crease in load-carrying capacity due to the ductility properties of the material and its strain hardening. Thus, for ductile materials the above estimate can be used only to deter- mine the level of the external shearing force corresponding to the beginning of the appear- ance of plastic strains at the point of the cross section liable to the greatest stress.

i.

2. 3.

4.

LITERATURE CITED

A. P. Zhukovets, "Study of the loading conditions of shearable elements," Probl. Prochn., No. 3, 48-50 (1983). S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, McGraw-Hill (1970). B. A. Obodovskii and A. P. Zhukovets, "Determination of contact strains of shear pins in safety clutches," in: Protection of ~tallurgical Equipment from Breakage [in Rus- sian], Moscow (1972), pp. 163-176. G. S. Pisarenko (ed.), Strength of Structural Materials and Elements Under Extreme Con- ditions [in Russian], Vol. I, Naukova Dumka, Kiev (1980).

EXPERIMENTAL STUDY OF RESIDUAL STRESSES IN REELS OF MAGNETIC

TAPE

E. S. Umanskii and N. S. Shidlovskii UDC 539.315:678

i. A sizable fraction of polymeric magnetic tapes are used and stored in the form of annular reels wound about cylindrical spools made of different materials.

The reel owes its existence to the presence of residual radial compressive stresses, the magnitude of which is determined by the coiling regime and the mechanical and geometric char- acteristics of the tape being wound. The level of these stresses has a significant effect on the load-carrying capacity of the reel under the influence of thermal, vibrational, and other service factors.

~lus, one of the tasks in evaluating the capacity of reels operating under extreme con- ditions is investigation of the stress state of the body of the reel.

Similar studies, both theoretical and experimental, have been conducted mainly for wound products made of fiberglass or carbon fibers on a polymeric binder [i-9~] and intended for use in the manufacture of various structural elements, principally shells. In contrast to such products, the above-discussed reels are subjected in service to repeated winding cycles. Here both the mechanical and tile physical parameters of the system may undergo a change.

The works [10-12] examined a theoretical model of a reel of magnetic tape on a poly- ethylene terephthalate (PETP) base, wound in different regimes. Experimental results from a study of the stress--strain state of the body of the reel were also presented. Certain ques- tions on the formation of residual stresses during coiling (formation of the reel) were ex- amined in [11-15] with allowance for other service factors.

Presented below are amethod and experimental results of studying residual stresses in reels of one of the con~nonly used magnetic tapes (type 1-4406) based on PETP. The distribu- tion of these stresses over time and with a change in temperature is also explored.

An important element in evaluating the stress state of formed reels is measurement of its interturn pressures. It should be mentioned here that the use of pressure transducers which are relatively large compared to the thickness of the tape may lead to a significant change in the residual-stress field.

In connection with this, it was decided expedient to use the following two measurement methods to record the interturn pressures. These methods have almost no effect on the stress-- strain state of the body of the reel.

~le first method is based on measurement of the tensile force on very thin polished steel strips previously introduced into tile reel before winding.

Kiev Polytechnic Institute. Translated from Problemy Prochnosti, No. i0, pp. 43-49, October, 1983. Original article submitted March ii, 1983.

1402 0039-2316/83/1510-1402507.50 �9 1984 Plenum Publishing Corporation

Fig. 1. Electromechanical scheme of unit for winding reels: i) drive motor; 2) drive shaft; 3) magnetic tape; 4) pinch roller; 5) guide rollers; 6) winding motor; 7) take-up spool; 8) reel being wound; 9) regulable voltage source; i0) reel being unwound; Ii) braking motor; 12) supply reel; 13) voltage source; 14) dynamometer; 15) strain gauges; 16) movable roller of dynamometer; 17) contactor- type relay; 18) pulse counter; 19) permanent magnet; 20) thermal chamber; 21) heating element; 22) centrifugal fan; 23) resistance thermometer; 24) voltage comparison block; 25) control block (KSP- 4M -- electronic potentiometer; VS 4-12, B5-8 -- direct ~oltage souces; RD-09, SD-2 -- electric motors; EMP-109 -- electronic bridge).

