Patent Publication Number: US-7595964-B2

Title: Method for reducing off track head motion due to disk vibration in a hard disk drive through the head gimbal assembly

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is a divisional of Ser. No. 10/619,163 filed Jul. 10, 2003, now U.S. Pat. No. 7,136,260. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to head gimbal assemblies and servo controller of a hard disk drive. 
   2. Background Information 
   Hard disk drives contain a plurality of magnetic heads that are coupled to rotating disks. The heads write and read information by magnetizing and sensing the magnetic fields of the disk surfaces. There have been developed magnetic heads that have a write element for magnetizing the disks and a separate read element for sensing the magnetic field of the disks. The read element is typically constructed from a magneto-resistive material. The magneto-resistive material has a resistance that varies with the magnetic fields of the disk. Heads with magneto-resistive read elements are commonly referred to as magneto-resistive (MR) heads. 
   Each head is embedded in a slider, which is attached to a flexure arm to create a subassembly commonly referred to as a head gimbal assembly (HGA). The HGA&#39;s are attached to an actuator arm. The actuator arm has a voice coil motor that can move the heads across the surfaces of the disks. 
   Information is stored in radial tracks that extend across the surfaces of each disk. Each track is typically divided up into a number of segments or sectors. The voice coil motor and actuator arm can move the heads to different tracks of the disks and to different sectors of each track. 
   A suspension interconnect extends along the length of the flexure arm and connects the head to a preamplifier. The suspension interconnect typically comprises a pair of conductive write traces w+, w− and a pair of conductive read traces r+ and r−. One pair of traces, such as the read traces, extend down one side of the flexure arm to the head and the remaining pair of traces extends down the other side of the flexure arm to the head. 
   The Tracks Per Inch (TPI) in hard disk drives is rapidly increasing, leading to smaller and smaller track positional tolerances. The track position tolerance, or the offset of the read-write head from a track, is monitored by a signal known as the head Positional Error Signal (PES). Reading a track successfully usually requires minimizing read-write head PES occurrences. The allowable level of PES is becoming smaller and smaller. A substantial portion of the PES is caused by disk vibration. 
   Track Mis-Registration (TMR) occurs when a read-write head tends to lose the track registration. This occurs when the disk surface bends up or down. TMR is often a statistical measure of the positional error between a read-write head and the center of an accessed track. Bending is defined in terms of bending modes. For a positive integer k, a bending mode of (k, 0) produces k nodal lines running through the disk surface center, creating k peaks and k troughs arranged on the disk surface. Bending mode (0, 0) produces no nodal lines, either the entire disk is bent up or bent down. 
   Two basic prior art approaches are known to lower the Track Mis-Registration (TMR) due to disk vibration. One approach uses head gimbal assemblies providing a radial motion capability. The other approach alters the servo-controller to reduce TMR. 
   In the first approach, a head gimbal assembly, including a biased load beam, creates a roll center (also known as a dimple center), which provides a radial motion capability as the load beam moves vertically due to disk vibration. This allows sliders to move in a radial direction as well as in a vertical direction with respect to the disks, reducing off-track motion due to disk vibration. 
   The first approach has some problems. An air bearing forms between the slider face and the disk surface. The slider face is tilted near the disk surface when it is flat. The air bearing becomes non-uniform when the disk surface is flat, adding new mechanical instabilities into the system. 
   One alternative prior art head gimbal assembly provides a slider mounted so that it pivots in the radially oriented plane about the effective roll axis, which is located within the disk. This scheme does not cause a non-uniform air bearing when the disk surface is flat. However, the way the effective roll axis is placed inside the disk requires a more complex mechanical coupling between the slider support assembly and the slider. This complex mechanical coupling may have a greater probability of mechanical failure, tending to increase manufacturing expenses and to reduce hard disk drive life expectancy. 
   The second prior art approach to lowering TMR due to disk vibration alters the servo-controller. These servo controllers favor optimization of PES in the disk vibration range without regard for strengthening rejection of low frequency disturbances. The disk vibration range will be considered to include frequencies between about 1K Hz and about 4K Hz. Low frequency disturbances will be considered to include at least the frequencies between about 0 Hz and about 800 Hz. 
   Accordingly, there exists a need for head gimbal assembly mechanisms providing a stable air bearing, able to follow a track when a disk surface bends, which are easy and reliable to manufacture. There exists a need for servo controllers optimizing PES in the disk vibration range and taking into account potential advantages from strengthened rejection of low frequency disturbances. 
   BRIEF SUMMARY OF THE INVENTION 
   The present invention includes improved head gimbal assemblies, which address TMR. These head gimbal assemblies are as mechanically simple as contemporary head gimbal assemblies, support parallel flying sliders over flat disk surfaces, and reduce TMR induced by disk vibration. They may be easier to build, more reliable, and cost less to make, than other known approaches, at comparable track densities and rotational rates. The improved head gimbal assemblies include mechanisms for moving the slider parallel the disk surface, when the disk surface is flat, and radially moving the slider toward the track, when the disk surface is bent, so that the head can more closely follow the track. 
   In a first set of mechanisms, the actuator arm moves by lever action through a principal axis, with the slider aligned at a bias angle and the slider face parallel to the flat disk surface. The lever action causes the slider to move radially toward the track, when the disk surface is bent. 
