JPH04212763A - Head supporting device - Google Patents

Abstract

PURPOSE:To offer a head supporting device where a magnetic head slider is not deformed in a moving direction and which can perform stable positioning control even though resonance accompanied with twist occurs when the magnetic head slider is moved at a high speed. CONSTITUTION:This device is constituted so that a contact point of a pivot with a load beam may be positioned in the shearing central surface of the load beam in a state where the load beam is deformed by load. Furthermore, a leaf spring part is constituted to be in a plate state.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a head support device that floats and supports a magnetic head slider, and more particularly to an in-line type head support device configured such that the longitudinal direction of the load beam of the head support mechanism is in the circumferential direction of a magnetic disk. The present invention relates to a supporting device.

0002

2. Description of the Related Art A magnetic head slider used in a magnetic disk device must read data accurately by making the posture of the magnetic head slider follow dynamic displacement such as surface runout during rotation of the magnetic disk. For this purpose, conventionally,
For example, there is one described in Japanese Patent Application Laid-Open No. 2-46578. FIG. 10 is a perspective view of a conventional head support device, and FIG. 11 is an exploded perspective view showing an enlarged tip of the head support device. In the figure, 1 is a magnetic head slider equipped with a magnetic head (not shown), 2 is a gimbal spring with a gimbal mechanism, 3 is a magnetic disk, 4 is a load beam, and 5 is a gimbal spring fixed to the magnetic head slider. One fixed part, 6 is a second fixed part fixed to the load beam of the gimbal spring, 7 is a pivot on which the first fixed part is formed, and the load beam 4 is in contact with the pivot at a contact point 4a. Reference numeral 4b denotes a spring section that generates a force to press the magnetic head slider 1 toward the magnetic disk 3 via a pivot section, and is bent in accordance with the spring force. In addition, 4c is the spring part 4
This is a rib portion other than b for increasing the rigidity of the load beam 4. In the figure, the X direction is the circumferential direction of the magnetic disk 3, the Y direction is the radial direction of the magnetic disk 3, and the Z direction is perpendicular to the X and Y directions, and is the pressure direction in which the magnetic head slider 1 is pressed against the magnetic disk 3. . Also, arrow A indicates the magnetic disk 3
The arrow B indicates the direction of rotation of the magnetic head, and the arrow B indicates the direction of movement of the magnetic head. The load beam 4 is arranged so that its longitudinal direction is in the circumferential direction of the magnetic disk 3, and the pivot 7 of the gimbal spring 2
is turned to press the magnetic head slider 1 toward the magnetic disk 3, that is, in the Z direction. The gimbal spring 2 is bonded to the magnetic head slider 1 at a first fixing portion 5, for example. Also,
The second fixing portion 6 on the rear end side of the gimbal spring 2 is fixed to the load beam 4 via a coupling means such as spot welding. The magnetic disk 3 rotates in the A direction, and the magnetic head slider 1 moves in the B direction. The magnetic head slider 1 is supported by a gimbal spring 2 to enable pitching and rolling movements around the X and Y directions, and is configured so that the attitude of the magnetic head slider 1 can follow dynamic changes in the magnetic disk 3. Further, when the magnetic disk 3 rotates, an air spring is generated which acts due to the air flowing between the magnetic disk 3 and the magnetic head slider 1. The force to apply the load necessary to maintain the force balance with the air spring to the magnetic head slider 1 is generated by the spring portion 4b of the load beam 4, and the force is applied to the magnetic head slider 1 via the contact point 4a with the pivot 7. The head slider 1 is pressurized.

