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Multibody systems simulation software 107<br />

12000.0<br />

FRONT DAMPER – SOLID, REAR DAMPER – DASH<br />

9000.0<br />

6000.0<br />

Force (N)<br />

3000.0<br />

0.0<br />

3000.0<br />

6000.0<br />

9000.0<br />

5000.0 3000.0 1000.0 1000.0 3000.0 5000.0<br />

6000.0 4000.0 2000.0 0.0 2000.0 4000.0 6000.0<br />

Velocity (mm/s)<br />

Fig. 3.30<br />

Non-linear force characteristics for front and rear dampers<br />

is described for use with tyre models. The format for this function expression<br />

used here is<br />

FUNCTION CUBSPL(x, z, id)<br />

where<br />

x the independent variable on the x-axis, in this case VR(1627,1728)<br />

z is set to zero to indicate that the data set is two dimensional<br />

id the id of the spline data set, in this case spline number 1<br />

An example of the spline data set used here to represent the non-linear<br />

damper force follows. In this case the velocities are defined in mm/s on the<br />

x-axis and the values of force (N) are returned on the y-axis. It is important<br />

that the data set has sufficient range at both the top and bottom end to<br />

encompass the conditions during the simulation. Should the independent<br />

variable used on the x-axis reach values outside of the range of the spline<br />

data then the program will have to extrapolate values that can lead to unreliable<br />

results.<br />

SPLINE/1<br />

,X 5000, 3150, 2870, 2450, 2205, 1925, 1610, 1260<br />

,910, 630, 470, 400, 350, 300, 250, 230, 200, 190<br />

,160, 120, 80, 55, 40, 20, 10, 1, 0.1, 0, 0.3, 3, 30, 40,<br />

60,80, 100, 200, 250, 400, 490, 770, 1050, 1330, 1820, 2060, 2485, 2590<br />

,2730, 2835, 2940, 3080, 5000<br />

,Y 10 425, 5800, 5200, 4400, 4000, 3600, 3200, 2800, 2400, 2000, 1800<br />

,1700, 1600, 1500, 1400, 1350, 1310, 1290, 1200, 1000, 700, 400, 210, 80<br />

,40, 4, 0.4, 0, 1, 10, 100, 123, 150, 182, 200, 260, 300<br />

,400, 500, 800, 1200, 1600, 2400, 2800, 3400, 3500<br />

,3600, 3700, 3800, 4000, 7840<br />

Although the method of modelling a non-linear force element has been<br />

demonstrated here using a damper the method is equally applicable to other

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