20. The gimbal component 40 may include outrigger members, arms, and the like.

FIG. 3 is a schematic cross-sectional view showing an example of a disk drive (HDD) 11. The disk drive 11 includes disks 12, a casing 70 (shown in part), a carriage 72, a positioning motor 73 for driving the carriage 72, and the like. The disks 12 rotate about spindles. The carriage 72 is pivotable about a pivot 71. The casing 70 is sealed by a lid. A suspension 10 is mounted at the tip of the arm portion 74 of the carriage 72.

When the carriage 72 is turned by the positioning motor 73, the suspension 10 moves in the radial direction of the disk 12. The sliders 31 thereby move to desired positions of the disks 12. When the disks 12 rotate, air flows from leading side portions 31a of the sliders 31 toward the trailing side portions 31b. Air bearing 80 is thereby formed between the disk 12 and the slider 31.

FIG. 4 schematically shows a surface 12a of the disk 12 along a flat reference plane N, the slider 31, and the dimple portion 50. The reference plane N is a virtual flat surface extending in a direction perpendicular to the central axis of the rotating disk 12. The slider-mounted portion 30 in a state of being elastically supported by the gimbal component 40 is in contact with the convex surface 51. Therefore, the slider-mounted portion 30 and the convex surface 51 are in contact with each other at a contact portion 90.

The slider-mounted portion 30 moves around center of curvature Z1 so as to roll over the convex surface 51, in a state of being in contact with the convex surface 51 at the contact portion 90. At this time, the convex surface 51 and the slider-mounted portion 30 are substantially in elastic contact (Hertzian elastic contact) between a plane and a sphere surface. Therefore, it has been considered that there is no slippage at the contact portion and that losses caused by friction are essentially negligible.

In fact, however, it was found that a force similar to friction acts on the contact portion 90 between the slider-mounted portion 30 and the convex surface 51. This force is the flexure pitching resistance Fpr discovered by the present inventors. The flexure pitching resistance Fpr can be obtained by analysis depending on the design of the flexure 21 (primarily, the design of the gimbal portion 45).

FIG. 5 schematically shows the slider 31 moving along the surface 12a with a negative pitch angle θ1 relative to the reference plane N. As shown in FIG. 5, when the slider 31 moves along the surface 12a with a negative pitch angle θ1, the contact portion 90 moves in a first direction P1 from a reference line Y1. The slider-mounted portion 30 rotates on the surface of the convex surface 51 without substantial slippage. At this time, the flexure pitching resistance Fpr in the direction opposite to the direction of movement of the slider-mounted portion 30 acts on the contact portion 90 in a tangential direction of the convex surface 51. The slider 31 is provided on the slider-mounted portion 30. Therefore, as described herein, the pitch angle of the slider 31 and the pitch angle of the slider-mounted portion 30 are synonymous with each other.

The flexure pitching resistance Fpr acts on the contact portion 90 as a moment of the radius of curvature R. Therefore, the torque around the center of curvature Z1 as expressed as a product of the flexure pitching resistance Fpr and the radius of curvature R (Fpr×R), acts on the slider-mounted portion 30. This torque increases as the radius of curvature R increases, supplying resistance to the slider-mounted portion 30 moving in the pitching direction.

FIG. 6 schematically shows the slider 31 moving along the surface 12a with a positive pitch angle θ2 relative to the reference plane N. As shown in FIG. 6, when the slider 31 moves along the surface 12a with a positive pitch angle θ2, the contact portion 90 moves in a second direction P2 from the reference line Y1. The slider-mounted portion 30 rotates on the convex surface 51 without substantial slippage. At this time, the flexure pitching resistance Fpr in the direction opposite to the direction of movement of the slider-mounted portion 30 acts on the contact portion 90 in a tangential direction of the convex surface 51.

FIG. 7 is a schematic diagram showing the motion system including the slider 31. In equations shown below and in FIG. 7, k1 is the pitch stiffness ([Nm/rad]) of a slider surface 31c facing the air bearing 80. k2 is the pitch stiffness (pitch stiffness [Nm/rad]) of the gimbal portion 45 of the flexible 21. c is the viscous damping coefficient between the slider surface 31c facing the air bearing 80 and the gimbal portion 45. ζ is the viscous damping ratio. 0 is the pitch angle of the slider [rad], a is the input amplitude [rad], Fpr is the flexure pitching resistance [N], R is the radius of curvature of the convex surface of the dimple R [m] and, ω is the angular frequency [rad/s]. I is the inertia (mass) of the slider 31 including the slider-mounted portion 30 but, to simplify the calculation, only the inertia of the slider 31 is considered.

Fpr×R is the resistance torque, which acts in the opposite direction to the rotation direction. Therefore, the equations of motion for one degree of freedom are the following equations (1) and (2).

- When {dot over (θ)}>0

I
⁢

θ
¨

=

-

k
1

(

θ
-

a
⁢

sin
⁢
ω
⁢
t

)

-

c
⁢

θ
.

-

k
2

⁢
θ

-

RF
pr

(
1
)

- When {dot over (θ)}<0

I
⁢

θ
¨

=

-

k
1

(

θ
-

a
⁢

sin
⁢
ω
⁢
t

)

-

c
⁢

θ
.

