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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