0003

[Problems to be Solved by the Invention] The conventional magnetic head support device is constructed as described above, and when the magnetic head slider 1 moves at high speed toward the inner circumferential side of arrow B, for example, the magnetic head slider 1 is accelerated. In addition, a force is applied to the contact point 4a of the load beam 4 in the Y direction due to the inertial force of the magnetic head slider 1, so that the load beam 4 is deformed. Figure 12
(a) and (b) are graphs showing the transfer function of the acceleration of the magnetic head support device in the Y direction with respect to the driving force of the head support device, where the horizontal axis shows the frequency of the driving force, and the vertical axis shows the phase in (a). , (b) shows the gain. As shown in the figure, two prominent peaks occur below 5 kHz due to the bending and torsion mode of the load beam 4. FIG. 13(a) is an explanatory diagram showing a modification of the head support device of peak ■ shown in FIG. 12(b), and FIG. 13(b) is an explanatory diagram showing a modification of the head support device of peak {circle around (2)}. In the figure, the solid line shows the load beam in a deformed state, and the dotted line shows the load beam in a normal state. Since these vibration modes are deformed in the positioning direction, a peak occurs and the positioning control system becomes unstable. Here, a detailed explanation will be given of the peak resonance that occurs below 5 kHz. The above vibration mode of peak ■ (Fig. 13(a)) is a mode in which the torsion of the load beam 4 in -θX (the right-handed screw direction of the X axis is +) coupled with the bending in the +Y direction (this causes the magnetic head to The slider moves in the +Y direction), and the peak ■ vibration mode (Fig. 13(b)) is a mode in which the -θX twist of the load beam 4 and the bending in the -Y direction are coupled (as a result, the magnetic head slider 1 moves -Y), and the above-mentioned peak (2) is a mode in which the twisting direction of the load beam 4 is in reverse phase with respect to the moving direction of the magnetic head slider 1.

Next, the reason why the first peak vibration mode is the above mode will be explained. FIG. 14(a) is an enlarged view of the load beam. Considering static deformation, in this figure, the shear center of the XZ cross section of the part where the rib 4c is located is Z<0
Therefore, a force F in the -Y direction is applied to the contact point 4a with the pivot.
If you add , it will always try to twist in the +θX direction. Also, the remaining spring portion 4b is affected by the pressure as shown in Fig. 14(b).
Therefore, even if force F is applied to the portion shown enlarged in FIG. 14(c), the direction of twisting cannot be determined unambiguously. However, the standard load to keep the air spring stable is 9.
．． In order to generate a force of 5gf, when a load is applied to the contact point 4a in the -Y direction while the spring part 4b is normally bent near the center, the entire body is twisted in the +θX direction as shown in FIG. 15.

When considered as a dynamic vibration mode, it can be considered as vibration of a two-degree-of-freedom system of bending and torsion of the load beam 4, and in the first mode, the torsion and bending of the load beam 4 are in phase (the torsion is -θX, The bending mode is +Y direction), and the second mode is the opposite phase (twisting is -θX, bending is -Y direction).
direction) mode. In a shape close to a plane like the load beam 4, the rigidity in the bending direction is very high, but the rigidity in the torsion is low, and these coupled modes will always have a low frequency, and as long as the bending is coupled, the positioning will always be determined. A peak occurs in the Y direction, which adversely affects positioning control. Furthermore, in order to maintain stable flying of the magnetic head slider, the torsional rigidity of the load beam 4 cannot be increased, so the frequency of resonance accompanied by torsion cannot be greatly increased.

The present invention was made to solve the above-mentioned problems, and even if resonance accompanied by torsion occurs when the magnetic head slider 1 is moved at high speed, the magnetic head slider 1 does not move. An object of the present invention is to provide a head support device that does not deform in any direction and enables stable positioning control.

Another object of the present invention is to provide a head support device that increases the rigidity of the suspension in the bending direction in the positioning direction, has no resonance peak in the positioning direction up to high frequencies, and enables stable positioning control.

[0008]

[Means for Solving the Problems] In the head support device according to the present invention, when the load beam is deformed by a load, the contact point of the pivot with the load beam is located within the shear center plane of the load beam. It is configured as follows.

Furthermore, when the magnetic head slider moves in the radial direction, the inertial force vector of the magnetic head slider acting on the contact point of the pivot with the load beam is included in the shear center plane of the load beam. It is composed of

Furthermore, the load beam is constructed such that, in its symmetrical axial cross-section in the longitudinal direction, the total area bulging toward the magnetic disk from the shear center is equal to the total area bulging away from the disk. It is.

Further, in the head support device according to another aspect of the present invention, when the load beam is deformed by a load, the leaf spring portion is in a flat state, and the shear center plane of the leaf spring portion and the spring The shear center plane of the portion ahead of the pivot is in the same plane that includes the contact point of the pivot with the load beam.

