Digital torsion pendulum

Polymer Testing 9 (1990) 127-135

Digital Torsion Pendulum

I. R. F a h m y , a M. S. A b d u l - W a h a b a & R . J. S h a l a s h b aElectronics and Computer Research Centre, bPetroleum Research Centre, Scientific Research Council, PO Box 2131, Jadiriah, Baghdad, Iraq (Received 22 June 1989; accepted 28 July 1989)

ABSTRACT The design of a digital torsion pendulum is described. It uses a single optoelectronic transducer for the measurement of the logarithmic decrement and period of oscillation. The measurement technique employed may be considered able to overcome experimental errors associated with application of two transducers or other techniques cited before. Data acquisition, data processing and temperature control can be performed manually or by a microcomputer. The instrument offers good potential for economical production and operation.

1 INTRODUCTION Dynamical mechanical techniques have been extensively used in realizing the important objectives of polymer research in the characterization of polymeric solids. This is aimed at relating macroscopic bulk properties to molecular structure by the correlation of their changes to the storage and dissipation of energy following molecular deformation as functions of temperature or time. To this end, the torsional p e n d u l u m has availed itself for characterizing the thermomechanical behaviour of such materials. Kuhn and Kunzle 1 have been accredited with the first instrument in 1947; it was used three years later by Nielsen 2,3 who developed his own instrument 4 in 1951 with a detection mechanism different from those 127 Polymer Testing 0142-9418/90/$03.50 © 1990 Elsevier Science Publishers Ltd, England. Printed in Northern Ireland

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L R. Fahmy, M. S. Abdul-Wahab, R. J. Shalash

used previously. Several designs have been reported, each rectifying the shortcomings of the preceding designs,s-12 Manual operation of a torsion pendulum can be prohibitively time-consuming. The long time-scale of operation is a consequence of the low thermal conductivity of most polymeric materials. This type of measurement usually involves prolonged periods of monotonous measuring steps that are bound to result in boredom and fatigue, which may in turn affect the overall accuracy of manual measurements. Therefore, automated measurements are considered ideal for repetitive procedures and their standardization; 13 they will not vary from operator to operator. The automation of the torsion pendulum has been reported by Gillham~4 in 1974 and more recently in 1985 by Xiang. ~5 In the present work, the design of an automatic torsion pendulum is reported which has aimed at simplicity, manual or microcomputerassisted operation overcoming several of the practical problems and inaccuracies associated with other designs.

2 THEORY The torsional pendulum in its simplest form consists of an inertia disc which can oscillate freely, and to which the test polymer specimen is attached, as shown in Fig. 2. The other end of the specimen is attached to a fixed clamp. When the polymer specimen is twisted, the inertia disc starts to oscillate and, due to the damping nature of the polymer, the oscillations start to decay gradually until they die out. Therefore, by measuring the time and amplitude of these oscillations, the dynamic mechanical parameters, i.e. logarithmic decrement and tan 6, can be calculated. The operation of the instrument requires an initial displacement of the inertia disc from its equilibrium position. The resultant equation of motion will assume the form: 0 + A~O + A 2 0 = 0

where 0 and O represent the second and first derivative of angular displacement 0 with respect to time. The solution of this equation of motion to a good approximation may take the form: O(t) = Ooe- ~' cos (o9t - ¢)

where ¢ is a phase angle depending on the timing of data acquisition, o~ is the damping coefficient and 00, A1 and A2 are constants (A1 = 2o~ and A2 = o92+ a2). The solution gives a damped sinusoidal wave (Fig. 4),

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reflecting the damping nature of polymeric materials. The damping is measured via A, the logarithmic decrement given by: A = In (An/An+~)/n where An is the amplitude of the nth peak and n is the number of oscillations. The mechanical damping in polymers can be understood by considering the shear modulus, G. It is assumed that G consists of real and imaginary parts as expressed below: G = G' + iG"

where G' is the real shear modulus which is proportional of energy recoverable from a deformed polymer. G" is shear modulus, which is proportional to the amount of dissipated as heat when the polymer is deformed. G" and to the mechanical damping by the following equation:

to the amount the imaginary energy lost or G' are related

G " / G ' = A/z~ = tan 6

where tan b is the loss tangent. The determination of the logarithmic decrement is performed by calculating the ratio Ai/Ai+l. This has not always proved easy; alternatively, the ratio of the velocities of two consecutive oscillations has been measured. This is based on the principle, for a sinusoidally oscillating system, that the instantaneous velocity of an oscillation at zero amplitude is proportional to the maximum amplitude, i.e. l]i/•i+l

-'~ Ai/Ai+l

However, in the present work, a different approach has been adopted. It involves the generation of clock pulses as light is reflected off alternate dark and highly reflecting strips on the inertia disc, where the pulse width is a measure of the velocity of the disc, i.e. a very wide pulse width represents the end-point of an oscillation (see Fig. l(a)). The logarithmic decrement is conveniently realized by counting the number of pulses between the two end-points of an oscillation which effectively represents peak-to-peak value. These counts are sent via a parallel interface to a microcomputer in which both logarithmic decrement and tan ~i are calculated.

