The Effect of Friction between a Cylindrical Guide and Magnetic Tape on Lateral Tape Motion

Transcription

1 The Effect of Friction between a Cylindrical Guide and Magnetic Tape on Lateral Tape Motion B. and F. E. Talke Center for Magnetic Recording Research University of California, San Diego 95 Gilman Drive La Jolla, CA bart@talkelab.ucsd.edu Abstract The reduction of lateral tape motion (LTM) in tape drives is a key requirement for improved performance of tape drives since read/write errors are likely to occur if lateral tape motion exceeds ten percent of the track width of the recorded magnetic signal. Lateral tape motion is a function of tape path and tape properties, mechanical design parameters such as speed and tension, and friction between tape and tape path components. This investigation deals with the effect of friction on LTM for a tape moving over the surface of a cylindrical guide. The effect of friction and mechanical design parameters on LTM is investigated numerically. The equation of motion for a moving tape on a cylindrical guide surface is determined and the effects of friction and design parameters are examined by calculating the ratio of LTM before and after a cylindrical guide. Keeping the tape velocity and guide radius constant, attenuation of the LTM signal is seen to occur for all frequency components of the signal. Attenuation of LTM is found to increase with increasing friction and roller radius. Increasing tape tension reduces LTM while keeping the friction coefficient constant. 1. INTRODUCTION Lateral tape motion (LTM) is the time-dependent displacement of magnetic tape perpendicular to the tape transport direction. Lateral tape motion can cause track misregistration between the read/write head and a previously written track, thereby limiting the recording density that can be achieved (Taylor et al., ). Currently, the track density of typical magnetic tape drives is approximately 4 tracks/mm (1 tracks per inch (tpi)). In order to increase the track density further, the lateral displacement of tape must be decreased (Richards and Sharrock, 1998). Two types of lateral tape motion are generally considered, namely, low frequency and high frequency LTM. High frequency lateral tape motion with frequencies above 1 H cannot be followed by the head servo actuator in a tape drive, while low frequency lateral tape motion can be followed. Thus, high frequency lateral tape motion is the more critical component of the two types. In commercial tape drives and tape manufacturing equipment, tape is guided over rollers and guides which interact with the tape surface through frictional contact. Rollers and guides in tape drives are typically small in diameter, on the order of tens of mm, due to limited space in a tape drive. On the other hand, rollers and guides in tape manufacturing process equipment can be much larger in diameter, since spatial constraints are less constringent. The lateral motion of a string or web has been studied extensively. Swope and Ames (1963) analyed the oscillations of a string that is being wound on a bobbin. They assumed a perfectly flexible string without lateral bending stiffness and solved the governing equations analytically. Shelton and Reid (1971) studied the lateral dynamics of a moving web and derived the differential equations for the lateral dynamic motion of a mass less, moving web (1971). Wickert and Mote (199) investigated the vibration and stability of an axially moving continuum casting the equations of motion in a canonical state space form. Gariero and Amabili () studied the effect of damping on the lateral vibration of an axially moving tape. The tape was modeled as a string, i.e., bending stiffness was neglected and only the lateral vibrations were investigated. Benson () used Euler-Bernoulli beam theory to predict the lateral motion of a long warped web that is transported between two rollers. The effect of guides on the lateral tape motion in a tape path has been studied by only a few researchers. Ono (1979) described the lateral displacement of an

2 axially moving string on a cylindrical guide surface. Bending stiffness was not included in his model. He showed that the lateral motion was governed by a second order differential equation similar to that for one dimensional heat flow. More recently, Taylor and Talke (5) investigated the interactions between rollers and flexible tape and showed that friction between the tape and the roller affects the lateral displacement of tape. In addition they correlated LTM with the axial run-out of a roller. and Talke (6) derived the equation of motion of an axially moving tape on a cylindrical guide surface and compared the effect of bending stiffness of tape to a string model without bending stiffness. In this paper we have studied the effect of friction and other design parameters on the lateral motion of magnetic tape as it passes over a stationary guide. We have included the effect of bending stiffness, since the moment of inertia of the wide tape for the transverse direction is very large. Bending stiffness is the major difference between a simplified string model and an actual magnetic tape. vertical ( µ ) direction, respectively. The tape makes contact with the guide at point s 1 and leaves the tape at point s. E is the Young s modulus, I is the moment of inertia of the tape s cross sectional area, is the vertical position of the tape, s is the coordinate along the tape s centerline, T is the nominal tape tension, a is the guide radius, v is the tape velocity and t represents time. The first term on the left hand side in eq. (1) denotes the bending stiffness of the tape. For the limiting case when the guide becomes a roller, µ = and µ since there is no relative sliding (slip) between a tape and an ideal roller. Furthermore, if the friction coefficients for the circumferential and vertical directions are the same, i.e., if µ = µ, eq. (1) becomes EI + = s s t 4 µ T T 4 va () since ν = 1in this case. If I = and µ = µ =, eq. () reduces to the following equation:. METHODOLOGY v d ds = (3) a y j i s=s s=s 1 x s=s s=s 1 k y j o The solution of this equation is a linear function of in terms of s, i.e., the tape moves in a straight line over the guide between points s1 and s. Since equation (1) is difficult to solve in closed form, numerical analysis was used to study the effect of friction and design parameters on the lateral motion of the tape. Fig. 1: Axially moving tape over a cylindrical guide surface The equation of motion for a tape travelling on a stationary cylinder (Fig. 1) is given by ( and Talke, 6): EI + 1 = s s a s t w 4 µ T µ T T 4 ( ν ) va µ (1) where ν = is the ratio of the friction µ coefficients in the circumferential ( µ ) and In order to first verify our model, we have compared the values of numerically calculated lateral tape motion in the middle of the cylindrical guide with experimentally measured LTM values at the same position. Using a stationary guide and an LTM edge sensor (Taylor et al., ) we measured LTM on the guide surface. Fig. shows simulated and experimentally measured values of lateral tape displacement in the middle of the cylindrical guide, while Fig. shows the simulated and experimentally determined frequency spectrum at the same position. From Fig. we observe that very good agreement exists between experimental measurements and numerical results, especially in the low frequency region (< 1 kh).

