### Analysis of the influence of the installation angle on the stiffness

The stiffness of the composite leaf spring is determined by the mechanical properties of each single-layer plate and affected by factors such as volume content of fiberglass, number of layers, laying angle and working temperature. In order to analyze the influence of the installation angle on the stiffness of the composite leaf spring, specimens 1, 2 and 3 were selected for stiffness comparison tests. The results of the stiffness tests are shown in Fig. 4.

Figures 4a-c show the stiffness curves of composite leaf springs with different lay angles when the glass fiber volume content is 60%. The curves show that the fiber lay angle has a significant effect on the stiffness of the composite leaf spring. The area bounded by the hysteresis loop is the work done by the applied load, which decreases with increasing pose angle. Under the same travel conditions, the larger the area, the greater the stiffness of the composite leaf spring. The stiffness of specimens 1, 2 and 3 is 118.3 N/mm, 87.8 N/mm and 70.3 N/mm respectively. When the laying angle is 0°, the stiffness is maximum, when the laying angle is 90°, the stiffness is minimum.

Figure 5 is the simulation and experimental curves of the leaf spring with different laying angles. When the laying angle is 0°, the agreement between the static stiffness test result and the static stiffness simulation result is 98.5%, when the laying angle is 45°, the agreement between the static stiffness test result and the static stiffness simulation result is 98.5%. The agreement is 96.3% and when the angle of exposure is 90°, the agreement is 95.8%. The comparison results show that the finite element model of the composite leaf spring is correct. The dynamic stiffness of the leaf spring is greater than the static stiffness, and the difference between the two data increases with the increase in the bending angle. Experimental data and simulation data show that when the volume content and the number of layers are constant, the larger the angle of lay, the lower the stiffness, and it has a nonlinear decreasing relationship with the angle of laid.

### Analysis of the influence of glass fiber volume content on stiffness

For a composite leaf spring with a bend angle of 0°, the glass fiber volume content mainly affects the longitudinal tensile modulus. The higher the volume fraction of fibers, the higher the longitudinal tensile modulus and the higher the stiffness of the leaf spring. In order to quantitatively analyze the relationship between the stiffness of the composite leaf spring and the volume content of glass fiber, specimens 1, 4 and 5 were selected for stiffness comparison tests. Figures 6a-c show the stiffness curves of composite leaf springs with different fiber volume contents when the lay angle is 0°. The stiffnesses of specimens 4, 1 and 5 are respectively 95.7 N/mm, 118.3 N/mm and 137.1 N/mm. When the volume content of fibers is 40%, the stiffness is minimum, when the volume content of fibers is 80%, the stiffness is maximum.

Figure 7 is the simulation and experimental curves of leaf spring with different volume content. When the volume content is 40%, the agreement between the static stiffness test result and the static stiffness simulation result is 92.5%, when the volume content is 60%, the agreement is 98.5% and when the volume content is 80%, the agreement is 93.5%. The dynamic stiffness of the leaf spring is greater than the static stiffness, and the difference between the two data decreases with increasing volume content. Experimental data and simulation data show that when the lay angle and the number of layers are constant, the larger the volume content, the higher the stiffness, and there is a linear increasing relationship with the fiber volume content .

### Analysis of the impact of the installation angle on damping

Specimens 1, 2 and 3 were installed between the rear axle and the frame, and the rear suspension shock absorbers were removed, and the leaf spring damping test was carried out. Figures 8a-c show the free vibration attenuation curves of the composite leaf spring. The amplitude of adjacent cycles does not change much, indicating that the damping of the composite leaf spring is weak. The damping coefficients of specimens 1, 2 and 3 are respectively 0.024, 0.031 and 0.044. The damping coefficient of the leaf spring with 0° layer is the smallest, and the damping coefficient of the leaf spring with 90° layer is the largest.

Fiber lay angles affect the overall stiffness, interlaminar friction, and shear properties of laminates. When the stiffness of the composite leaf spring is too large, the deformability of the polyurethane will be affected and the relative sliding between the reinforcement and the matrix will be hindered, thus reducing the damping characteristics of the composite leaf spring.^{23.24}. Sample 1 is placed at 0°, the layer of fibers plays the main role of support and the stiffness of the leaf spring is the greatest. Under the same external load, the composite leaf spring consumes less vibration energy and has the smallest damping coefficient. The specimen 5 is placed at 90° and the polyurethane layer acts as the main support, which results in the lower stiffness of the leaf spring. Under the same external load, the composite leaf spring consumes more vibration energy and has the largest damping coefficient.

Figure 9 shows the leaf spring damping contrast curves with different laying angles. When the exposure angle is 0°, the agreement between the test result and the simulation result is 93.8%, when the exposure angle is 45°, the agreement is 96, 6% and when the exposure angle is 90°, the agreement is 95.0%. Experimental data and simulation data show that when the fiber volume content and the number of layers are constant, the larger the laying angle, the higher the damping coefficient of the composite leaf spring, and it has an approximate linear growth relationship with lay angles.

### Analysis of the influence of glass fiber volume content on damping

Specimens 1, 4, 5 were selected for damping tests. Figures 10a-c show free vibration attenuation curves of composite leaf spring specimens. The damping coefficients of specimens 4, 1 and 5 are respectively 0.032, 0.024 and 0.0197. When the fiber volume content is 40%. The damping coefficient of the leaf spring is the largest. When the fiber volume content is 80%, the damping coefficient of the leaf spring is the smallest.

The main damping contribution of the composite leaf spring comes from the polyurethane matrix. Polyurethane is viscoelastic. When a force is applied to the leaf spring, the polyurethane matrix undergoes tensile deformation, bending deformation and shear deformation, which consumes vibration energy to achieve the vibration reduction effect. The higher the glass fiber volume content, the lower the polyurethane content, the worse the viscoelasticity of the composite leaf spring, and the lower the damping coefficient.

Figure 11 shows the damping contrast curves of leaf springs with different volume contents. When the volume content is 40%, the agreement between the test result and the simulation result is 95.5%, when the volume content is 60%, the agreement is 94.1% and when the volume content is 80%, the agreement is 93.4%. Experimental data and simulation data show that when the laying angle and the number of layers are constant, the higher the fiber volume ratio, the lower the damping coefficient. However, when the fiber volume content increases to a certain extent, the influence of the fiber volume content on the damping coefficient of the composite leaf spring will become insignificant.