履带式车辆黏弹性悬架分数阶模型及其减振效果分析

Fractional order model of viscoelastic suspension for crawler vehicle and its vibration suppression analysis

为了准确掌握黏弹性悬架减振效果及参数影响规律,针对传统整数阶黏弹模型的不足,引入分数阶Kelvin-Voigt模型,建立了考虑结构几何参数的分数阶黏弹性悬架动力学模型,利用Grumwald-Letnikov分数阶导数定义及矩阵函数理论推导出动力学方程数值解。以某型履带拖拉机为例,利用所提模型分析了其黏弹性悬架减振性能,并进行了参数分析,包括黏弹性悬架黏弹件径厚比、分数阶次和激励频率。结果表明,该型悬架具有较好的减振效果,尤其在系统固有频率处效果显著;径厚比与减振效果负相关,分数阶次与减振效果正相关。该研究成果为大功率重载履带黏弹性悬架的开发提供相应的理论基础。

Viscoelastic suspension is a newly applicable suspension for a large power and heavy crawler vehicle. The viscoelastic suspension can support a heavy load efficiently when walking and working on the offroad, raise the adhesion property of a vehicle, and decrease the impact vibration level of the vehicle. The suspension consists of a metal part and viscoelastic material which are spaced and arranged to notably control vibration by transforming vibration energy into thermal energy to dissipate it into the air due to the hysteretic characteristic of viscoelastic materials. To predict and accurately study the dynamic behavior of viscoelastic suspension and evaluate its vibration damping capability, fractional calculus was introduced because of the facts that the fractional calculus exhibits global correlation and data-fitting well when describing theological phenomenon. In this context, a fractional order Kelvin-Voigt model considering the geometric factors i.e. A radius-thickness ratio incorporated into a dynamic model of viscoelastic suspension for crawler vehicle was established. In this model, the viscoelastic part was represented by a parallel-combination of a spring whose stress is in direct proportion to the strain and a spring pot whose stress is in direct proportion to the fractional derivative of the strain differentiating from the conventional damping pot with stress being proportional to the first derivative of the strain. A numerical solution was obtained by adoption of a Grumwald-Letnikov fractional derivative definition and a matrix function theory and its calculating codes were programming in Matlab. A history correlation coefficient was achieved to embody the afore-history influence of the viscoelastic suspension on its dynamic behavior. Parameters of a fractional model was acquired by fitting data using a least-square method based on a viscoelastic material tensile test carried out on a Testometric M350-10kN according to GB/T 528-1998 and GB/T 9865.1. For a pragmatic study case, a heavy crawler tractor installed with 8 viscoelastic suspensions was considered to analyze its vibration control effect by establishing its fractional model. Also the parameter influence on the vibration control effect, including exciting frequency, fractional order, and ratio of radius to thickness, was examined. The results showed that, compared with rigid suspension, the viscoelastic suspension exhibited remarkable vibration control capability, especially at the resonant frequency of about 4.5 Hz by reducing the response magnitude of the vehicle body by 64.10% in max value and 66.40% in RMS, thus satisfying the supporting and stable demands of the crawler tractor walking and working on the offroad. Radius-thickness has a negative influence on the response magnitude of viscoelastic suspension, that is to say there is an effective way to reduce the vibration by introducing a geometry-modified viscoelastic suspension with higher thickness and lower action aero. Fractional order, however, exhibits a positive correlation to the behavior of the response magnitude, which inspires another valid method of altering the viscoelastic material parameter to perfect the vibration of the crawler tractor. The history-dependent factor gives evidence of the long range correlation of the fractional model, i.e., the system response at current time relates to the whole history whose influence increases with time closer to the current time. This research provides an essential theoretical basis for multi-objective optimization and dynamic design of a viscoelastic suspension for a higher power and heavy load crawler vehicle. Experiment study is an essential procedure as a further study. So our future work will stress the indoor test of a dynamic mechanical analysis （DMA） of viscoelasitc materials, deriving a fractional constitutive model considering the temperature-frequency effect of viscoelastic material, and carrying out an in-situ test of a real crawler vehicle establishing a different-parameter viscoelastic suspension to investigate stable/dynamic stiffness, fatigue features, and vibration control capability under working conditions of cutting, pulling, digging, and crossing over an obstacle.