The second method is based on measurement of the strains of the elastic spool on which the reel is coiled, with the stiffness of the spool differing little from that of the spools used in magnetic tape recorders.

Experience in the use of magnetic tape storage devices in the form of annular reels shows that the level of the residual compressive stresses depends to a large degree on the reel winding conditions (the ambient temperature, t~e condition of the working surface of the magnetic tape and base, the geometric dimensions of the reels, the change in the tensile forces on the tape during formation of the reel, etc.).

To study the effect of these factors on the stress state of the reels, we developed an experimental unit. The principle of operation of the unit is clear from the diagram shown in Fig. i.

The tape drive used in the unit is based on a standard design [16, 17]. The pinion drive provides for translation of the tape at one of four standard speeds -- 0.0953, 0.1905, 0.3810, and 0.7620 m/sec. The system of removable guide rollers makes it possible to wind magnetic tapes 6.25, 12.5, or 25.4 mm wide and 18 to 55 ~m thick.

During coiling, the tension on the tape can be changed within the range H = 0-4 N by means of the regulable voltage source which powers the winding motor.

~e tensile force on the tape on the section between the drive shaft and the reel being wound is measured by an extensometric dynamometer, which is in an elastic ring with glued-on semiconductor strain gauges. The tension on the tape during winding is transmitted through a movable roller to the elastic element, and tlle error signal from thegauges~ connected to a bridge circuit, is recorded by a KSP-4M potentiometer. The bridge circuit is powered by a V5-8 stabilized direct voltage source.

The supply and take-up spools are located in a thermal compartment made of a heat-re- sistant material.

1403

Fig. 2.

~,N ls

j o fA

0 2 4 6 u, m m

ql /2

I' l' Electromechanical circuit of unit for measuring radial

stresses in reels.

The system for delivering hot air into the compartment consists of a heating element made of a Nichrome spiral filament and a centrifugal fan to create an air flow. The heating element is placed with the fan in a special compartment which is covered by a protective housing containing holes for escape of the air.

The temperature is recorded and controlled by an EMP-109 IMZ electronic bridge together with an electromechanical servo system similar to that described in [18].

The temperature transducer is a copper resistance thermometer made in the form of coils embedded in one of the walls along the thermal compartment.

Use of the temperature control system has shown it to be reliable over long periods of time, maintaining the temperature to within •176 in the range 20-80~

The interturn-stress field of the reel is measured by the two methods mentioned earlier, with most of the tests having been conducted by the method of thin strips.

Preliminary experiments involving the insertion of different numbers (from one to 12) of 50-~m-thick measurement strips into one reel showed that the perturbations introduced by the strips are negligible. Thus, the tensile force acting to pull the strip out of the reel is almost unambiguously determined by the interturn pressure acting at the site of insertion of the strip.

Using the above-described unit under prescribed conditions, we wound reels of magnetic tape and inserted 0.8-mm-wide measurement strips of the indicated thickness into the reel every certain number of turns.

The measurement strips were pulled out on a special stand (Fig. 2) which includes a dynamometer translation mechanism, a block for recording the tensile force, and a system to maintain the prescribed temperature.

The wound reel 1 with its measurement strips 2 is placed in the thermal chamber 3, made of a thermally insulating material, and is fastened securely to the frame 4. The strips 2 are secured in a special clamp 5 which is connected to a proof-ring dynamometer 6. The lat- ter is in turn connected to a movable crossbeam 7. The crossbeam is moved vertically on guides 8 by means of a screw-nut pair.

The screw 9 is rotated through a planetary reduction gear i0 by a UT-II dc motor ii. The speed of translation of the strip being pulled, V = 2.3.10 -= m/min, is kept constant by a stabilized source of direct voltage 12.

1404

Semiconductor strain gauges 13 glued onto the elastic ring of the dynamometer are con- nected to a bridge circuit and are powered by a B5-8 stabilized direct-voltage source. The error signal sent from the bridge circuit during pulling of the strip and deformation of the elastic ring is measured with a KSP-4M potentiometer.

