Energy analysis and optimization design of vehicle electro-hydraulic compound steering system

Applied Energy 255 (2019) 113713

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Energy analysis and optimization design of vehicle electro-hydraulic compound steering system

T

Wanzhong Zhao , Xiaochuan Zhou, Chunyan Wang, Zhongkai Luan ⁎

College of Energy & Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

HIGHLIGHTS

GRAPHICAL ABSTRACT

novel vehicle electro-hydraulic • Acompound steering (EHCS) system is proposed.

mechanical-electro-hydraulic • The coupling relationship affects steering energy.

key parameters are optimized by • The an improved MOPSO algorithm. road test verifies the optimized • The EHCS system can reduce the steering energy.

energy flow of the EHCS system • The under real road traffic scene is analyzed.

ARTICLE INFO

ABSTRACT

Keywords: Electro-hydraulic compound steering Energy consumption Steering road feeling Coupling relationship Multi-objective optimization Road traffic scene

In order to reduce the vehicle steering energy consumption and improve the steering road feeling, this work proposes an electro-hydraulic compound steering (EHCS) system, which combines the functions of electric power steering (EPS) and electro-hydraulic power steering (EHPS). For this novel steering system, there is a complex mechanical-electrohydraulic coupling relationship that affects the steering performance. Thus, how to choose the appropriate parameters to ensure the system of good energy-saving characteristics and steering road feeling is one of the key issues. The power flow of mechanical, electrical and hydraulic subsystems is used to test the coupling relationship between the parameters of the motor, hydraulic pipe, hydraulic valve, power cylinder, and mechanical steering structure, and analyze their influence on the steering energy consumption. According to the results of energy consumption sensitivity analysis, the main coupling parameters are selected as design variables, and the steering energy consumption, steering road feeling and steering wheel return error are taken as optimization objectives. To add population diversity and accelerate convergence velocity, the improved competitive multi-objective particle swarm optimization (CMOPSO) algorithm is proposed and used for optimization. The optimization results illustrate that the CMOPSO has better convergence compared with the basic MOPSO, and the EHCS system optimized by CMOPSO has a better steering economy, with better steering road feeling and smaller steering wheel return error. To verify the comprehensive steering performance, the optimized EHCS system is installed on the vehicle for an on-field road test. Compared with original EHPS, the road test results show that the energy consumption of the modified vehicle under the steering condition significantly decreases, and can also meet the steering assistance and driver road feeling requirements. Furthermore, the real road traffic scene around Nanjing University of Aeronautics and Astronautics is reconstructed to analyze the relationship between the whole vehicle energy consumption and energy characteristics of the EHCS system in the intelligent traffic environments, which verifies the steering energy consumption is reduced by 51.7% under the 15 km test road.

⁎

Corresponding author. E-mail address: [email protected] (W. Zhao).

https://doi.org/10.1016/j.apenergy.2019.113713 Received 2 June 2019; Received in revised form 24 July 2019; Accepted 6 August 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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1. Introduction

similar, but the steering road feeling of EPS could be adjusted by the motor to provide improved feedback to the driver. Hanifah et al. [21] optimized the PID parameters of EPS motor controller by particle swarm optimization and ant colony optimization, effectively improving the controller performance and reducing the energy loss of EPS. Hung et al. [22] proposed a wavelet fuzzy neural network to control the motor of EPS that improve the stability of the vehicle and the steering road feeling of the driver. An H-infinity-controller was proposed by Dannöhl et al. [20] to make the assist motor torque track the ideal torque and provide sufficient steering road feeling. Wilhelm et al. [23] proposed a strategy of actively compensating to suppress adverse effects caused by friction, but it also transmits the road interference signal to the driver. A Takagi-Sugeno fuzzy was used to express the nonlinear characteristics caused by friction and disturbances of the road condition in EPS by Saifia et al. [24], which is applied to improve the steering road feeling levels perceived by the driver. These studies mainly improved the steering road feeling of EPS through the control strategy of the motor, and the output torque of the motor can produce a direct road feeling response and is easy to adjust with the speed of the vehicle. However, compared with the road feeling transmitted to the driver through the hydraulic system directly, the steering road feeling generated by the motor is still not clear, accurate and smooth enough [25]. In addition, due to the factors such as the safety limitation of on-board power and the installation space of high-power motor, the assist power provided by existing EPS is too small to meet the steering assist demand of the vehicles with a large load on the front axle, such as buses, trucks, and engineering vehicles. The above research has analyzed and improved the performance of EPS and EHPS respectively. However, due to the inherent characteristics of the electric system and hydraulic system, it is difficult for EPS and EHPS to balance good steering feeling, sufficient assist power and low energy consumption at the same time. Therefore, this paper proposes an electro-hydraulic compound steering (EHCS) that combines the functions of traditional EPS and EHPS to achieve the coordination of steering road feeling and steering economy, and improve the overall steering performance of the vehicle. The structure of the EHCS system is shown in Fig. 1, which consists of two power-assisting units. One is the power assist motor directly acting on the steering column, and the other is the pump providing hydraulic force to the piston connected to the steering rack. Based on the signal transmitted by the sensor, the EHCS system judges the steering condition of the vehicle and distributes the proportion of the electro-hydraulic assist power. Normally, the two units work at the same time at low speed, the hydraulic unit provides large steering assist power, and the electric unit can reduce energy consumption. As the vehicle speed increases, the electro-hydraulic

