The ride comfort and energy-regenerative characteristics analysis of hydraulic-electricity energy regenerative suspension

2.1. HESA model

HESA as a new kind of rotary regenerative shock absorbers may not only isolate vibration but also recover a part of energy dissipation, whose operating principle was presented in detail by Fang [18]; moreover, there is no significant difference in damping effects between the jounce and rebound strokes.

Fig. 1Schematic diagram of a HESA unit

Thus, improvement was carried out to meet the vehicle shock absorption requirement. The new structure of HESA is shown in Fig. 1, which is composed of a hydraulic cylinder, check valves, accumulator, a hydraulic motor, a generator, and pipelines and so on and Where: the red and blue arrows indicate fluid flows in jounce and rebound strokes, respectively. The compression damping force should be smaller than the expansion one according to the vehicle shock absorption demand. The current HESA structure contributes to satisfy the demand based on various hydraulic circuits. The target vehicle’s shock absorber was reprocessed based on the operating principle of HESA, whose schematic diagram is shown in Fig. 2 and whose rebound valve (on the piston) rather than other valves is removed. The original piston rod is replaced with a hollow bar whose lower end is connected with the upper operating chamber to transfer oil from the upper operating chamber. In addition, the connecting holes are designed in the bottom of the storage tank and the upper end of the piston rod, to connect any external motor-generator system.

When the body moves downwards, the lower operating chamber B is pressurized so that a part of oil may flow into the upper operating chamber through the flow valve on the piston. Due to there being a piston rod in the operating chamber A, other oil flows into the compensation chamber C through the compression valve and the same oil flowing path as the that during the compression process represents a traditional shock absorber.

The compression damping force occurs in the compression stroke, when upper operating chamber A is pressurized while the body moves upwards so that oil may flow into the external energy recovery system through the hollow piston rod and the hydraulic motor may be driven from the compensation chamber C to the lower operating chamber B. Due to there being no rebound valve, the damping force is chiefly provided by the external motor-generator system during rebound stroke.

In conclusion, HESA works as a traditional shock absorber when its piston moves downwards; on the other hand, the damping force is not only similar to that of an ordinary damper in this process but also provide the damping force represents isolating vibration and recycling a part of vibration energy while the piston moves upwards.

It is found that the rebound damping force dominate major differences in major mechanical differences based on the previous analysis; however, the damping force is primarily from hydraulic pipelines, check valves and the motor-generator system in a HESA while the local pressure loss is neglected. While ignoring the internal leakage of the oil cylinder and the pressure of the compensation valve, the following pressure balance equation may be obtained to the upper operating chamber under high pressure in expansion stroke:

where: $P_A$ represents the pressure of the upper operating chamber; $P_B$ represents the pressure of the lower operating chamber, ${∆P}_i$ represents the pressure drop of the check valve $i$ ($i=$1, 2); ${∆P}_e$ represents the pressure drop of a hydraulic motor; and ${∆P}_p$ represents the pressure drop of a hydraulic pipe.

Fig. 2Plane diagram of a HESA prototype

While ignoring the fiction force between the piston and the cylinder wall, the damping force may be expressed by:

where: $F_c$ represents the damping force in the expansion stroke; $A_a$ represents the piston ring area on the side of the upper operating chamber; and $A$ represents the piston cross-sectional area.

While neglecting the pressure drop of any compensation valve, the following equation comes into existence for $P_B$ and $P_{acc}$:

where: $P_{acc}$ represents the pressure of an accumulator.

Thus, the following equation may be obtained:

where: $A_r$ represents the cross-sectional area of a piston rod, $A_r=A-A_a$.

While simplifying a check valve as a thin wall orifice, the pressure drop of a check valve may be calculated by:

where: $Q_i$ represents the oil flowrate of the check valve$\mathrm{}i$ ($i=$1, 2), $A_{ci}$ represents the orifice area of the check valve $i$; $c_q$ represents the oil flow coefficient ($c_q=\mathrm{}$0. 6); and $\rho$ represents the oil density.