Furthermore, the portion beyond the leaf spring portion is bent in a U-shape in a direction perpendicular to the magnetic disk, and the height in the magnetic disk direction with respect to the shear center of the leaf spring portion is h1.
, a rib portion is provided so that the moment of inertia of the section h1 and h2 in the direction perpendicular to the magnetic disk are approximately equal when the height in the antimagnetic disk direction is h2.

[0013]

[Operation] By aligning the contact point of the pivot with the shear center axis of the load beam in the present invention, even if a force is applied in the direction of movement of the head, only bending deformation occurs at the tip of the load beam and no twisting occurs. Therefore, even if torsional resonance of the suspension occurs, the magnetic head slider has no amplitude in the positioning direction and no resonance peak occurs.

Specifically, when the magnetic head slider moves in the radial direction, the inertial force vector of the magnetic head slider acting on the contact point of the pivot with the load beam is included in the shear center plane of the load beam. If this is done, the excitation force that generates torsional force will not be applied to the suspension, so torsional deformation will not occur, resonance peaks will not occur, and the vibration of the suspension itself will be reduced, making the flying characteristics of the magnetic head more stable. do.

[0015] More specifically, the load beam is constructed such that, in its symmetrical axial cross section in the longitudinal direction, the total area that bulges toward the magnetic disk from the shear center is equal to the total area that bulges away from the disk. With this configuration, it becomes possible to easily design a suspension in which a resonance peak does not occur in the positioning direction even if torsional resonance occurs.

[0016] Also, with a suspension like this one,
In order to maintain a stable flying height of the magnetic head slider, it is not possible to increase the rigidity in the torsional direction. However, because the leaf spring part is in a flat state when a load is applied, and the shear center plane of the leaf spring part and the shear center plane of the part beyond the spring part are in the same plane, a resonance peak occurs in the positioning direction. It is possible to increase the rigidity in the bending direction without causing any resonant peaks to occur, and without substantially changing the rigidity in the torsional direction, and it is possible to increase the frequency at which resonance peaks occur in the positioning direction.

Specifically, the portion beyond the leaf spring portion is bent in a U-shape in a direction perpendicular to the magnetic disk, and the height in the direction of the magnetic disk is h1 with respect to the shear center of the leaf spring portion. Cross section 2 of the above magnetic disk in the vertical direction of h1 and h2 when the height in the magnetic disk direction is h2
By providing rib portions configured such that the second moments are approximately equal, the position of the shear center in the rib portion can be changed without changing the design or manufacturing method of conventional suspensions.

[0018]

[Embodiment] First, the shear center, shear main axis, shear center axis, and shear center plane will be explained. When a force is applied to a beam structure like the suspension in question, deformation usually occurs, which involves bending and torsion. (Figure 3 shows the load beam 4
This is a perspective view showing the deformation when a force is applied to the tip of the tip, where the dotted line shows the deformation before force is applied, and the solid line shows the deformation when force F is applied. ) However, in each cross section of the beam, there is a point S and direction where no twisting occurs, only bending occurs. Such a point is defined as the shear center, and the direction that passes through the shear center and does not cause twisting even when force is applied is defined as the shear principal axis. There are such points and directions in each cross section of the beam, and the principal shear axis exists in a direction perpendicular to each cross section. Furthermore, the axis connecting the shear centers of each cross section is defined as the shear center axis. If the cross section of the beam is not uniform or curved, it is not possible to easily determine the shear center axis or shear center plane, but the above-mentioned axes always exist. In addition, the plane formed by the shear center axis and the shear principal axis is defined as the shear center plane. In the case of the following suspension, the description will focus on the shear center plane, which is a plane formed by the shear center axis and the shear principal axis that is nearly parallel to the xy plane direction.

Example 1. FIG. 1 shows a head support device according to an embodiment of the present invention.
Explain using. When a force F is applied to the contact portion 4a with the pivot in the −Y direction, the rib portion 4c tends to twist in the +θX direction because the shear center P1 is located at Z<0 in any cross section of the rib portion 4c. Therefore, in the pressurized state, the shape of the spring part 4b is set in a position opposite to the rib part 4c, that is, the shear center P2 is located at a place where Z>0.
In total, the contact point 4 is located at the contact point 4a where force is applied.
a can be made to coincide with the shear center. In addition, since the excitation force is applied in a direction parallel to the disk, by making the suspension symmetrical with respect to the ZX plane, the shear center plane can be made parallel to the disk, and the inertial force vector acting on the contact point 4a is It can be included in the shear plane passing through the center. Thereby, even if twisting occurs near the boundary between the spring portion 4b and the rib portion 4c, it is possible to prevent twisting from occurring near the contact point 4a. When a suspension that achieves this is vibrated, the inertial force of the magnetic head slider 1 is applied only in the direction of bending the load beam 4. Therefore, the bending and twisting of the load beam 4 vibrate independently.

