Influence of semi-trailer truck operating conditions on road surface friendliness

2.1. Full vehicle dynamic model

A 5-axle semi-trailer truck with a dependent suspension system for the front axle and a walking beam suspension system for the rear axles are selected for the consideration of road-friendliness. A semi-trailer truck dynamic model with 14 degrees of freedom is established for analyzing the influence of semi-trailer truck operating conditions on road-friendliness, as shown in Fig. 1.

In Fig. 1, $K_{ij}$ are the suspension stiffness coefficients; $C_{ij}$ are the suspension damping coefficients; $K_{Tkj}$ are the stiffness coefficients of tires; $C_{Tkj}$ are the damping coefficients of tires; $M_1$ and $M_2$ are the sprung mass of the tractor and trailer, respectively; $m_{Ai}$ are the unsprung mass of the front axles, respectively; $l_n$ and $b_m$ are the distances; $z_{ai}$ and $z_{bm}$ are the vertical displacements at the centre gravity of the axles tractor and trailer; ${\theta }_k$ are the angle deflection at the centre gravity of the axles, tractor and trailer; ${\phi }_h$ are the angle deflection at the centre gravity of tractor and trailer; $v$ is the speed of vehicle; ($i=$1, 2, 3; $j=r$, $l$; $k=$1, 2,…, 5; $n=$1, 2,…, 10; $m=$1, 2; $h=$1, 2, 3, 4).

A combined method of the multi-body system theory and D’Alembert’s principle is chosen in this study. The general dynamic differential equation for 5-axle semi-trailer truck is given by the following matrix form:

where $M$, $C$, $K$, $C_T$ and $K_T$ are the mass matrix of the vehicle, damping matrix of the suspension system, stiffness matrix of the suspension system, damping matrix of the wheel system and stiffness matrix of the wheel system, respectively; $z$ is the vector of displacement; $Q$ is the vector of excitation of road surface.

Fig. 1Vehicle and air suspension system dynamic model

a) Side view

b) Front view

2.2. Road surface roughness

The random excitation of road surface roughness can be represented with a periodic modulated random process. The general form of the displacement PSD of the road surface roughness is determined by the experimental formula [5]:

where space frequency $n$ is the reciprocal of the wavelength $\lambda$. It means wave numbers in a meter. $n_0$ is reference space frequency, it’s defined as 0.1 m^-1. $S_q\left(n\right)$ is PSD of road surface under the reference space frequency $n_0$ known as the road surface roughness coefficient and $\omega$ is the frequency index which decides the frequency configuration of PSD of road surface $(\omega =$ 2$)$.

The road surface roughness is assumed to be a zero-mean stationary Gaussian random process. It can be generated through an inverse Fourier transformation:

where ${\varphi }_i$ is random phase uniformly distributed from 0 to 2$\pi$.

In this study, typical road surface roughness is adopted according to the standard ISO 8068 [6] and the simulation results of the typical road surface roughness are shown in Fig. 2.

Fig. 2Typical road surface roughness according to the standard ISO 8068

a) Level B

b) Level C

c) Level D

d) Level E

4.1. Effect of road surface roughness

In order to analyze the influence of the road surface roughness on the tire dynamic load, dynamic load coefficient and road -friendliness, five road surface conditions from level A (very good) to level E (very poor) in ISO/TC 80686 have been considered as inputs to the vehicle-road coupled model when vehicle moves with a velocity of 20 m/s and fully loaded. The dynamic left tire loads acting on road surface at 2nd axle and the values of the left tire dynamic load coefficients of 1st axle, 2nd axle, 3rd axle, 4th axle and 5th axle when vehicle moves on five different road surface conditions are shown in Fig. 3 and Fig. 4.

