Vehicle Dynamics Modeling and Control of the TowPlow, A Stee(4)

Chen and Velinsky (1992) suggested a kinematic design methodology to optimize the geometry of the vehicles and the roadways for low-speed maneuverability. Also, they ascertained that the low-speed maneuverability of an articulated vehicle can be improved through steering of trailer axles as a linear function of the articulation angle and front-wheel-steer angle, as shown in Figure 1.5 [10].

Figure 1.4. Instantaneous centers of logging trucks by Erkert et al [9]

(a)(b)

Figure 1.5. Cornering of tractor-trailer combination: (a) without trailer steering, (b) with trailer

steering by Chen and Velinsky [10]

Manesis (1998) introduced a sliding kingpin mechanism, shown in Figure 1.6, to eliminate the off-tracking of heavy duty trucks with semi-trailers, and also designed various types of sliding control

[11-13].

Figure 1.6. Manesis’ sliding kingpin mechanism [12]

1.2.2

Dynamics of the articulated vehicle From the 1930s, a substantial amount of work has been performed concerning the directional dynamics of articulated vehicles. Vlk (1985) comprehensively reviewed and summarized studies on handling performance of truck-trailer vehicles. According to his review, the early theoretical works of articulated vehicles are limited to only unstable states of the trailer until Schmid (1964) and Jindra (1965) introducing the interdependence between truck and trailer motions [14]. In the 1960s, Jindra (1965) and Bundorf (1967) developed linear differential equations for the simplified mechanical model of a tractor double trailer combination and an automobile-trailer combination, respectively, and examined the directional instability and steady-state turning performance through steady-state and transient responses to steering inputs [15, 16]. Ellis (1969) developed both linear and simplified nonlinear models for the planar motion of articulated vehicles neglecting the roll motion of the vehicles, and analyzed dynamic responses to show how instability of the trailer occurs [17]. Segal and Ervin (1981) classified handling instability of

articulated vehicles into: (1) jack-knifing – occurring when the tractor oversteers and the trailer

understeers or slightly oversteers above a critical speed; (2) trailer swing – occurring when the tractor oversteers and the trailer oversteers strongly above a critical speed [18]. Vlk (1985) also characterized three typical directional unstable states of articulated vehicles: (1) snaking – trailer yaw oscillation that occurs at high speed; (2) jack-knifing – instability of tractor yaw motion; and (3) trailer swing – instability of trailer yaw motion [14].

Figure 1.7. Typical unstable states of articulated vehicles by Vlk [14]

Later, a more complex nonlinear model of articulated vehicles considering the lateral, yaw and roll motions together was developed by Chen and Tomizuka (1995) [19].

Figure 1.8. Coordinate system for the articulated vehicle by Chen and Tomizuka [19]

Analysis on non-linear dynamics of the vehicle had been enhanced through development of non-linear tire friction models because forces and moments generated by the friction between tire and road surface influence vehicle dynamics significantly. The tire models that have been used commonly for vehicle dynamics are the LuGre model, Pacejka’s model, and Dugoff’s model. The LuGre friction model is originally suggested by Canudas de Wit et al. [20]. It describes the mechanism of friction as contact of two rigid bodies through elastic bristles. When one body travels on the other, the bristles randomly deflect like springs, and the bending of the bristles generates the friction force. Initially, the LuGre model was only used for the longitudinal friction force. However, it was extended to the combined longitudinal and lateral motion [21].

Figure 1.9. Concept of friction between bristles for the LuGre model [20]

Pacejka’s model, also known as the Magic Formula tire model, is mathematical equations composed of several tunable coefficients to accurately describe the measured data of the longitudinal and lateral tire force [22]. The coefficients in the model may not have physical interpretation.

Dugoff’s model is a derivative of the freely rolling tire by Fiala [23]. Dugoff extended the previous work to general tire-road interaction either for pure-slip or combined-slip condition [24]. A simplified Dugoff’s model assuming that both longitudinal and lateral forces are linearly dependent on the normal force of the tire is developed by Krauter [25]. In addition to the simplified model, Guntur and Sankar implemented the friction circle concept to Dugoff’s model; i.e., if the desired friction is less than

or equal to half of the available friction, described by inside of the circle in Figure 1.10, the longitudinal

and lateral tire forces have linear relationship with the slip ratio and slip angle, respectively; however, if the desired friction outside of the circle, the tire forces attenuate nonlinearly. They also presented a procedure of the tire forces calculation for vehicle simulation [26].

Figure 1.10. Friction circle concept for the Dugoff’s tire friction model by Guntur and Sankar [26]

1.2.3

Snow resistance model The snow resistance model is significant in modeling of the TowPlow because forces on the plows affect the dynamics of the TowPlow, and may cause instability. There has been an effort to estimate forces on the plow during the snow removal operation. Some of the models found in the literature are based on Croce’s model, which is a simple Bernoulli fluid flow model under the assumption that the velocity of the snow is constant throughout the entire process. The model approximates the snow resistance force more closely at highe …… 此处隐藏：4408字，全部文档内容请下载后查看。喜欢就下载吧 ……