Analysis of Operating Safety of Tractor-Trailer under Crosswind in Cold Mountainous Areas

Abstract

To investigate the driving safety of tractor-trailers under extreme conditions in cold mountainous areas, this paper used numerical simulation software to construct a driving scenario of cold mountainous road, to simulate and analyze the driving safety of tractor-trailers under different wind speed and driving speed conditions, and then the critical deriving speed for safe driving was obtained. Four main factors were considered: low adhesion coefficient, strong crosswind, road radius, driving speed, lateral acceleration, and vertical load-deflection rate (LTR) were selected as the main safety response indexes for the determination of sideslip and rollover. The results show that strong crosswinds have an obvious effect on the tractor-trailer sideslip, and the safe operating speed range of the tractor-trailer is from 0 to 30 km/h, with the value of safe driving speed decreasing as the wind speed increases; the speed range where sideslip occurs is from 30 to 37 km/h, with the dangerous driving speed also decreasing as the wind speed increases; accidents when the driving speed exceeds 38 km/h. In addition, simulation experiments show that tractor-trailers generally skid first without rollover on a combination of curved road sections with a low coefficient of adhesion and super-elevation. Finally, the driving simulator was used to test the driving conditions of the tractor-trailer on the cold curved slope combination section with different crosswind speeds, and the experimental results proved the validity of the simulation’s safe speed threshold.

1. Introduction

With the development of e-commerce, the demand for logistics transport is growing, and the tractor-trailer has a large loading capacity, so that it accounts for an increased proportion of cargo transport vehicles, but because of its high centre of gravity, large volume, and the interaction between tractor and trailer interactions, and other characteristics [1], when driving in the mountain highway, vulnerable to road alignment, crosswind and other factors. In particular, in the complex mountainous terrain, the crosswind has a significant acceleration effect impact [2,3], in addition to the low adhesion coefficient of snow and ice in winter, tractor-trailer driving safety hazards are great. In addition, once an accident occurs, the tractor-trailer will cause great economic losses, especially in mountainous sections, which will easily cause secondary accidents and traffic jams. According to the U.S. Department of Transportation Bureau of Hazardous Materials Safety, statistics show that each year the tank semi-trailer in the transport process led to traffic accidents of about 16,000–20,000 [4]; Chinese automobile safety transport accident statistics also show: the proportion of major traffic accidents due to lateral instability is around 90% [5]. Therefore, in order to reduce accidents or reduce the severity of accidents of tractor-trailers, their driving characteristics in complex environments need to be analyzed.

In terms of crosswinds affecting the operational safety factors of tractor-trailers, experts, and scholars have conducted research in terms of road conditions [6,7], crosswind conditions [8], and complex environments [9,10]. Tunay T et al. found that different road radio and wind deflection angles have the greatest impact on the safety of tractor-trailer driving in a conventional road environment [11].

In the early years, Baker et al. [12,13,14] investigated the safety of a range of vehicles travelling on roads in crosswind conditions, while defining three types of accidents due to wind based on analysis results: overturning, sideslip, and excessive rotation. Later, many scholars have studied different road environments through wind tunnel experiments, based on the studies of Baker et al. For example, Guo [15] found that compared with ordinary roads, tractor-trailers are more likely to have lateral instability on long-span bridges. Dorigatti et al. [16] conducted a series of wind tunnel tests on various large vehicles (a van, a bus, and a lorry) driving on long-span bridges. The results show that lorry has become the most affected by crosswinds because of the highest rolling moment coefficient. Xianzhi Liu [17] focused on the aerodynamic characteristics of different vehicles under different wind flow conditions (smooth flow, turbulent flow, and boundary layer flow) through a wind tunnel. The results show that the center of gravity of the vehicle will significantly affect the aerodynamic characteristics of the vehicle, and further point to the driving safety problem for large vehicles, such as heavy trucks.

