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Modelling and assembly of the full vehicle 337 trajectory and orientation as it moves vertically between full bump and rebound positions. Scapaticci and Minen (1992) describe this approach as the implementation of synthetic wheel trajectories. Such a method has been adopted within MSC.ADAMS where the model is referred to as a ‘Concept Suspension’ and is the basis of many dedicated vehicle dynamics modelling software tools such as Milliken Research Associate’s VDMS, MSC’s CarSim, University of Michigan’s ArcSim, and Leeds University’s VDAS. The way in which such a model is applied is summarized in Figure 6.11. In essence the vehicle model containing the concept suspension can be used to investigate the suspension design parameters that can contribute to the delivery of the desired vehicle handling characteristics without modelling of the suspension linkages. In this way, the analyst can gain a clear understanding of the dominant issues affecting some aspect of vehicle dynamics performance. A case study is given in section 6.14 describing the use of a reduced (3 degree of freedom) linear model to assess the influence of suspension characteristics on straight-line stability. These models belong very firmly in the ‘analysis’ segment of the overall process diagram described in Chapter 1, Figure 1.6. The functional representation of the model is based on components that describe effects due to kinematics dependent on suspension geometry and also elastic effects due to compliance within the suspension system. A schematic to support an explanation of the function of this model is provided in Figure 6.12. ∆v ∆γ X Z ∆z Y ∆x Fxt ∆δ Fig. 6.12 Fy Mz ∆y Fxb Wheel trajectory Concept Suspension system model schematic
338 Multibody Systems Approach to Vehicle Dynamics If we consider first the kinematic effects due to suspension geometry we can see that there are two variables that provide input to the model: z is the change in wheel centre vertical position (wheel travel) v is the change in steering wheel angle The magnitude of the wheel travel z will depend on the deformation of the surface, the load acting vertically through the tyre resulting from weight transfer during a simulated manoeuvre and a representation of the suspension stiffness and damping acting through the wheel centre. The magnitude of the change in steering wheel angle v will depend on either an open loop fixed time dependent rotational motion input or a closed loop torque input using a controller to feed back vehicle position variables so as to steer the vehicle to follow a predefined path. The modelling of steering inputs is discussed in more detail later in this chapter. The dependent variables that dictate the position and orientation of the road wheel are: x is the change in longitudinal position of the wheel y is the change in lateral position (half-track) of the wheel is the change in steer angle (toe in/out) of the wheel is the change in camber angle of the wheel The functional dependencies that dictate how the suspension moves with respect to the input variables can be obtained through experimental rig measurements, if the vehicle exists and is to be used as a basis for the model, or by performing simulation with suspension models as described in Chapter 4. For example, the dependence of camber angle on wheel travel can be derived from the curves plotted for Case study 1 in Chapter 4. The movement of the suspension due to elastic effects is dependent on the forces acting on the wheel. In their paper Scapaticci and Minen (1992) describe the relationship using the equation shown in (6.1) where the functional dependencies due to suspension compliance are defined using the matrix F E : ⎡x⎤ ⎡ ⎢ y ⎥ ⎢ ⎢ ⎥ ⎢F ⎢⎥ ⎢ ⎢ ⎥ ⎢ ⎣⎦ ⎣ E ⎤ ⎡ Fxt ⎤ ⎥ ⎢ Fxb ⎥ ⎥ ⎢ ⎥ ⎥ ⎢ Fy ⎥ ⎥ ⎢ ⎥ ⎦ ⎣ Mz ⎦ (6.1) and the inputs are the forces acting on the tyre: Fxt is the longitudinal tractive force Fxb is the longitudinal braking force Fy is the lateral force Mz is the self-aligning moment Note that the dimensions of the matrix F E are such that cross-coupling terms, such as toe change under braking force, can exist. The availability of such data early in the design phase can be difficult but the adoption of such a generalized form allows the user to speculate on such values and thus use the model to set targets for acceptable behaviour.
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Modelling and assembly of the full vehicle 337<br />
trajectory and orientation as it moves vertically between full bump and<br />
rebound positions. Scapaticci and Minen (1992) describe this approach as<br />
the implementation of synthetic wheel trajectories. Such a method has been<br />
adopted within MSC.ADAMS where the model is referred to as a ‘Concept<br />
Suspension’ and is the basis of many dedicated vehicle dynamics modelling<br />
software tools such as Milliken Research Associate’s VDMS, MSC’s<br />
CarSim, University of Michigan’s ArcSim, and Leeds University’s VDAS.<br />
The way in which such a model is applied is summarized in Figure 6.11. In<br />
essence the vehicle model containing the concept suspension can be used to<br />
investigate the suspension design parameters that can contribute to the<br />
delivery of the desired vehicle handling characteristics without modelling of<br />
the suspension linkages. In this way, the analyst can gain a clear understanding<br />
of the dominant issues affecting some aspect of vehicle dynamics<br />
performance. A case study is given in section 6.14 describing the use of a<br />
reduced (3 degree of freedom) linear model to assess the influence of suspension<br />
characteristics on straight-line stability. These models belong very<br />
firmly in the ‘analysis’ segment of the overall process diagram described in<br />
Chapter 1, Figure 1.6.<br />
The functional representation of the model is based on components that<br />
describe effects due to kinematics dependent on suspension geometry and<br />
also elastic effects due to compliance within the suspension system. A<br />
schematic to support an explanation of the function of this model is provided<br />
in Figure 6.12.<br />
∆v<br />
∆γ<br />
X<br />
Z<br />
∆z<br />
Y<br />
∆x<br />
Fxt<br />
∆δ<br />
Fig. 6.12<br />
Fy<br />
Mz<br />
∆y<br />
Fxb<br />
Wheel<br />
trajectory<br />
Concept Suspension system model schematic