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Simulation output and interpretation 433
Signal
Noise
Design
variables
System
Response
Fig. 7.31
A generic system from the robust design perspective
stiffness, master cylinder mounting stiffness and pipe stiffness come together
under ‘system stiffness’. As long as our tests incorporate some contribution
from each of the compounded ‘sub-variables’ then the conclusions will be
valid. Similarly, noise inputs can be compounded together to give a ‘noise
reducing performance the most’ and ‘noise increasing performance the
most’. For example, the former condition might be very cold brakes, fully
loaded, worn brake pads. The latter condition might be optimally warm
brakes, driver only, new bedded-in brake pads.
Each variable could be varied individually while maintaining the others
constant. While this is a valid method, it rapidly leads to a large number of
experiments with only a small number of variables. For example, with eight
variables the number of experiments required to test two levels of each
variable is 2 2 2 2 2 2 2 2 256 experiments. The use
of orthogonal arrays allows meaningful results to be produced from a
reduced set of experiments. With only eight variables, results can be obtained
from only 72 runs. Adhering to so-called ‘Taguchi’ principles and using
dynamic signal-to-noise ratios as described allows interactions between
inputs to be ruled out, allowing eight variables to be handled in just 16
experimental runs. Modern multibody system codes usually come with
some form of experimental design built into them, although not necessarily
the dynamic signal-to-noise ratio calculations described.
To perform the experiment, several levels of ‘signal’ are set and the design
configuration is set. Results are collected at each signal level, in each
design configuration for both noise conditions. The nature of those results
should be such that the comparison with the ideal function is a meaningful
one. For the brake system, mean deceleration between two speeds is
suggested as a suitable response variable. Any modern data logging or
multibody system analysis software can easily capture and process such
data. Signal factors should be chosen to give a reasonable spread of results
over the operating envelope. In the case of a brake system, three levels of
deceleration might be suggested as 0.2g, 0.5g and 0.8g, with the pedal
inputs selected to give results around these levels. Note that the signal factors
(i.e. pedal inputs) should remain as consistent as possible. The actual array
to be used is best selected from an existing library of such arrays; there is
no particular need to derive one’s own. Figure 7.32 shows a typical such
array.
Once the results have been generated – either by an experiment or by
simulation – they are processed to calculate signal-to-noise ratio and
sensitivity for each of the conditions in the orthogonal array. For vehicle
dynamic behaviour, the most useful form for the signal-to-noise ratio
calculation is the so-called ‘linear’ form, which presumes that output is