A N O N - C O N T A C T I N G O P T I C A L D I S P L A C E M E N T T R A N S D U C E R S. E. S E M E R C I G I L
D e p a r t m e n t of M e c h a n i c a l E n g i n e e r i n g K. M c L A C H L A N
D e p a r t m e n t of C i v i l E n g i n e e r i n g N. P O P P L E W E L L
D e p a r t m e n t © f M e c h a n i c a l E n g i n e e r i n g U n i v e r s i t y of M a n i t o b a
W i n n i p e g , M a n i t o b a R 3 T 2N2 A B S T R A C T
A n o n - c o n t a c t i n g o p t i c a l s y s t e m is d e s c r i b e d w h i c h can m e a s u r e not o n l y a b s o l u t e d i s p l a c e m e n t s li k e c o m p a r a b l e , m o r e t r a d i t i o n a l t r a n s d u c e r © but a l s o r e l a t i v e d i s p l a c e m e n t s . It can be c h e a p and, ev e n u n d e r n o r m a l l i g h t i n g c o n d i t i o n s , o p e r a t e d n o n - i n t r u s i v e l y at s o m e d i s t a n c e f r o m a test o b j e c t w h i c h n e e d not b e r e f l e c t i v e . S e v e r a l e x a m p l e s a r e p r e s e n t e d to i l l u s t r a t e the s y s t e m ’s v e r s a t i l i t y in a p p l i c a t i o n s i n v o l v i n g f r e q u e n c i e s b e l o w 100 Hz.
R E S U M E
U n e m é t h o d e o p t i q u e p o u r m e s u r e r les d é p l a c e m e n t s dans un s y s t è m e est d is cu te r. Les m e s u r e s p e u v e n t ê t r e fait a une d i s t a n c e du s y s t è m e et il n ’y a a u c u n c o n t a c t a v e c le systèae.
Un e n v i r o n n e m e n t s o m b r e n ’est pas n é c e s s a i r e et la s é t h o d e d o n n e non s e u l e m e n t des r é s u l t a t s a b s o l u s m a i s a u s s i r e l a t i v e s . P l u s i e u r s a p p l i c a t i o n s sont i n c l u qui d é m o n t r e la f l e x i b i l i t é de
la m é t h o d e p o u r m e s u r e r les d é p l a c e m e n t s en b a s de 100 Hz.
1 . I N T R O D U C T I O N
A n o n - c o n t a c t i n g t r a n s d u c e r , u n l i k e an a c c e l e r o m e t e r , does not h a v e to be p l a c e d on a v i b r a t i n g o b j e c t to d e t e r m i n e the d y n a m i c c h a r a c t e r i s t i c s . Th i s f e a t u r e is p a r t i c u l a r l y u s e f u l for l i g h t w e i g h t o b j e c t s w h o s e b e h a v i o u r w o u l d b e i n f l u e n c e d b y the a d d i t i o n a l w e i g h t of a c o n t a c t i n g probe. H o w e v e r , c o n v e n t i o n a l n o n - c o n t a c t i n g t r a n s d u c e r s like l a s e r s or c a p a c i t i v e p r o b e s are e i t h e r q u i t e e x p e n s i v e or h a v e to b e l o c a t e d v e r y c l o s e to the v i b r a t i n g o bj e c t [1]. F u r t h e r m o r e , t h e y are o n l y abl e to m e a s u r e a b s o l u t e d i s p l a c e m e n t s . A n o n - c o n t a c t i n g o p t i c a l t r a n s d u c e r w i l l be d e s c r i b e d w h i c h l a r g e l y o v e r c o m e s t h e s e d i s a d v a n t a g e s . Fo u r e x a m p l e s of its u s e w i l l be p r e s e n t e d to p o r t r a y v a r i o u s a p p l i c a t i o n s .
2.PRINCIPLE OF O P E R A T I O N All EXP E R I M E N T A L IMPLEMENTATION
The p rinciple of m e as ur i ng an absolute displaceaent with the optical transducer is illustrated in Figure 1(a). A light source is used to form a slit of light on the opening created between the object, v ib r ating about an e q uilibrium position, and a s tationary reference post. The additional iris and collimator in Figure 1(a) are optional components w hich a ay be introduced to isprove the u n i f omity of this slit of light. If uniform, light p assing through the opening will fluctuate by an a i o u D t which is proportional to the aoveaent of the v i b rating object.
Such fluctuations can be d etermined by using a biconvex lens to focus the transmitted light on a photocell and me a s u r i n g the p h o t o c e l l ’s amplified electrical output on an oscilloscope.