~le dynamometric system makes it possible to measure tensile forces up to 50 N to within • -2 N.

The system for recording and ensuring the prescribed temperature in the working volume of chamber 3 consists of an automatic temperature regulator 14, copper resistance thermom- eters 15, heating element 16, Dewar flask 17, evaporator 18, and centrifugal fan 19. The coolant used is liquid nitrogen. The scheme for controlling the temperature and agitating the air is no different from that presented in Fig. i.

During the pulling of the measurement strip from the reel, a diagram was recorded on the KSP-4M in the coordinates pulling force Q--strip displacement u. A typical diagram is shown in the upper right corner of Fig. 2.

The diagram can be tentatively divided into four basic sections. Section AB corresponds to an increase in the force in the strip up to point B, the ordinate of which is equal to the static friction. The decrease in pulling force on the section BC corresponds to the tran- sitional period from static friction to sliding friction at the site of contact of the strip with the magnetic tape. The sliding frictional force stabilizes on the section CD, and the decrease in the force on the section DE corresponds to the exit of the strip from the body

of the reel.

Preliminary tests showed that, due to considerations involving the scatter of the empir- ical results, in analyzing the data it would be best to use the value of the sliding fric- tion, i.e., to measure the ordinate of section CD.

Each strip was calibrated by measuring the pulling force for different values of com- pressive stresses applied to a packet composed of samples of magnetic tape.

The resulting calibration curves make it possible to use the pulling force on the strips removed from the reels to determine the level of the residual radial compressive stresses in reels which have been fully formed and, when necessary, have been subjected to further proc-

essing.

To realize the second method for measuring stresses in reels, tapes were wound about an appropriately calibrated dynamometric ring installed in place of spool 7 (see Fig. i). We thus obtained values of the residual stresses on the internal radius of the reel.

We succeeded in monitoring the roughness of the magnetic tape in the range (0.2-4)-10-" ~mm and thereby evaluating the effect of the quality of the working surface of the tape on the residual-stress field in the reel by including a special device in the kinematic circuit of the unit. The device consisted of a high-speed motor with an abrasive attachment mounted on its shaft and a clamping element which ensured close contact between the abrasive and the magnetic tape. We also used different types of abrasive to achieve the above range.

We tested reels of 1-4406-6 and 1-4406-25 magnetic tape 6.25 and 25.4 mm wide, respec- tively. The reels of the first tape were wound on a 90-mm-diameter spool, while the reels of the second tape were wound either on a ll4-mm-diameter spool or on a 170-mm-diameter elas-

tic ring.

The reels were wound at the maximum tape speed possible in the tape transport channel (V w = 0.762 m/sec). This helped reduce the amount of relaxation of the residual stresses that occurred. Such stress relaxation could significantly affect the test data.

The need to avoid significant viscoelastic strains, leading to distortion of the infor- mation recorded on the tape, limited the maximum force that could be used to wind the 25.4-

mm-wide tapes to H = 4 N.

To obtain reliable data, we tested 10-12 reels of tapes in each series of tests and sub-

sequently analyzed the results statistically.

2. Figure 3a illustrates the character of the distribution of the radial compressive stresses created during the winding of the reels. The diagram shows the measured levels of o r for different values of relative radius 0 = r/R a (r is the running radius of the reel; R a

1405

tO r2 I~ t6 r8 p a " i

~t/, [ MPa ...,:,2- " "

/ ' t

t0 I2 I.~ tO 1,8 k b

Fig. 3. Dependence of the radial residual stresses on the tension of 1-4406-25 tape

during winding (a) and on the maximum rela- tive radius of the reel (b). (Curves i, 2, 3 correspond to tensile forces on the tape

H = 2, 3, 4 N.)

