allow effective minimisation to the instability of hydraulic circuit, thus altering the performance of the system and power capability.Figure 5
Hydraulic motor shaft speed, pressure, mechanical power, and regenerated power at different 16 tests.
(a)
(b)
(c)
(d)It can be summarised that the change of component combinations can not only affect the stability of system dynamics but also dramatically impact on the level of regenerated power.


## 4. Parameter Optimisation Analysis

16 sets of simulation tests have been designed and performed to provide desirable solutions of the system parameters to enhance the system behaviours and power level. After that, mean response analysis is used to take the average value of all test results for each factor level and determine the extent that the factor affects the indicator based on the range mean values, which is called the comprehensive equilibrium method. It can be applied to perform the multi-indicator analysis of shaft speed, hydraulic motor pressure, regenerative power, and regeneration efficiency.


### 4.1. Shaft Speed

As shown in Figure6, the size of cylinder has the greatest influence on shaft speed with a visibly large range. The larger cylinder size can deliver faster flow which is capable of providing larger rotational torque on motor shaft. The smaller motor displacement is also beneficial on the motor rotation, which is more effective than other three factors. Compared to the size of check valves, the electrical load has an equivalent degree of influence to the shaft speed. In addition, it is obvious that the capacity of accumulator is less significant than other factors for shaft speed. It can be concluded that the optimal combination of the shaft speed as the evaluation criterion is A1B1C1D1E1, where A1 = 50/28 mm, B1 = 6.35 mm, C1 = 0.63 L, D1 = 5.77 cc, and E1 = 10 Ω.Figure 6
The index level of shaft speed at different factors.


### 4.2. Hydraulic Motor Pressure

As shown in Figure7, the displacement of motor and the load of generator have almost equivalent influences on working pressure, and they take slightly lower impacts in comparison to the size of hydraulic cylinder. Additionally, it reveals that smaller check valve diameter can significantly lead to higher pressure. The higher average pressure means much more power can be produced by the generator to raise the regenerated power level. Therefore, optimal combination of hydraulic motor pressure is A1B1C1D1E1, where A1 = 50/28 mm, B1 = 6.35 mm, C1 = 0.63 L, D1 = 5.77 cc, and E1 = 10 Ω.Figure 7
The index level of motor pressure at different factors.


### 4.3. Regenerated Power

As shown in Figure8, the size of the cylinder has significant influence on the power output of the power circuit which is more important than other factors. Obviously, the small values of other factors can also contribute positive effects for more regenerated power. From the mean response analysis of Figure 8, the optimal combination of the regenerated power is A1B1C1D1E1, where A1 = 50/28 mm, B1 = 6.35 mm, C1 = 0.63 L, D1 = 5.77 cc, and E1 = 10 Ω.Figure 8
The index level of regenerated power at different factors.


### 4.4. Regeneration Efficiency

Regeneration efficiency is a significant indicator to assess the performance of HERSA. As shown in Figure9, the electrical load has the greatest influence on the regeneration efficiency. When the electrical load is 20 Ω, the proposed system can reach a high regeneration efficiency, which increases slowly with the larger value of electrical load. Compared to other three indicators, higher regeneration efficiency can be found with larger the size of check valve port and the capacity of accumulator. It is clear that the larger size of hydraulic cylinder also contributes to regeneration efficiency. However, the optimal combination of regeneration efficiency is A1B4C2D1E4, where A1 = 50/28 mm, B4 = 19.05 mm, C2 = 1 L, D1 = 5.77 cc, and E4 = 40 Ω.Figure 9
The index level of regeneration efficiency at different factors.