3 THE INSTRUMENT A schematic diagram of the instrument is shown in Fig. 2. It operates inside a chamber with the test specimen surrounded by a temperature-

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Pulse shapes at points a, b, c, d, e and f of Fig. 3. controlled hollow cylindrical enclosure. The test temperature is adjusted and controlled by a temperature controller. A thin circular aluminium glass mirror (D) serves as the inertial mass of the pendulum on the surface periphery of which equally spaced black strips of equal width are printed. The instrument can operate over a temperature range between room temperature and 300 °C. Free oscillations are initiated by angular displacement of the inertial mass using a lever-arm mechanism and small stepper motor (M). The initial angle of twist is selected via a thumbwheel switch connected to the stepper motor driving circuit. Angular twist is initiated by pressing down lever A, which lowers the motor driver onto the mirror surface and simultaneously raises the needle mechanical fixture upwards. The fixture is incorporated to ensure no sideways movement of the disc on its release at the start of a test run, which is effected when switch B is pressed. Conversion of the damped oscillations to electrical signals is realized by using a single transducer (S) positioned above the periphery of the disc. The transducer consists of an infrared transmitter and receiver encapsulated in a single package. Light is transmitted, incident at 45 ° to

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the disc surface, and detected by the receiver after reflection at the surface. Pulses are produced as the disc oscillates, a consequence of reflection of light from highly reflecting and dark srips. The pulses are taken to a pulse-shaping circuit whose output is clock pulses suitable for the digital system (Fig. 3). Pulses shapes shown in Fig. l(a-f) refer to corresponding points a - f shown in Fig. 3. The electronic system consists of three modules: oscillations profile tracking, peak-to-peak digital display and period-of-oscillation digital display. These modules facilitate the use of the instrument when no microcomputer is available.

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Fig. 4. Experimental trace: amplitude, A (Arbitrary Units) versus time scale, T (25 s/era). to be noted that for positioning the trace in the middle of a paper, the number 127 needs to be loaded into the counters while the disc is stationary, before commencing the oscillations. This is required because the maximum limit of the counters is 256. A typical experimental trace is illustrated in Fig. 4.

3.2 Peak-to-peak digital display In this modul e, three BCD counters are used to count up to 256. In order to allow the counters to count in an ascending or descending order, depending on the direction of rotation, the clock pulses are fed to a retriggerable monostable whose set time is adjusted to be slightly longer than the width of the pulse preceding the end-point pulse. This, then, secures a change of state in the monostable at the end-points of oscillation. The monostable output is taken to a toggle flip-flop to obtain an up/down signal. This signal is fed to a negative and positive edge pulser to freeze the digital display for the top and bottom peaks of the oscillation (Fig. 3).

3.3 Period-of-oscillation digital display A 1 MHz crystal oscillator is used for this purpose. The output frequency is stepped down to 10 Hz in order to achieve a more realistic

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L R. Fahmy, M. S. Abdul-Wahab, R. J. Shalash

maximum time of 99-9s, which can cover a very wide range of materials. In order to display the period of each oscillation, the output of the toggle flip-flop is divided by two to obtain the time between two consecutive peaks. This is realized by utilizing a negative and positive edge pulser, where, at the end of each oscillation, the period of oscillation is displayed digitally. This is approximately the same for each material. A delay circuit has been incorporated to allow for storage of data before fresh counting commences. The use of a torsion pendulum usually necessitates the determination of the direction of the inertial disc rotation. This may be accomplished by using two transducers placed above the disc so that their output signals are in quadrature. However, practical problems are encountered in view of the free movement of the disc. These problems have been completely overcome by employing one transducer and the technique of dependence on the time the disc is stationary at the end-points of each cycle. In addition, the instrument offers the capability of manual operation, if no microcomputer is available. In such a case, experimental data relevant to the calculation of tan 6 and logarithmic decrement (upper and lower peaks and period of oscillation) can be conveniently read off the digital displays on the instrument for processing later.

REFERENCES 1. Kuhn, W. & Kunzle, O. Heir. Chim. Acta, 30 (1947) 839-43. 2. Nielsen, L. E. Some instruments for measuring the dynamic mechanical properties of plastic materials. A S T M Bull., 165 (1950) 48-52. 3. Nielsen, L. E., Buchdahl, R. & Levereault, R. Mechanical and electrical properties of plasticized vinyl chloride compositions. J. Appl. Phys., 21 (1950) 607-14. 4. Nielsen, L. E., A recording torsion pendulum for the measurement of the dynamic mechanical properties of plastics and rubbers. Rev. Sci. Inst., 22(9) (1951) 690-3. 5. Schmeider, V. K. & Wolf, K. Kolloid-Z. 127 (1952) 65-78. 6. Koppelmann, V. J., Uber das dynamisch-elastische Verhalten hochpolymerer. Kolloid-Z., 144 (1955) 12-41. 7. Lord, P., Pithey, E. R. & Wetton, R. E., Improved instrument for the continuous determination of dynamic mechanical properties of high polymers. Lab. Practice, (Dec. 1961) 884-8. 8. Swartz, J. C., Apparatus for measuring internal friction and modulus changes of metals at low frequency. Rev. Sci. Inst. 32(3) (1961) 335-8. 9. Adicoff, A. & Yukelson, A. A., Torsional braid as a kinetic tool for the study of the polymerization of viscous materials. J. Appl. Polym. Sci., 10 (1961) 159-69.

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10. Gillham, J. K., A semimicro thermomechanical approach to polymer characterization. Appl. Polym. Symp., 2 (1966) 45-57. 11. Gillham, J. K., Torsional braid analysis: a semimicro thermomechanical approach to polymer characterization. Crit. Rev. Macromol. Sci., (Jan. 1972) 83. 12. Wheeler, A., Evaluation of flexible materials by means of an automatic torsion pendulum. Plastics and Polymers, 37(131) (1969) 469-74. 13. Bibbero, R. J., Microprocessors in Instruments and Control. John Wiley & Sons, New York, 1977. 14. Gillham, J. K., A semimicro thermomechanical technique for characterizing polymeric materials: torsional braid analysis. AIChE J., 20(6) (1974) 1066-79. 15. Xiang, P. Z., Ansari, Ii & Pritchard, G., Torsion pendulum automation by a single microcomputer. Polymer Testing, 5 (1985) 321-39.