3 3. RESULTS In the following section we have presented results for the case of a commercial tape drive, where guides are subject to tight space constraints, and where guide diameters are typically on the order of mm. In addition we have presented results for dimensions that are in line with those used in tape manufacturing process equipment, where guide diameters of mm are used. In Fig.4, the influence of tape speed on the amplitude ratio is shown. Fig. 4 shows the amplitude ratio versus the frequency for a mm diameter guide while Fig. 4 shows the amplitude ratio for a mm diameter guide. A wrap angle of 9 deg was used along with a nominal tape tension of 1 N Fig. : Comparison of experimental measurements and numerical predictions in the midspan of the cylindrical guide ( in time domain and ( in frequency domain To characterie the effect of a tape guide on lateral tape motion, we have introduced the amplitude ratioζ, defined by the output amplitude of the LTM divided by the input amplitude, i.e., LTM ( f ) ( f ) ζ = out LTM (4) in A normalied sine wave was used as input LTM (Fig. 3). By varying the frequency f of the input we have determined the attenuation of LTM versus frequency. sin LTM in V LTM out ( π ft ) ζ sin ( π ft ) Fig. 3:.1 V=4 m/s V=6 m/s V=8 m/s V=1 m/s V=4 m/s.1 V=6 m/s V=8 m/s V=1 m/s Fig. 4: Influence of tape speed on amplitude ratio for a mm diameter guide and a mm diameter guide We observe that for a small guide diameter, the amplitude ratio is independent of speed. For the mm diameter guide, the amplitude ratio is one order of magnitude smaller than that for the mm case, i.e., LTM is attenuated significantly more. A small increase of the amplitude ratio is observed as a function of speed. In addition, we observe from Fig. 4 that the attenuation is almost independent of the frequency for a small diameter guide. From 3

4 Fig 4 we observe that at H the amplitude is six times larger than at 1 kh. Fig.5 shows the influence of the friction coefficient on the amplitude ratio for a mm diameter guide and a mm diameter guide. Again, a wrap angle of 9 deg was used and a nominal tape tension of 1 N f=.5.1 f=.3 f=.1 f=.5 f= f=.5. f=.3 f=.1 f=.5 f= Fig. 5: Influence of friction coefficient on amplitude ratio for a mm diameter guide and We observe that the amplitude ratio is (almost) independent of the friction coefficient for both the mm (Fig. 5 ) and mm (Fig. 5 ) diameter guide. The influence of the guide radius is depicted in Fig. 6 for a typical friction coefficient of., a wrap angle of 9 deg and a nominal tension of 1 N. We observe that the amplitude ratio is a strong function of the guide radius a. As the guide radius increases, the contact length between magnetic tape and guide increases. This causes an increased friction force which will dampen out lateral tape vibrations. Fig. 7 shows the influence of the wrap angle on the amplitude ratio for a friction coefficient of. and a guide diameter of mm with a nominal tape tension of 1 N. We observe that the wrap angle has a significant influence on the amplitude ratio deg 3 deg 6 deg 9 deg Fig. 7: Influence of the wrap angle on the amplitude ratio for a friction coefficient of. and a mm guide diameter This is due to the change of contact length between the tape and the guide as a function of the wrap angle. Fig. 8 illustrates the influence of the nominal tape tension on the amplitude ratio a=. m a=.1 m a=.5 m a=. m a=.1 m.1.5 N 1 N 1.5 N N Fig. 6: Influence of guide radius on amplitude ratio for a friction coefficient of. 4