~-.MPa ~r. MPa

~02~ - - - w . . . . F - - - --~

~0 U .',7 ~3 t,, ~5 ;; r ~2 t,~ t,6 t8 ' b

a

Fig. 4. Effect of the material of the spool (a) and the condition of the work- ing surface of the magnetic tape (b) on the value of the residual stresses in

the reel: i) silumin; 2) AG-4; 3) acrylonitrile butadiene styren e resin;

4) R z = 0.26"10 ~ ram; 5) R z = 0.78"10 -4 mm; 6) R z = 1.84"10 -4 mm; 7) Rz = 3.80" 10 -4 ram.

is the outer radius of the spool). As can be seen, the graphs of the residual radial stresses are monotonic curves which reach a maximum at p = i, i.e., near the external radius of the spool.

The character of the effect of the geometric dimensions of the reels on the radial- stress distribution is shown in Fig. 3b. The radial stresses in the reel increase with an increase in the number of turns in the reel, i.e., with an increase in the maximum relative radius of the reel k = Rb/Ra, where R b is the outer radius of the wound reel. Here the rate of increase in the pressure of the reel on the spool decreases with an increase in the reel radius. It is fairly high for the first turns of the reel and then begins to decrease smoothly. Beginning with roughly p = 1.3, it is nearly constant.

To evaluate the effect of the stiffness of the take-up spool on the stress state of the body of the reel of tape, we performed a series of measurements of the residual radial stresses in reels with spools made of different materials (Fig. 4a).

We wound 1-4406-6 magnetic tape on a single type of annular spool with an outer diam- eter R a = 114 mm, inner diameter R c = 76 mm, and thickness h = 25.4 mm. The material of the spool was changed: silumin (elastic modulus E = 7.1-104 MPa); acrylonitrile butadiene sty- rene (ABS) resin (E = 3.2-103 MPa); a composite based on fiberglass impregnated with AG-4 phenol--formaldehyde resin (E = 3.5-10" MPa). The winding was done with a constant force H = 1.0 N.

As might have been expected, a decrease in the stiffness of the take-up spool was ac- companied by a decrease in the level of the residual radial stresses (Fig. 4a) and, thus, a decrease in the capacity of the formed reel.

1406

-i=-t . . . . + - + . . . . . t . . . . . . . L :

-QT~ -- 1 .................

"02~

~0 f.I k2 t,5 ~t, ~ p a

o~ U, MPa

0

b

Fig. 5. Change in the residual stresses in reels of magnetic tape in relation to temperature: a) wound on an ABS spool: i) initial state at T = 20~ 2) T = -5~ 3) T = --10~ 4) T = --15~ b) wound on different spools: 5) acrylonitrile bu- tadiene styrene; 6) silumin; 7) AG-2; 8) AG-4.

3. The various types of polymer-based magnetic tapes used in modern tape recorders have different surface roughnesses. The surface roughness also changes during use of the tapes, which affects the magnitude of the residual stresses and the character of their relaxation.

This practically important question was studied by the above-described method on reels of 1-4406-6 magnetic tape taken from a single batch.

~le height of the roughness R z was determined in accordance with GOST 2789--73 from pro- filograms obtained on a 201-series profilograph--profilometer.

The residual-stress levels measured in reels of tapes with different surface rough- nesses are shown in Fig. 4b, where each value of radial compressive stress was obtained by averaging 5-6 test points. It is apparent that variation of the degree of roughness of the working layer of the magnetic tape has a significant effect on the magnitude of the stress o r for a given level of tape tension. This property can be explained by a change in the yield of the body of the reel with an increase in the roughness of the working layer. A de- crease in the actual area of contact of adjacent turns of the reel due to the formation of additional irregularities leads to a decrease in the nominal radial elastic modulus of the reel Er. This was confirmed by appropriate experiments involving compression of packets of

magnetic tapes.

4. The temperature of reels may change within the range from--60 to +800C during use of a magnetic tape recorder, this range being the GOST specification. Thus, in evaluating the integrity of reels and selecting optimum winding regimes, it is important to have data on the character of the effect of temperature change on the residual-stress distribution. Ex- perience in the use of magnetic tape recorders has shown that there is a substantial reduc- tion in interturn radial stresses Or at certain temperatures, and this reduction may alter

the load-carrying capacity of the reel.

