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Modelling and analysis of suspension systems 159 A more detailed discussion of suspension analysis methods, such as those used to investigate body isolation issues, will follow later in this chapter but using a virtual rig such as this the following are typical of some of the analyses performed: (i) The wheels may be moved vertically relative to the vehicle body through a defined bump–rebound travel distance. For the half model shown in Figure 4.20 the vertical movement may involve single, opposite or parallel wheel travel representing ride or roll motions for the vehicle. The measured outputs allow the analyst to consider, depending on the model used, aspects of kinematic and compliant wheel plane control. (ii) Lateral force and aligning torque may be applied at the tyre contact path allowing measurement, for example, of the resulting toe angle change and lateral deflection of the wheel (compliant wheel plane control). In addition to the above basic types of analysis it is also possible to use an MBS suspension model to consider wheel envelopes where under the full range of suspension travel and steering inputs an envelope mapped by the outer surface of the tyre can be developed allowing the clearance with surrounding vehicle structure to be checked. In practice this has been achieved by using the wheel centre position, orientation and tyre geometry from the MBS simulation as input to a CAD system where the clearances can be checked. An example of the graphic visualization of a wheel envelope, for vertical wheel travel only, using superimposed animation frames is shown in Figure 4.21. Fig. 4.21 Superimposed animation frames giving visual indication of wheel envelope
160 Multibody Systems Approach to Vehicle Dynamics 4.5 Suspension calculations 4.5.1 Measured outputs A glossary of terms providing a formal specification of various suspension characteristics has been provided by the Society of Automotive Engineers (1976). In the past variations in formulations and terminology have been provided by researchers, authors and also practising engineers following corporate methodologies. The concept of a roll centre has also been subject to a number of definitions (Dixon, 1987). As discussed in Chapter 3 programs such as ADAMS/Car and ADAMS/ Chassis offer a range of pre-computed outputs for suspension characteristics. The user documentation provided with those software systems includes an extensive description of each output and need not be repeated here. For completeness those outputs considered to be most common in their usage and most relevant only to the following discussion in this textbook will be described in this chapter. As discussed in the previous sections, one of the main uses of a multibody systems model of a suspension system is to establish during the design process geometric position and orientation as a function of vertical movement between the rebound and bump positions. As the output required does not include dynamic response it is suitable to use a kinematic or quasistatic analysis to simulate the motion. It should be noted that this information could also be obtained using a CAD package or a program developed solely for this purpose. The fact that a multibody systems program is used is often associated with the stages of model development described in Chapter 1 that lead through from the individual suspension model to a model of the full vehicle. A large number of parameters can be measured on an existing suspension system and laboratory rigs such as the Kinematics and Compliance measurement facility (or K&C Rig) described by Whitehead (1995) have been developed specifically for this purpose. The descriptions provided here will be limited to the most commonly calculated outputs, these being: ● ● ● ● ● ● ● ● ● ● ● Bump movement (spindle rise) Wheel recession Half track change Steer (toe) angle Camber angle Castor angle Steer axis inclination Suspension trail Ground level offset Wheel rate Roll centre height
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Modelling and analysis of suspension systems 159<br />
A more detailed discussion of suspension analysis methods, such as those<br />
used to investigate body isolation issues, will follow later in this chapter<br />
but using a virtual rig such as this the following are typical of some of the<br />
analyses performed:<br />
(i) The wheels may be moved vertically relative to the vehicle body<br />
through a defined bump–rebound travel distance. For the half model<br />
shown in Figure 4.20 the vertical movement may involve single, opposite<br />
or parallel wheel travel representing ride or roll motions for the<br />
vehicle. The measured outputs allow the analyst to consider, depending<br />
on the model used, aspects of kinematic and compliant wheel<br />
plane control.<br />
(ii) Lateral force and aligning torque may be applied at the tyre contact<br />
path allowing measurement, for example, of the resulting toe angle<br />
change and lateral deflection of the wheel (compliant wheel plane<br />
control).<br />
In addition to the above basic types of analysis it is also possible to use an<br />
MBS suspension model to consider wheel envelopes where under the full<br />
range of suspension travel and steering inputs an envelope mapped by the<br />
outer surface of the tyre can be developed allowing the clearance with surrounding<br />
vehicle structure to be checked.<br />
In practice this has been achieved by using the wheel centre position, orientation<br />
and tyre geometry from the MBS simulation as input to a CAD<br />
system where the clearances can be checked. An example of the graphic<br />
visualization of a wheel envelope, for vertical wheel travel only, using<br />
superimposed animation frames is shown in Figure 4.21.<br />
Fig. 4.21 Superimposed animation frames giving visual indication of<br />
wheel envelope