h the right
;, and no
the right
n neither
load had
methods
from one
il of the
sing con-
"tromag-
50 Mk1)
hine and
orced vi-
d during
'e modes
lcer was
sonance
nd made
frequen-
r on our
e finally
am, and
ed. We
chine to
down in
iat to get
ject and
average
rements
ving the
of the il-
| 1/10 to
nachine
z). The
| to the
Fig. 17. Conventional time average hologram recorded when the arm
was excited at its lowest resonance mode. The frequency was 76 Hz,
and the fringes indicate a simple bending motion, the node being the
bright, broad, almost vertical band.
vertical represents the nodal line. The upper part of
the machine simply vibrates forward and backward as
if it rotates around the nodal line. The maximum am-
plitude at its left end was 7 X 0.254 2 0.9 um. The vi-
bration amplitude of the lower parts of the machine was
too small to be detected.
The second lowest resonance mode (325 Hz) is shown
in Fig. 18. If the top part of the machine had vibrated
in a single torsional mode around a horizontal axis, there
would have been a long bright horizontal fringe. The
nodal island indicates a vibration mode made up mainly
of torsion but also of a slight bending. The two sup-
ports that go down to the shaft are also fringe covered
so that it can be seen that the shaft close to the left
support was vibrating with an amplitude of 9 X 0.25^
= 1.16 um. The vibration amplitude of the main body
and the knee was too small to be detected, but it is
possible to see vibration patterns on the sign plate and
the cable to the right of the machine.
VIII. Double Pulse Holography
During studies of the milling machine in Stockholm
some holographic measurements were also made during
the actual cutting process. Because of the random
motions and vibrations produced by the working ma-
chine we had to use a double pulsed Q-switched laser
with a pulse separation of about 1 msec. The resulting
patterns in the holographic image were very similar to
those obtained by using a static load. The patterns
were, however, difficult to evaluate because the sign of
the displacement was not preknown and could not be
found from the conventional double exposure hologram
Fig. 18. "The same situation as in Fig. 17, but a higher resonance
mode was excited. The frequency was 325 Hz, and the fringes indi-
cate a mainly torsional motion of the over arm. Vibrations of the
shaft and the sign plate (upper right) are also seen.
we used. Therefore, it was decided to develop a sand-
wich hologram method that could be used even for
double pulsed holography with a pulse separation in the
millisecond range. Preliminary results made by Bjel-
khagen? have been very promising, and the new method
will soon be ready for practical applications.
I thank Bertil Colding, head of Production Engi-
neering Division of the Royal Institute of Technology
in Stockholm, and E. Matthias, head of Machine Tool
and Production Engineering Division (IWF) of the
Swiss Federal Institute of Technology (ETH) in Zürich,
for their valuable interest and support; R. Dandliker,
Brown Boveri Research Center, Baden, for the loan of
a Spectra-Physics argon laser; W. Schuman head of
Photoelasticity Laboratory, ETH, and M. Dubas who
lent optical equipment; St. Hrovat who gave the most
valuable metrologic assistance and E. Müller, IWF, who
made some of the holograms; G. Berter and P. Schultz
who made most of the practical work around the ex-
periments in Stockholm; and finally the National
Swedish Board for Technical Development which
sponsored much of the research.
References
1. J. Burch, Prod. Eng. 44, 431 (1965).
. N. Abramson, Appl. Opt. 8, 1235 (1969).
. N. Abramson, Appl. Opt. 15, 1018 (1976).
P. Hariharon and Z. Hegedus, Appl. Opt. 15, 848 (1976).
N. Abramson, Appl. Opt. 14, 981 (1975).
. R. Powell and K. Stetson, J. Opt. Soc. Am. 55, 1593 (1965).
. K. Stetson and K. Singh, Opt. Las. Tech. 3, 104 (1971).
. H. Bjelkhagen, Appl. Opt. 16, 1727 (1977).
WwW N
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September 1977 / Vol. 16, No. 9 / APPLIED OPTICS 2531
