## 2 Model Establishment and Analysis
### Strength Analysis of the Fifth Wheel Under Pavement Excitation  
#### 2.5.1 Establishment of Time Domain Model Based on White Noise Pavement Roughness  
Pavement roughness refers to the displacement of the actual pavement surface relative to the reference plane, and it is also known as random excitation of the pavement surface. Due to the unevenness of the pavement, the tractor tires experience vertical oscillations during driving. The resulting impact forces are transmitted from the tires to the suspension, fifth wheel, and semi-trailer compartment, causing stress and deformation in these components.  
According to the \"Mechanical vibration-pavement pavement spectrum measurement data report\" issued in 2005, the pavement power spectral density can be expressed as:  
\[G_{q}(n)=G_{q}(n_{0})\bigg{(}\frac{n}{n_{0}}\bigg{)}^{-\omega} \tag{3}\]  
In Equation (3), \(n\) is the spatial frequency, which is the reciprocal of the wavelength, where the units are m\({}^{-1}\); \(n_{0}\) is the reference spatial frequency, usually set to 0.1 m\({}^{-1}\); \(G_{q}(n_{0})\) is the power spectral density of the pavement surface under the reference spatial frequency, also known as the pavement roughness coefficient, which is m\({}^{3}\); and \(\omega\) is the frequency index, which determines the frequency structure of the pavement power spectral density, usually set to 2.  
According to the relevant standards, the pavement surface can be divided into eight grades, A-H, according to the pavement roughness coefficient \(G_{q}(n_{0})\), as shown in Table 8.  
According to statistics on relevant pavement conditions, the power spectrum range of expressway pavement falls between grades A and C, with grades B and C accounting for a significant proportion. Among these, the C-grade pavement spectrum is larger than  
Figure 5: The fatigue life distribution diagram of the original fifth wheel under condition 3.  
that of B-grade pavement. Therefore, this study focuses on establishing and simulating the pavement roughness model for C-grade pavements.  
In this study, the first-order band-limited white noise filtering method was used to establish a random pavement excitation model. The time pavement excitation signal is expressed as:  
\[\dot{q}(t)=2\pi n_{0}\cdot\sqrt{\text{G}_{q}(n_{0})v}\cdot\omega(t)-2\pi f_{0} \cdot q(t) \tag{4}\]  
In Equation (4), \(q(t)\) is the pavement random excitation signal; \(\text{G}_{q}(n_{0})\) is the pavement roughness coefficient, with a C-grade pavement surface value range of \(1.28\times 10^{-4}\) m\({}^{3}\)-5.12 \(\times\)\(10^{-4}\) m\({}^{3}\) and a geometric mean of \(2.56\times 10^{-4}\) m\({}^{3}\); \(v\) is semi-trailer velocity, set to 60 km/h, which is 16.7 m/s; \(\omega(t)\) is the Gaussian white noise signal with a mean value of 0; and \(f_{0}\) is the lower cutoff frequency, set to 0.0628 Hz.  
The simulation analysis was performed using Simulink (R2020a) with a sampling time of 0.001 s. The time-domain simulation model of pavement unevenness is shown in Figure 6, and the random pavement excitation signals obtained from a 30 s simulation are shown in Figure 7. The height range of the C-grade pavement fluctuations was within \(\pm\)0.04 m.