The works [ii, 12, 14] presented results of studies of the effect of temperature change oll the stress distribution in reels wound on steel and aluminum spools. To evaluate the ef- fect of the stiffness and thermophysical properties of the spool and the dimensions of the reel on the stress state of the latter, we conducted a further study of the distribution of o r in the above temperature range for spools made of different materials.

Reels of 1-4406-6 magnetic tape were wound at normal and elevated temperatures, and their residual compressive stress field in their original state was determined. After the reels were cooled by the amount ~, we again measured the radial stresses.

Figure 5a shows the radial-stress distribution in reels, wound on an ABS spool, during cooling. It can be seen that a 15~ temperature reduction from the initial value signifi- cantly reduces the radial compressive stresses and, in essence, leads to lamination of the reel. A similar pattern is seen in the cooling of reels wound on spools made of a material with a lower coefficient of thermal expansion. A decrease in the latter is accompanied by an increase in the critical temperature drop at which the danger of reel lamination ap-

pears.

1407

TABLE i. Permissible Temperature Drops

for Reels Wound on Different Spools

Spool material =-Ira, deg--I r c r , ~

Sf lum~ AG -2 AG-4 ABS

2,3 1,47 2,0 7,2

--36 --45 --39 --13

I \

lO t.g 1> ;~ ~S F ~O t~ r~ tO 1.8 a b

F i g . 6. Change i n r e s i d u a l s t r e s s e s i n r e e l s o f magne t i c tape i n r e l a t i o n to t ime and temperature: a) holding time t = 120 min at temperatures T = 400C (2), T =

60~ (3), T = 80~ (4); b) temperature T =

60~ holding time t = 30 min (5); t = 60 min (6); t = 240 min (7). (Curves 1 show the initial stress state at tempera- ture T = 20~

Figure 5b shows the change in the maximum residual stresses in the reel near the spool with a temperature reduction, while Table 1 shows values of permissible temperature drops for reels wound on spools with different coefficients of thermal expansion ~.

~le completed experiments show that with a change in the coefficient of thermal expan- sion of the spool during cooling, there is a substantial reduction in the radial stresses in regions near the inside radius of the body of the reel. The level of stresses near the outer edge of the reel changes little in this case. With an increase in ~, the region of lamina- tion shifts toward the inside edge.

5. The rheological properties of polymeric materials are such as to cause stress re- laxation in wound reels of PETP-based magnetic tapes. This is particularly evident with long storage or use of the reels at elevated temperatures. In this case, lamination occurs due to a reduction in the magnitude of the radial compressive stresses in the reel. In con- nection with this, it is important to study the stress redistribution over time in reels within the working temperature range.

Figure 6 shows experimental curves of the radial-stress distribution in reels of 1-4406-6 magnetic tape obtained in the temperature range 20-80~

Holding the reels at nigh temperatures and st~sequent cooling to room temperature (the cooling was done over 15 min by an air jet at 20~ led to a sharp drop in the radial stresses, the appearance of excessive slack in the reel, and slipping of the turns relative

to one another. For example, after holding a reel at 80~ for 2 h and cooling it to room temperature, the radial stresses in it on the section p = 1.2-2.0 nearly dropped to zero and the reel lost its load-carrying capacity (Fig. 6a).

The radial-stress distribution in reels held at 60~ for different times is shown in Fig. 6b. It is apparent that an increase in the temperature at which the reel is stored ac- tivates stress relaxation processes and adversely affects the strength of the reel. As in- dicated above, whereas long holding of reels of magnetic tape at room temperature leads to a radial-stress reduction of no more than 20-30%, holding the reel for 4 h at 60~ reduces these stresses at least 50% from their initial value.

1408

Thus, the results presented above make it possible to evaluate the effect, on the stress state of reels of magnetic tape, of such important factors as the force parameters of the winding regime, the geometric characteristics of the system, the stiffness of the spools, and the service time and temperature. Such an evaluation will prove useful in de- signing and operating magnetic recording apparatus intended for use under variahle -- in- cluding extreme -- conditions.

LITERATURE CITED

I. V. V. Bolotin and K. S. Bolotina, "Calculation of residual stresses and strains in wound products made of reinforced plastics," Mekh. Polim., No. i, 134-139 (1969).

