7. V. P. Andreev, "Damping capacity of thin structural components," in: Energy Dissipation in Oscillating Mechanical Systems [in Russian], Naukova Dumka, Kiev (1985), pp. 295-301.

8. G. S. Pisarenko, "Structural energy dissipation in an oscillating material," Proceedings of the Scentific-Technical Conference on the Investigation of Energy Dissipation in Oscillating Elastic Bodies [in Russian], Izd. Akad. Nauk UkrSSR, Kiev (1958), pp. 247- 254.

9. N. M. Mukhin and G. S. Pisarenko, "Effect of a specimen's sectional dimensions on the decrement of the damping of torsional oscillations," in: Energy Dissipation in Oscilla- ting Elastic Systems [in Russian], Izd. Akad. Nauk UkrSSR, Kiev (1963), pp. 214-219.

i0. A. P. Yakovlev and R. G. Shumilova, "Effect of the dimensions of metal-ceramic specimens on the logarithmic decrement of damping during transverse oscillations," Proceedings of the Scientific -Technical Conference on the Damping of Oscillations [in Russian], Izd. Akad. Nauk UkrSSR, Kiev (1960), pp. 127-129.

ii. V. A. Leonets, "Effect of absolute dimensions of low-carbon-steel rods on the logarithmic decrement of torsional oscillations," Probl. Prochn., No. 12, 107-111 (1978).

12. G. S. Pisarenko and O. T. Bashta, "Effect of the absolute dimensions of carbon-steel specimens on the damping characteristics during transverse oscillations," Probl. Prochn., No. 9, 80-84 (1970).

13. V. V. Matveev and B. S. Chikovskii, "Evaluation of the effect of static tension on the damping capacity of a material during investigation of the bending oscillations of ten- sion rods," Probl. Prochn., No. 9, 85-88 (1970).

EFFECTS OF VIBRATION AND TEMPERATURE ON THE CARRYING CAPACITY

OF A MAGNETIC TAPE REEL

E. S. Umanskii, N. S. Shidlovskii, and L. K. Stezhko

UDC 539.3/5:678

Certain regularities have been established [i] in the failure of magnetic-tape reels (MTR) on operation under various conditions of vibration but otherwise safe working condi- tions at room temperature.

On the other hand, the technical specifications for operating magnetic-recording equip- ment envisaged the reels working under considerable vibrational load between -60 and +60~ [i, 2]. To increase the reliability in systems based on tape recording, considerable interest attaches to the variation in MTR capacity under extreme conditions, particularly when vibra- tion is combined with elevated temperatures.

The effects of temperature on the residual stresses in MTR, which are monolithic, have been examined in [4-6], where in particular it has been shown that MTR based on polyethylene terephthalate wound on steel or aluminum cores show reduction in the pressure between turns in the body of the winding as the temperature is reduced. Operating the reels at elevated temperatures activates relaxation and in some cases causes loss of carrying capacity.

Here we give results on the effects of temperature and vibrational loads, either alone or together, on the carrying capacities of PETP reels as used in recording and data process-

ing.

The experiments were performed with an apparatus based on a VEDS-100B electrodynamic tester [7] fitted with a thermal chamber, which maintains a set temperature in the range 20 to 80~ with an accuracy of ZI~ The temperature was monitored with copper-constantan

thermocouples placed between the turns.

The tape reels of width 6.25 mm were wound on solid aluminum cores of diameter 90 mm and height 8 mm with a given tape tension in the range from 0.50 to 1.25 N at normal temperature. During the winding, copper-constantan thermocouples were inserted between the turns at cer- tain radii, with the junctions in the median plane. The maximum thickness of the thermo- couple junctions was 0.i n~ and had virtually no effect on the residual-stress distribution.

Kiev Polytechnic Institute. Translated from Problemy Prochnosti, No. ii, pp. 69-72, November, 1986. Original article submitted December 29, 1985.

0039-2316/86/1811-1509512.50 �9 1987 Plenum Publishing Corporation 1509

. . . . . . . . . . . . . . . . . . .

1.0 ;.2 m.4 ZN ~8 ~ f,O f .2 ~'/~ ~r~ gO' p a b

Fig. 1

;5

zo

y

o

a ~ - . . . . ; . . . . . . . . . . . . . . . . . ~ - ,

I - S - - J ...........