### 4.5. Optimisation Results

From the mean response analysis of Figures6–9, it can be concluded that the optimal combination of each parameter for more regenerated power on the HERSA is A1B1C1D1E1. However, a high regeneration efficiency is also one of the important criteria. It is necessary to adjust the optimal combination for the higher regeneration efficiency. According to the range mean values of different factors, the extent that the factor affects the indicator can be determined. The rank of factors based on their degree of importance and their corresponding best combination are shown in Table 10.Table 10
The rank of factors and their combination.
Indicators
Rank of factors
Best level combinations
Shaft speed
A D E B C
A
1
D
1
E
1
B
1
C
1
Hydraulic motor pressure
A E D B C
A
1
E
1
D
1
B
1
C
1
Regenerated power
A D E B C
A
1
D
1
E
1
B
1
C
1
Regeneration efficiency
E A D B C
E
4
A
1
D
1
B
4
C
2It is obvious that the largest size of cylinder (A1) and the smallest displacement of motor (D1) can provide better dynamics and power level for the proposed HERSA. According to the principle of the comprehensive equilibrium method, the selection of other factors is as follows:(a)
Given the rank of factor B on different indicators is fourth, the superior level selection is considered as the one that occurs most frequently. The selection of factorB therefore is level 1, where B1 = 6.35 mm.(b)
Identically, the rank of factorC is fifth on different indicators. Given the best level selection of factor C for three indicators is level 1, which is the one that occurs most frequently. Therefore, the selection of factor C is level 1, where C1 = 0.63 L.(c)
When the factor has a different degree of influence on all indicators, the more important indicators should be satisfied firstly. The regeneration efficiency and regenerated power are the main criteria of this system. When the factorE is selected, the level 2 may be better. As shown in Figures 8 and 9, the efficiency at level 2 is over 60%, which is much higher than that at level 1 and nearly to that at level 3 and 4. Meanwhile, the regenerated power at level 2 is also high. The selection of factor E is level 2, where E2 = 20 Ω.Therefore, the optimal combination of parameters in HERSA isA1B1C1D1E2, which is capable of delivering a large electrical power as well as a high regeneration efficiency. The optimisation results are shown as follows: The size of cylinder is 50 mm (piston) and 28 mm (rod), the diameter of check valve is 6.35 mm, the accumulator capacity is 0.63 L, the displacement of motor is 5.77 cc, and the electrical load of generator is 20 Ω, respectively. Furthermore, for the general HERSA system (including hydraulic cylinders, check valves, accumulators, motors, and generators), a set of optimisation methods about power regeneration performance can be summarised as follows:(a)
Determine the range of key parameters(b)
Design the corresponding orthogonal test(c)
Conduct the mean response analysis(d)
Discuss the optimisation resultsIt is considered that the proposed optimisation procedure is suitable for the general HERSA system. Figure10 shows the results of the HERSA applied with the optimal component combinations.Figure 10
The results with optimal parameter combinations.As shown in Figure10, the shaft speed is 1634 rpm, the accumulator pressure is about 30 bar, the power output is about 331 W, and the regeneration efficiency is approximately 65%. Both larger power and higher regenerated efficiency are achieved.