Fig. 3Dynamic left tire loads acting on road surface at 2nd axle with two different road conditions

Fig. 4Effect of road surface roughness

Fig. 3 could be determined the $F_{T2l,RMS}$ values of the 2nd axle when vehicle moves on the average road surface condition (level C) to very poor road surface condition (level E). The $F_{T2l,RMS}$ value of the 2nd axle increases 3.13 times when the road condition is very poor for the specific case of 5-axle semi-trailer truck with a velocity of 20 m/s and full loaded. Fig. 4 shows that the DLC values of the five different axles increase quickly when vehicle moves on the poor road surface conditions and that makes the negative effects on the road surface. When the vehicle changing road surface condition moves on the average road surface condition (level C) to poor road surface condition (level D) and then to very poor road surface condition (level E), the DLC values of the 3rd axle increase from 23.97 %, and 34.88 %. Therefore, the road surface condition of level D (the DLC value ≤ 3.0) is chosen as the intervention limit for road surfaces. In this case, traffic management need to intervene quickly to give a safe speed limit for vehicle when it moves on these roads and need to repair the road surface. To improve the safety of movement and reduce the negative impact on the road surface, this study proposes that the speed limit for 5-axle semi-trailer truck is $v_{max}\le$ 12.5 m/s for the road surface condition of the ISO level D, $v_{max}\le$ 8.3 m/s for the road surface condition of the ISO level E.

4.2. Effect of vehicle speed

The vehicle speeds of 5 m/s, 7.5 m/s, 10 m/s, 12.5 m/s, 15 m/s, 17.5 m/s, 20 m/s, 22.5 m/s, 25 m/s, 27.5 m/s, 30 m/s and 32.5 m/s were considered to analyze the influence of vehicle speed on the tire dynamic load, dynamic load coefficient and road friendliness when vehicle moves on the road surface condition of the ISO level B and full loaded. The dynamic left tire loads acting on road surface at 3rd axle and the values of the left tire dynamic load coefficients of 1st axle, 2nd axle, 3rd axle, 4th axle and 5th axle when vehicle moves on the different vehicle speed are shown in Fig. 5 and Fig. 6.

As can be seen from Fig. 5, the $F_{T3l,RMS}$ values of the 3rd axle when vehicle moves on the good road surface condition (level B) with $v=$10 m/s and $v=$20 m/s are determined by 1533.7 N and 1958.8 N, respectively and increased by 27.7 %. Fig. 6 shows that when vehicle speed value is $v\ge$22.5 m/s, the DLC values increase the most quickly in the direction of the un-friendly road surface. Therefore, the vehicle speed values $v\le$22.5 m/s is chosen as the road-friendly limit of driving speed for 5-axle semi-trailer truck when vehicle moves on the good road conditions and full loaded.

Fig. 5Dynamic left tire loads acting on road surface at 3rd axle with two different velocity conditions

Fig. 6Effect of vehicle speed

4.3. Effect of vehicle load

Vehicle load not only affects the durability of the part of vehicle, but also affects the fatigue life of road surface. In order to the influence of the vehicle load on road surface damage, the load values of 5-axle semi-trailer truck which include 25 % loaded, half loaded, 75 % loaded, fully loaded, over 25 % loaded and over 50 % loaded are discussed when vehicle moves on the road surface condition of the ISO level B at a velocity of 20 m/s. The dynamic left tire loads acting on road surface at 3rd axle and the values of the left tire dynamic load coefficients of 1st axle, 2nd axle, 3rd axle, 4th axle and 5th axle when vehicle moves under the different vehicle load at the velocity of 20 m/s are shown in Fig. 7 and Fig. 8.

From Fig. 7, we can see that the amplitude values of the maximum vertical dynamic left tire force of the 3rd axle when vehicle operates under vehicle load of 50 %, 100 % and 150 % are determined by 7893.4 N, 7827.5 N and 7459.1N, respectively and increased by 0.84 % and 4.94 %, respectively. Fig. 8 shows that the DLC values of all axles of vehicle increase most quickly when vehicle operates under 25 % loaded condition and half loaded condition which it has impact negatively on road surface and has no benefit to the durability of the part of vehicle and the safe movement of vehicle.

Fig. 7Dynamic left tire loads acting on road surface at 3rd axle with three different loading conditions

Fig. 8Effect of vehicle load