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Modelling and analysis of suspension systems 185 UNI SPH REV BUSH SPH CYL BUSH BUSH REV I marker at wheelbase MOTION 15 900 N SPH FIX ZP for marker 3 BUSH 12 360 N Z Fig. 4.48 ZP for marker 1 ZP for marker 2 X Y GRF Application of pothole braking loads to suspension model that demonstrates the dynamic input of a road load but are not used for the initial phase where the load is applied quasi-statically. A schematic for the model is shown in Figure 4.48 where it can be seen that the jack that was used earlier to move the suspension between the rebound and bump positions has been replaced by applied forces acting on a marker located at the bottom of the road wheel. The loads are applied as action-only single forces acting on the I marker at the contact patch. In this example we are treating the wheel as a single rigid body and ignoring any compliance in the tyre. The I marker is in this case located at an undeformed radius directly below the wheel centre. The motion statement associated with the road wheel revolute joint has a function set to zero to effectively lock the rotation of the wheel. The loads are applied parallel to the axes of the Ground Reference Frame (GRF) at the start and remain parallel to the GRF during the simulation. They do not rotate with the wheel as the suspension deforms under the loading. For an action-only force it was shown in Chapter 3 that the point of application for the force is given as the I marker and the line of action and direction of the force is given by the z-axis of the J marker. A convenient way to create a set of J markers that may be used for each loadcase is to define three markers that are used for this purpose alone as follows: PART/01, GROUND MARKER/01, ZP 1, 0, 0 ! Global x direction MARKER/02, ZP 0, 1, 0 ! Global y direction MARKER/03, ZP 0, 0, 1 ! Global z direction Note that in this case the QP vectors have been omitted so that by default all three markers are located at the GRF on the ground part. The ZP vectors

186 Multibody Systems Approach to Vehicle Dynamics orientate the markers so that each z-axis aligns with one of the axes of the GRF. The ZP definition on Marker/03 is included for completeness although if this were left out Marker/03 would by default still be parallel to the GRF. It is now possible to include a set of three single forces to define the pothole braking case. To allow the use of animation the loads will be applied as an initial static analysis where only the vertical static tyre load is applied followed by a quasi-static analysis where the additional loads are applied as a function of time. As the analysis is quasi-static the time taken to ramp on the loads is arbitrary. In this example a period of 1 second is used by way of example. The following SFORCE statements may be used to implement this: SFORCE/01, I 1029, J 1, TRANS, ACTION ,FUNCTION 15900 * TIME SFORCE/02, I 1029, J 2, TRANS, ACTION, FUNCTION 0 SFORCE/03, I 1029, J 3, TRANS, ACTION ,FUNCTION 3727 8633 * TIME From this it can be seen that for the pothole braking case a longitudinal load in the x direction and a vertical load in the z direction are applied. The lateral load in the y direction is set to zero. The functions are set for this example so that for the initial static analysis a vertical load of 3727 N is applied with the additional components due to pothole braking being added over 1 second. It can be seen from this that the functions used to define the forces can be quickly changed to correspond with each of the loadcases given in Table 4.8. The graphics showing the suspension deformed under full load are shown in Figure 4.49 with additional graphics showing the force components at the contact patch. An XY plot showing the development of force magnitude in the spring is shown in Figure 4.50. Examination of the numerical values associated with the components of this force at full load, after 1 second, would provide the inputs for any subsequent finite element models. It should be noted that with the quasi-static example used here there is no velocity dependent load transmission through the damper. To increase the validity of the results it would be necessary to estimate an equivalent load and apply this as an additional static force. An alternative would be to develop the analysis of the suspension to apply the force as a function of time and carry out a dynamic simulation as described next. Fig. 4.49 case load MSC.ADAMS graphics of suspension at maximum pothole braking

Modelling and analysis of suspension systems 185<br />

UNI<br />

SPH<br />

REV<br />

BUSH<br />

SPH<br />

CYL<br />

BUSH<br />

BUSH<br />

REV<br />

I marker<br />

at wheelbase<br />

MOTION<br />

15 900 N<br />

SPH<br />

FIX<br />

ZP for<br />

marker 3<br />

BUSH<br />

12 360 N<br />

Z<br />

Fig. 4.48<br />

ZP for<br />

marker 1<br />

ZP for<br />

marker 2<br />

X<br />

Y<br />

GRF<br />

Application of pothole braking loads to suspension model<br />

that demonstrates the dynamic input of a road load but are not used for the<br />

initial phase where the load is applied quasi-statically. A schematic for the<br />

model is shown in Figure 4.48 where it can be seen that the jack that was<br />

used earlier to move the suspension between the rebound and bump positions<br />

has been replaced by applied forces acting on a marker located at the<br />

bottom of the road wheel.<br />

The loads are applied as action-only single forces acting on the I marker at<br />

the contact patch. In this example we are treating the wheel as a single rigid<br />

body and ignoring any compliance in the tyre. The I marker is in this case<br />

located at an undeformed radius directly below the wheel centre. The<br />

motion statement associated with the road wheel revolute joint has a function<br />

set to zero to effectively lock the rotation of the wheel. The loads are<br />

applied parallel to the axes of the Ground Reference Frame (GRF) at the<br />

start and remain parallel to the GRF during the simulation. They do not<br />

rotate with the wheel as the suspension deforms under the loading.<br />

For an action-only force it was shown in Chapter 3 that the point of application<br />

for the force is given as the I marker and the line of action and direction<br />

of the force is given by the z-axis of the J marker. A convenient way to<br />

create a set of J markers that may be used for each loadcase is to define<br />

three markers that are used for this purpose alone as follows:<br />

PART/01, GROUND<br />

MARKER/01, ZP 1, 0, 0 ! Global x direction<br />

MARKER/02, ZP 0, 1, 0 ! Global y direction<br />

MARKER/03, ZP 0, 0, 1 ! Global z direction<br />

Note that in this case the QP vectors have been omitted so that by default<br />

all three markers are located at the GRF on the ground part. The ZP vectors

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