Micromechanics - Neural Networks and Micromechanics - page 167

Fig. 8.23 Test pieces employed for the second prototype evaluation

length was the distance between marks 1 and 2. This magnitude corresponds to the
programmed displacement of 1,050 motor steps. The results of the measurements
are X 1 2 = 1978 m m, s = 6.07 m m. The standard deviation s gives information over

62.8 % of the samples.
In order to obtain a better sample range, it is necessary to triplicate the value of
this result to get a sampling of 99.3%, i.e., 3 s = 18.2 m m. Because of this, the error
of this sample is Error = m. This is the average error, and it can be

interpreted as the error of the Y -axis displacement because all measurements were
made in different positions on the axis. The displacement resolution for each step is
X DPSM = 1.88

18.2 m

m. In this case, the standard deviation is helpful only
to give us an idea about the behavior of the resolution compared with the theoretical
expectations for the deviation, but it is not a result that we can trust because the
error is lower than the equipment accuracy. This standard deviation might be an
estimation of the random error.
In order to define the backlash presented on the Y -axis, we measured the distance
between marks 1-3 of the testing pieces (Fig. 8.23 ). The average backlash of the Y -
axis is B g = 345.3

m m, s = 0.005 m

m. There are different backlash error sources, the
first of which is connected with the gearbox. The second and most important source
is produced by the transmission and the carriage on each axis. The leading screw
and the nut that is coupled to the carriage on each axis produce the third source
(Fig. 8.24 )[ 52 - 55 ]. It is possible to estimate the backlash produced by the gearbox
using the measurements of gear and shaft parameters. The measurement of trans-
mission and leading screw parameters is much more complicated. Therefore, we
calculate the gearbox backlash B g and then obtain transmission and lead screw
backlash B a as a difference between real backlash B t and gearbox backlash B g .

m m, s = 7.8 m