Handling instability is a serious threat to driving safety. In order to analyze the handling stability of a tractor semitrailer, a handling diagram can be used. In our research, considering the impact of multiple nonsteering rear axles and nonlinear characteristics of tires on vehicle handling stability, the handling equations are developed for description of stability of tractor semitrailer. Then we obtain handling diagrams so as to study the influence of driving speed, loaded mass, and fifth wheel lead on vehicle handling stability. The analysis results show that the handling stability of a tractor semitrailer when the tractor has two nonsteering rear axles is better than that when the tractor has only one nonsteering rear axle. While the stability in the former case is slightly influenced by driving speed and loaded mass, the latter is strongly influenced by both. The fifth wheel lead is found to only slightly influence handling stability for both tractor semitrailers. Therefore, to ensure the driving safety of tractor semitrailers when the tractor has only one nonsteering rear axle, much stricter restraints should be imposed on driving speed, and the loaded mass must not exceed the rated load of the trailer.
Tractor semitrailers make up a large proportion of road transport vehicles due to their high transportation efficiency and economy. In 2010, the number of lorries in China reached 17 million, of which 8.7% were tractor semitrailers, and the number is growing at a rate of 20% per year.
At the same time, the number of traffic accidents involving tractor semitrailers remains high, and these accidents often cause serious personal injuries and property damage. Chinese statistics show that more than 1 in 3 tractors caused an accident on the highway in 2010, leaving 10,881 people dead.
Steering instability is one of the main contributors to traffic accidents involving tractor semitrailers. But, until now, little attention has been paid to it, and there are relatively few works on the topic [
Two different approaches are generally used to analyze vehicle handling stability: open and closed loop measurements. Unlike the former, the latter does not reflect the vehicle’s inherent stability because driver behavior is taken into consideration [
There are many methods of analyzing the open loop handling stability of vehicles, including (among others) dynamic theory [
To date, there has been too much focus on the handling stability of trucks and passenger cars, but few studies have attempted to characterize that of tractor semitrailers. Therefore, in this paper, the handling stability of tractor semitrailers is studied using handling diagrams, and the impact of vehicle design parameters and motion variables on the vehicle handling stability is analyzed. The research results have great importance for the development of active/passive safety control systems and for ensuring driving safety.
Given the importance of the number of nonsteering rear axles (on the tractor) on the handling stability of a tractor semitrailer and given that most tractors have one or two, tractor semitrailer when the tractor has two nonsteering rear axles and that when the tractor has one nonsteering rear axle are the two cases discussed in this paper. For simplicity, we refer to them as tractor semitrailers with two rear axles/one rear axle.
First, we establish the handling equation to be used in plotting the handling diagram.
In [
The compliance factor
Based on the handling equation for simple vehicles, Winkler [
Different from (
It can be seen from (
According to market surveys, most tractors have one or two nonsteering rear axles, those with two being most popular. Considering the impact of multiple nonsteering axles on vehicle handling stability, the following handling equation introduced by Winkler [
To simplify our analysis of the handling stability, we define the following quantity:
The nonlinear characteristics of tires on heavy vehicles mainly reflect the relationship between the tires’ vertical loads and cornering stiffness, which is commonly described by the following equation introduced by Frendo et al. [
Heavy vehicle tires have more stiffness, which makes the tire sideslip angle smaller and keeps the relation between the cornering force and the cornering stiffness fairly linear. This fact can be expressed by
Now we define the following quantities:
According to (
The total differentials of
According to (
Supposing that the turning radius remains constant, we can substitute (
Now, supposing that the driving speed remains constant, we can substitute (
Equations (
The handling diagram that is obtained by holding the turning radius constant is called the
For a tractor semitrailer with one rear axle, the handling equation and partial differential with respect to
From Section
For analytical clearness, the tractor and its trailer are separated at the articulated point, and corresponding forces are applied to both vehicle units, as shown in Figure
Representation of tractor semitrailer: main dimensions and lateral forces.
Under steadystate turning, the articulated angle
The semitrailer is partly supported by the tractor once the two are connected. The load that comes from the trailer and is carried by the tractor can be expressed by
The fifth wheel is installed on the rear of the tractor, which moves the center of gravity (CG) of the tractor’s sprung mass backwards when it is towing a trailer. The distance the CG moves can be expressed by
According to (
Sidetoside lateral load transfer is generated when a lateral force acts on the vehicles. As seen from Figure
Roll plane model of tractor.
From (
First, we introduce the characteristics of the handling diagram before looking at the handling stability simulation for a tractor semitrailer.
A handling diagram for a passenger car under different driving conditions, obtained using (
Handling diagram for a passenger car.
Based on the characteristics of the handling diagram shown, equivalent definitions for understeer, neutral steer, and oversteer for complex vehicles are given in Table
Equivalent definitions for understeer, neutral steer, and oversteer of a complex vehicle.
At a constant radius  Oversteer 