Then, the pressure drop of a check valve may be expressed as follows:

As an energy conversion unit, a hydraulic motor converts the oil pressure in the hydraulic system to the mechanical energy so that the expansion pressure energy may be turned into the torque to the generator. The hydraulic motor rotary speed and output torque may be calculated by the following equations:

where: $n$ represents the hydraulic motor rotary speed; $Q_e$ represents the flux of hydraulic motor; $q$ represents the displacement of the hydraulic motor; ${\eta }_v$ represents the volume efficiency of the hydraulic motor; $T_n$ represents the output torque of the hydraulic motor; and ${\eta }_m$ represents the mechanical efficiency of the hydraulic motor.

The generator is driven by a hydraulic motor so that its voltage and torque shall meet the following equations:

where: $V_e$ represents the induction electromotive force; $k_v$ represents the back electromotive force constant; $w$ represents the rotate speed of the generating rotor ($w=2\pi n)$; $T_n$ represents the output torque of the hydraulic motor; $J$ represents the rotary inertia of the generating rotor; $k_t$ represents the torque constant of the generator; and $I$ represents the inductive current.

The induction electromotive force may be expressed as $V_e=IR$, where $R$ represents the total resistance of the circuit. While ignoring the rotary inertia of the generating rotor, the following equation may be obtained:

As above, the accumulator is primarily to absorb redundant oil due to contraction of the rod cylinder. By taking the initial and final charging states into account and ignoring any middle course, the compression pressure of the accumulator may be calculated based on the Boyle’s law:

where: $\kappa$ represents the gas polytrophic index; $P_0$ and $V_0$ represent the initial pressure and volume of the accumulator, respectively; and $s\left(t\right)$ represents the displacement of the piston at the time ($t$). When the input is sinusoidal wave ($s\left(t\right)=s_{max}\sin \left(2\pi ft\right)$, $s_{max}$ denotes the maximum distance of piston), the linear friction loss of a hydraulic circuit during the expansion stroke may be expressed as:

where: $l$ and $d$ represent the length and inner diameter of the oil pipe, respectively; ${\upsilon }_v$ represents the fluid kinematic viscosity; and $Q$ represents the flowrate of a hydraulic circuit.

While assuming the same flowrate in each hydraulic circuit during the expansion stroke, namely, $Q_1=Q_2=Q_e=Q$, then:

From Eqs. (1)-(12), the expansion damping force may be calculated by:

For verifying the accuracy of the mathematical model, the measured and simulated results in Fig. 3 were compared under the sinusoidal frequency and amplitude (1.67 Hz and 50 mm).

Owing to the oil transportation characteristics, there exists oil loss travel distortion in actual tests so that the damping force may be distorted locally as shown in the lower right corner of Fig. 3. However, performances of the damper may not be influenced distinctly. It is found based on the verification experiments that the actual maximum damping force is 4516 N and the simulated one is 4370 N with the difference of only 3.23 %; thus, the simulated and measured damping forces are in good agreement and the proposed HESA as a damper is reliable in the vehicle suspension system.

Fig. 3Comparison of test and simulation results

a) Force vs. displacement

b) Force vs. velocity

Fig. 4Traditional shock absorber and HESA test rig

Based on experiments of the HESA prototype without battery load, the compression damping force was obtained, which is shown in Fig. 4. By combining the expansion damping force, the indicator diagram of HESA was presented. In comparison with those of the traditional shock absorber (TSA) under the same parameters, the results are shown in Fig. 5.

The comparison compression damping force results are in good agreement for the HESA and traditional shock absorber. On the other hand, the expansion damping forces are different under the same battery load.

Fig. 5Comparison of indicator diagrams of HESA and TSA

a) Frequency: 1 Hz, Amplitude: 10 mm

b) Frequency: 1 Hz, Amplitude: 50 mm

c) Frequency: 5 Hz, Amplitude: 10 mm

d) Frequency: 1. 67 Hz, Amplitude: 50 mm

2.2. HERS model

When the sprung mass allocation proportion is close to 1, the front and rear suspension systems are almost under independent vibration conditions. A quarter car was modeled to analyze the vehicle dynamics under certain road excitation conditions. As shown in Fig. 6, while the damping force of HESA is represented by $F_a$, the modeling dynamics may be easily written as:

where: $m_b$ and $m_w$ represent the sprung and unsprung masses, respectively; $z_2$ and $z_1$ represent the vertical displacements of sprung and unsprung masses, respectively; $z_0$ represents the road input displacement; $k_s$ and $k_t\mathrm{}$represent the suspension stiffness and the tire stiffness, respectively.

