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Simulation output and interpretation 431
where d is the allowable range for the attribute d and d is the standard
deviation of the attribute d as produced by the process. If C p is greater than
unity, the process is ‘capable’ and if not, it isn’t. This notion is used to
assess production methods for intended tolerances and to focus attention
on the least capable processes where resources are limited. As previously
noted, the capability for the vehicle dynamics measurement process is
questionable at best – though analytical methods improve the capabability
of the process at the risk of introducing systematic inaccuracies through
modelling errors and the like.
As part of a design process, the idea of a signal-to-noise ratio (SN ratio)
becomes much more useful. If we imagine that same manufacturing process,
SN ratio is the ability of the process to produce any desired value of d.
Thus, for some form of CNC machine tool, some dimension d might be
anywhere from 10 mm to 500 mm. A snapshot of the device’s ability to produce,
say, 276 mm is less useful than an overall knowledge of the relationship
between input (desired dimension) and output (dimension produced).
There are three types of ‘lack of quality’ that concern us:
●
●
●
Linearity: the proportionality of output to input. For example, if on small
dimensions the stiffness of the workpiece reduced, the machine might
systematically make smaller things than required but as the dimension
increases this effect might become less significant.
Variability: the consistency of output to input. If the machine is insufficiently
stiff then random vibrations induced by the cutting action might
lead to random variations in the size of the workpiece.
Sensitivity: the scale of output to input. If some calibration error were present
between sensors and tool positioning shafts, it could be that so-called
‘millimetres’ in one axis were different to ‘millimetres’ on another axis.
A fourth effect is the ability of our measuring technique to discern the output
to the required resolution. If we ask for a 0.1 mm change in size of the
product but can only measure to the nearest millimetre, we are unable to
discern whether or not we have been successful. This, however, is a matter
of good experimental or analytical technique rather than something innate
in the process itself and so it is laid aside as a difficulty for the moment.
To capture all three types of ‘lack of quality’, a single measure is used – the
SN ratio. This is simply defined as
2
⎛ ⎞
SN 10 log 10 ⎜ 2 ⎟
⎝ ⎠
(7.37)
where is the sensitivity of the process (i.e. the amount the output changes
for a unit input change) and is the standard deviation of the results from
the nominal.
To successfully use the idea of SN ratio in vehicle dynamics design, a
process is required that looks something like that shown in Figure 7.30.
Notice the similarity between this and Figure 1.6 in Chapter 1. This type of
process is variously and vaguely known as robust design, parameter design
or the Taguchi method.