BLYTHE W [18] analyzed the potential possibility of truck rollover by crosswind through complex modelling, and Chen Feng et al. conducted a series of studies on truck driving safety, for example, simulation-based single-vehicle accident evaluation models where extreme conditions, such as wind and snow are taken into account to predict the potential crash and injury risk of vehicles [19], a single vehicle safety index is introduced into the model to provide a reasonable assessment of accident risk by taking into account the uncertainty of key variables [20], after that, the driving safety of the truck platoon was considered and a safe driving model for the trucks platoon was developed [21]. The safety evaluation models already available have some reference significance for the analysis of truck-driving safety under crosswind conditions. In respect to mountain roads, experts and scholars have analyzed the safety of driving on mountain bridges under the influence of crosswinds [22], the stability of trucks in bridge-tunnel connection sections under crosswind environment [23,24,25], and the safety of trucks driving under crosswinds in complex linear road conditions in mountainous areas [26], all of which have analyzed the influence of different crosswind speeds on truck driving safety and given such suggestions as limiting vehicle speed, adding transition. The recommendations and prevention methods, such as limiting speed, and adding transition sections and wind shields on bridge and tunnel sections were given.

In summary, the analysis of the driving safety of tractor-trailers under the coupling effect of various influencing factors is still scarce, especially in the analysis of the operating safety and stability discrimination under comprehensive conditions, such as complex alignment in mountainous areas with crosswinds and low road adhesion coefficient, which still needs further research. Therefore, this paper applies TruckSim software to establish extreme environment scenarios in cold mountainous areas, to study the operational safety of tractor-trailers under the coupling effect of various factors, such as strong crosswind conditions, low adhesion coefficient and small radius of curvature, to analyze the influence of crosswind on the driving of tractor tractor-trailers under such extreme conditions, and to give the threshold values for the safe driving of tractor-trailers under complex conditions, so as to provide reference for traffic management control or research on operation stability control strategies for tractor-trailers. The rest of this paper is organized as follows. In Section 2, the model is built and simulated within TruckSim; in Section 3, the simulation results are presented and discussed and analyzed; in Section 4, the experimental validation of the driving simulator is carried out; and in Section 5, some conclusions and shortcomings are shown.

2. Construction of Tractor-Trailer Operation Scenario

2.1. Model of the Tractor-Trailer

The tractor model and the trailer four-axle model were built on Trucksim software which integrated speed control, steering, braking, variable speed, tires, suspension, aerodynamics, and other subsystems, shown in Figure 1. The tractor has one steering axle and one solid axle, the trailer has two solid axles, and the box payload is used instead of the cargo in the trailer. The parameters of the four-axle complete vehicle model are shown in

Table 1. Four axle box trailer and trailer vehicle parameters.

Name	Value	Unit
Lead unit sprung mass	4455	kg
Tractor size	6750 × 2438 × 3030	mm
Tractor wheelbase	4000	mm
Trailer sprung mass	5925	kg
Trailer size	10,000 × 2800 × 3200	kg
Trailer wheelbase	1300	mm
Load mass	21,340	kg
Load size	9000 × 2500 × 3000	mm

.

The vehicle is affected by the air force while driving on the road. According to the SAE Road Vehicle Aerodynamics Committee standard (Vehicle Aerodynamics Terminology J1594_201007), the location of the aerodynamic reference point for a tractor-trailer is shown in Figure 2, and the equations for the aerodynamic forces and aerodynamic moments to which it is subjected under the action of side winds are as follows.

$$\left\{\begin{array}{c}{F}_x=-C_{F_x}\left(\beta \right)AQ=-\frac{1}{2}{C}_{F_x}\left(\beta \right)A\rho v^2\hfill \\ F_y=-C_{F_y}\left(\beta \right)AQ=-\frac{1}{2}{C}_{F_y}\left(\beta \right)A\rho v^2\hfill \\ F_z=-C_{F_z}\left(\beta \right)AQ=-\frac{1}{2}{C}_{F_z}\left(\beta \right)A\rho v^2\hfill \\ M_x=-C_{F_x}\left(\beta \right)ALQ=-\frac{1}{2}{C}_{F_x}\left(\beta \right)AL\rho v^2\hfill \\ M_y=-C_{F_y}\left(\beta \right)ALQ=-\frac{1}{2}{C}_{F_y}\left(\beta \right)AL\rho v^2\hfill \\ M_z=-C_{F_z}\left(\beta \right)ALQ=-\frac{1}{2}{C}_{F_z}\left(\beta \right)AL\rho v^2\hfill \end{array}\right.$$