-

k
2

⁢
θ

-

RF
pr

(
2
)

- k₁; Pitch stiffness of ABS, k₂; Pitch stiffness of Fx,
- c; Viscous damping coefficient of Fx,
- R; Radius of dimple, Fpr; Flexure pitching resistance,
- θ; Slider pitching angle,
- a; Input amplitude, I; Slider inertia,
- ω; Angular frequency.

By transforming the equations (1) and (2), the following equations (3) and (4) are obtained.

- When {dot over (θ)}>0

θ
¨

+

2
⁢
ζ
⁢

ω
0

⁢

θ
.

+

ω
0
2

⁢
θ

=

ak
1

I

⁢
sin
⁢
ω
⁢
t

-

RF

p
⁢
r

I

(
3
)

- When {dot over (θ)}<0

θ
¨

+

2
⁢
ζ
⁢

ω
0

⁢

θ
.

+

ω
0
2

⁢
θ

=

ak
1

I

⁢
sin
⁢
ω
⁢
t

+

RF

p
⁢
r

I

(
4
)

Here,

ω
0

=

k
1

+

k
2

I

is the circular natural frequency, and

ζ
=

c

2
⁢

I
⁡
(

k
1

+

k
2

)

is the viscous damping ratio.

In equations (3) and (4), the principle of linear superposition is established. Therefore, the steady-state vibration solution is assumed to be the following equation (5).

θ
p

=

U
⁢
sin
⁢
ω
⁢
t

+

V
⁢
cos
⁢
ω
⁢
t

+
C

(
5
)

If θp. {dot over (θ)}p, {umlaut over (θ)}p are substituted into equations (3) and (4),

- When θ>0

{

(

ω
0
2

-

ω
2

)

⁢
U
-
2
⁢

ζω
0

⁢
ω
⁢
V

}

⁢

sin
⁢
ω
⁢
t

+

{

2
⁢
ζ
⁢

ω
0

⁢
ω
⁢
U

+

(

ω
0
2

-

ω
2

)

⁢
V

}

⁢

cos
⁢
ω
⁢
t

+

ω
0
2

⁢
C

=

ak
1

I

⁢
sin
⁢
ω
⁢
t
-

RF
pr

I

- When {dot over (θ)}<0

{

(

ω
0
2

-

ω
2

)

⁢
U
-
2
⁢

ζω
0

⁢
ω
⁢
V

}

⁢

sin
⁢
ω
⁢
t

+

{

2
⁢
ζ
⁢

ω
0

⁢
ω
⁢
U

+

(

ω
0
2

-

ω
2

)

⁢
V

}

⁢

cos
⁢
ω
⁢
t

+

ω
0
2

⁢
C

=
 

ak
1

I

⁢
sin
⁢
ω
⁢
t
-

RF
pr

I

When the left and right sides are compared,

- When è>0

(

ω
0
2

-

ω
2

)

⁢
U
-
2
⁢

ζω
0

⁢
ω
⁢
V

=

ak
1

I

2
⁢

ζω
0

⁢
ω
⁢
U

+

(

ω
0
2

-

ω
2

)

⁢
V

=
0

ω
0
2

⁢
C

=

-

RF
pr

I

- When {dot over (θ)}<0

(

ω
0
2

-

ω
2

)

⁢
U
-
2
⁢

ζω
0

⁢
ω
⁢
V

=

ak
1

I

2
⁢

ζω
0

⁢
ω
⁢
U

+

(

ω
0
2

-

ω
2

)

⁢
V

=
0

ω
0
2

⁢
C

=

-

RF
pr

I

When U, V, and C are obtained from the above equations,

U and V are the same as expressed by the following equations when è>0 and when {dot over (θ)}<0.

U
=

ak
1

(

ω
0
2

-

ω
2

)

I
⁢

{

(

ω
0
2

-

ω
2

)

2

+

(

2
⁢
ζ
⁢

ω
0

⁢
ω

)

2

}

(
6
)

-
V

=

2
⁢

ak
1

⁢
ζ
⁢

ω
0

⁢
ω

I
⁢

{

(

ω
0
2

-

ω
2

)

+

(

2
⁢
ζ
⁢

ω
0

⁢
ω

)

2

}

(
7
)

C varies as expressed by the following equations when {dot over (θ)}>0 and when {dot over (θ)}<0.

- When {dot over (θ)}>0

C
=

-

RF
pr

I
⁢

ω
0
2

=

-

RF
pr

k
1

+

k
2

(
8
)

- When {dot over (θ)}<0

C
=

RF
pr

I
⁢

ω
0
2

=

RF
pr

k
1

+

k
2

(
9
)

The steady-state solution Op was obtained from equations (6) to (9).

θ
p

=

U
⁢
sin
⁢
ω
⁢
t

+

V
⁢
cos
⁢
ω
⁢
t

+
C

=

A
⁢

sin
⁡
(

ω
⁢
t
-
δ

)

+
C

When the resistance torque (flexure pitching resistance Fpr) is zero, each of the amplitude A and phase δ is expressed by the following equation.

Amplitude