The vehicle steering system is a bridge and link connecting the human-vehicle-road closed-loop system. Its performance not only affects the handling feeling [1,2] but also is an important part of the vehicle energy flow [3]. With the increasing requirements for energy conservation, environmental protection and safety, the energy saving and electrification of steering systems have become inevitable trends of its development [4–7]. The electro-hydraulic power steering (EHPS), which is developed based on the hydraulic power steering, can changes the power source of the hydraulic pump from the engine to the motor and reduce the steering energy consumption [8–10]. It can also adjust the flow to change the power-assisting characteristics of the steering system while retaining the clear road feeling of the hydraulic transmission [11]. Kemmetmüller et al. [12] provided a novel electro-hydraulic closedcenter power-steering system and established the mathematical modeling and devised the nonlinear controller of it, which enhanced the energy efficiency of the steering system and could supply the variable steering assistance while keeping the good steering feeling. Cho et al. [13] designed a flow control valve of the fixed displacement and pressure balanced type vane pump for the steering system, and the simulation results from AMESim software showed that the design parameters largely affect the flow control characteristics. Tang et al. [14] optimized the rotary valve parameters of EHPS and changed the hydraulic assist characteristics to improve the road feeling. Zhao et al. [15] proposed a multi-mode hybrid steering system and optimized the steering performance based on an improved MOPSO algorithm. Pan et al. [16] analyzed the speed deviation characteristics of the doubleaction vane pump in a specific speed range and designed a new pump with speed offsetting to overcome the energy consumption of the steering system. Cheng et al. [17] optimized the parameters of the extended state observer to improve the performance of EHPS. The above research shows that the steering economy of EHPS has great advantages over traditional hydraulic power steering system, and it can achieve better steering performance through parameters optimization and controller design. However, EHPS has certain limitations due to the disadvantages of the inherent hydraulic energy loss, which leads to its further development towards electrification. The electric power steering (EPS) uses the motor to provided assist power acquired for steering, which overcomes the shortage of the hydraulic steering system, and effectively improves the steering economy [18–20]. Baharom et al. [18] presented a new method of designing EPS and compared the vehicle fitted with EPS and EHPS, and it was concluded that the steering assist performances of both systems were

Fig. 1. Electro-hydraulic compound steering system. 2

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assist ratio also changes. Both the electric unit and the hydraulic unit simultaneously work with a small power output, which ensures a certain steering road feeling while making the EHCS system consume less energy. In addition, in the case of a very small steering resistance torque or a system failure, the electric power unit and hydraulic power unit can also work independently according to the needs of the vehicle, thereby providing a certain steering assist to ensure the steering ability of the vehicle. For the electro-hydraulic compound steering system, the value of the structural parameters has a great influence on steering performance. Hence, it is the focus of research to obtain the ideal parameters through reasonable structural design, model construction and parameters optimization. There exists a coupling relationship of mechanical, electrical, hydraulic, control and other disciplines in the EHCS system, and the coupling between the parameters of each discipline has a complex nonlinear effect on the steering performance, so the choice of optimization variables is greatly limited. In addition, due to the conflict between the optimization objectives of the steering road feeling and steering energy consumption, it is difficult to obtain good comprehensive steering performance through the traditional single-objective optimization method [26]. Therefore, this paper focuses on the performance analysis and multi-objective optimization of the EHCS system. The remaining of this paper is organized as follows. In Section 2, the power flow model of the mechanical, electrical and hydraulic subsystem are analyzed and the dynamics model is built. In Section 3, the simulation model is established and the steering energy characteristics of the EHCS system is analyzed. In Section 4, the influence of parameters on steering energy consumption, steering road feeling and steering wheel return error is analyzed, and then improved competitive multi-objective particle swarm optimization (CMOPSO) algorithm is used to carry out the parameters optimization of the EHCS system. In Section 5, the optimization results and real vehicle road test results are discussed. The conclusions of this paper are given in the sixth section.

hydraulic systems, and the above dissipation phenomena cause the main energy consumption of the EHCS system. The major difference between resistive source power and resistive power is that the resistive source power is converted from another energy form into heat, used in the system by another component, or kept in the component itself. The source power is produced from gravity or the pressure difference between the absolute pressure and the relative pressure, and it has been implemented in the component where energy is supplied in an implicit manner. Due to the motion of a solid with proper weight, mass element and rotary load element also lead to inertial power. Inertial power also occurs when there is an inductance or solid movement in the circuit of the electrical system. Capacitive power is associated with a capacitor present in an electric circuit, and in hydraulic system, it is especially associated with elasticity elements, such as a spring or a fluid volume. This paper applies the power-energy-based modeling metric and model reduction algorithm to the EHCS system, and the power and energy flow are used to measures the total amount of energy that flows in and out of the EHCS system shown in Fig. 2. It can be seen from the figure that in the power flow of the EHCS system, the energy loss is mainly based on resistive power and is a one-way irreversible loss. The capacitive and inertial energy are used as energy in storage components in the EHCS system, and energy can be bidirectionally transmitted. The resistive source power does not appear in the power flow because it is only transformed from a mechanical, hydraulic or electrical power type to heat that kept in the AMEsim model of the EHCS system. 2.2. Mechanical system power flow The mechanical steering structure of the EHCS system is made up of the steering column, torsion bar, worm gear, rack-pinion, steering joint, spring, damper, rotary load, wheels and so on. The dissipation phenomena of the above mechanical elements involve a loss of mechanical power:

2. Power flow model and dynamic model 2.1. Power flow model

PR = Ffri · vf = cd· vf2

(1)

PI = FI ·vI

(2)

where Ffri is the friction force, vf is the velocity associated with Ffri , cd is the damping coefficient, FI is the total force applied to the solid, vI is the body velocity.