(1)

where, $\rho$ is the air density, this paper takes 1.206 $\mathrm{kg}/{\mathrm{m}}_3$; v is crosswind speed, m/s; $F_{\mathrm{x}}$ is the aerodynamic drag, $F_{\mathrm{y}}$ is the side force, and $F_{\mathrm{z}}$ is the aerodynamic lift, N; $M_{\mathrm{x}}$ roll moment, $M_{\mathrm{y}}$ is the pitch moment and $M_{\mathrm{z}}$ is the yaw moment, N/m; $C_{{\mathrm{F}}_{\mathrm{x}}}$ is aerodynamic drag coefficient, $C_{{\mathrm{F}}_{\mathrm{y}}}$ is lateral force coefficient and $C_{{\mathrm{F}}_{\mathrm{z}}}$ is lift coefficient; $\beta$ is the angle between the forward direction of the vehicle and the crosswind direction, that is, the aerodynamic slip angle, deg; A is the projected area of the vehicle, ${\mathrm{m}}^2$; L is the vehicle length, m.

Because of the structure of the tractor-trailer, compared with ordinary vehicles, the impact of the crosswind is more obvious, and its aerodynamic coefficient is also very different from that of ordinary vehicles, so it is necessary to measure its aerodynamic coefficient before analysing the impact of the crosswind. TruckSim provides the aerodynamic force coefficients and aerodynamic moment coefficients for tractor-trailer, as shown in Figure 3.

2.2. Road Model

According to the Design Specification for Highway Alignment (JTG D20-2017), a two-way, two-lane mountainous tertiary road with a radius of 60 m, a circular curve with a super-elevation of 5% and a longitudinal slope with a 5% composite alignment was established in TruckSim. The model and parameters are shown in Figure 4.

2.3. Crosswind Setup

The speed of the gale in the natural environment is between 62 and 74 km/h, which is generally unsteady wind; however, unsteady wind is extremely random and difficult to calculate and simulate. At the same time, the sudden turbulence of unsteady wind is often the factor that affects the operating stability the most, this research replaces the influence of unsteady wind conditions on vehicle operation by applying different gradients of constant wind. The experimental wind speed was set at 62 km/h, 68 km/h, and 74 km/h, respectively, covering the strongest, weakest, and intermediate wind conditions in windy weather. A crosswind parallel to the X-axis was applied at the bend, and due to the road alignment, the angle between the driving direction of the tractor-trailer and the crosswind direction gradually changed from 0° to 180°, and the wind direction reached 90° in the middle of the bend with the vehicle driving direction. The crosswind direction and the area of the road covered by the wind are shown in Figure 5.

2.4. Experimental Procedure

The purpose of this study was to analyze the driving safety of a tractor-trailer under strong crosswind in a cold mountainous section, so the tractor-trailer was designed to drive at a certain speed in a mountainous section with a coefficient of adhesion of 0.3, and the speed was set in the simulation test with reference to Equation (2).

$$\begin{array}{c}\hfill R_{min}=\frac{v_{\mathrm{c}}^2}{127({\mu }_{max}+i_{max})}\end{array}$$

(2)

where ${\mu }_{max}$ is the lateral force coefficient corresponding to the ultimate minimum radius and imax is the maximum ultra-high transverse slope. The values of the maximum lateral force coefficient and the maximum ultra-high cross slope for different driving speeds are shown in

Table 2. Ultimate minimum radius transverse force coefficient and ultra-high transverse slope values.

Design Speed (km/h)	120	100	80	60	40	30	20
${\mu }_{max}$	0.1	0.11	0.12	0.13	0.14	0.15	0.16
$i_{max}$(%)	8	8	8	8	8	8	8

.