Neutral steer 



Understeer 



 
At a constant velocity  Oversteer 


Neutral steer 



Understeer 


The vehicle characteristics that were used in our numerical simulation of the handling stability of a tractor semitrailer with two rear axles are listed in Table
Characteristics of the tractor semitrailer with two rear axles.
Parameter  Value  Parameter  Value 


5069 kg 

2431 kg 

790 kg 

1590 kg 

1.288 m 

2.687 m 

140000 N/rad 

0.3 m 

202000 N/rad 

2.2 m 

1.8 m 

0.5 m 

0.5 m 

0.242 m 

6000 kg 

4.77 m 

3.34 m 

3.975 m 

8.11 m 

0.36 m 
For the tractor semitrailer with one rear axle, the characteristics are the same as for the two rear axle case, except for the tractor’s wheelbase, which is 3.5 m, and the number of tractor tires, which is 8.
The load distribution across the tractor’s front and rear axles when it is towing a trailer is determined by the fifth wheel lead, which can be adjusted within a certain range to allow the fifth wheel to engage with the kingpin. The fifth wheel for the tractor with two rear axles is arranged between the two rear axles, and the fifth wheel lead is about 0.3 m. According to collected statistics, the distance between the two rear axles is generally 1.45 m, 1.4 m, 1.37 m, 1.35 m, 1.3 m, and so forth, and 1.35 m is the most common distance. Therefore, the adjustment range for the fifth wheel lead for a tractor with two rear axles is somewhere between 0 and 0.675 m.
To analyze the influence of the fifth wheel lead on the handling stability of a tractor semitrailer with one rear axle, we assume that the adjustment range is the same as for the tractor with two rear axles.
All rear tires are assumed to be the same and to support equal loads. Taking lateral load transfer into consideration, tire cornering stiffness can be calculated as the average of the right and left tires’ cornering stiffness, and the vertical load can also be assumed to be the average of the right and left loads.
The constants in (
Based on the vehicle characteristics presented in Table
Tire cornering stiffness as a function of vertical load.
Ratio of rear tire’s to front tire’s cornering stiffness.
We use Matlab to simulate the influence of different vehicle parameters on the handling stability of the tractor semitrailer with one or two rear axles.
We use (
As can be seen in Figures
The most important finding that can be drawn from Figures
Therefore, the excellent handling stability of a tractor semitrailer with two rear axles owes more to its rear tires than to its multiple nonsteering rear axles. Unlike the conclusions drawn in [
A handling diagram for a tractor semitrailer with two rear axles and varying fifth wheel leads is presented in Figure
Handling diagram for a tractor semitrailer with two rear axles and varying fifth wheel leads.
For a tractor semitrailer with one rear axle, the
As Figures
Figure
Figure
Based on the previous analysis, a vehicle handling stability threshold defined by driving speed is more appropriate than one defined by lateral acceleration. This implies that it is important to set limits on the driving speeds of heavy vehicles on highways.
The handling diagram for a tractor semitrailer with one rear axle and varying fifth wheel leads is presented in Figure
Handling diagram for a tractor semitrailer with one rear axle and varying fifth wheel leads.
In this paper, we analyze the handling stability of tractor semitrailers with one or two rear axles, based on handling diagrams. The following conclusions are obtained.
Tractor semitrailers with two rear axles have better handling stability than those with just one. Within the rated load range, the former always show good steering performance. This result is due to the larger number of rear tires on the tworearaxle vehicle.
For a tractor with one rear axle, towing a trailer with a suitable total mass and driving at a low speed are quite important. This tractor semitrailer will lose handling stability when overloaded or if driven at high speeds. The vehicle may even lose steering capacity at high speeds.
Driving speed has much more influence on vehicle handling stability than the turning radius. Even on a gentle curve, these vehicles should not be driven at speeds above a certain level.
Fifth wheel lead has a slight influence on the handling stability of tractor semitrailers with one and with two rear axles. However, for tractors with one rear axle, it is especially important that the fifth wheel lead should be as large as possible in order to improve vehicle handling stability.
Since we make the assumption in deriving the handling equations that the tireground adhesion coefficient is sufficiently large, the handling equations are limited to analyzing handling stability for vehicles driven under certain road and driving conditions only. Thus, handling stability analysis for tractor semitrailers driven on slippery roads will be conducted in a future study.
This research is supported by “Research on Evaluation and Detection Technology of Handling and Driving Stability for Commercial Vehicles (no. 2009BAG13A04)” as part of the Major Project of the 11th FiveYear National Science and Technology Support Program: serious road traffic accident prevention and integrated disposal technology development and demonstration applications, organized by the Ministry of Science and Technology, Public Security, and Transportation of China.