The overall energy loss of the EHCS system is obtained by analyzing the power flow of subsystems such as mechanical system, electrical system and hydraulic system. In the analysis, the types of energy include resistive power (PR ), resistive source power (PRS ), source power (PS ), capacitive power (PC ) and inertial power (PI ). Resistive power is related to energy dissipation phenomena, such as friction loss or damping loss in the mechanical system, Joule effect in the electrical system, and restrictions or friction along pipes in

2.3. Electrical system power flow The EHCS system uses an engine-driven alternator to charge the battery, and the energy consumption of the alternator is given by:

Pm = Pe/eff

Fig. 2. Power flow and energy flow of the EHCS system. 3

(3)

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dh = Pm

(4)

Pe

P = t

(5)

PRS = Pdis

where Pe is the electrical power, Pm is the mechanical power, eff is the efficiency function, dh is the thermal loss, is the efficiency of thermal port, Pdis is the total power loss. In order to adapt to the development of electrification and meet the needs of electric vehicles, the EHCS system use battery to drive the hydraulic pump motor and the power assist motor. The equivalent circuit connection as well as the voltage and currents is defined with the convention and the energy consumption of the battery given by:

PC = UI

(6)

PRS = I 2R

(7)

PS = dh = (U

dIsq dt

=

=

Usq

PS = dh =

Usd

Lsd e Isd

3 / 2 e fl

Lsq 2 Rs Isq

+

2 Rs Isq

The mechanical system dynamic model of the EHCS system is:

Js

(9)

sign( P )

ks (

e)

s

Tw Fz

e ..

.

e

.. ..

m1

m2

+ Bm1 + Bm2

. .

Tehps = qPs = q

(16)

m1

= Tem1

Teps

m2

= Tem2

Tehps

(17)

8(Cq A1)2

(Q

s

+ Ap

)

dxr 2 dt

Fhyd = Ap (PA Teps = Km1 (

m1

+

8(Cq A2 )2

(Q

s

Ap

)

dxr 2 dt

PB ) e G)

(18)

where Ap is the hydraulic cylinder cross-sectional area, PA is the inlet pressure of the power cylinder, PB is the outlet pressure of the power cylinder, Km1 is the rotation stiffness of the power assist motor, q is the displacement of hydraulic pump, Ps is the output pressure of the hydraulic pump, Ai is the throttling area of the rotary valve port, Qs is the flow rate of the rotary valve port.

(11)

3. Energy flow analysis 3.1. Simulation model and verification AMEsim is an integrated multi-domain and multi-disciplinary system modeling and simulation platform, which is applied in automotive, aerospace and other fields [27–29]. According to the structure of the vehicle, this paper adopts the modular modeling method and builds a fifteen degrees of freedom vehicle model in AMEsim software, including suspension system module, damper module, tire module, road module, sensors module, brake system module, powertrain system module and external load module. Based on the EHCS system structural principle and power flow analysis, the simulation model of the electrohydraulic compound steering system is established in AMEsim shown in Fig. 3. The EHCS system simulation model consists of an electrical power unit, hydraulic power steering unit, mechanical transmission unit, signal unit and the energy source is the battery. In this paper, the energy exchanged between the submodule and the surrounding

(12)

where P is the pressure drop, is the density, Cq is the flow coefficient, Ao is the opening area. The compressibility and friction of hydraulic pipes are critical to energy consumption. The energy consumption of the pipes is given by Eqs. (11) and (13):

PC = pcham · qcham

Tdri

where Jm1, Bm1, Tem1, m1 respectively denote the moment of inertia, damping coefficient, armature torque and angle of the power assist motor, Jm2 , Bm2 , Tem2 , m2 respectively denote the moment of inertia, damping coefficient, armature torque and angle of the hydraulic pump motor, Tehps is the hydraulic pump working torque, The hydraulic system dynamic model of the EHCS system is:

where pin is the inlet absolute pressure, Qvin is the inlet volumetric flow rate, pout is the outlet absolute pressure, Qvout is the outlet inlet volumetric flow rate. The rotary valve is a key component of the EHCS system, which greatly affects the energy consumption and power-assisting characteristics of the steering system. The rotary valve can be represented as a Wheatstone bridge, where each branch is a way of the valve. The flow area depends on the relative deformation of the torsion bar, and the flow area on the valve is controlled by the relative deformation of the torsion bar. The energy consumption of the rotary valve is given by Eq. (11), and the flow rate is given by Eq. (12):

2| P|

s = .

= GTeps + Tsen

Jm2

Due to the complicated structure of the hydraulic pump, there are many nonlinear energy losses such as frictional resistance loss, viscosity and temperature loss of hydraulic oil, volume loss caused by leakage, power matching loss, etc. This paper selects the ideal hydraulic pump in which the flow loss or mechanical loss is ignored, the simplified energy consumption is mainly given by:

(0)

+ Bds

.

mr x r + Br x r = Tw / rp + Fhyd

Jm1

2.4. Hydraulic system power flow

Q = Cq Ao

+ Bs

s ..

where. Js ., s , Tdri , Bs , ks are the moment of inertia, angle, input torque, damping coefficient and stiffness of steering wheel, respectively. e , Jds , Bds are the pinion angle, moment of inertia, damping coefficient of steering column, G is the reduction ratio, Tw , mr , Br , Rp are torque, mass, damping coefficient and radius of rack, respectively, Teps is the power assist motor torque, x r is the pinion displacement, Fz , Fhyd are the tire resistance and hydraulic force, respectively. The motor dynamic model of the EHCS system is given as:

(10)

pout Q vout

..

Jds

where Isd and Isq are the stator currents, Rs is the stator winding resistance, Usd and Usq are the stator voltages, Lsd and Lsq are the stator cyclic inductance, is the magnetic flux, e is the rotor rotary velocity.

