1、 1 Turning characteristics of multi-axle vehicles Abstract： This paper presents a mathematical model for multi-axle vehicles operating on level ground. Considering possible factors related to turning motion such as vehicle configuration and tire slip velocities, equations of motion were constructed
2、to predict steer ability and driving decency of such vehicles. Turning radius, slip angle at the mass center, and each wheel velocity were obtained by numerically solving the equations with steering angles and average wheel velocity as numerical inputs. To elucidate the turning characteristics fault
3、y-axle vehicles, the eject of fundamental parameters such as vehicle speed, steering angles and type of driving system were examined for a sample of multi-axle vehicles. Additionally, field tests using full-scale vehicles were carried out to evaluate the basic turning char-ataractics on level ground
4、. Keywords: Multi-axle vehicles； Turning maneuverability； Mathematical model 1. Introduction Track laying running gear has been mainly used in the fields of military and construction for heavy vehicle applications. Recently, running gear with pneumatic tires has been expanding to heavy vehicles in s
5、uch fields, since tire equipped vehicles excel in speed, silence and energy e?-cogency. Several papers have been published on the subject of tractability and maneuverability of multi-axle vehicles 1,2. A theoretical study to evaluate the turning motion of skid steering vehicles was also developed by
6、 Renoir and Cravat 3. More recent army vehicles, such as the MODIX, are designed to be equipped with independent wheel drive and steering, and load control suspensions 4. The MODIX can turn by normal steering, skid steering, or a mixture of both. Additionally, the conversion from mechanical drive to
7、 an electric drive unit controlled by each in-hub motor has been examined 57. A hybrid wheel steer system is being developed to complement the independent drive capability of the in-hub wheel motors. However, there has not been a paper or technical publication dealing with the subject comprehensivel
8、y and in a logical sequence because the phenomenon of dynamic motions of the multi-axle vehicle is complex. This paper describes a computer simulation model to predict turning characteristics of multi-axle vehicles. The equations of motion for the vehicles are constructed for level ground. Tractate
9、and side forces acting under pneumatic tires due to interaction with the ground are of fundamental importance to predict the motion of vehicles. In the numerical simulation, the brush 2 model based on a physical approach was adopted for the tire model 8. The brush model is an idealized representatio
10、n of tires in the region of contact. In order to determine the turning motion of multi-axle vehicles, the ejects of fundamental parameters such as vehicle speed, steering angles and type of driving system are examined by using specification of an example vehicle. Field tests on multi-axle vehicles w
11、ere also conducted and compared to the predicted results with the data numerically obtained by the model. The results demonstrated that the proposed mathematical model could accurately assess the turning characteristics of multi-axle vehicles. 2. Mathematical model of multi-axle vehicles 2.1. Coordi
12、nate system and kinematics of the vehicle Fig. 1 shows coordinate systems used to describe a multi-axle vehicle with velocity vector V and yaw angular velocity h at the mass center. The coordinate system (X1, X2) is fixed on the level ground with unit base vectors E1, E2. A moving coordinate system
13、(x1, x2) is attached to the vehicle, whose origin is located at the mass center, with unit base vectors e1, e2. 2.2. Equations of motion Newtons second law applied to the vehicle yields: where m and I are the mass and the moment of inertia for the vehicle, respectively. The frictional force Q is def
14、ined under the itch wheel, and xi denotes the position vector of the itch wheel. In a steady state turn, the equilibrium equations for the vehicle are obtained by setting V and zero. 2.3. Tire slip and frictional forces Modeling of shear force generation for pneumatic tires has been reviewed by Paci
15、fica and Sharp 8 who covers physical and empirical models. The brush model, an analytical model physically derived, has been widely used for vehicle dynamics studies. The relation between deformations of tire treads and shear forces, i.e., side force and tractate force, is simplified and the model i
16、dealizes the representation of tires in the region of contact. The horizontal shear forces 3 acting under the tire due to interaction with the ground are assumed to be linearly dependent on the tread displacement from the tread base. In this paper, the brush model has been adopted to the vehicle mod
17、el. A schematic slip motion of a tire with slip angle is shown in Fig. 2. The slip velocity vector ViS is defined by the relative velocity of tread surface and the ground as follows: Where Vi and ViR denote the traveling velocity vector and the peripheral speed vector, respectively, of the itch whee
18、l. A non-dimensional slip ratio S is defined by the ratio of the norm of slip velocity with the magnitude of the peripheral velocity: Frictional force yields at the limit of the adhesion and the coincident of yielding friction is expressed as a function of slip ratio as follows: where K is a positiv
19、e constant dependent on the staidness of the tire, and l0 is the maximum coincident of friction. The limit of slip ratio Sm represents the full sliding state of the tire throughout the tread, expressed by Sm =1/K. Fig. 4 shows the lateral force versus the longitudinal force (braking or traction forc
20、e) plotted at given values of slip angles (rod) for a tire with the property of K= 5.0. As the driving power from the engine is transmitted to the wheel through the deferential, the driving force and the rotational speed of each wheel are influenced by power train types. The general type of driving system for multivalve vehicles is illustrated in Fig. 5. Deferential are