I ~ i I I i l i ]

JS' ~'0 ~ s rain Z6o 7~ J40 2~ too ~ o ~ . Hz

Fig. 2 Fig. 3

Fig. i. Distribution of the excess temperature over the radius on dissipative heating by forced transverse vibrations: i, 2, 3, and 7) H = 1.25 N; 4) H = 0.75 N; 5) H = i00 N; 6) H = i.i0 N (the solid line has been recorded with a ~ 200 m/sec 2, and the dot-dash lines with & = 300 m/sec2).

Fig. 2. Variation in excess temperature on dissipative heating by forced transverse oscilla- tion: i) H = 1.25 N; 2) H = i.i0 N; 3) H = 1.0 N.

Fig. 3. Dependence of excess temperature on resonant vibrational frequency in dissipative heating by forced transverse oscillation with an acceleration of 200 m/sec 2 (vibration time

2 h): i) p = 1.0; 2) 0 = i.i; 3) p = 1.3;4) 0 = 1.5; 5) 0 = 1.9.

The temperatures in the winding were measured with a V7-21 digital voltmeter.

The radial residual stresses in the wound reels were measured not only by a method based on the stretching of thin plates [6] but also from an analysis based on a cylindrical ortho- tropic disk [4, 5, 7].

MTR Carrying Capacity on Prolonged Vibration. Under working conditions, vibrational loads can be present for long periods in magnetic-recording equipment, which represent a sub- stantial hazard to the body of the coil on account of dissipative heating. The additional (excess) temperature patterns active at residual-stress relaxation, which can cause premature loss of carrying capacity.

The dissipative heating was examined, together with the reduction in carrying capacity, by the use of transverse vibrations with accelerations of 100-300 m/sec 2 under resonant con- ditions without forced air flow.

Figure 1 shows the distributions of the excess temperature AT over the radius; as the acceleration increases, and consequently also the amplitude of the cyclic strain, AT rises substantially, but the radial temperature distribution is much the same. In reels wound with less tension, i.e., having lower o r , the most heated region is displaced towards the middle turns.

This is evidently due to change in the relation between the amount of heat produced by cyclic bending and the amount of heat dissipated by the periodic mutual displacements of the turns in the axial direction. In a reel with a sufficiently high residual-stress level, the first of these predominates, and the maximal excess temperature occurs near the core, i.e., where the maximum bending stresses arise. When the pressure between the turns is less, there is not only a general reduction in the excess temperature but also a shift to heat production associated with friction between turns, which occurs mainly in parts with lower pressure be- tween turns, i.e., far from the core.

Figure 2 shows heating kinetics and the related reduction in carrying capacity; the dis- sipative heating by transverse vibration with acceleration a = 200 m/sec 2 essentially stabil- izes after 2 h.

The resonant frequency fr affects the excess-temperature distribution (Fig. 3); as the resonant frequency increases (as the tape tension in winding increases), the excess tempera- tures at the various radii increase substantially. The point of maximum heating also alters.

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~2 mlsec 2

)

L f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,

o 7c 5o 9OK, m_n

Fig. 4

o8~ ...... i iJ o.8

o - i rf o ~ " -

Fig. 5 Fig. 6

P

Fig. 4. Variation in damaging acceleration in dissipative heating due to transferse vibration for H = 1.00 N.

Fig. 5. Radial-stress relaxation on vibration with an acceleration of i00 m/sec 2 at room temperature (i), at 60~ without vibration (2), and with the joint effects of temperature and vibration (3) (p = i.i, ~ is the initial radial-stress level).

Fig. 6. Variation in radial stresses for vibration with an accelera- tion of i00 m/sec 2 at room temperature (i), at 60~ without vibration (2), and with the joint action of temperature and vibration (3).

For example, for a reel wound at 0.50-0.75 N (fr 250-280 Hz), the maximum excess temperatures occurred at the relative radii p = r/R a = 1.5-1.6 (r is current radius and R a is core radius). Reels wound with the maximum permissible tension of 1.25 N (fr = 360 Hz) show that region displaced close to the core (p = 1.0-i.i).

Some reels were vibrated with a = 200 m/sec 2 for 30-120 min and were then cooled to room temperature before being caused to fail by brief forced transverse oscillation at frequency f = (0.5-0.6)fr; Fig. 4 illustrates the reduction in the failure acceleration for reels wound at 1N.