PR = pin Q vin

(15)

2.5. Dynamic model

Rs Isd + Lsq e Isq Lsd

Rs Isq

9.8 L sin( )| L ff

where pcham is the absolute pressure, qcham is the volumetric flow rates, B is the bulk modulus, ff is the friction factor, A , dp , L , are the crosssectional area, diameter, length, inclination of the pipe, respectively.

where U is the difference of electrical potential, I is the electrical current, R is the value of the ideal resistance. ocv is the open circuit voltage, r is the internal resistance. Because of the advantage of high efficiency, permanent magnet synchronous motor is used in the power assist motor and hydraulic pump motor of the EHCS system: dIsd dt

(14)

2dp | P

Q=

(8)

ocv )/ r

B Q · A x

(13)

The derivative of the input pressure is: 4

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environment is calculated by:

EX (t ) =

PX (t ) dt + EX (0)

speed include alternator, battery, three-phases inverter and motors. At the high speed, the energy is mainly depleted in the alternator, battery and motors. Similar to the mechanical system, the electrical system consumes more energy at lower speeds than at high speeds, but due to the loss of the energy conversion process of the alternator, the total energy consumption of the electrical system is about two orders of magnitude larger than that of the mechanical system. Fig. 8 shows the energy flow and power flow of the hydraulic system. According to the results from simulation analysis, it can be found that the energy consumption of the hydraulic system is mainly concentrated on the loss of the rotary valve and the hydraulic pipe. Among them, the peak power of the hydraulic rotary valve at low speed reaches 2.3kw, which is the most energy-consuming component in the hydraulic system, and the hydraulic system is also the subsystem with the largest energy consumption in the EHCS system.

(19)

where X represents either resistive elements, capacitive elements, inertial elements or source elements, PX is the power, EX is the energy consumption, EX (0) is the initial energy. The basic steering assist characteristics of the EHCS system are shown in Fig. 4. When the vehicle speed is 10 km/h, the electric assist torque is greater than the driver's torque. The superimposed torque is output through the rack and pinion steering module and combined with the output force of the hydraulic power steering unit. At this time, the hydraulic accounts for 53% of the total power provided by the EHCS system. As the vehicle speed increases, the steering resistance torque decreases and the total assist required of the EHCS system also decreases. When the vehicle speed is 80 km/h, the torque provided by the power assist motor is less than the driver's torque, and the hydraulic output accounts for 65% of the total power. It can be seen that the electro-hydraulic compound steering simulation model can adjust the size of the electric power assist and the hydraulic power assist with the vehicle speed, thereby achieving the coordination of the steering economic and the steering road feeling.

3.3. Overall performance analysis Based on the analysis of energy flow in the second section, the simulation experiment is carried out, and the comprehensive energy consumption of the EHCS system is shown in Fig. 9. It can be seen that at low speed the most energy-consuming part is the hydraulic system, which accounts for approximately 81% of the total energy consumption. At high speed, the assist power required for steering decreases drastically, and the energy consumption of the hydraulic system reduces significantly from approximately 36KJ at low speed to approximately 0.4KJ. Although the energy consumption of the electrical system has also decreased from about 7KJ at low speed to about 1.2KJ at high speed, its proportion of total energy consumption has increased from 16% to 72%. Under different vehicle speeds, the energy loss of mechanical system changes little, and its proportion in total energy consumption is extremely low, which has a little direct impact on the energy consumption of the EHCS system. The steering road feeling is the state of the road and the feedback force felt by the driver through the steering wheel, which mainly refers to the movement and force of the vehicle and the tires. The driver quickly and accurately receives the good steering feeling, and then can adjust the steering wheel in real time according to the driving condition of the vehicle, ensuring the safety of driving and obtaining a good driving experience [30]. There are many methods to express the steering road feeling [31]. In this paper, when the steering wheel is fixed, a wheel force is input, and the force exerted by the steering wheel

3.2. Subsystem power flow and energy flow analysis Two typical vehicle steering conditions are selected for the simulation and analysis of steering performance. One is the single linechange condition at low speed, which simulates the driver to perform the lane change operation during low-speed driving. The other condition is the double line-change condition, where the driver performs two consecutive lane-change operations to complete the overtaking of the preceding vehicle during the high-speed driving of the vehicle. Fig. 5 shows the two kinds of steering conditions for simulation. The dissipation power and energy losses of the mechanical, hydraulic and electrical systems are analyzed separately as shown in Figs. 6–8. Fig. 6 shows the energy flow and power flow of the mechanical system under different driving conditions. It can be seen from Fig. 6 that the energy consumption of the mechanical system at low speed is about 4 times that of high speed, and the loss of the worm is the largest, followed by the friction and spring-damper. Fig. 7 investigates the energy flow and power flow of the electrical system. It shows that the main energy consuming components at low

Fig. 3. Simulation model of the EHCS system. 5

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Fig. 4. Steering assist characteristics, (a) V = 10 km/h, (b) V = 80 km/h.

is calculated to express the steering road feeling. When the steering wheel input angle is zero, the steering wheel reaction torque represents the road feeling of the driver:

Tdri = rp Fhyd

rp Fz

(Jds + Rp2mr )

.. e

+ (Bds + rp2Br )

. e

+ GTeps

is 3Nm and the torque fluctuation is smoother than that at 10 km/h. It also can be seen from Fig. 10 that during 3–4 s the input tire force return to zero, but steering wheel still has some residual force, which means the steering wheel couldn’t return to the initial position accurately, so the EHCS system has a certain steering wheel return error and it will have an adverse effect on the steering performance.