Substituting the road radius $R=60$ m into the Equation (2) and looking up at the Table 2, could obtain the simulation conditions of the tractor-trailer limit maximum speed of 40 km/h, while the Design Specification for Highway Alignment (JTG D20-2017) standard provisions, in the mountain road section driving speed should not exceed 30 km/h. In order to investigate the driving safety of the tractor-trailer, if only the standard specified speed was simulated, many possible dangerous situations would be lost and no prevention could be provided for the possible danger, so the driving simulation speed was selected as 30 km/h, 40 km/h to study the operating stability of the tractor-trailer in extreme environment, and 35 km/h was added to transition.

When the tractor-trailer driving on the combination ramp, it would be affected by a side wind perpendicular to the x-axis with wind speeds of 62 km/h, 68 km/h, and 74 km/h, respectively, until it drove out of the curved combination section and stopped being affected by the side wind, while the wind deflection angle changed between [0, 180] degrees during the driving process. The vehicle was driven without speed control and gear shifting, and the stability and safe speed of the vehicle was analyzed by changing the vehicle’s speed and wind speed in the extreme linear section with a low coefficient of adhesion. The environmental conditions and speed conditions of the simulation experiment are shown in

Table 3. Simulation experiment condition parameters.

Simulation Conditions	Symbol	Value	Unit
Road radius	R	60	m
Superelevation	$i_{\mathrm{h}}$	5%	–
Longitudinal slope	$i_{\mathrm{l}}$	5%	–
Road adhesion coefficient	$\phi$	0.3	–
Wind speed	$v_{\mathrm{c}}$	62	km/h
		68	km/h
		74	km/h
Driving speed	$v_{\mathrm{w}}$	30	km/h
		35	km/h
		40	km/h

.

3. Analysis and Discussion of Driving Safety Results for Tractor-Trailers

3.1. Safety Quantitative Indicators

Usually, lateral-load transfer ratio (LTR) [27] refers to the ratio of the sum of the difference between the vertical loads of the left and right tires of the vehicle to the sum of the vertical loads of the vehicle, which can be judged by the formula:

$$\begin{array}{c}\hfill \mathrm{LTR}=\frac{\parallel {\sum }_i^n(F_{\mathrm{ri}}-F_{\mathrm{li}})\parallel }{{\sum }_i^n(F_{\mathrm{ri}}+F_{\mathrm{li}})}\end{array}$$

(3)

where $F_{\mathrm{ri}}$ is the vertical load of the right-hand wheel of the vehicle, $F_{\mathrm{li}}$ is the vertical load of the right-hand wheel, unit N, i denotes the i-th axle, n denotes the total number of axles, and ${\sum }_i^n(F_{\mathrm{ri}}+F_{\mathrm{li}})=m\mathrm{g}$, that is, the total mass of the load. LTR takes the value range of [0, 1], when the vehicle is stable driving without deflection, LTR = 0, when LTR = 1 the vertical load of a side wheel of the vehicle is 0, the vehicle is in the critical state of a rollover. In general, when LTR = 0.6, the vehicle has the risk of rollover, and LTR = 0.8 when the vehicle has the trend of a rollover. Vehicle rollover safety can be obtained by combining the rollover angle analysis.

Yaw rate $\omega$ and lateral acceleration $a_y$ are used to characterize the vehicle stability. If the vehicle acceleration and speed are known, the yaw rate can be calculated by formula $\omega =\frac{a_{\mathrm{y}}}{v_{\mathrm{c}}}$. If the vehicle speed and turning radius or curvature are known, the yaw rate $\omega$ can be calculated by the formula $\omega =v_{\mathrm{c}}\times cur$, where $cur$ is curvature. Under general conditions, when the yaw rate is less than 16.5 deg/s, the lateral stability is good, otherwise, it is poor.