2. V. V. Bolotin and A. N. Vorontsov, "Formation of residual stresses in products made of layered and fibrous composites during hardening," Mekh. Polim., No. 5, 790-795 (1976).

3. V. L. Biderman, I. P. Dmitrenko, V. I. Polyakov, and N. A. Sukhova, "Determination of residual stresses in the manufacture of rings made of glass-fiber-reinforced plastic," Mekh. Polim., No. 5, 892-898 (1969).

4. R. ~. Brivmanis, "Experimental determination of residual stresses in the winding of unidirectional glass-fiber-reinforced plastics," Mekh. Polim., No. i, 123-129 (1966).

5. I. I. Bugakov and V. S. Ekel'chik, "Initial thermal stresses in a ring made of an anisotropic viscoelastic glass-fiber-reinforced plastic," Vopr. Sudostr., No. 12, 26- 37 (1976).

6. V. L. Blagonadezhin, V. G. Perevozchikov, V. D. Merkulov, and V. L. Polyakov, "Mechani- cal properties of a carbon-plastic and residual stresses in wound products made of com- bined composites," Mekh. Polim., No. 6, 996-1004 (1975).

7. V. P. Nikolaev and V. M. Indenbaum, "Calculation of the residual stresses in wound products made of glass-fiber-reinforced plastics," Mekh. Polim., No. 6, 1026-1030 (1970).

8. G. G. Portnov and A. I. Bell', "Model for consideration of the nonlinearity of the properties of a semifinished product in a force analysis of the winding of composites," Mekh. Polim., No. 3, 231-240 (1977).

9. Yu. M. Tarnopol'skii, G. G. Portnov, Yu. B. Spridzans, and V. N. Bulmanis, "Load-carry- ing capacity of rings made by winding composites reinforced with high-modulus aniso- tropic fibers," Mekh. Polim., No. 4, 673-683 (1973).

I0. E. S. Umanskii, V. V. Kryuchkov, and V. A. Rakovskii, "On determining the stress-strain state of a reel of magnetic tape," Probl. Prochn., No. 3, 83-85 (1978).

ii. E. S. Umanskii, V. V. Kryuchkov, and N. S. Shidlovskii, "Load-carrying capacity of coilable polymer films," Probl. Prochn., No. i0, 104-113 (1980).

i2. E. S. Umanskii, V. V. Kryuchkov, and N. S. Shidlovskii, "Evaluating the effect of the temperature factor on the load-carrying capacity of a reel of magnetic tape," Probl. Prochn., No. 8, 62-65 (1981).

13. E. S. Umanskii, V. V. Kryuchkov, V. A. Rakovskii, et al., "Study of stress relaxation in magnetic tape wound into a reel," Vestn. Kiev. Politekh. Inst., Ser. Mashinostr., 17, 3-7 (1980).

14. ~. S. Umanskii, N. S. Kryuchkov, N. S. Shidlovskii, et el., "Effect of the temperature factor on the magnitude of the radial stresses in a reel of magnetic tape," Tekh. Sredstv Svyazi, Ser. Obshchetekh., No. 2, 83-94 (1978).

15. E. S. Umanskii. V. V. Kryuchkov, N. S. Shidlovskii, et al., "Evaluating the integrity of a reel of magnetic tape during work in the start-stop regime," Tekh. Sredstv Svyazi, Ser, Obshchetekh., No. 2, 82-86 (1980).

16. E. N. Travnikov, Mechanics of ~gnetic Tape Recorders [in Russian], Tekhnika, Kiev

(1976). 17. V. I. Antonov, V. P. Veklich, L. P. Vodyanitskii, et el., Handbook of Magnetic Record-

~ng Technology [in Russian], Tekhnika, Kiev (1981). 18. E. S. Umanskii, V. V. Kryuchkov, I. V. Debrivnyi, et el., "Stand for studying creep and

rupture strength of magnetic-tape-type composite films at elevated temperatures,"

Probl. Prochn., No. 5, 103-107 (1973).

1409