(20)

In order to automatically return the steering wheel to the original position and maintain the direction of travel of the vehicle when the steering wheel is deflected, the wheel positioning parameters such as the kingpin inclination angle and the kingpin caster angle are designed to generate an aligning torque. The aligning torque is reversely transmitted to the mechanical steering structure and then the steering wheel has an automatic returnability. However, due to the frictional damping of the motor rotor and speed reduction mechanism, the steering system's returnability is deteriorated. The steering wheel returning accuracy is not ideal without the return control strategy, especially at low speed, the steering wheel cannot return to center, which affects the driver's manipulation feeling and even interfere with the normal operation of the steering system. The aligning torque is given as:

Tre = kre (T1 + T2 M1 M2 ) T1 = k1 sin(k2 ) T2 = eK cos

4. Optimization design 4.1. Parameters sensitivity analysis According to the above analysis, the steering energy consumption under the single line-change condition at low speed is more than 40KJ, which is much higher than that at high speed, so it is of great significance to analyze the influence of parameters on steering energy consumption at low speed. The systematic sensitive analysis is performed by the united simulation of AMEsim and Isight, and the AMEpilot module is used to output the design variables and objective functions, The Latin Hypercube method was chosen as the design of experiment (DOE) technique to analyze the correlation of the system, and 300 samples were selected randomly in the eight-dimensional vector space, established on the parameters of K a , dp , Rp , Ks , Ap , Jm1, G , q. Fig. 11 shows the correlation between parameter and steering energy consumption after a large number of simulation experiments. The key parameters highly correlated with the steering energy consumption are selected as the major optimization variables to further analyze, including the valve area gain K a , rack radius Rp , stiffness Ks and pipe diameter dp . The effects of parameters on steering energy consumption are shown in Fig. 12. Although the energy consumption of the mechanical system is very low compared to the electrical and hydraulic system, the mechanical parameters such as stiffness Ks and rack radius Rp greatly affect the energy consumption of the hydraulic system and electrical system. Similarly, the hydraulic parameter K a is not only closely related to the energy consumption of the hydraulic system but also has an influence on the electrical energy consumption. So the impact of each parameter on steering energy consumption is not a simple one-to-one correspondence, but a complex coupling relationship. The steering road feeling, which is associated with the driver

M3 (21)

where Tre is the aligning torque, T1 is aligning torque of positional parameter, T2 is aligning torque of lateral force, k1 and k2 are constant coefficient, M1 is friction resistance torque of mechanical steering construction, M3 is the moment of friction resistance between tires and road, M3 is the moment of friction resistance caused by EHCS system. When the steering wheel is fixed or the steering wheel torque input by the driver is zero, the steering road feeling is expressed by the steering wheel reaction torque that transmitted from the tire of the vehicle. The steering resistance torque transmitted by the road surface to the tire is different under different steering conditions. Within a certain range, the steering resistance torque decreases with the increase of the vehicle speed. Fig. 10 shows the steering road feeling of the EHCS system at different vehicle speed. The periodic force with different amplitude is input to simulate the road surface resistance torque on the tire. When the speed is 10 km/h, the steering wheel peak torque is about 8Nm and the steering wheel torque has a certain fluctuation near the peak. When the speed is 80 km/h, the peak torque felt by the driver

Fig. 5. Simulation condition, (a) Single line-change, (b) Double line-change. 6

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Fig. 6. Results for the mechanical system power flow and energy flow, (a) V = 10 km/h, (b) V = 80 km/h.

comfort and safety, is an important performance index of the EHCS system, especially at high speed. The hydraulic cylinder cross-sectional area Ap , rack radius Rp , power assist motor moment of inertia Jm1 and stiffness K s are the key parameters that affect the steering performance. Fig. 13 shows the effect of parameters at high-speed conditions on steering road feeling. In Fig. 13, the driver steering torque represents the steering road feeling during 1–3 s, and the torque after 3 s when the periodic force input on the wheel is zero indicates the steering wheel return error. It can be seen that Ap and K s have a greater influence on the steering road feeling peak and Ks also affects the steering wheel return error greatly, Rp has a very small impact on return performance but it still affects the peak torque felt by driver, Jm1 has little effect on the peak torque, but has a great influence on the returning performance of the steering wheel. So the impact of parameters on steering comfort is not a simple linear relationship, but a complex mechanical-electrohydraulic coupling relationship.

4.2. Optimization model For the multi-objective optimization problem, a multi-objective optimization model needs to be built to find the Pareto frontier [32]. This paper uses the ratio of yaw rate to steering wheel angle to indicate the stability of the EHCS system [33]. The stability constraints of the EHCS system are established based on the Routh criterion, where Cij represents the element of line j in column i of the Routh table, Qi denotes the coefficient of the term whose order is equal to i. r (s ) s (s )

=

K s·(A3 s3 + A2 s 2 + A1 s + A0 ) Q6 s6 + Q5 s5 + Q4 s 4 + Q3 s 3 + Q2 s 2 + Q1 s + Q0

A3 = muIx N + h2ums2 N huIxz ms Y A2 = muLp N + Ix N Y Ix N Y A1 = muL N Lp N Y + L p N Y hums N Y + hums N Y A0 = L N Y + L N Y

(22)

where m , ms are the vehicular mass and sprung mass, u , h are the velocity and centroid height of the vehicle, Ix , Ixz are the moment of

Fig. 7. Results for the electrical system power flow and energy flow, (a) V = 10 km/h, (b) V = 80 km/h. 7

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Fig. 8. Results for the hydraulic system power flow and energy flow, (a) V = 10 km/h, (b) V = 80 km/h.

