# Rubber Creep Model and Its Influence on Mounting Stiffness
## 4 Influence of Rubber Creep on Static and Dynamic Characteristics of Mount
### Influence of Rubber Creep on Dynamic Characteristics of Engine-Mounted Main Spring  
#### 4.3.1 Frequency Variation Characteristics of Engine-Mounted Main Spring  
The main spring of engine suspension is made of pure rubber. The dynamic characteristics of the main spring are described by the constitutive models of hyperelasticity and viscoelasticity. The hyperelastic parameters adopt the Mooney-Rivlin constitutive parameters [22]. The viscoelasticity involved is different from that of creep. In creep analysis, static viscoelasticity is used to describe the creep process, while dynamic viscoelasticity is used to describe the dynamic process of the main spring. In ABAQUS, there are two kinds of viscoelastic domain. One is a kind of viscoelastic time domain--a frequency domain of viscoelasticity; the other is a two-domain viscoelasticity defined through the Prony series, mounting the main spring dynamic characteristic analysis using frequency domain viscoelasticity. The Prony series needs inputs of \(g_{i}\), \(k_{i}\) and \(\tau_{i}\), three parameters (provided by the enterprise), as shown in Table 1.  
Main spring: the dynamic stiffness of the simulation analysis to set up for two-step analysis. One is a static general analysis step, and the other is a viscosity analysis step, in order to accurately calculate the main spring dynamic stiffness, loading in a way consistent with the actual working condition. The first step was analysis, with the main spring axial preload set to 1000 N; in the second step, the analysis applied a sine along the main spring axial displacement. Figure 12 shows the sinusoidal displacement loading function.  
\[x=A\sin(\omega t) \tag{11}\]  
\[\omega=2\pi f \tag{12}\]  
\begin{table}
\begin{tabular}{c c c c} \hline _prony_ & \(g_{i}\) & \(k_{i}\) & \(\tau_{i}\) \\ \hline  & 0.1954 & 0.0401 & 0.5737 \\  & 0.14 & 0.0035 & 0.019 \\  & 0.0604 & 0.004 & 0.000303 \\ \hline \end{tabular}
\end{table}
Table 1: Dynamic viscoelastic parameters.  
Figure 11: Displacement cloud diagram of the suspended structure. (**a**) Non-creep displacement cloud map. (**b**) 2.98 mm creep displacement cloud map. (**c**) Creep displacement cloud map of 3.83 mm.  
In the formula, the frequency \(f\) is taken as 1-49 Hz, and the frequency is taken once every interval. A represents the vibration amplitude, and the value is 1. Under the condition of no creep, 2.98 m creep and 3.83 mm creep, the dynamic stiffness simulation analysis of the suspended main spring is carried out, and the corresponding dynamic stiffness value of each frequency point is obtained, in N/m. The calculation results of dynamic stiffness of three kinds of creep suspension main springs are drawn into a curve, as shown in Figure 13. According to the curve, when the creep is constant, the dynamic stiffness of the suspension main springs increases with the increase of frequency, and when the frequency is 1-15 Hz, the increase rate of dynamic stiffness is relatively large, and then the dynamic stiffness increases slowly. When the frequency is constant, the dynamic stiffness of the suspended main spring increases with the increase of creep, and when the creep increases from 0 to 2.98 mm, the dynamic stiffness value increases greatly. For example, when the frequency is 15 Hz, the corresponding dynamic stiffness of the suspended main spring without creep, 2.98 mm creep and 3.83 mm creep are 287.2 N/mm and 322.0 N/mm, respectively. When the creep variable increases from 0 mm to 2.98 mm, the dynamic stiffness increases by 12.1%, and when the creep variable increases from 0 mm to 3.83 mm, the dynamic stiffness increases by 15.0%.  
Figure 12: Displacement loading function.  
Figure 13: Dynamic stiffness curves of suspension main springs under different creep conditions.