## 1 Introduction  
The handling stability is one of the extremely important performances that affect the driving safety of trucks. How to obtain the strong handling stability for improving the driving safety is an important issue in vehicle design [1; 2; 3]. The suspension is an important system connecting the truck frame and wheel [4]. The leaf spring is the most widely used elastic element in the suspension system for trucks. Moreover, it plays a crucial role in the handling stability for trucks. At present, the lightweight design of trucks is of great importance to enhance the load capacity and reduce the production cost [5; 6; 7]. For leaf springs, the lightweight design of trucks is mainly reflected in replacing the multi-leaf spring with the taper-leaf spring, so as to reduce the trucks' weight, to improve the power performance, and to reduce the fuel consumption and the exhaust pollution [8; 9; 10]. In modern society, with the development of people's living standard, people have higher and higher requirements for the handling stability of trucks [11; 12; 13]. However, the changes of the handling stability after the replacement have not been revealed. Due to the advantages of light weight and low noise, the taper-leaf spring is more and more used in trucks. At present, scholars mainly focus on its dynamic property, stress, and strain. Moreover, most of the studies of its mechanical properties mainly were conducted by using simulation software packages, such as Ansys, Nastran, Abaqus, and Adams. [PERSON] et al. created the dynamic model of the tandem suspension equipped with the taper leaf spring for trucks based on Adams software [14]. In order to research the stress of a taper leaf spring, [PERSON] et al. established a flexible multi-body dynamic model [15]. [PERSON] et al. proposed a calculation method of the stiffness of the taper-leaf spring based on the combine superposition method and the finite difference method [16]. [PERSON] et al. analyzed the mechanical properties of the taper leaf spring considering the friction between the leaf springs on the basis of the FE (Finite Element) contact analysis [17]. To improve the kinematics characteristics of a midsize truck, [PERSON] et al. selected the optimal combination parameters based on a vehicle model with a taper leaf spring [18]. Some scholars improved the performance of leaf springs from the perspective of materials. For example, [PERSON] et al. researched the high-temperature quality of the accelerated spheroidization on SUP9 leaf spring and the machining performance of Sup9 leaf spring can be significantly improved under high temperature [19]. [PERSON] et al. optimized the development of 56 SiCr7 leaf springs and micro-hardness measurements show surface degradation effects [20]. [PERSON] et al. optimized the key design parameters of EN45A flat leaf spring and the developed leaf spring program can be used to optimize various parameters of the leaf spring quickly and reliably [21]. [PERSON] proposed carbon/glass epoxy composite as a leaf spring material and analyzed the leaf spring by using Ansys software [22]. [PERSON] et al. proposed a new method on the basis of testing and simulation for the durability of leaf springs [23]. In their study, the finite element method and the multi-body simulation were used to calculate the fatigue life. Some scholars researched the fatigue life of leaf springs. For example, [PERSON] et al. proposed a method to predict the fatigue life of Z Type leaf spring and created an approach to validate the proposed method [24]. [PERSON] et al. researched the correlation of simulation, test bench, and rough road testing in terms of strength and fatigue life of a leaf spring [25]. [PERSON] et al. conducted the failure evaluation of a leaf spring eye design under various load cases [26] and this study provides a valuable reference for preventing the failure of leaf spring in engineering design. [PERSON] et al. carried out the fatigue analysis of leaf-spring pivots [27].