However, it is beneficial to place the photocell not quite at the b i convex l e n s ’ focal point so that the light iiaage is formed over the p h o t o c e l l ’s entire surface. This precaution alleviates the consequences of slight misalig n m e n t s between the the optical components. Furthermore, if a displaceaent is needed at more than one location of the v ib rating object, as in a modal analysis, openings first formed at the different locations with the object at rest should be prefer a bl y identical. Then the initial light transmissions associated with each location will be the same so that the gain of the optical system will be constant. Finally, if the reference post itself was to move then the same procedures may still be used to determine the vibrating o b j e c t ’s displacement relative to the post.
The first embodiment of the optical transducer was made from avaiiible components and is shown in Figure 1(b). The light source was a small, high intensity bulb with an internal coil and the iris and collimator were absent. Seasonable accuracy was obtained p r ov i di ng p ea k- to-peak absolute or
relative displacements were smaller than 1.0 mm. Larger
displacements would need better and more costly components. The following components were purchased p ri marily from Ealing Scientific Limite d + :
1. A very high intensity halogen light bulb, Type 28-8407.
2. An iris with a 2mm opening, Type 22-8801, to transmit only the most homogeneous centre section of the light source.
3. A collimator, Type 28-8506, with a focal length of 95 mm to transpose diverging light into parallel rays. (The inclusion of a collimator made sure that the sens i ti v it y of the optical transducer did not change when the distances between the collimator to opening and opening to b iconvex lens were varied.
However, the distances betw ee n the source and iris, iris and collimator and biconvex lens and photocell must then be kept c o n s t a n t .)
+
Ealing Scientific Limited
6010 Vanden Abeele, Saint-Laurent, Quebec, C a nada H4S 1R9.
1 10 m m s o u r c e
5 7 m m
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b i c o n v e x lens
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F i g u r e 1. S h o w i n g (a) a g e n e r a l a r r a n g e m e n t a n d (b) t h e c o m p o n e n t s o f t h e $ 5 0 s y s t e m .
( l ) L i g h t s o u r c e ( 2 ) b i c o n v e x l e n s (3) p h o t o c e l l
4. A good quality b i convex lens, Type 23-8972, with a focal length of 50 mm to better focus the light on the p h o t o c e l l ,MRD Type 3055 [5].
These additions brought the total cost of the optical coapoaents
•roi $50 to under $1500 and extended the w o r k i n g displacement range a p proxiaately five tiaes.
The sensitivity and linearity of the u pgraded optical systes were found from comparisons with reference absolute displacessents a e asured i n dependently by using a Wayne Kerr ME I capacitive probe and aeter. Easily detectible displacements with various amplitudes and frequencies were created by firmly securing a solid metal bracket to an e lectromagnetic shaker controlled by a power amplifier and a sinewave generator.
An opening was forced between the bracket and an adjacent stationary post in a similar fashion to that shown in Figure 1(b).Signals from both tranducer systems were displayed s i m u ltaneously on a Tektronix 7313 storage oscilloscope to facilitate calculation of the upgraded s y s t e m ’s sensitivity.
Percentage deviations"*” from 24 aV/am, the average sensitivity in the frequency range 1 to 100 H z , are p r e s ented in Figure 2.
The greatest deviations of 11 X from the linear abscissa of this figure h a p p e n s regardless of the peak absolute d i s p l a c e m e n t , at frequencies above 40 Hz. They were caused by resonances of the structure supporting the optical components. Experiments also indicated that linearity was r easonably p r e s erved when the bracket's displacement was changing the size of the opening
(between the bracket and post) by 4% to 30%.
3. TYPICAL A P P L I C A T I O N
3.1 Biliaear Hysteretic O scillator
The upgraded optical system was used, as illustrated in Figure 3, to measure the absolute displacement hist o r y of an experimental bilinear h ysteretic oscillator. In addition, the displacement was p r o c essed el e c t r o n i c a l l y in a feedback loop to give the required b i linear h ysteretic features. Details may be found in references 2 and 3.
3.2 Modal Analysis
The fundamental mode shape of an inverted brass T-plate, s t anding on two rubber strips, was determined by using the optical system. The plate was excited s i n u s oidally at its fundamental natural frequency by c onnecting it through a light sp ring to an elect r o m a g n e t i c shaker. To avoid interference with +
S e n sitivity at any one frequency - Average sensitivity
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( l ) L i g h t s o u r c e (2) iris (3) c o l l i m a t o r (4) b i c o n v e x lens (5) p h o t o c e l l (6) v i b r a t i n g m a s s (7) o p e n i n g (8) f i x e d r e f e r e n c e f r a m e .
the M e t a l plate* the elements of the o p t ic a l system could not be set in a single row as before. I n s t e a d 9 two rows w e r e formed on each side and p e rpendicular to the p l a t e 9s vertical component as shown in Figure 4(a). Light was transferred b e t w e e n the rows by employing two off-set but parallel mirrors each p ositioned at 45° to the p l a t e ’s vertical component. Absolute deflections and phases at regularly spaced points of the plate were found with the help of a lovable cardboard strip appended c o nsecutively to each point. This arrangement m ay be seen in Figure 4(a) together with the stationary reference post. Reasonable agreement is shown in Figure 4(b) with the mode shape determined c o n v entionally [4] by traver s i n g a Bruel and Kjaer Type 4344 accelerometer across the much heavier plate.