In comparison with a traditional suspension unit, a HESA includes an energy-harvesting shock absorber so that the vehicle ride comfort and the recovery of suspension vibration energy may be achieved.

3.1. Optimization constraints

The hydraulic-electricity energy regenerative suspension unit shall ensure the satisfactory characteristics of comfort and handling performances so that the following constraints shall be satisfied.

3.2. Optimization objectives

The vibration acceleration of the sprung mass is broken into the vertical, longitudinal and lateral components at the centroid of the whole vehicle for studying the vehicle ride comfort, among which the vertical vibration acceleration in the center of the sprung mass is taken as the objective function $J_1$, whose RMS value is expressed by:

where: $a_w$ represents the RMS value of vertical vibration acceleration in the center of the sprung mass; $G_a\left(f\right)$ represents the acceleration power spectral density function; and $W\left(f\right)$ represents the frequency weighting function, which is expressed by:

Besides, the ride performance, the recovered power should also be regarded as representation of the hydraulic-electricity energy regenerative suspension. The more recovered power is desired on the premise that the ride comfort may be guaranteed. The RMS value of the recovered power is taken as another objective function $J_2$, which is defined as:

where: $P_{rms}$ represents the RMS value of the recovered power; and $P\left(t\right)$ represents the function of recovered power time with time, which may be determined based on testing results.

3.3. Analysis of influencing factors

HESA dominate performances of a hydraulic-electricity energy regenerative suspension unit. As for HESA in Fig. 2, the primary influencing factors are listed in Table 1.

Because the HESA prototype is manufactured based on the traditional shock absorber of the target vehicle, diameters of the piston and the piston rod is taken into account in this study. Moreover, the initial pressure of accumulator $P_0\left(A\right)$, the volume of accumulator $V_0\left(B\right)$, the load current $I\left(C\right)$, the internal resistance of the generator $R_0\left(D\right)$ and the hydraulic motor displacement $q\left(E\right)$ are regarded as primary influencing factors. The orthogonal tests were carried out to analyze their sensitivities.

For rational assessment of the level interval of each factor, the constraints were set up hereby in light of: (1) 1.3 $\le n_1\le \mathrm{}$1.8; (2) $f_d\le \mathrm{}$65; and (3) $\xi \le$ 1/3; Class D road and the speed of 36 km/h are taken for calculation; and the standardized orthogonal table $L_{16}\left(4^5\right)$ is applied. By combining the characteristics of the hydraulic-electricity energy regenerative suspension unit, those influencing of factors were analyzed for the ride comfort and recovered suspension energy, whose orthogonal experiment design and results are listed in Table 2.

Based on the above orthogonal experiment results, the ranges of various factors were calculated, as in Tables 3 and 4, where $K_i$ represents the arithmetic average of the evaluation index in $i$ level test for each factor. The impact degree of any factor on the test evaluation index is reflected by its range; and the larger the range is, the greater the impact is.

The influencing tendency of performances of the reclaiming energy suspension unit may be obtained for each influencing factor based on above analysis results, as in Fig. 7.

Fig. 7Diagrams of influencing factors

a) Accumulator initial pressure

b) Accumulator volume

c) Load current

d) Generator rotor resistance

e) Hydraulic motor displacement

It is found from the above diagrams that those selected factors significantly impact the characteristics (especially the recovered power) of the reclaiming energy suspension unit; thus, they shall be taken into account to optimize performances of the hydraulic-electricity energy regenerative suspension unit, whose variable ranges are shown in Table 5.

The optimization model may be expressed by:

where: ${\mathbf{X}}_{min}$ and ${\mathbf{X}}_{max}$ represent the minimum and maximum of each design variable, respectively.