The change in carrying capacity on dissipative heating is as follows. According to [4, 6], these polyethylene terephthalate reels wound on aluminum cores show considerable increases in the radial compressive stresses as the temperature rises, while the initial stage of dissi- pative heating is characterized by some strengthening. However, the subsequent relaxation and cooling mean that the level of pressure between turns is less than the initial value, i.e., as measured directly after winding, which l~ads to an overall reduction in the carrying capacity.

For example, resonant vibrations with a = 200 m/sec 2 operating for 2 h did not cause failure in heated reels, but after cooling to room temperature, they failed at accelerations of 100-150 m/sec 2 (Fig. 4), i.e., the failure acceleration was reduced by more than a factor three by comparison with the initial value.

State of Strain Caused by Thermal and Vibrational Loads. The carrying capacity of a reel is maintained by the pattern of compressive radial stresses due to the winding on a rigid core. The main at tension in the experiments has been given to the variation in these stresses caused by vibration and temperature.

These polyethylene terephthalate rolls were wound on aluminum cores of diameter 90 mm at a tension of 1 N; the outside diameter of the finished reel was 180 mm. Preliminary experi- ments were made with 12 reels, which indicated the initial radial-stress level as measured directly after winding.

Reels fail under vibration and heating mainly in the region adjoining the core (p = 1.00-1.15), so the main attention was given to stresses there, which enabled us to reduce the

volume of experiments considerably.

Three tests modes were used:

i) resonant vibration at 199 m/sec 2 at room temperature;

2) treatment at 60~ for 0.5-4 h; and

3) resonant vibration at i00 m/sec 2 at 60~

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The radial stresses were determined on reels cooled to room temperature by an air jet acting for 15 min at 0.5, I, 2, 3, and 4 h after the start.

Figure 5 shows the radial-stress relaxation curves in ~,/~reot coordinates, where o r is the current radial stress, ~ is the initial radial stress, and t is time.

Combined or separate treatment with heat and vibration causes rapid stress relaxation, which reduces the carrying capacity considerably. Resonant forced oscillations for I-4 h at 60~ reduced the radial stresses by 70-90%. The reduction is most rapid in the initial period the first 30-60 min), after which there is stabilization at low residual stress levels.

The stresses are reduced most substantially when temperature and vibration act together; in 4 h of vibration at 60~ a reel has virtually completely lost its carrying at p = 1.1 (curve 3 in Fig. 5).

The temperature makes the main contribution to stress relaxation; Fig. 5 shows that the difference in stress levels after pure temperature treatment and after vibrational treatment at elevated temperatures does not exceed 10% by comparison with the initial level. The dif- ference between stress level after pure vibrational treatment and after the combined treat- ment is substantially larger (45% at p = 1.3)o

Figure 6 shows the variation in radial stress over the radius of the winding for vari- ous working conditions over 4 h. The most rapid changes occur at p ~ i.i, because this part of the reel is the most heated (Fig. I) so rheological effects are most pronounced. There- fore, the reels are most likely to fail on combined temperature and vibrational treatment at p ~ i.i, as is confirmed by experiment.

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LITERATURE CITED

~. S. Umanskii, N. S. Shidlovskii, and L. L. Stezhko, "The carrying capacity of a mag- netic-tape reel under vibrational loading," Probl. Prochn., No. ii, 52-56 (1986). GOST 16962-71: Components in Electronic Engineering and Electronics: Mechanical and Climatic Effects: Specifications for Test Methods [in Russian], introduced May 12, 1971. V. I. Antonov, V. P. Veklich, L. P. Vodyanitskii, et al., Handbook on Magnetic Recording Techniques [in Russian], O. V. Poritskii and E. N. Trapeznikov (ed.), Tekhnika, Kiev (1981).

E. S. Umanskii, V. V. Kryukov, and N. S. Shidlovskii, "Estimating the effects of temper- ature on the carrying capacity of a magnetic tape reel," Probl. Prochn., No. 8, 62-65 (1981). E. S. Umanskii, V. V. Kryukov, and N. S. Shidlovskii, "The carrying capacity of reeled polymer film," Probl. Prochn., No. i0, 104-113 (1980). E. S. Umanskii and N. S. Shidlovskii, "An experimental study of the residual stresses in magnetic tape reels," Probl. Prochn., No. i0, 43-49 (1983). E. S. Umanskii, N. S. Shidlovskii, V. V. Kryukov, et al., "A study of the resonant fre- quencies in transverse vibrations of ma{netic tape reels," Probl. Prochn., No. 5, 81-85.

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