4569846498
Multibody systems simulation software 105 I I As markers approach VR(I,J ) is negative As markers separate VR(I,J ) is positive J J Fig. 3.28 Damper force is positive Damper force is negative Sign convention for damper forces and velocities An alternative form of definition that could be used with MSC.ADAMS involves the use of the SPRINGDAMPER statement. In this case this would have exactly the same effect as the SFORCE statement above: SPRING/0509,I0205,J0409,TRANS,K40,L250 In a similar manner to the definition of a spring force the representation of a damper force will involve using the line-of-sight method to formulate an action–reaction force between an I marker on one part and a J marker on another part. We will again start with the linear case where we formulate a damper force F D using F D c • VR(I, J) (3.46) where VR(I, J) radial line of sight velocity between I and J marker c damping coefficient Since the force generated in a damper is related to the sliding velocity acting along the axis of the damper we introduce another system variable VR(I, J) that will take a positive sign when the markers are separating, as in suspension rebound, and a negative sign when the markers are approaching, as when a suspension moves upwards relative to the body in bump. The formulation of the damper force F D in (3.46) is such that the damper forces are consistent with those of a spring. The force generated is positive in a repelling mode and negative in an attracting mode as illustrated in Figure 3.28. The formulation of the damper force F D is shown graphically in Figure 3.29. An example of the syntax that could be used to formulate this in MSC.ADAMS, using an SFORCE statement, would be SFORCE/0509,I0205,J0409,TRANS,FUNCTION -5*VR(0205,0409)
106 Mutibody Systems Approach to Vehicle Dynamics F D VR (I,J ) Approaching F C c · VR (I,J ) Separating Fig. 3.29 Formulation of a linear damper force where using the units that are consistent throughout this text we would have: FUNCTION the damper force F D (N) The damping coefficient C 5 Ns/mm VR(0205,0409) the radial line of sight velocity between I and J (mm/s) An alternative form of definition that could be used with MSC.ADAMS involves the use of the SPRINGDAMPER statement. In this case this would have exactly the same effect as the SFORCE statement above: SPRINGDAMPER/0509,I0205,J0409,TRANS,C5 The definitions of spring and damper forces so far has been based on the assumption that the force element can be modelled as linear. This can be extended to consider the modelling of a non-linear element. The example used will be based on the front and rear dampers for a typical road vehicle. The non-linear damper forces are defined in MSC.ADAMS using xy data sets where the x values represent the velocity in the damper, VR(I, J), and the y values are the force. During the analysis the force values are extracted using a cubic spline fit. The damper forces are not only non-linear but are also asymmetric, having different properties in bump and rebound. The curves for the front and rear dampers are shown in Figure 3.30. An example of the syntax that could be used to formulate the non-linear characteristics of the front damper force in MSC.ADAMS, using an SFORCE statement, would be SFORCE/2728,I1627,J1728,TRANS,FUNCTION CUBSPL(VR(1627,1728),0,1) The function formulation used here, CUBSPL, is based on a cubic curve fitting method (Forsythe et al., 1977). Note that although the function is used here to fit values to xy pairs of data it is also possible to use the function to fit values to three-dimensional xyz data sets of the type used for carpet plots. In these cases MSC.ADAMS uses a cubic interpolation method to interpolate with respect to the x independent variables and then uses linear interpolation between curves of the second z independent variables. This will be covered in more detail in Chapter 5 when the interpolation method
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Multibody systems simulation software 105<br />
I<br />
I<br />
As markers<br />
approach VR(I,J )<br />
is negative<br />
As markers<br />
separate VR(I,J )<br />
is positive<br />
J<br />
J<br />
Fig. 3.28<br />
Damper force is positive<br />
Damper force is negative<br />
Sign convention for damper forces and velocities<br />
An alternative form of definition that could be used with MSC.ADAMS<br />
involves the use of the SPRINGDAMPER statement. In this case this<br />
would have exactly the same effect as the SFORCE statement above:<br />
SPRING/0509,I0205,J0409,TRANS,K40,L250<br />
In a similar manner to the definition of a spring force the representation of<br />
a damper force will involve using the line-of-sight method to formulate an<br />
action–reaction force between an I marker on one part and a J marker on<br />
another part. We will again start with the linear case where we formulate a<br />
damper force F D using<br />
F D c • VR(I, J) (3.46)<br />
where<br />
VR(I, J) radial line of sight velocity between I and J marker<br />
c damping coefficient<br />
Since the force generated in a damper is related to the sliding velocity acting<br />
along the axis of the damper we introduce another system variable VR(I, J)<br />
that will take a positive sign when the markers are separating, as in suspension<br />
rebound, and a negative sign when the markers are approaching, as<br />
when a suspension moves upwards relative to the body in bump. The formulation<br />
of the damper force F D in (3.46) is such that the damper forces are<br />
consistent with those of a spring. The force generated is positive in a repelling<br />
mode and negative in an attracting mode as illustrated in Figure 3.28.<br />
The formulation of the damper force F D is shown graphically in Figure 3.29.<br />
An example of the syntax that could be used to formulate this in<br />
MSC.ADAMS, using an SFORCE statement, would be<br />
SFORCE/0509,I0205,J0409,TRANS,FUNCTION<br />
-5*VR(0205,0409)