The standard stipulates that the lateral acceleration of ordinary vehicles driving on the normal road should not exceed 0.4 g, and that of heavy vehicles should not exceed 0.3 g. Otherwise, the driving safety and stability of vehicles are affected, and there is a danger of sideslip. On the road with different adhesion coefficients, the influence of lateral acceleration on the vehicle is also different. Since the driving state of the vehicle at the bend is similar to that at the lane-changing, the specific quantitative index of the lane changing lateral acceleration is introduced to evaluate the sideslip safety of the low-speed (10 m/s–15 m/s) tractor-trailer driving at the low adhesion coefficient bend [28,29] as follows:

Limiting level lateral acceleration: $\left(0.22-0.002v\right)\mathrm{g}\le a_{\mathrm{y}}<0.67\phi \mathrm{g}$;

Maximum level lateral acceleration: $0.67\phi \mathrm{g}\le a_{\mathrm{y}}<0.85\phi \mathrm{g}$;

The meaning of the symbols in the formula is the same as above.

According to the quantitative index of lateral acceleration, under the condition of road adhesion coefficient $\phi =0.3$, the relationship between the speed of the tractor-trailer and lateral acceleration is shown in

Table 4. Simulation experiment condition parameters.

Driving Speed	Lateral Acceleration
	Limited Level	Maximum Level
30	[0.16, 0.201)	[0.201, 0.255)
40	[0.14, 0.201)	[0.201, 0.255)
50	[0.12, 0.201)	[0.201, 0.255)

.

The lateral acceleration is recommended to be lower than the limit level when the vehicle is running safely. Additionally, the maximum lateral acceleration should be less than 0.255 g which is the maximum value of the maximum level in extreme environments to ensure the safety of driving.

3.2. Analysis of Rollover Stability Results under the Influence of Different Crosswind

Through the analysis of the vertical load on the left and right sides of the tire and the LTR value in Figure 6, Figure 7 and Figure 8, it could be found that under the same wind speed conditions, as the driving speed increased, the vertical load on the left and right sides of the tractor-trailer varied more when entering the curved section and the instability increases. It could also be seen that when the driving speed reached 35 km/h, the tractor-trailer would produce a sudden change in the left and right side loads when entering the crosswind area, that is, when it was affected by a sudden appearance of crosswind, and would recover within a short time, indicating that when the tractor-trailer was disturbed by a sudden appearance of crosswind, which could be interpreted as a sudden increase in the speed of non-stationary wind, it would have a greater impact on driving safety.

Under the same speeds condition, with the increase in wind speed, the load distribution on the left and right sides of the vehicle also changed. The maximum LTR values are 0.42 ($v_{\mathrm{w}}=62$ km/h), 0.52 ($v_{\mathrm{w}}=68$ km/h) and 0.54 ($v_{\mathrm{w}}=74$ km/h), respectively. As can be seen from the figures, with the change of the distance into the curve, the wind deflection angle increased continuously, in the direction of the crosswind was perpendicular to the direction of the tractor-trailer driving, that was the direction of driving speed and the direction of the crosswind reached 90°, the crosswind had the greatest influence on the body, at this time the LTR value reached the maximum, after that the LTR value decreased continuously, until driving out of the crosswind area.

3.3. Analysis of Side Slip Stability under the Influence of Different Crosswinds

Simulation results of tractor-trailer driving on cold mountainous road conditions at different wind speeds were also analyzed, and the trend of lateral acceleration and lateral displacement of the tractor-trailer under each condition were obtained as shown below.

By analyzing and comparing the lateral acceleration curves of the tractor-trailer under different crosswind speeds and vehicle speeds, it can be found in Figure 9, Figure 10 and Figure 11 that the lateral acceleration peak appeared when the vehicle entered the curved slope section and then decreased suddenly. At this time, the vehicle had a slight sideslip. Compared with the tractor-trailer, the tractor that was the power source was more sensitive to the influence of road adhesion coefficient and lateral wind, and the response was also more obvious. Therefore, a sudden change occurred immediately after the lateral acceleration reached the maximum, indicating that a certain degree of sideslip occurred. When the driving speed reached 40 km/h, the lateral displacement of the tractor-trailer exceeded 0.15 m and close to 0.2 m, although there was no danger. However, it was still below the recommended speed.