inertia around the x-axis and the plane x-z of the vehicle, Lp , L are the equivalent sprung mass coefficient and elevation angle coefficient, N , N , N are the wheelbase front-wheel corner coefficient, pitch angle coefficient and side slip angle coefficient, Y , Y , Y are the yaw rate coefficient, front wheel angle coefficient and side slip angle coefficient of the suspension. According to the performance analysis results, the coupling parameters that have a great influence on the steering economy and the road feeling are selected as the optimization variables. The optimization objectives include steering energy consumption f1 (X ) , steering road feeling f2 (X ) and steering wheel return error f3 (X ) . The comprehensive optimization model can be given by:

min

algorithm based on swarm intelligence evolution technology that simulates the social behavior of groups such as the birds [34]. The process of finding the best design point is seen as the process of foraging activities and each individual of the population is called a particle. The position of the individual in the search area is called the state, and the state of the particle is constantly changing to find the best position [35]. PSO algorithm has the advantages of convenient implementation, strong global search ability and fast convergence, so it is suitable for optimization problems in fields such as complex engineering applications [36–38]. Multi-objective particle swarm optimization (MOPSO) proposes a finite-scale external storage set to preserve the non-inferior solutions currently searched [39,40]. Individuals in the set don’t have a priority relationship, and the size of the set is kept within a reasonable range by certain criteria, and the variation of the non-inferior solution set is increased by taking a certain probability of variation. In order to add the population diversity and accelerate convergence velocity, the improved competitive multi-objective particle swarm optimization (CMOPSO) algorithm is proposed in this paper, which replacing the method of updating particles in classical PSO with an update strategy based on paired particle competition and learning mechanism [41,42]. At the same time, the external storage collection in basic MOPSO is retained to maintain the elitist solutions. After analyzing the steering economy and steering energy consumption of the EHCS system, the major design parameters were optimized by the CMOPSO, and the optimized parameters are fed back to

[f1 (X ), 1/ f2 (X ), f3 (X )]

where X = [Ks, Rp, Ap , dp, Jm1, K a] s.t. 0.1 < Ks < 2, 6 < Rp < 10, 1e 5 < Jm1 < 5e

4

250 < Ap < 800, 3 < dp < 15, 0.7 < K a < 1.3 Q6 > 0, Q5 > 0 C13 = C15 =

Q4 Q5

Q6 Q3 Q5

Q14 C23 C13 C24 C14

> 0, C14 = > 0, C16 =

Q3 C13 Q5 C23 C13

>0

C15 C24 Q0 C14 C15

>0

(23)

4.3. Optimization algorithm Particle swarm optimization (PSO) is an intelligent random search

Fig. 9. Results for comprehensive energy consumption of the EHCS system, (a) V = 10 km/h, (b) V = 80 km/h. 8

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Fig. 10. Results for steering road feeling of the EHCS system, (a) V = 10 km/h, (b) V = 80 km/h.

AMEsim for performance analysis to get a better design value. The complete flow chart of the EHCS system optimization is shown in the Fig. 14 [43–45]. The specific steps of the MOPSO optimization are as follows: Step 1. Build a model and define initial parameters. The specific steps of the CMOPSO optimization are as follows: Step 1.1 Build the optimization model including the optimization objective, constraints and design variables given as Section 4.2. Step 1.2 Set the algorithm parameters, the maximum number of iterations Ite , particle number N , inertia weight , individual learning factor c1, global learning factor c2 . Step 1.3 Initialize the particle swarm position and velocity information within a given solution space. Step 1.4 Calculate fitness function and filter the Pareto solution, then place it in the external storage set Eset and determine the initial personal optimum Pbest and global optimum Gbest Step 2.1 Calculate the crowded distance and select the Gbest from the top 5% in descending order.

Fig. 11. Correlation between parameter and steering energy consumption.

Fig. 12. Effect of parameters on steering energy consumption, (a) K a , (b) Rp , (c) K s , (d) dp . 9

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Fig. 13. Effect of parameters on steering road feeling, (a) Ap , (b) Rp ,(c) Jm1, (d) K s .

Step 2.2 Paired particles are selected for the competition from the parent population P (It ) , Step 2.3 Particles of better fitness are labeled as winner particles, which directly into the next generation of the population P (It + 1) . The poorer particles are labeled as loser particles, which into the next generation after updated by the learning mechanism based on the winner particles.

Vst (It + 1) = R (k, It ) Vl, k + R2 (k, It )(Xw, k (It ) + R3 (k, It )(X¯ k (It ) Xl, k (It ))

vehicle speed, and by 13% at high speed. When CMOPSO is applied to the optimization, the energy consumption is reduced by 34% and 14% respectively. Thus, the steering economy of the EHCS system is improved significantly. Furthermore, after the optimization of MOPSO, the steering road feeling and steering wheel return error at high speed is changed by 16% and 19%, and at low speed they are 42% and 14% respectively, and after the optimization of CMOPSO, these indices are correspondingly changed by 8.3%, 5% at high speed respectively, and 41%, 18% at low speed respectively. Therefore, the optimized parameters can improve the steering economy and the driver's steering feeling, obtaining good comprehensive steering performance.

Xl, k (It ))

Xl, k (It + 1) = Xl, k (It ) + Vl, k (It + 1)

(24)

Step 2.4 Calculate fitness function and filter the Pareto solution. Step 3.1 Judge the dominant relationship between the new Pareto solution and the solution of Eset . Step 3.2 if the new Pareto solution dominates the solution of Eset , replace the dominated solution with the new Pareto solution. Step 3.3 add the new Pareto solution into Eset if it doesn’t dominate the solution. when Eset is full, perform maintenance strategy by replacing a small crowded particle with the new Pareto solution randomly. Step 3.4 Generate the new Eset and update Gbest . Step 3.5 When the number of iterations exceeds Ite , output the Pareto set, otherwise return to step 2.1.