4.1. Road excitation input

The road excitation is a primary external input for any suspension system. The random road profile is generated by Gaussian white noise passing through a first order filter [20] in this study:

where: $u$ is the vehicle speed; $w\left(t\right)$ is the zero-mean Gaussian white noise input with intensity 1 in time domain; $f_0$ is the low cut-off frequency, $f_0=$0.1 Hz hereby; and $G_q\left(n_0\right)$ is the road roughness coefficient, whose geometric mean values are listed in Table 6.

It is known from Eq. (22) that $z_0$ correlates closely with the vehicle velocity. The velocity varies from 10 m/s to 30 m/s in this study.

4.2. Optimal design

Based on our optimization model, the sobol sequence was selected to 30 initial points in the variable range. An improved non-dominated ranking based MOGA (MOGA-II) was used to perform the optimization process [21]. Since the design evaluation is very fast, a high number of generations was taken as 300 in this study. According to the recommended range, the probabilities of directional cross-over, selection and mutation were taken as 0.5, 0.05 and 0.1, respectively. DNA string mutation ratio was taken as 0.05. Thus, optimization results are shown in Fig. 9.

Fig. 9Optimization results for different grade roads

a) Road level: $A$

b) Road level: $B$

c) Road level: $C$

d) Road level: $D$

It is found from Fig. 9 that the Pareto Frontier occurs for various grade roads; and the relationship ($a_w$ vs. $P_{rms}$) may be obtained; in addition, the greater the acceleration RMS value is the more energy may be recycled within the same velocity context.

Fig. 10Optimized Pareto frontier

The relationship ($a_w$ vs. $P_{rms}$) in Fig. 10 reflect the monotone effect so that the tire dynamic load shall be introduced in the optimal design, in which the fitted curve 1 characterize the relation ($P_{rms}$ vs. $F_d/G$); moreover, the intersection area was taken as the optimal solution range to tolerate a small dynamic load. The optimal design was in Table 7.

4.3. Comparative analysis

In view of the above optimal solution, comparison and analysis were carried out to ride comfort effects for the energy regenerative suspension unit and the traditional one under different random pavements, whose results are shown in Table 8.

In comparison with that of the traditional suspension unit, the optimized reclaiming energy suspension unit brings about marginally improved ride comfort. Moreover, a part of vibration energy is recovered by HESA, as in Fig. 11.

Fig. 11Recovery power vs. velocity

For performance of ride comfort of the energy regenerative suspension unit, the amplitude-frequency characteristic was analyzed under a step excitation including the body acceleration, the suspension dynamic displacement and the relative dynamic load of wheels, whose results are given in Figs. 12, 13 and 14.

It may be known based on the amplitude-frequency characteristic of the body acceleration that their acceleration responses are basically the same within the range $\left(0.\mathrm{}1,\mathrm{}{f}_2\right)$Hz; whereas, the acceleration response is smaller for the energy regenerative suspension unit while the excited frequency is more than $f_2$. Especially, it is of great significance to improve the ride comfort under high frequency excitation conditions.

Fig. 12Amplitude-frequency characteristic of z¨2/z0

Fig. 13Amplitude-frequency characteristic of fd/z0

Fig. 14Amplitude-frequency characteristic of Fd/Gz0

Their amplitude-frequency characteristics include almost the consistent suspension dynamic displacement responses; on the other hand, the dynamic deflection response is intensified to a certain extent around two peak frequencies.

The tire dynamic load is dominant for choice of the optimal solution. It may be seen from Fig. 14 that the dynamic load response is improved between the two peak frequencies, which are very important for improving the driving stability.

The two peak frequencies represent the resonance frequencies of the sprung mass and the unsprung mass frequencies, respectively. The HESA energy recovery system may relieve the suspension effect so that the resonance frequency of the sprung mass shall be decreased correspondingly. Since the tire stiffness is much more than the suspension stiffness, the resonance frequency of the unsprung mass does not change significantly.

In contrast, the damping characteristics of a traditional shock absorber are given in Table 9. Based on the optimal parameters, different damping characteristic curves may be obtained under various battery load currents, as in Fig. 15. In comparison with the traditional shock absorber, the HESA may be utilized to control the recovery resistance by adjusting the load current, which is an important measure to perform control of the HERS.

Fig. 15Damping characteristic curves of HESA