As can be seen from the Figure 9, Figure 10 and Figure 11, under the same wind speed conditions, with the increase in driving speed, both lateral acceleration and lateral displacement values changed considerably. When the speed of the tractor-trailer was 30 km/h, there was a small fluctuation in lateral acceleration and the stability of the vehicle decreased; when the speed reached 35 km/h it could be found that when driving into the crosswind area, the lateral acceleration and lateral displacement changed abruptly and recovered quickly, at which time the tractor-trailer underwent a small sideslip. Considering that the direction of travel changed continuously when the tractor-trailer was driving at a curve, while the direction of the crosswind remained unchanged, the wind deflection angle between the two also changed continuously, so the wind deflection angle also had an impact on the tractor-trailer. Comparing the lateral displacement at different wind speeds, a two-factor ANOVA showed that the wind speed had a significant effect on the lateral displacement ($F(2,1392)=1569.66,p<0.01)$ and the wind deflection angle ($F(696,1392)=77.15,p<0.01$), both at 30 km/h and 35 km/h speeds.

3.4. Analysis of Hazardous Conditions for Tractor-Trailers

When the speed was increased to 40 km/h and the tractor-trailer was experimented with different side wind speeds, the simulation analyzed its operating state, at which point the Trucksim issued a warning that the hinge of the tractor-trailer exceeded a deflection of 500 mm, and it was found that the tractor-trailer had experienced a sideslip and a torsional folding phenomenon occurred. The distribution of the yaw rate and lateral acceleration under these conditions are shown in Figure 12; the vertical load and LTR values for different wind speeds are shown in Figure 13.

It can be found from Figure 12a that when the tractor-trailer passed through the low adhesion road bend at the driving speed of 40 km/h, it started to slip after entering the bend, and the yaw rate reached the maximum at about 12 s, which was 12.95 deg/s ($v_{\mathrm{w}}=62$ km/h), 12.90 deg/s ($v_{\mathrm{w}}=68$ km/h), 12.80 deg/s ($v_{\mathrm{w}}=74$ km/h), respectively. Additionally, in Figure 12b, it could be known that When a towed tractor-trailer skidded sideways, a sudden change in lateral acceleration occurred, that a sudden change in lateral acceleration was the sign that a sideslip had occurred. Additionally, an increase in wind speed did not affect the maximum of the ultimate lateral acceleration when sideslip, and the lateral accelerations at this point all exceeded 0.28 g, with a maximum of 0.284 g. At this time, the tractor-trailer had a serious sideslip, and it could not return to normal course by adjusting steering wheel angle. That gave a value of 0.284 g for the lateral acceleration of a tractor-trailer in the event of a severe accident on the cold mountainous road. In addition, it can be seen from the left and right load distribution of the vehicle in Figure 13b that the maximum LTR value was only 0.598 ($v_{\mathrm{w}}=62$ km/h) even when the vehicle slipped out of the lane, which was still relatively safe for vehicle rollover instability. On the road with a low adhesion coefficient ($\phi =0.3$), vehicle sideslip accidents occur preferentially compared with rollovers.

From the above analysis it can be concluded that when the sideslip occurs, with the increase in wind speed, the vehicle rollover index LTR value decreases, and the vehicle yaw rate decreases, but the maximum value is still less than the safety theoretical value of the ordinary road 16.5 deg/s. On the one hand, the low adhesion coefficient of ice and snow pavement reduces the safety threshold of vehicle sides lips. On the other hand, the effect of crosswind on vehicles also reduces the side slip threshold under the conditions of ice and snow pavement. Therefore, sideslip risk should be focused on this type of road condition.

Setting the road adhesion coefficient $\phi =0.3$ in extreme weather conditions, road conditions for the curve radius $R=60$ m without slope, by changing different crosswind conditions, to investigate the safe speed of tractor-trailer. The results of the simulation of the proposed maximum speed of the tractor-trailer with severe sideslip and just sudden changes in lateral acceleration are shown in

Table 5. Correlation between lateral acceleration, critical speed, and crosswind wind speed.

Wind Speed/($\mathbf{km}·{\mathbf{h}}^{-1}$)	0	10	20	30	40	50	60	70	80	90
Lateral acceleration/g	0.19	0.19	0.185	0.181	0.174	0.165	0.155	0.145	0.137	0.12
Critical speed/($\mathrm{km}·{\mathrm{h}}^{-1}$)	37.6	37.5	37.1	36.7	36	35.1	34	33.1	32.1	30
Suggested maximum speed/($\mathrm{km}·{\mathrm{h}}^{-1}$)	26	25	23.8	22	19	15	10	5	0	0

.