5. Experimental results and discussion 5.1. Road experiment preparation During the current study, the Shenlong SLK6118ALE0BEVS6 passenger bus was selected in the on-field road test, and the basic parameters of the tested vehicle are shown in Table 2. In order to verify the steering energy consumption and other characteristics of the optimized EHCS system, the original EHPS system of the passenger bus was converted into an optimized EHCS system. According to the results of the previous energy consumption analysis, the speeds of the test conditions are set to a low speed of 10 km/h and a high speed of 80 km/h. Fig. 16 illustrates that the road test is carried out by the vehicle with the EHCS system and the EHPS system respectively under the typical test conditions of the single line-change and the snake-shaped pile. The steering wheel angle and torque was recorded by LW35 sensor installed on the steering column, and two BPR-40 resistance strain press sensors were used and installed in the hydraulic power cylinder of the steering system to record the inlet pressure and return pressure, and the LWGY10 turbine flowmeter was mounted on the oil inlet and oil outlet of valve to collect the flow signal. In addition, the LMS SCADAS multifunction data acquisition system was used to acquire the real-time signals during the steering road test, which were performed by the portable computer to collect experimental results [46].

4.4. Optimization results Two algorithms are used in the multi-objective optimization of the EHCS system which is carried out under the low speed single linechange condition. The results of Pareto solution sets are shown in Fig. 15, and it can be seen from the convergence trend of feasible solutions that the CMOPSO algorithm has better convergence than the MOPSO algorithm. In order to obtain the optimal solution, the satisfaction function given by Eq. (25) is used to judge and select the final result of optimization variables.

sf =

f3 f3 min 1/ f1 1/ f1 min f2 f2 min + + 1/ f1 max 1/f1 min f2 max f2 min f3 max f3 min

(25)

Table 1 shows the values of the design variables and optimization goals before and after the optimization of MOPSO and CMOPSO. It can be seen from Table 1 that the energy consumption of the EHCS system with MOPSO optimization is reduced by 29% at the condition of low 10

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Fig. 14. Flow chart of the CMOPSO optimization.

5.2. Road experimental results

ripple and a small torque amplitude. The steering torque is fed back to the steering wheel and is in the proper range of driver's hand. It can be seen from the output pressure curve of the hydraulic cylinder that the EHCS and EHPS system pressures are established more quickly and can respond to changes in steering torque. At low speeds, the maximum pressure of EHCS and EHPS is basically close. At high speed, the electric assist unit of EHCS system has a large proportion of assisting force. The output pressure of the hydraulic cylinder is significantly lower than that of EHPS, and it can meet the steering assist demand.

The comprehensive performance of the two systems was compared by many times of experiments. Fig. 17 shows the experimental results of steering torque, hydraulic cylinder output pressure, and steering power under single line-change steering conditions. Among them, the steering torque at low speed is slightly higher than the high-speed steering, which is in line with the actual situation that the steering resistance torque decreases as the vehicle speed increases. Compared with the EHPS system, the optimized EHCS system has little difference in torque 11

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Fig. 15. Pareto-optimal solution sets, (a) MOPSO, (B) CMOPSO.

Fig. 18 shows the experimental results under the snake-shaped pile turning condition. It can be seen from the steering torque diagram that the steering torque decreases with the increase of the vehicle speed, and the optimized EHCS system responds faster at high speeds. The output pressure curve of the hydraulic cylinder shows that the output pressure amplitude of the EHCS system is smaller than that of the EHPS system at both speeds, and the pressure drop is more obvious at high speed. The steering power curve shows that the steering power of the EHCS system is significantly lower than that of the EHPS during the continuous steering of the snake-shaped pile condition. Table 3 shows the results of vehicle dynamic characteristic and steering performance under the realistic road test condition. The indices of the vehicle yaw rate and roll angle show the stability of vehicle with the EHCS system in the steering process. Especially, compared with the Table 1, the steering energy consumption of single line-change condition at 10 km/h is 5.94 KJ lower than the optimization result, that is because of the road test only calculate the dissipation of the hydraulic system. According to the analysis result in Fig. 9, it can be seen that one-fifth of the comprehensive energy dissipation is produced by the electrical and mechanical system, and the total dissipation of test vehicle is calculated approximately to be 29.26 KJ according to this proportion, so the steering energy consumption of the experiment accords with the optimization result. Moreover, the steering wheel average torque and residual torque are used to represent the steering road feeling and steering wheel return error during the analysis of experimental results, which illustrate the steering performance of the tested vehicle are close to the theoretical value in Table 1.

Table 1 Optimization results. Initial V = 10 Parameters Ka K s /Nm/degree dp /mm

Ap /mm2 Rp /mm

Jm1/kg*m2 Objectives Steering energy consumption/kJ Steering road feeling Steering wheel return error

MOPSO V = 80

V = 10

CMOPSO V = 80

V = 10

0.95 0.9 7

0.89 1.25 8

0.88 1.33 7.5

8.5

7.8

7.5

615

735

1.5e-4

V = 80

766

2.8e-4

2.6e-4

44.45

1.69

31.39

1.47

29.35

1.45

9.65 0.44

3.10 0.21

5.58 0.38

3.59 0.25

5.69 0.36

3.36 0.22

Table 2 Basic parameters of the test vehicle. Parameters

Unit

Value

Body length/height/width/ Wheelbase Vehicle mass center distance from front axle ssssVehicle curb weight Vehicle full load mass Vehicle no-load front wheel load Vehicle full load front wheel load

mm mm mm kg kg N N

10995 × 2500 × 3695 5550 3689 12,200 16,400 4100 5500

5.3. Road traffic scene verification

The steering power curve shows that the steering power at high speed is lower than that at low speed due to the change in steering resistance torque. At low speed steering, the steering power of the EHCS is closer to that of the EHPS. The steering power of the EHCS system is lower than that of the EHPS during high-speed steering, and the energysaving effect is more obvious.

The actual vehicle test obtained the steering system performance under the steering conditions of single line-change and snake-shaped pile. However, the steering conditions of the vehicle in the traffic system are different from the test conditions. To verify the energy consumption characteristics of the EHCS system in the real road traffic environment, this paper takes the real open road around Nanjing

Fig. 16. On-field road experiment of the realistic vehicle, (a) Test vehicle with EHCS system; (b) Typical test condition of single line-change and snake-shaped pile. 12

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Fig. 17. Experimental results of the single line-change, (a) V = 10 km/h, (b) V = 80 km/h.