### 4.6. Experimental Validation

The setup of the test rig is shown in Figure11. According to the schematic in Figure 3, the parameters of the key components are listed in Tables 6 and 11. A corresponding test rig was designed and fabricated according to the design concept and model development to validate the prediction of the optimised HERSA model. Based on the result of parameter optimisation, the key components of the test rig, including hydraulic cylinder, hydraulic accumulator, hydraulic motor, DC generator, inline check valve, and hydraulic circuits of the HERSA system, are carefully selected and equipped on the designed test bench. The HERSA test rig selected the parameters of the main components that are closest to the optimal results of the parameter optimisation. Table 11 shows the main parameter differences between model and test rig.Figure 11
The HERSA test rig.Table 11
Key component differences between model and test rig.
Parameters
Simulation
Experiment
Hydraulic cylinder
50–28
50–30
Bore rod (mm)
Check valve (mm)
6.35 (1/4 inch)
6.35 (1/4 inch)
Accumulator capacity (L)
0.635
0.60
Hydraulic motor displacement (cc)
5.77
6.00
Electrical load (Ω)
20
20The input controller and road actuator are designed which are able to provide predicted input excitations including excitation displacement, excitation velocity, and frequency. Data acquisition and transducers are also applied to synchronise and measure the regenerated voltage and current across the electrical load.The voltage and current across the electrical load were measured on the design test rig. The measured regenerated power is compared with predicted power, as shown in Figure12. The both results of simulation and measurement are under the harmonic excitation of 1 Hz-25 mm with an electrical load of 20 Ω. It is worth to mention that the measured average regenerated power is approximately 326 W compared to the predicted power of up to 331 W, and the results show a good agreement, especially for the visible variation trend in compression and extension strokes of cylinder.Figure 12
The validation of regenerated power (1 Hz-25 mm).In Figure12, it also indicates that the peaks of power are slightly different and predicted peak is higher than that of the measured. This is because the smaller motor displacement can provide high pressure to obtain higher shaft speed with more generated power. Additionally, in real experiment, the road actuator cannot practically provide absolute stability of sinusoidal excitation due to unaccepted input error in the operating process, especially on the top and bottom of the sinusoidal waveform. It is also the underlying cause of reducing the nadir of measured value.


## 4.1. Shaft Speed

As shown in Figure6, the size of cylinder has the greatest influence on shaft speed with a visibly large range. The larger cylinder size can deliver faster flow which is capable of providing larger rotational torque on motor shaft. The smaller motor displacement is also beneficial on the motor rotation, which is more effective than other three factors. Compared to the size of check valves, the electrical load has an equivalent degree of influence to the shaft speed. In addition, it is obvious that the capacity of accumulator is less significant than other factors for shaft speed. It can be concluded that the optimal combination of the shaft speed as the evaluation criterion is A1B1C1D1E1, where A1 = 50/28 mm, B1 = 6.35 mm, C1 = 0.63 L, D1 = 5.77 cc, and E1 = 10 Ω.Figure 6
The index level of shaft speed at different factors.


## 4.2. Hydraulic Motor Pressure

As shown in Figure7, the displacement of motor and the load of generator have almost equivalent influences on working pressure, and they take slightly lower impacts in comparison to the size of hydraulic cylinder. Additionally, it reveals that smaller check valve diameter can significantly lead to higher pressure. The higher average pressure means much more power can be produced by the generator to raise the regenerated power level. Therefore, optimal combination of hydraulic motor pressure is A1B1C1D1E1, where A1 = 50/28 mm, B1 = 6.35 mm, C1 = 0.63 L, D1 = 5.77 cc, and E1 = 10 Ω.Figure 7
The index level of motor pressure at different factors.


## 4.3. Regenerated Power

As shown in Figure8, the size of the cylinder has significant influence on the power output of the power circuit which is more important than other factors. Obviously, the small values of other factors can also contribute positive effects for more regenerated power. From the mean response analysis of Figure 8, the optimal combination of the regenerated power is A1B1C1D1E1, where A1 = 50/28 mm, B1 = 6.35 mm, C1 = 0.63 L, D1 = 5.77 cc, and E1 = 10 Ω.Figure 8
The index level of regenerated power at different factors.


## 4.4. Regeneration Efficiency

Regeneration efficiency is a significant indicator to assess the performance of HERSA. As shown in Figure9, the electrical load has the greatest influence on the regeneration efficiency. When the electrical load is 20 Ω, the proposed system can reach a high regeneration efficiency, which increases slowly with the larger value of electrical load. Compared to other three indicators, higher regeneration efficiency can be found with larger the size of check valve port and the capacity of accumulator. It is clear that the larger size of hydraulic cylinder also contributes to regeneration efficiency. However, the optimal combination of regeneration efficiency is A1B4C2D1E4, where A1 = 50/28 mm, B4 = 19.05 mm, C2 = 1 L, D1 = 5.77 cc, and E4 = 40 Ω.Figure 9
The index level of regeneration efficiency at different factors.