FIG. 2(a) shows the first vibration mode when the position and radius of the bent portion satisfy the above conditions. As can be seen from the figure, the magnetic head slider 1 is hardly deformed in the positioning direction and is in a twisting mode only. In addition, in the second case, as shown in FIG. 2(b), twisting occurs near the boundary between the rib portion 4c and the spring portion 4b, but the load beam 4
This is a bending mode in which no twist occurs near the tip. A graph (
Looking at Figure 2 (c) and (d)), the peak occurs only in the second mode, and compared to the conventional method, it is possible to eliminate the low-order resonance peak that has a particularly large effect on positioning control, and the stable Positioning control can be realized. Here, the height of the rib 4c is set at such a position that a torsional force in the opposite direction is generated in response to the torsional force of the spring portion 4b, and the contact point 4 of the pivot is
The center of shearing is made to coincide with a, and the center of shearing is made to be symmetrical. As a result, the contact point 4a coincides with the shear center, and the direction of the inertial force is made within the shear center plane at the contact point 4a. Here, the shear center plane is lowered without changing the vertical strength of the rib 4c itself as much as possible, and it is bent in two stages as shown in Figure 1, making it easy to replace with the previous suspension. , it is also easy to create a suspension.

[0021] Here, the ribs 4c may be provided in one stage as in the conventional case, or may be provided in more stages. Moreover, the height of the rib 4c does not have to be constant.

Example 2. Another embodiment of the invention is shown in FIGS. 4(a) and 4(b). Figure 4
(b) shows an enlarged view of the main part of (a). In this example, ribs 4c are provided on the top and bottom of the plate to balance the torsional force. That is, the rib portion 4
c is bent in a direction perpendicular to the magnetic disk 1 into a U-shape 4e. The height h1 of each rib portion 4c
, h2 is the height in the magnetic disk direction with respect to the shear center of the leaf spring part when h1 is the height in the direction of the magnetic disk and h2 is the height in the antimagnetic disk direction when the spring part 4b is made to be flat after applying a load. The moment of inertia of h1 and h2 in the direction perpendicular to the magnetic disk are determined to be approximately equal. In this way, the position of the shear center in the rib portion can be changed without changing the conventional suspension design or manufacturing method, and the position of the shear center in the rib portion can be changed, as shown in FIG.
) to (d), the peaks become one and stable positioning control can be realized.

Note that if the spring portion 4b cannot be made flat after applying the load, the height h1 of the rib portion 4c
, h2 are determined so as to be balanced depending on the deformed shape of the spring portion 4b. In this case, the second moments of inertia of h1 and h2 in the direction perpendicular to the magnetic disk are not necessarily equal.

Example 3. In addition, in this embodiment, the rib portion 4c has a U-shaped bend 4.
However, as shown in FIG. 5, the same effect can also be obtained by combining L-shaped rib portions 41c and 42c provided at both ends and the center of the load beam 4 with different bending directions. .

Example 4. Furthermore, the same effect can be obtained by bonding as shown in FIG. 6 instead of bending as shown in FIGS. 4 and 5. In this example, the shape of the spring portion 4b before pressurization is determined so that it becomes flat in the pressurized state. Therefore, in the pressurized state, the shear center plane of the spring portion 4b is located at the center plane of the spring portion 4b. Here, by making the rib portion vertically symmetrical, the shearing center plane of the rib portion and the shearing center plane of the spring portion 4b can be made to be on the same plane. As a result, the contact point coincides with the shear center, the direction of the inertial force is in the shear center plane, and the spring portion 4b bends within the plane against the excitation force, making it possible to make the rigidity extremely high. Furthermore, in order to improve productivity and reduce the thickness of the suspension, in the embodiment shown in FIG. 6, flat plates 8 are provided at the top and bottom instead of ribs. The primary mode of this suspension is only twisting as shown in FIG. 7(a), and the secondary mode is in-plane bending as shown in FIG. 7(b), so the rigidity is high and the resonance frequency is high. As an example, the plate thickness of the conventional load beam 4 (80μ
Figures 7(c) and 7(d) show the frequency response when a plate 8 with half the thickness of the plate 8 is provided, making the total plate thickness twice as high as 160 μm, and the spring portion 4b becomes flat under pressure. Shown below. From these figures, there is one resonance peak, and the frequency of the bending resonance has increased by about 1 kHz, making more stable control possible.

