## 1 Introduction  
The suspension system of multi-axle trucks is an important component that affects the driving performance of vehicles. In previous studies, the optimization and control of truck suspensions mainly targeted road-friendliness, ride comfort, and steering stability [1; 2; 3], but not enough attention has been paid to an important performance index that affects the safety of the road traffic, namely, the dynamic load-sharing performance of the multi-axle groups. The dynamic load-sharing performance of the multi-axle groups refers to the ability to distribute the load evenly between the axles within the multi-axle groups during driving [4]. Favorable dynamic load-sharing can reduce the peak forces from tires: on the one hand, it can prevent tire blowout caused by single-axle overloading and the braking failure caused by load transfer during braking; on the other hand, it is closely related to the road-friendliness, able to delay the occurrence of ruts, cracks, looseness, pits, and peeling on roads [5]. Therefore, the dynamic load-sharing of multi-axle trucks is a comprehensive index covering driving safety and road-friendliness. Load-sharing is relatively weak for leaf springs (usually employing centrally pivoted walking beams, trunnion shafts, etc.) and unconnected air suspensions of multi-axle trucks [6; 7]. To address this issue, an Australian design for longitudinal-connected air suspensions connects the air springs in the axle groups on the same side through larger-than-industry air lines and connectors so that air could be exchanged between air bags more readily. This kind of suspension not only has a damping effect similar to that of air suspension with additional air chambers, but also, when applied to the multi-axle groups of tractors or semi-/full-trailers, can have the air bag force transferred rapidly between different axles through the air lines and connectors, thus effectively improving the load-sharing of vehicles [8]. Many on-road tests have been performed to analyze the performance of the longitudinal-connected air suspension. The Organization for Economic Co-operation and Development (OECD) indicated that the load-sharing coefficient (an indicator for load-sharing capacity) of multi-axle trucks in western countries ranged from 0.904 to 0.925 [9]. Studies commissioned by the National Road Transport Commission of Australia found that installation of larger air lines on multi-axle air suspension increased longitudinal air flow between air springs on adjacent axles [10]. The Queensland Department of Main Roads discovered that improvements in dynamic load-sharing coefficient (_DLSC_) of 4-30% for a tri-axle coach and 37-77% for a tri-axle semi-trailer were obtained by altering the conventional-sized longitudinal air connection (three 6.5 mm inside diameter connectors connecting 6.5 mm inside diameter air lines) to a larger air connection (three 20 mm inside diameter connectors at the air springs connecting 50 mm inside diameter air lines) [8]. However, due to the limitations of on-road tests, only vehicle speed and a limited number of air connections were considered in most tests, such that the effect of some other factors, e.g., the static absolute air pressure of the air spring, static height of the air spring, and load-sharing, were not able to be taken into account. Limitations of on-road tests can be addressed by developing realistic models of connected air suspension. [PERSON] et al. developed a 4-degrees-of-freedom (DOF) half-vehicle model and compared the transferring characteristics between the laterally interconnected and non-interconnected air suspension. It was found that the laterally interconnected air suspension could significantly decrease the amplitude of roll angle [11]. [PERSON] et al. developed an 8-DOF mathematical model of a car with laterally interconnected air suspension [12; 13]. It is indicated that these suspensions outperformed unconnected suspensions in terms of vibration isolation and torsion elimination.