4569846498

Simulation output and interpretation 427
Steering angle spectrum (degrees)
10
1
0.1
Normal road driving
Professional rally driver
0.01
0 1 2 3 4 5
Frequency (Hz)
Fig. 7.28 A frequency-domain comparison between road and competition
driving
vehicle vary with frequency. Substantially below the resonant frequency,
the behaviour of the vehicle is as already described. Around the resonant
frequency, the gain is controlled by the level of damping present and above
the resonant frequency the gain is controlled by the mass and inertia of the
vehicle.
Also like any other vibrating system, a phase shift builds up between input
and output as input frequencies approach resonance. At resonance, response
is 90 degrees behind input and beyond resonance, response is 180 degrees
behind input. For normal drivers this is particularly problematic. When
driving normally, the significant frequency content of steer input is very
low, typically below the primary ride frequencies at around 1 Hz. A professional
rally driver, in contrast, makes rapid and high frequency steering
inputs. Figure 7.28 shows a pair of spectral estimates made from handwheel
angle recorded over time. The spectral density measure of degrees/Hz is
multiplied by the spectral resolution of the two estimates to allow meaningful
overplotting of signals sampled at different rates. A single 4096 point
buffer, tapered using the ‘Hanning’ (cosine) window function has been used
for both signals. At the lowest frequency, the professional driver (Petter
Solberg during the third special stage of the 2002 Argentina round of the
World Rally Championship) is using around three times as much steering
input as the road driver, the author (Harty) on a Saturday in Warwickshire.
By 0.5 Hz, the normal road driver’s steer input is nearing the noise floor
and is around one eighth of its peak. In contrast, the professional driver’s
input is more or less flat to 1 Hz and tails off slowly, extending all the way
to 5 Hz before reaching the same levels as the normal road driver’s input at
0.5 Hz. At 0.5 Hz, the professional driver is using between eight and nine
times the normal road driver’s steer input – and this on a rack ratio that is
some 50% faster than the road car on which the data was gathered.
Thus the Milliken assertion (Milliken and Milliken, 1995) that for road use
the vehicle can be treated as a series of connected quasi-static events is mostly
true – this is the basis of the automotive statics analysis embodied in the
MRA Moment Method software (Milliken and Milliken, 1995). However,