# Design and Stability Analysis of Six-Degree-of-Freedom Hydro-Pneumatic Spring Wheel-Leg
## 1 Introduction
The authors of [20] designed a suspension configuration that elastically connects the in-wheel motor to the wheel support shaft using rubber bushings. By establishing a dynamic model of the in-wheel motor suspension with actuators, the smoothness of vehicle driving and tire grounding have been improved. The authors of [21] designed a suspension configuration with an in-wheel motor electric wheel featuring a motor stator suspension by establishing a vehicle dynamics model of the damper and optimizing the stiffness and damping coefficients of the rubber bushings in the damper system with the objective function being the acceleration response values of the motor stator and vehicle center of mass. The authors of [22] analyzed the structure and vertical vibration characteristics of in-wheel motor electric vehicles and designed a vibration damping mechanism to transfer the motor stator mass to the sprung mass, thereby reducing vertical vibrations during vehicle operation. The above literature review indicates that current research has mainly addressed the vertical vibration issues of in-wheel motor-driven vehicles. Various in-wheel motor suspension system configurations were designed, system parameters were optimized through intelligent algorithms or parameter optimization models, and the enhancement of ride comfort of vehicles was evaluated to verify the advantages of the designed configurations over the traditional configuration with regard to vertical vibration. In the present study, given the significant technological changes introduced by the in-wheel motor drive mode--particularly the dual in-wheel motor wheelset unit--we designed a new six-arm hydro-pneumatic spring suspension structure. It expands the single degree of freedom to six degrees of freedom, effectively resisting impact forces and torques from different directions. Therefore, it has high flexibility and good applicability. Combined with four tension springs, the suspension has strong self-stabilizing property within a certain range. The suspension and dual in-wheel motor wheelset unit are combined into an independent wheel-leg system, which not only has flexible driving functions, but also has the nonlinear damping characteristics of hydro-pneumatic springs. It can meet the application needs of different vehicles in various working environments. The structure of this article is arranged as follows: Section 1 introduces the characteristics of hydro-pneumatic springs and the significant technological changes brought about by in-wheel motor technology, which puts forward new design requirements for the configuration of in-wheel motor vehicle suspension systems. Section 2 explains the structural composition and functional characteristics of the designed suspension. Section 3 introduces the structure and working principle of the external single-chamber hydro-pneumatic spring; derives the mathematical formulas of the damping valve, accumulator, pipeline, and hydro-pneumatic spring; and establishes the simulation models of the hydro-pneumatic spring in Matlab/Simulink (R2018b). Section 4 studies the instability problem of hydro-pneumatic suspension in horizontal steering and obtains the relationship between torque and rotation angle. Section 5 summarizes the completed work in this article and points out the potential application of the hydro-pneumatic suspension.