The thickness and shape of the plate 8 to be attached are determined depending on the required dynamic characteristics.

The plate 8 may have a hole or the like in it, and if it is ring-shaped or U-shaped with the outside left open, it will have the same effect as a rib.

Further, the plate 8 to be attached may be attached to only one side or may be attached in multiple stages.

Further, it is also possible to use only one plate 8 without adding the plate 8. In this case, the entire load beam 4 becomes the spring part 4b, and the contact point and the shear center coincide with each other under pressure, and the force is reduced. The shape before pressurization is determined so that the direction of application and the center plane of shear coincide. At this time, if it is set so that it becomes flat under pressure, the frequency of bending can be increased.

Furthermore, as shown in FIG. 8, a mounting plate 8
An adhesive 9 which also serves as a damper may be used as the fixing means, and the peak gain that occurs can be lowered compared to spot welding, and more stable positioning control can be performed.

Example 5. In addition, in each of the above embodiments, the load beam 4
is deformed, the leaf spring portion 4b and the rib portion 4c
If it is substantially difficult to make the plate into a flat plate state, the generation of torsion moment can be prevented by doing the following. That is, as shown in FIG. 9, the load beam 4 has a total area S1+S2 that bulges toward the magnetic disk from the shear center R in a cross section along its longitudinal axis of symmetry (indicated by T in FIG. 1), and a total area S1+S2 that bulges away from the disk. The total area S3+S4 is configured to be equal.

Although the embodiment shown in FIG. 9 has been described with respect to the case where the rib portion 4c is provided, it can also be applied to the case where the plate 8 is attached as shown in FIG. It is preferable to adjust the thickness and direction so that the total area bulging toward the magnetic disk from the shear center R is equal to the total area bulging away from the disk.

[0033]

As described above, according to the present invention, when the load beam is deformed by a load, the contact point of the pivot with the load beam is located within the shear center plane of the load beam. With this structure, there is no resonance peak in the positioning direction even when torsional resonance occurs, and stable control is possible.

Furthermore, when the magnetic head slider moves in the radial direction, the inertial force vector of the magnetic head slider acting on the contact point of the pivot with the load beam is included in the shear center plane of the load beam. With this configuration, no excitation force that generates torsional force is applied to the suspension, so torsional deformation does not occur, resonance peaks do not occur, and the vibration of the suspension itself is reduced, making the flying characteristics of the magnetic head more stable.

Furthermore, if the load beam is configured so that the total area bulging toward the magnetic disk from the shear center is equal to the total area bulging away from the disk in its symmetrical axial cross section in the longitudinal direction, torsion can be reduced. It becomes possible to easily design a suspension in which a resonance peak does not occur in the positioning direction even if resonance occurs.

According to another aspect of the present invention, when the load beam is deformed by a load, the leaf spring portion is in a flat state, and the shear center plane of the leaf spring portion and the tip of the spring portion are Since the shear center plane of the part is configured to be in the same plane that includes the contact point of the pivot with the load beam, the resonance peak in the first positioning direction is eliminated and the resonance frequency of bending is increased. Therefore, stable control is possible.

Furthermore, the portion beyond the leaf spring portion is bent into a U-shape in a direction perpendicular to the magnetic disk, and the height in the direction of the magnetic disk with respect to the shear center of the leaf spring portion is h1.
If a rib section is provided so that the second moments of area in the direction perpendicular to the magnetic disk of h1 and h2 are approximately equal when the height in the anti-magnetic disk direction is h2, the design of the conventional suspension can be improved. The position of the shear center in the rib portion can be changed without changing the manufacturing method.

[Brief explanation of the drawing]

FIG. 1 is a perspective view showing a head support device according to an embodiment of the present invention.

