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Modelling and analysis of suspension systems 153 Spring Upper mount Damper Wheel knuckle (stub axle) (kingpin) Lower bushes (mounts) Road wheel Lower wishbone (control arm) Connection to rack Track rod Lower ball joint Track rod end Fig. 4.15 McPherson strut suspension system established and will be discussed further in the next section of this chapter. The output from this type of analysis is mainly geometric and allows results such as camber angle or roll centre position to be plotted graphically against vertical wheel movement. The inclusion of bush compliance in the model at this stage will depend on whether the bushes have significant influence on geometric changes in the suspension and road wheel as the wheel moves vertically relative to the vehicle body. With the development of multi-link type suspensions, such as the rear suspension on the Mercedes Model W201 (von der Ohe, 1983), it would appear difficult to develop a model of the linkages that did not include the compliance in the bushes. This type of suspension was used as a benchmark during the IAVSD exercise (Kortum and Sharp, 1993) mentioned in Chapter 1 comparing the application of multibody systems analysis programs in vehicle dynamics. This modelling issue is best explained by an example using the established double wishbone suspension system. The modelling of the suspension using bushes to connect the upper and lower arms to the vehicle body is shown in Figure 4.16. Vertical motion is imparted to the suspension using a jack part connected to the ground part by a translational joint. A translational motion is applied at this joint to move the jack over a range of vertical movement equivalent to moving between the full bump and full rebound positions. Although the jack is shown below the wheel in Figure 4.16 the jack is connected to the wheel using an inplane joint primitive acting at either the wheel base or the wheel centre as described in Chapter 3. The joint primitive constrains the wheel centre or wheel base to remain in the plane at the top of the jack but does not constrain the wheel to change

154 Multibody Systems Approach to Vehicle Dynamics BUSHES SPHERICAL BUSHES REVOLUTE SPHERICAL MOTION UNIVERSAL SPHERICAL INPLANE MOTION TRANSLATIONAL Fig. 4.16 Double wishbone suspension modelled with bushes. (This material has been reproduced from the Proceedings of the Institution of Mechanical Engineers, K2 Vol. 213 ‘The modelling and simulation of vehicle handling. Part 2: vehicle modelling’, M.V. Blundell, page 121, by permission of the Council of the Institution of Mechanical Engineers) Table 4.2 Degree-of-freedom calculation for suspension system with bushes Component Number DOF ΣDOF Parts 6 6 36 Translationals 1 5 5 Revolutes 1 5 5 Universals 1 4 4 Sphericals 3 3 9 Inplanes 1 1 1 Motions 2 1 2 ΣDOF for system 10 orientation or to move in the lateral or longitudinal directions. A zero motion input is applied at the revolute joint connecting the wheel to the wheel knuckle in order to constrain the spin freedom of the wheel. For the suspension modelled in this manner it is possible to calculate the degrees of freedom for the system as shown in Table 4.2. The double wishbone suspension model shown in Figure 4.16 can be simplified to represent the bushes connecting the upper arm and the lower arm to the vehicle body by revolute joints as shown in Figure 4.17. For the suspension modelled in this manner it is possible to calculate the degrees of freedom for the system as shown in Table 4.3.

Modelling and analysis of suspension systems 153<br />

Spring<br />

Upper mount<br />

Damper<br />

Wheel knuckle<br />

(stub axle) (kingpin)<br />

Lower bushes (mounts)<br />

Road wheel<br />

Lower wishbone<br />

(control arm)<br />

Connection to rack Track rod<br />

Lower ball joint<br />

Track rod end<br />

Fig. 4.15 McPherson strut suspension system<br />

established and will be discussed further in the next section of this chapter.<br />

The output from this type of analysis is mainly geometric and allows<br />

results such as camber angle or roll centre position to be plotted graphically<br />

against vertical wheel movement.<br />

The inclusion of bush compliance in the model at this stage will depend on<br />

whether the bushes have significant influence on geometric changes in the<br />

suspension and road wheel as the wheel moves vertically relative to the<br />

vehicle body. With the development of multi-link type suspensions, such as<br />

the rear suspension on the Mercedes Model W201 (von der Ohe, 1983), it<br />

would appear difficult to develop a model of the linkages that did not<br />

include the compliance in the bushes. This type of suspension was used as<br />

a benchmark during the IAVSD exercise (Kortum and Sharp, 1993) mentioned<br />

in Chapter 1 comparing the application of multibody systems analysis<br />

programs in vehicle dynamics.<br />

This modelling issue is best explained by an example using the established<br />

double wishbone suspension system. The modelling of the suspension<br />

using bushes to connect the upper and lower arms to the vehicle body is<br />

shown in Figure 4.16. Vertical motion is imparted to the suspension using<br />

a jack part connected to the ground part by a translational joint. A translational<br />

motion is applied at this joint to move the jack over a range of vertical<br />

movement equivalent to moving between the full bump and full<br />

rebound positions. Although the jack is shown below the wheel in Figure<br />

4.16 the jack is connected to the wheel using an inplane joint primitive acting<br />

at either the wheel base or the wheel centre as described in Chapter 3.<br />

The joint primitive constrains the wheel centre or wheel base to remain in<br />

the plane at the top of the jack but does not constrain the wheel to change

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