## 4.5. Optimisation Results

From the mean response analysis of Figures6–9, it can be concluded that the optimal combination of each parameter for more regenerated power on the HERSA is A1B1C1D1E1. However, a high regeneration efficiency is also one of the important criteria. It is necessary to adjust the optimal combination for the higher regeneration efficiency. According to the range mean values of different factors, the extent that the factor affects the indicator can be determined. The rank of factors based on their degree of importance and their corresponding best combination are shown in Table 10.Table 10
The rank of factors and their combination.
Indicators
Rank of factors
Best level combinations
Shaft speed
A D E B C
A
1
D
1
E
1
B
1
C
1
Hydraulic motor pressure
A E D B C
A
1
E
1
D
1
B
1
C
1
Regenerated power
A D E B C
A
1
D
1
E
1
B
1
C
1
Regeneration efficiency
E A D B C
E
4
A
1
D
1
B
4
C
2It is obvious that the largest size of cylinder (A1) and the smallest displacement of motor (D1) can provide better dynamics and power level for the proposed HERSA. According to the principle of the comprehensive equilibrium method, the selection of other factors is as follows:(a)
Given the rank of factor B on different indicators is fourth, the superior level selection is considered as the one that occurs most frequently. The selection of factorB therefore is level 1, where B1 = 6.35 mm.(b)
Identically, the rank of factorC is fifth on different indicators. Given the best level selection of factor C for three indicators is level 1, which is the one that occurs most frequently. Therefore, the selection of factor C is level 1, where C1 = 0.63 L.(c)
When the factor has a different degree of influence on all indicators, the more important indicators should be satisfied firstly. The regeneration efficiency and regenerated power are the main criteria of this system. When the factorE is selected, the level 2 may be better. As shown in Figures 8 and 9, the efficiency at level 2 is over 60%, which is much higher than that at level 1 and nearly to that at level 3 and 4. Meanwhile, the regenerated power at level 2 is also high. The selection of factor E is level 2, where E2 = 20 Ω.Therefore, the optimal combination of parameters in HERSA isA1B1C1D1E2, which is capable of delivering a large electrical power as well as a high regeneration efficiency. The optimisation results are shown as follows: The size of cylinder is 50 mm (piston) and 28 mm (rod), the diameter of check valve is 6.35 mm, the accumulator capacity is 0.63 L, the displacement of motor is 5.77 cc, and the electrical load of generator is 20 Ω, respectively. Furthermore, for the general HERSA system (including hydraulic cylinders, check valves, accumulators, motors, and generators), a set of optimisation methods about power regeneration performance can be summarised as follows:(a)
Determine the range of key parameters(b)
Design the corresponding orthogonal test(c)
Conduct the mean response analysis(d)
Discuss the optimisation resultsIt is considered that the proposed optimisation procedure is suitable for the general HERSA system. Figure10 shows the results of the HERSA applied with the optimal component combinations.Figure 10
The results with optimal parameter combinations.As shown in Figure10, the shaft speed is 1634 rpm, the accumulator pressure is about 30 bar, the power output is about 331 W, and the regeneration efficiency is approximately 65%. Both larger power and higher regenerated efficiency are achieved.