3.3 Vibroi mpact Damper
A vibroimpact damper is e s s entially a rigid nass (m) whose motion, upon collision, opposes and reduces that of a larger resonant mechanical system. It is important, therefore, to know the relative displacement when "tuning" the damper. This measurement was achieved s t r a i g h t f o r w a r d l y by employing the optical system and stiff, lightweight cards fixed firmly to both the damper and an oscillator representation of a mechanical system to exaggerate their intermediate gap. Typical relative and absolute displacement measurements are presented in Figure 5 together with a schematic of a vibroimpact damper.
3.4 Multi-e x p o s u r e Phot o g r a p h y
The optical systea was employed as a trigger for a 35 mm camera when photogr a p h i n g the progressive deformation of a pendulum impacting a rigid wall. The pendulum cut the optical s y s t e m ’s light beam just befo r e the collision. Then the sudden change in the electrical output of the s y s t e a ’s photocell triggered a stroboscope. By leaving the c a m e r a ’s aperture open, the ensuing stroboscopic light flashes p roduced multi-e x p o s e d photographs around the instant of collision. Resulting photographs like that shown in Figure 6 gave a visual representation of the p e n d u l u m ’s deformation history.
4 . CONC LU SI ON S
A n o n - c o n t a c t i n g optical system has been developed to a ccurately measure b o t h absolute and relative displacements b e l o w 100 Hz. The s y s t e m ’s cost depends upon the peak displacement to be m e a s u r e d but remains very competitive when compared with alternatives. Several typical examples have been presented to illustrate the p o t entially wide range of the s y s t e m ’s applications.
( a )
(1) Light s o u r c e (2) iris (3) c o l l i m a t o r (4) m i r r o r (5) b i c o n v e x lens (6) p h o t o c e l l (7) e l e c t r o m a g n e t i c s h a k e r (8) light s p r i n g (9) i n v e r t e d T - p l a t e (10) f i x e d r e f e r e n c e post (11) c a r d b o a r d s t r i p ( s e c u r e d to the edge of the plate).
F i g u r e 4. M o d a l a n a l y s i s of an i n v e r t e d T-pla t e . I l l u s t r a t i n g (a) the two row o p t i c a l s e t - u p and (b) the c o m p a r i s o n of the r e s u l t i n g f u n d a m e n t a l m o d e s h a p e (-■-•) w i t h that d e t e r m i n e d
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F i g u r e 5. S h o w i n g (a) a s c h e m a t i c and (b) the d i s p l a c e m e n t h i s t o r i e s of the m a s s e s in a v i b r o i m p a c t system.
F i g u r e 6. A m u l t i - e x p o s e d p h o t o g r a p h s h o w i n g the d e f o r m a t i o n h i s t o r y of a r e s i l i e n t p e n d u l u m » The i n t e r v a l b e t w e e n e x p o s u r e s was 2.4 msec.
5 . REFERENCES
1. W. G. R I C H Â R Z 1985 C a n a d i a n A c o u s t i c s . Vol. 13, no 4, 19-23.
N o n - C o n t a c t iïîg D i s p l a c e m e n t Sensor.
2. W. J. M C A L L I S T E R 1985 M. Sc. ( E n g i n e e r i n g ) Thesis, U n i v e r s i t y of M a n i t o b a . A S t u d y of a B i - l i n e a r H y s t e r e t i c System.
3. K. M c L A C H L â N , N. P Q P P L E W E L L , W. J. M c A L L I S T E H a n d C. S. C H A N G 1983 S h o c k a n d V i b r a t i o n B u l l e t i n Proc. 53, Pt. 4, 13-17. An E x p e r i m e n t a l H y b r i d M o d e l for a B i l i n e a r H y s t e r e t i c Systea.
4. D. J. E W I N S 1984 M o d a l T e s t i n g : T h e o r y a nd P r ac t i c e . N e w York, R e s e a r c h S t u d i e s P r e s s L t d . , J o h n W i l e y & Son s Inc.
5 . The S e s i c o n d u c t o r D a t a Libr ar y, M o t o r o l a S e m i c o n d u c t o r P r o d u c t s Inc., Vol. II, p. 3 . 9 3 5 — 3.938, M o t o r o l a Inc., 1972.
ACKNOWLEDGEMENTS
The f i n a n c i a l a s s i s t a n c e of the N a t u r a l S c i e n c e s and E n g i n e e r i n g R e s e a r c h C o u n c i l of C a n a d a is a c k n o w l e d g e d g ra t ef u ll y .