University of Aeronautics and Astronautics Ming Palace Campus as the test environment and carries out the hardware-in-the-loop simulation test. The test process is shown in Fig. 19. The selected vehicle trajectories are the main traffic trunks of Nanjing city, including typical X-shaped intersections, Y-shaped intersections, and T-type intersections. The total length is about 15 km, and the average speed is 20 km per hour. The test vehicle completes common steering actions such as lane change, overtaking, obstacle avoidance, 90 degree turn, and the real-time steering wheel angle, vehicle speed, GPS and other information in real traffic scenes are collected. Then, a physical simulation model is established based on the real map of the corresponding road system in the Prescan software, and the data collected by the test vehicle is imported to reconstruct the traffic scene, and the Simulink model is generated, and the experiment is performed based on the real-time simulation platform

and the steering system test bench. The test results are shown in Fig. 20. Fig. (a) shows the steering wheel angle of the driver's input in a real road traffic environment. The steering wheel angle is about 500° when performing a right-angle turn, and the corner is about 30–100 degrees when performing obstacle avoidance and overtaking. Fig. (b) shows the output power of the battery. The peak power reaches 3.6 kW when turning at a large angle. Fig. (c) shows that the trend of electric steering power is consistent with the input angle. Fig. (d) shows that the hydraulic system provides about three times the power of the electric steering and it is also more sensitive to changes in steering angle. Fig. 21 shows the energy flow process of a vehicle equipped with an EHCS system in a test road traffic environment. As can be seen from the figure, the total energy supplied by the battery to the EHCS system is about 3.16 kW, which accounts for 2.23% of the vehicle's output

Fig. 18. Experimental results of snake-shaped pile, (a) V = 10 km/h, (b) V = 80 km/h. 13

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Table 3 Experimental results of the tested vehicle with the EHCS system. Single line-change

Objectives Steering wheel angle/drgree Yaw rate/degree/s Roll angle/degree Hydraulic energy consumption/kJ Steering wheel average torque/Nm Steering wheel residual torque/Nm

Snake-shaped pile

V = 10 km/h

V = 80 km/h

V = 10 km/h

V = 80 km/h

−180.96 ∼ 178.65 −5.88 ∼ 6.25 −1.52 ∼ 1.76 23.41 5.96 0.28

−102.36 ∼ 114.32 −11.61 ∼ 11.64 −5.81 ∼ 7.29 1.23 3.89 0.17

−120.95 ∼ 113.54 −2.79 ∼ 4.97 −0.83 ∼ 1.36 178.08 3.92 0.22

−118.71 ∼ 131.62 −9.58 ∼ 10.47 −9.92 ∼ 10.25 11.83 2.11 0.18

energy. The total energy consumption of the EHCS system is 3271.5 kJ, of which the energy loss of the electric power-assist system is about 5.4%, the energy loss of the hydraulic power-assist system is about 88.4%, and the maximum energy loss is in the rotary valve. The energy consumption of the traditional passenger car steering system accounts for 3%-5% of the total energy consumption of the vehicle. It can be seen that the EHCS system reduces steering energy consumption by 51.7% under the 15 km test road. Assuming that a vehicle travels 15000 km per year in the city, the EHCS system can save the energy about 9.63e06kJ, which increase 24.26 km cruising range in urban conditions. Therefore, the application of the EHCS system has great significance for energy saving and emission reduction of the whole vehicle and can improve the sustainability of the entire road

energy system. The above test results verify the accuracy of the simulation and optimization results, which indicates that the optimized EHCS system has lower comprehensive energy consumption than the traditional EHPS system, and has a better energy-saving effect and sustainability. 6. Conclusion An electro-hydraulic compound steering (EHCS) system combining the function of electric power steering (EPS) and electro-hydraulic power steering (EHPS) is proposed, which can realize the coordination of the steering system energy saving, sustainability, economy and maneuverability.

Fig. 19. Test process of hardware-in-the-loop under real road traffic environment.

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Fig. 20. Hardware-in-the-loop simulation test results of real traffic road system, (a) Input steering wheel angle, (b) Power of battery, (c) Power of electric system, (d) Power of hydraulic system.

The energy characteristic analysis is implemented under typical steering conditions of the single line-change and the double linechange. Simulation results show that the mechanical-electro-hydraulic coupling relationship has a great influence on steering energy consumption. According to the results of parameters sensitivity analysis, the main mechanical, electrical and hydraulic parameters that have a great influence on the EHCS system are selected as design variables. The improved competitive multi-objective particle swarm optimization (CMOPSO) algorithm is used in the optimization of the EHCS system, and receive better convergence compared to the basic MOPSO algorithm. The optimization results show that the average steering energy consumption is reduced by 34% at high speed and 14% at low speed respectively. Besides, the average steering road feeling is changed by 24%, and the average steering wheel return error is changed by 11.5%. The on-field road test results under single line-change and snake-

shaped pile show that, compared with the traditional EHPS system, the optimized EHCS system has excellent overall steering performances. Based on the road traffic scene around Nanjing University of Aeronautics and Astronautics, the hardware-in-the-loop simulation test of the real road traffic system is performed, and the test results show that the EHCS system accounts for 2.23% of the vehicle's output energy and reduces steering energy consumption by 51.7% under the traffic environment. Therefore, this study provides a theoretical and experimental basis for the development of the EHCS system. Further research on the influence of the coupling of structural and control parameters will be conducted in the future, and design a learning-based intelligent controller to achieve global energy optimization under an uncertain driving environment.

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Fig. 21. Total energy flow of the steering system in the road traffic scene.

Acknowledgment

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