When the wind speed reached 90 km/h, even in a stationary state, the tractor-trailer had a sideslip displacement situation, while the safe speed under different crosswind conditions was reduced accordingly, as shown in Figure 14, so the recommended speed is limited to the green part and the critical speed is limited to the yellow part, when the speed reaches the yellow area, the tractor-trailer has a side slip, and when the speed reaches the red area, a serious side slip occurs.

After the simulation of different ultimate safety speeds, it was found that the lateral displacement of the tractor-trailer was within $[-0.1,1.5]$ m under different wind speeds, which was in a relatively safe range. As shown in Figure 15, it could be seen that the tractor-trailer was affected by the lateral force of the crosswind and the centrifugal force, and the maximum lateral displacement to the outside of the road was maintained at about 0.15 m, and the maximum displacement to the inside of the road was less than 0.1 m. The green range indicates the displacement of the right side of the vehicle, and the blue range indicates the displacement of the left side of the vehicle.

4. Validation of the Simulation Results on the Driving Simulator

The simulation results are calculated by theoretical models, such as mathematics. Whether there are differences with the actual situation requires experiments to test the validity of the results. Then, the reliability of the simulation results, the driving simulator experiments were conducted on the tractor-trailer with the same environmental conditions.

4.1. Design of the Experimental Environment for the Driving Simulator

The driving simulator used for the experiments was a six-degree-of-freedom (6DOF) simulator from the Northeast Forestry University Transport Laboratory (Figure 16), which was used for experimental scenario design, operation control and data acquisition through Simlab software to control the vehicle movement through the driver. The equipment mainly consists of a 6DOF dynamic system, a control system, an audio-visual system, a data acquisition system and an operation and feedback system, which provides a realistic driving experience with 360° sound surround and real-time driving feedback. The driving scenario is constructed in real time using three projectors with a horizontal viewing angle of 180° and a vertical viewing angle of 40°.

The tractor-trailer model used the same data as that used in the Trucksim, with internal loads; the road conditions were a road adhesion coefficient of 0.3, S-curves with a radius of 60 m, both curves were 5% high, the longitudinal gradient was 5%, and the straight line length between the curves was 200 m, so that the driver could adjust the body state and avoided the influence of the previous curve on the driving state of the next curve; the crosswind was set to a constant steady wind perpendicular to the centre of the curve. The wind speed conditions were 62 km/h, 68 km/h, and 74 km/h to test the effect of different flow speeds in the wind range, as shown in Figure 17.

4.2. Experimental Procedure of the Driving Simulator

Drivers were subjected to three wind conditions and two speed conditions, for a total of six different driving conditions, with the wind speed and driving speed increasing one by one and a 5–10 min break to adjust after driving the entire section to avoid driver fatigue over a long period of time.

In order to ensure the reliability of the experimental data, the drivers involved in the experiments were all over 4 years of driving experience, and five experiments were conducted on the same experimental scenario, eliminating data with obvious driving anomalies (such as driving out of the lane, driving speed fluctuating greatly, driving process interruption, etc.), and selecting a group of data with stable driving speed without large fluctuations and normal driver operation for analysis.

4.3. Analysis of Experimental Results

The results of measured lateral acceleration under different wind speeds and different driving speed conditions are shown in the Figure 18 and Figure 19, which show that at a speed of 30 km/h, the maximum lateral acceleration of the truck was around 0.15 g, and the steering wheel angle was within a small range, so the truck could still drive safely on ice and snow roads. When the speed reached 40 km/h, the maximum lateral acceleration of the truck reached 0.33 when the wind speed was 74 km/h, which was already beyond the safe lateral acceleration threshold, and the truck then slid sideways to a certain extent, and the driver made the truck return to the right track by frequently adjusting the steering wheel.

