**1. Introduction**

Since the issue of energy depletion was raised, energy harvesting technology has received extensive attention [1–3]. In the automotive industry, extensive research and applications, including braking energy harvesting [4], exhaust thermo-electric recovery [5] and suspension vibration energy recovery [6–8], have also been conducted. Among them, braking energy recovery were gradually applied in electric vehicles. Considerable research has been carried out on energy harvesting suspensions. Zuo et al. [9] proved that the harvestable power in the suspensions of a middle-sized vehicle was 100–400 W, when driven at 60 mph on good and average roads. Zhang et al. [10] harvested 46 W from the suspension system of a passenger car. The research indicated that the energy harvesting suspension is feasible in theory and practice.

Among all traffic accidents, a large number of accidents are due to vehicle rollovers. It is reported that over one-third of 4WD fatalities involved rollover [11]. A percentage of 18.9 of rollover-related fatal crashes happened in the year of 2014 in the United States [12]. Suspension systems play a key role in reducing vehicle roll rates, and superior suspensions can greatly reduce the vehicular rolling propensity. Hydraulic interconnected suspension (HIS), with lower cost and easier structure than semi-active and active suspensions, was

**Citation:** Guo, S.; Chen, L.; Wang, X.; Zou, J.; Hu, S. Hydraulic Integrated Interconnected Regenerative Suspension: Modeling and Characteristics Analysis. *Micromachines* **2021**, *12*, 733. https:// doi.org/10.3390/mi12070733

Academic Editors: Kai Tao and Yunjia Li

Received: 13 May 2021 Accepted: 18 June 2021 Published: 22 June 2021

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verified to be useful in reducing the roll rate [13] and, thus, became a potential alternative to the transmission of conventional suspensions.

To simultaneously enhance the vehicle safety and harvest energy, novel suspensions, which combine energy regeneration and hydraulic interconnection features, have been proposed recently and are of great value to the automotive industry.

## *1.1. Interconnected Suspensions*

The "interconnected" idea of suspension was initially proposed by Hawley in 1927 as "oil pipe interconnected shock absorber" [14]. Since then, various layouts of interconnected suspension and research on the corresponding modeling have been carried out. At present, the main layouts of hydraulic interconnected suspensions are anti-roll [15], anti-pitch [16], anti-bounce and diagonal layout [17], etc. Among them, the most widely studied one is the anti-roll interconnected suspension, whose modeling is highlighted here.

Zhang et al. [18] proposed a frequency domain method to study the hydraulic interconnected suspension system, derived the coupled frequency-related equations and obtained the free vibration solution and frequency response function of a half-vehicle system. Wang et al. [19] did further research. He applied this method to a 7-degree-of-freedom model and studied the effects of several parameters on the roll, pitch and bounce modes of the vehicle. The results were verified by vehicle drop tests. Wang et al. [20] indicated that the HIS system can improve the vehicle stability in both roll and lateral aspects. Ding et al. [16] extended the application of the HIS system to tri-axle trucks, and the modal analysis results indicated that the HIS system can reduce the pitching motion of the sprung mass while maintaining smoothness.

Time-domain analyses on interconnected suspensions have also been conducted. Zhang et al. [21] proposed a new damper for hydraulically interconnected suspension. The AMESim model of hydraulic interconnected suspension was established and simulated. The results showed that the setting time and the overshoot were, respectively, reduced by 42.2 and 14.7%, and the largest roll angle and steady roll were, respectively, decreased by 9.9 and 5.9◦ . Wang et al. [22] derived the vehicle dynamics model of the hydraulically interconnected inertial device-spring-damper suspension (HIISDS). Two road excitations were used to verify the effectiveness of the suspension. Cao et al. [23] developed a generalized 14 degree-of-freedom nonlinear vehicle model to evaluate the vehicle dynamics of the interconnected suspension. The results showed that the coupled hydro-pneumatic suspension had considerable potential in enhancing the ride comfort and anti-roll/pitch performances.

The existing modeling methods of the mechanical–hydraulic coupled vehicle systems were either in time domain [21–23] or in frequency domain [18–20]. The frequency-domain modeling research mostly utilized the transfer matrix method to evaluate the impedance matrix of the hydraulic subsystem. With the model in the frequency domain, the modal analysis of the system could be performed and the system's own characteristics could be analyzed. The corresponding results disclosed a good agreement with experiments [19].

#### *1.2. Energy Harvesting Shock Absorbers*

Researchers noticed the energy-dissipating nature of shock absorbers and began to study energy harvesting shock absorbers [24,25]. The number of publications per year on energy regenerative shock absorber has been exponentially increased over the last decade [26], including piezo-electric [27] and electromagnetic [28,29] energy harvesting techniques. Among all the energy harvesting shock absorbers, the hydraulic energy harvesting shock absorber was put into the application earlier than other types, attributable to its relatively simple structure [30]. Wu et al. [31] established a mathematical model of the hydraulic energy regenerative shock absorber and conducted a series of bench tests. The results showed that the peak recovery power reached 505.52 W, and the recovery efficiency was 14.5%. Samn et al. [32] designed a hydraulic regenerative shock absorber and demonstrated that it cannot only collect part of the wasted energy in the suspension system, but also improve the vehicle ride comfort and road holding. Fang et al. [33] presented

a hydraulic electromagnetic energy-regenerative shock absorber and demonstrated that the damping force varied with the magnitude of the load current. Guo et al. [34,35] demonstrated the method and steps for the size matching and parameter setting of the hydraulic components in the hydraulic electromagnetic energy-harvesting shock absorber (HESA) system. Test results indicated that the proper matching of the parameters can make the HESA system work efficiently and improve the energy conversion efficiency. Peng et al. [36] applied the HESA in a commercial vehicle suspension and indicated that the root mean square energy regenerative power were 41.72 and 339.88 W on Class-B and Class-C roads at speeds of 30–70 km/h.