5 N 1 N 1.5 N N Fig. 9 shows the amplitude ratio for a mm diameter guide while Fig. 9 shows the amplitude ratio for a mm diameter guide. We observe that the amplitude ratio is almost independent of the tape thickness. However, for the mm guide we observe that the amplitude ratio decreases slightly with decreasing tape thickness. 4. DISCUSSION Fig. 8: Influence of nominal tension on amplitude ratio for a mm diameter guide and a mm diameter guide Fig. 8 shows the amplitude ratio for a mm diameter guide while Fig. 8 shows the amplitude ratio for a mm diameter guide. In each case a wrap angle of 9 deg, a friction coefficient of. and a nominal tension of 1 N were used. We observe that the amplitude ratio is almost independent of tape tension. The influence of the tape tension is very small compared to the guide diameter and wrap angle. Fig. 9 shows the influence of tape thickness µm 6 µm 9 µm µm 6 µm 9 µm Fig. 9: Influence of tape thickness on amplitude ratio for a mm diameter guide and a mm diameter guide The amplitude ratioζ can be defined in terms of tape design parameters as Vb ζ = A (5) µat We observe that the amplitude ratio ζ is inversely proportional to the tape/guide friction coefficient µ, the wrap angle, the nominal tape tension T and the guide radius a, and proportional to the tape speed V and tape thicknessb. A is a proportionality constant. From eq. (5) it is apparent that an increase in the guide diameter increases the guide/tape contact length. The larger friction force that is created will dampen out the LTM. In the case of commercial tape drives, the guide diameter cannot be increased arbitrarily due to space constraints. In tape manufacturing process equipment, where spatial constraints are less important, there is greater freedom to increase the diameter of the guides, which would reduce LTM. However, increased friction force due to increased contact length may lead to increased tape wear, and the balance between those effects must be found. From eq. (5) we also note that an increase of the tape increases the contact length between tape and guide. This effect is the same as that observed by increasing the guide diameter. The friction force F f increases with increasing wrap angle and can be determined from ( ( ) ) Ff = T exp µθ 1, (6) where T is the downstream tape tension, µ is the friction coefficient and θ is the wrap angle. In tape drives, the wrap angle is constrained by spatial considerations. Typical wrap angles for commercial tape drives vary between 5 3 degrees. 5

6 The tape industry is moving towards using thinner tapes that require lower tension, to increase the volumetric storage density of a tape cartridge. Increased storage density calls for higher data rates (faster tape speeds). Our results showed that the tape speedv, the tape thicknessb, the nominal tape tension T and the friction coefficient µ have only a secondary effect on the amplitude ratio. From the results presented it is apparent that LTM can be reduced by positioning guides in the tape path before the tape passes over the read/write head. This would yield increased track density and thus better performance of a tape drive. Reducing LTM during the tape slitting process would produce tapes with improved edge quality, i.e., straighter edges. Straight edges are important for tape guiding (Bhushan et al., 1994) and especially for avoiding tape edge contact (Taylor and Talke, 5). 5. CONCLUSION The simulation results show that roller radius, wrap angle, friction coefficient, tape thickness, tape tension and tape speed affect the amplitude ratioζ, i.e., the ratio that describes the attenuation of LTM due to the frictional contact between a guide and a magnetic tape in the tape path. We conclude that: 1. The guide radius as well as the wrap angle influence the amplitude ratio most significantly.. The nominal tape tension, friction coefficient, tape thickness and tape speed affect the amplitude ratio; however their influence is negligible with respect to the influence of the guide radius and the wrap angle. Ono K., (1979), Lateral Motion of an Axially Moving String on a Cylindrical Guide Surface, J. Appl. Mech., Vol. 46, pp B., Talke F.E., (6), Lateral Motion of an Axially Moving Tape on a Cylindrical Guide Surface, submitted to J. Appl. Mech. Richards D.B., Sharrock M.P., (1998), Key Issues in the Design of Magnetic Tape for Linear Systems of High Track Density, IEEE trans. mag., Vol. 34(4), pp Shelton J.J., Reid K.N., (1971), Lateral Dynamics of an Idealied Moving Web, J. Dyn., Syst., Meas. and Control, Vol. 3, pp Shelton J.J., Reid K.N., (1971), Lateral Dynamics of a Real Moving Web, J. Dyn., Syst., Meas. and Control, Vol. 3, pp Swope R.D., Ames W.F., (1963), Vibrations of a Moving Threadline, J. Franklin Institute, Vol. 75, pp Taylor R.J., Talke F.E., (5), High Frequency Lateral Tape Motion and the Dynamics of Tape Edge Contact, J. Microsyst. Technol., Vol. 11, pp Taylor R.J., Talke F.E., (5), Investigation of Roller Interactions with Flexible Tape Medium, Tribology International, Vol. 38, pp Taylor R.J., Strahle P., Stahl J., Talke F.E., (), Measurement of Cross-Ttrack Motion of Magnetic Tapes, J. Info. Storage Proc. Syst., Vol., pp Wickert J.A., Mote Jr. C.D., (199), Classical Vibration Analysis of Axially Moving Continua, J. Appl. Mech., Vol. 57, pp REFERENCES Benson R.C., (), Lateral Dynamics of a Moving Web with Geometrical Imperfection, J. Dyn., Syst., Meas. and Control, Vol. 14, pp Bhushan B., Hinteregger H.F., Rogers A.E.E., (1994), Thermal Considerations for the Edge Guiding of Thin Magnetic Tape in a Longitudinal Tape Transport, Wear, Vol. 171, pp Gariera R., Amabili M., (), Damping Effect of Winding on the Lateral Vibration of Axially Moving Tapes, J. Vibrations and Acoustics, Vol. 1, pp