2 (a) and (b) are explanatory diagrams showing vibration modes of the one in FIG. 1, respectively, and (c) and (d) are characteristic diagrams showing frequency response in the positioning direction of the head part of the one in FIG. 1, respectively.

FIG. 3 is an explanatory diagram illustrating how the object in FIG. 1 deforms when force is applied.

FIG. 4(a) is a perspective view showing a head support device according to another embodiment of the present invention, and FIG. 4(b) is an enlarged perspective view showing a main part of FIG.

FIG. 5 is a perspective view showing a head support device according to another embodiment of the invention.

FIG. 6 is a perspective view showing a head support device according to another embodiment of the invention.

7(a) and (b) are explanatory diagrams showing the vibration mode of the one in FIG. 6, respectively, and FIGS. 7(c) and (d) are characteristic diagrams showing the frequency response in the positioning direction of the head part of the one in FIG. 1, respectively.

FIG. 8 is a perspective view showing a head support device according to another embodiment of the invention.

FIG. 9 is a perspective view showing a head support device according to another embodiment of the invention.

FIG. 10 is a perspective view showing a conventional head support device.

FIG. 11 is an enlarged exploded perspective view showing the main parts of the device shown in FIG. 10;

FIGS. 12(a) and 12(b) are characteristic diagrams each showing the frequency response of a conventional head support device in the positioning direction of the head portion.

FIGS. 13(a) and 13(b) are explanatory diagrams showing vibration modes of a conventional head support device, respectively.

14(a), 14(b), and 14(c) are explanatory diagrams each explaining the reason why the first vibration mode of a conventional head support device is as shown in FIGS. 13(a) and 13(b).

FIG. 15 is an explanatory diagram showing deformation when a force in the positioning direction is statically applied to the contact portion.

[Explanation of symbols]

1 Magnetic head slider 2 Gimbal spring 3 Magnetic disk 4 Load beam 4a Contact point 4b Spring part 4c Rib part 5 First fixed part 6 Second fixed part 7 Pivot 8. Flat plate 9 Damping adhesive

Claims (5)

[Claims] 1. A magnetic head slider mounted with a magnetic head that moves in the radial direction of a magnetic disk, the longitudinal direction of which is disposed in the circumferential direction of the magnetic disk, and a spring force of a leaf spring section against the magnetic head slider A head support device comprising a load beam that applies a load to the magnetic disk side, and a gimbal mechanism that supports the magnetic head slider so as to be capable of rolling and pitching movements around the radial direction of the magnetic disk using a pivot in contact with the load beam as a fulcrum. A head support device characterized in that, in a state where the load beam is deformed by the load, a contact point of the pivot with the load beam is located within a shear center plane of the load beam. 2. When the magnetic head slider moves in the radial direction, the inertial force vector of the magnetic head slider acting on the contact point of the pivot with the load beam is included in the shear center plane of the load beam. The head support device according to claim 1. 3. The load beam is configured such that, in its longitudinal symmetrical axial cross section, the total area bulging toward the magnetic disk from the shear center is equal to the total area bulging away from the disk. The head support device according to claim 1 or 2, characterized in that: 4. A magnetic head slider equipped with a magnetic head that moves in the radial direction of a magnetic disk, the longitudinal direction of which is disposed in the circumferential direction of the magnetic disk, and the magnetic head slider is provided with a magnetic head that moves in the radial direction of the magnetic disk. A head support device comprising a load beam that applies a load to the magnetic disk side, and a gimbal mechanism that supports the magnetic head slider so as to be capable of rolling and pitching movements around the radial direction of the magnetic disk using a pivot in contact with the load beam as a fulcrum. , when the load beam is deformed by the load, the leaf spring part is in a flat state, and the shear center plane of the leaf spring part and the shear center plane of the part beyond the spring part are aligned with the pivot. A head support device characterized in that the head support device is configured to be located within the same plane that includes a point of contact with the load beam. 5. A portion beyond the leaf spring portion is bent in a U-shape in a direction perpendicular to the magnetic disk, and has a height h1 in the direction of the magnetic disk with respect to the shear center of the leaf spring portion.
The above h1 when the height in the antimagnetic disk direction is h2
5. The head support device according to claim 4, further comprising a rib portion configured such that the second moments of inertia of and h2 in the direction perpendicular to the magnetic disk are approximately equal.