By comparing the simulation results and experimental results in Figure 20, it is not difficult to find that the lateral acceleration results of the semi-trailer are similar under different running speeds and wind speeds. In actual driving, the vehicle is more sensitive to crosswind. Considering the influence of driver factors, the change of steering wheel angle will change the magnitude of lateral acceleration. On the one hand, the experimental results verify the influence trend of wind speed and vehicle speed changes on driving stability in the simulation. On the other hand, it also illuminates the changing trend of lateral acceleration. The results are in line with the above conclusions on the recommended speed and safe lateral acceleration.

As can be seen from Figure 21, under the same speed conditions, with the wind speed increased, the vehicle’s driving stability decreased continuously; similarly, under the same wind speed conditions, vehicle’s driving stability changed drastically with the speed change. When the speed exceeded the suggestion speed, the lateral displacement changed amplitude and changed frequently, the vehicle could have been involved in an accident if the driver had not constantly adjusted the direction.

5. Discussion

Compared with the existing research, this research focuses on the study of curved slope pavement with a small curvature radius and low adhesion coefficient under the fresh gale environment, which supplements the mountainous limit condition that is ignored in the driving safety analysis of the tractor-trailer. Through the analysis of the results of simulation experiments, the sensitivity of the evaluation index of tractor-trailer lateral instability is improved, and the recommended safe driving speed of tractor-trailer under different wind speeds is given.

However, due to the limitation of conditions, there are still some deficiencies in the safety analysis of the tractor-trailer, mainly including: firstly, the road adhesion coefficient is single and constant steady wind is used in this paper, while the actual crosswind environment is mostly unsteady wind, and the actual adhesion coefficient of different sections is different, which has a greater impact on the safety of the tractor-trailer. Secondly, some indexes of driving safety are improved to some extent in this paper, but a comprehensive evaluation system is not formed. In future experimental studies, it is necessary to model the simulation environment more reasonably and effectively, conduct more detailed experiments and analyze the results, so as to further improve the defects of the theoretical system.

6. Conclusions

In this research, taking the tractor-trailer as the research object, the driving situation of the tractor-trailer in the extreme road environment was simulated and analyzed. Firstly, the-trailer model and road and environment model were established. Secondly, the driving state of the tractor-trailer under different conditions was analyzed by changing the crosswind speed and speed. Finally, the recommended speed to maintain safe driving and the accident results that may occur beyond the safe driving speed was obtained. The main research results are as follows:

(1)

Under the condition of low adhesion coefficient of ice and snow pavement, the lateral acceleration limit of the vehicle is lower than that of the dry pavement. In the crosswind speed of 0–10 km/h, the maximum lateral acceleration of the tractor tractor-trailer without side slip instability is about 0.19 g; the maximum lateral acceleration at the wind speed of 20 km/h is about 0.188 g; 30 km/h is 0.185 g; 40 km/h is 0.18 g; 50 km/h is 0.173 g; 60 km/h is 0.134 g; 70 km/h is 0.153 g; 80 km/h is 0.137 g; and 90 km/h is 0.12 g. In comparison with the lateral acceleration evaluation indicators in Table 4, the maximum acceleration values given in this research for safe driving under extreme environmental conditions are reduced by approximately 26%, improving the sensitivity of the evaluation indicators for the safety of tractor tractor-trailer driving on cold mountain roads.

(2)

Under the condition of the fresh gale (wind speed is 62–74 km/h), when the lateral acceleration exceeds 0.28 g, the vehicle will appear with a serious side slip and cannot return to normal driving line by adjusting the steering wheel. Due to the influence of crosswind, the safety threshold of lateral acceleration decreases with the increase in wind speed. Generally, the vehicle driving on the low adhesion coefficient road has not yet reached the rollover instability condition, but the side slip instability occurs first, so the side slip accident should be prevented. It is suggested that the safe speed threshold of tractor-trailer driving under extreme environmental conditions is limited to 30 km/h, and the lateral displacement of vehicle driving is also within the safe range. Due to the low road adhesion coefficient, When the speed is higher than 40 km/h the vehicle will slide directly out of control and taking the emergency brake or jerking the steering wheel at this point may cause the tractor-trailer to bend over.