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Modelling and analysis of suspension systems 189 One method that could be used to input a motion associated with the profile of the road surface would be to use a SPLINE statement as follows: MOTION/20, JOINT20, TRANS, FUNCTIONCUBSPL(TIME, 0, 10) SPLINE/10 ,X 0, 0.10, 0.12, 0.14, 0.16, 0.18, 0.20, 0.22, 1.22 ,Y 0, 0, 50, 100, 100, 100, 50, 0, 0 Caution is needed here, however, for although the data points may be sufficient to capture the profile of the bump there may not be enough to ensure a good spline fit. A more elegant but elaborate method might be to forgo the use of interpolation and use a combination of arithmetic IF and step functions. This method requires care in formatting but may be applied as follows: MOTION/20, JOINT 20, TRANS ,FUIF(TIME0.14: STEP(TIME, 0.1, 0, 0.14, 100), 100 ,STEP(TIME, 0.16, 100, 0.22, 0)) The MSC.ADAMS graphics showing the suspension deflecting on the jack and the subsequent departure of the tyre from the road surface are shown in Figure 4.53. A plot showing the time histories for the vehicle body and road wheel vertical displacement is shown in Figure 4.54. The force in the Time = 0 sec Time = 0.14 sec Time = 0.18 sec Fig. 4.53 MSC.ADAMS graphics of suspension deflecting on a speed bump 600.0 SPEED BUMP IMPACT – DYNAMIC ANALYSIS Vehicle body and road wheel vertical displacements Displacement (mm) 500.0 400.0 300.0 200.0 Body displacement Road wheel displacement 100.0 0.0 0.2 0.4 0.6 0.8 1.0 Time (s) 1.2 1.4 1.6 1.8 2.0 Fig. 4.54 MSC.ADAMS plot vehicle body and road wheel displacements for speed bump strike

190 Multibody Systems Approach to Vehicle Dynamics 500.0 SPEED BUMP IMPACT – DYNAMIC ANALYSIS Magnitude of force in the bump stop 400.0 Force (N) 300.0 200.0 100.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Time (s) 1.2 1.4 1.6 1.8 2.0 Fig. 4.55 MSC.ADAMS plot of bump stop force time history for speed bump strike bump stop is provided by way of example (Figure 4.55). It should be noted that at this stage the analysis only represents vertical force input and not longitudinal force input from the road surface. 4.9 Ride studies (body isolation) The determination of vehicle ‘ride’ quality is associated with the extent to which the occupants of the vehicle are affected by vehicle motion. Automotive companies will often have departments concerned with ride and handling where multibody systems analysis will be deployed to support design and analysis work. Another area of activity is referred to as Noise Vibration and Harshness (NVH). In general vibrations with frequencies up to 25 Hz are generally said to be associated with ride. These modes of vibration are usually amenable to analysis with the multibody techniques described in this textbook. Vibrations with frequencies above 25 Hz are usually referred to as noise. The analysis of these modes and other acoustic type problems is more in the domain of advanced finite element analysis and as such is not covered here. Vehicles should be thought of as dynamic systems, a mixture of masses, springs and dampers, where vibration is exhibited in response to excitation. The source of excitation may be due to out-of-balance loads from rotating bodies such as the road wheel or from other sources in the vehicle including the engine and driveline. The other main source of vibration will be associated with the profile of the road surface. At this stage it is easy to envisage that the excitation of vehicle pitch may be in response to a road with an undulating type profile of relatively long wavelength whereas the excitation of a smaller mass such as the road wheel will occur at higher frequencies. This might, for example, occur while driving on a cobbled type of road surface.

Modelling and analysis of suspension systems 189<br />

One method that could be used to input a motion associated with the profile<br />

of the road surface would be to use a SPLINE statement as follows:<br />

MOTION/20, JOINT20, TRANS, FUNCTIONCUBSPL(TIME, 0, 10)<br />

SPLINE/10<br />

,X 0, 0.10, 0.12, 0.14, 0.16, 0.18, 0.20, 0.22, 1.22<br />

,Y 0, 0, 50, 100, 100, 100, 50, 0, 0<br />

Caution is needed here, however, for although the data points may be sufficient<br />

to capture the profile of the bump there may not be enough to ensure<br />

a good spline fit. A more elegant but elaborate method might be to forgo<br />

the use of interpolation and use a combination of arithmetic IF and step functions.<br />

This method requires care in formatting but may be applied as follows:<br />

MOTION/20, JOINT 20, TRANS<br />

,FUIF(TIME0.14: STEP(TIME, 0.1, 0, 0.14, 100), 100<br />

,STEP(TIME, 0.16, 100, 0.22, 0))<br />

The MSC.ADAMS graphics showing the suspension deflecting on the jack<br />

and the subsequent departure of the tyre from the road surface are shown in<br />

Figure 4.53. A plot showing the time histories for the vehicle body and<br />

road wheel vertical displacement is shown in Figure 4.54. The force in the<br />

Time = 0 sec<br />

Time = 0.14 sec<br />

Time = 0.18 sec<br />

Fig. 4.53<br />

MSC.ADAMS graphics of suspension deflecting on a speed bump<br />

600.0<br />

SPEED BUMP IMPACT – DYNAMIC ANALYSIS<br />

Vehicle body and road wheel vertical displacements<br />

Displacement (mm)<br />

500.0<br />

400.0<br />

300.0<br />

200.0<br />

Body displacement<br />

Road wheel displacement<br />

100.0<br />

0.0<br />

0.2<br />

0.4<br />

0.6<br />

0.8<br />

1.0<br />

Time (s)<br />

1.2 1.4 1.6 1.8 2.0<br />

Fig. 4.54 MSC.ADAMS plot vehicle body and road wheel displacements for<br />

speed bump strike

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