## 4.6. Experimental Validation

The setup of the test rig is shown in Figure11. According to the schematic in Figure 3, the parameters of the key components are listed in Tables 6 and 11. A corresponding test rig was designed and fabricated according to the design concept and model development to validate the prediction of the optimised HERSA model. Based on the result of parameter optimisation, the key components of the test rig, including hydraulic cylinder, hydraulic accumulator, hydraulic motor, DC generator, inline check valve, and hydraulic circuits of the HERSA system, are carefully selected and equipped on the designed test bench. The HERSA test rig selected the parameters of the main components that are closest to the optimal results of the parameter optimisation. Table 11 shows the main parameter differences between model and test rig.Figure 11
The HERSA test rig.Table 11
Key component differences between model and test rig.
Parameters
Simulation
Experiment
Hydraulic cylinder
50–28
50–30
Bore rod (mm)
Check valve (mm)
6.35 (1/4 inch)
6.35 (1/4 inch)
Accumulator capacity (L)
0.635
0.60
Hydraulic motor displacement (cc)
5.77
6.00
Electrical load (Ω)
20
20The input controller and road actuator are designed which are able to provide predicted input excitations including excitation displacement, excitation velocity, and frequency. Data acquisition and transducers are also applied to synchronise and measure the regenerated voltage and current across the electrical load.The voltage and current across the electrical load were measured on the design test rig. The measured regenerated power is compared with predicted power, as shown in Figure12. The both results of simulation and measurement are under the harmonic excitation of 1 Hz-25 mm with an electrical load of 20 Ω. It is worth to mention that the measured average regenerated power is approximately 326 W compared to the predicted power of up to 331 W, and the results show a good agreement, especially for the visible variation trend in compression and extension strokes of cylinder.Figure 12
The validation of regenerated power (1 Hz-25 mm).In Figure12, it also indicates that the peaks of power are slightly different and predicted peak is higher than that of the measured. This is because the smaller motor displacement can provide high pressure to obtain higher shaft speed with more generated power. Additionally, in real experiment, the road actuator cannot practically provide absolute stability of sinusoidal excitation due to unaccepted input error in the operating process, especially on the top and bottom of the sinusoidal waveform. It is also the underlying cause of reducing the nadir of measured value.


## 5. Conclusions

In this paper, a hydraulic electric regenerative shock absorber (HERSA) is designed, modelled, and fabricated to regenerate the kinematic energy of the suspension system. To maximise the level of regenerated power and power efficiency, a parameter optimisation approach has been proposed, and the result has been validated.A mathematical model has been proposed firstly, which consists of hydraulic cylinder, check valves, accumulator, hydraulic motor, and other components. In the dynamic model, it considers the flow variation in different chambers of cylinder (compression stroke and extension stroke), the fluid bulk modulus, and the accumulator smoothing, which are beneficial to comprehensively understand the system behaviours in order to further contribute and develop the corresponding prototype.The parameters needed to be optimised in HERSA system have been pointed out, which consist of the size of hydraulic cylinder, the size of check valves, the capacity of accumulator, the displacement of hydraulic motor, and the electrical load. The optimal values of the key components can be determined by using the orthogonal method.In parameter optimisation, 16 tests were designed and the corresponding simulated results were obtained. According to the principle of the comprehensive equilibrium method, the optimal component combinations of the HERSA were determined and contribute to the selection of the components of the test rig. The best combinations of the key components have been determined: the size of cylinder: 50 mm (piston) and 28 mm (rod), the diameter of check valve: 6.35 mm, the accumulator capacity: 0.63 L, the displacement of motor: 5.77 cc, and the electrical load of generator: 20 Ω, respectively. It is considered that the proposed optimisation procedure based on the orthogonal test is suitable for any general HERSA system.It is worth mentioning that the model prediction has confirmed that the recoverable power can be achieved with the average of 331 W at 1 Hz-25 mm sinusoidal excitation with the efficiency of up to 65%. In addition, the HERSA test rig is designed and fabricated in terms of the optimisation results. As a result, the experimental validation has been done and the measured results show good agreement with the simulated results, which verifies the optimisation approach’s effectiveness and reliability.It is worth noting that a HERSA system has many other objectives, such as comfort and vehicle handing stability. Particularly, feasibility study only needs to focus on the power regeneration in this paper. The studies about comfort and stability rely on the road test. Therefore, further research needs to pay more attention for the dynamic model in the future, which can satisfy irregular road profiles. And the integration of HERSA needs to be optimised for the real application.



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*Source: 5727849-2019-06-11.xml*