   In a second set of mechanisms, the actuator arms couple to load beams via two fingers. The first finger flexes differently from the second finger when the disk surface is bent. The fingers are constructed so that, when the disk surface is bent, the slider is moved radially toward the track. 
   A third set of mechanisms move the actuator arm by lever action through the principal axis. The actuator holds the slider parallel to the disk surface, when it is flat. The slider is mounted by a flexure at a second bias angle to the principal axis. The flexure responds as the disk surface bends through the second bias angle, causing the slider to move radially toward the track. 
   The present invention provides head gimbal assemblies incorporating mechanisms of the first set operating with mechanisms of the third set. The invention alternatively provides head gimbal assemblies incorporating mechanisms of the second set operating with mechanisms of the third set. 
   The present invention provides a distinctive servo-controller scheme resulting in overall improvement in PES performance, particularly when applied to hard disk drives employing the invention&#39;s TMR reduction mechanisms. 
   The servo-controllers trade off gain in the disk vibration frequency range in favor of increased rejection of low frequency disturbances. This leads to the lowest PES statistics, when applied to hard disk drives with the TMR reduction mechanisms of the invention. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The objects and features of the present invention, which are believed to be novel, are set forth with particularity in the appended claims. The present invention, both as to its organization and manner of operation, together with further objects and advantages, may best be understood by reference to the following description, taken in connection with the accompanying drawings, in which: 
       FIG. 1  is a simplified schematic of the relationship between a principal axis of the actuator arm, head gimbal assembly, slider, and radial vector from the center of the spindle hub; 
       FIG. 2  is a simplified schematic of a disk drive controller controlling a hard disk drive; 
       FIG. 3A  is a cross section view through a disk of a first inventive mechanism operating when the disk surface bends down; 
       FIG. 3B  is a radial-directional view through the disk of the first inventive mechanism, when the disk surface bends down; 
       FIG. 3C  is a cross section view through the disk of the first inventive mechanism operating when the disk surface bends up; 
       FIG. 3D  is a radial-directional view through the disk of the first inventive mechanism operating when the disk surface bends up; 
       FIGS. 4A to 6A  are top views of head gimbal assemblies of the first and second inventive mechanisms; 
       FIGS. 6B to 6E  are views of head gimbal assemblies of the second inventive mechanism; 
       FIG. 7A  is a top view of a head gimbal assembly of the first and second inventive mechanisms; 
       FIGS. 7B to 8D  are views of a head gimbal assembly of the third inventive mechanism; 
       FIGS. 9A ,  9 C, and  9 E are side views of the radial head motions for head gimbal assemblies of  FIG. 8D , resulting from the bending motion of the flexure gimbal induced by disk axial vibration; 
       FIGS. 9B ,  9 D, and  9 F are top views of the radial head motions for head gimbal assemblies of  FIG. 8D , resulting from the bending motion of the flexure gimbal induced by disk axial vibration; 
       FIGS. 10A ,  10 C, and  10 E are side views of the radial head motions for head gimbal assemblies of  FIG. 7B , resulting from the bending motion of the flexure gimbal induced by disk axial vibration; 
       FIGS. 10B ,  10 D, and  10 F are top views of the radial head motions for head gimbal assemblies of  FIG. 7B , resulting from the bending motion of the flexure gimbal induced by disk axial vibration; 
       FIGS. 11A and 11B  are cross section and radial-directional views, through the disk, of the mechanisms of  FIGS. 7B through 8D  operating when the disk surface bends down; 
       FIGS. 11C and 11D  are cross section and radial-directional views, through the disk, of the mechanisms of  FIGS. 7B through 8D  operating when the disk surface bends up; 
       FIG. 12  is a graph of the results of the bending slope per unit of axial displacement for four common bending modes for various radial positions and ID through OD; 
       FIGS. 13A ,  13 B, and  13 C are graphs summarizing results regarding the power spectral density function in terms of axial vibration frequency versus displacement in meters at ID, at MD, and at OD, respectively; 
       FIG. 14A  is the geometric analysis used for the roll bias angle formula for the mechanisms of  FIGS. 7B to 8D  when the disk surface bends down as in  FIG. 11A ; 
       FIG. 14B  is the geometric analysis used for the roll bias angle formula for the mechanisms of  FIGS. 7B to 8D , when the disk surface bends up as in  FIG. 11C ; 
       FIG. 14C  is the geometric analysis used for the roll bias angle formula for the roll center mechanisms of  FIGS. 4A to 7A  when the disk surface bends down as in  FIG. 8A ; 
       FIG. 14D  is the geometric analysis used for the roll bias angle formula for the roll center mechanisms of  FIGS. 4A to 7A  when the disk surface bends up as in  FIG. 9A ; 
       FIGS. 15A and 15B  are graphs of the results of the bending angle versus the roll bias angle at OD when the disk is respectively bent down and bent up; 
       FIG. 16A  is a graph summarizing the spectral density of NRRO PES/Track pitch measure in percent versus vibrational frequency for a disk-head gimbal assembly with a roll bias angle of zero degrees, which is standard in conventional hard disk drives; 
       FIGS. 16B and 16C  are graphs summarizing the spectral densities of NRRO PES/Track pitch measure in percent versus vibrational frequency for a disk-head gimbal assembly with a roll bias angle of one degree and of two degrees, respectively; 
       FIG. 17  is a graph of a weight function for PES feedback in the frequency domain trading servo controller gain in disk vibration frequency range for increased rejection of low frequency disturbances; 
       FIG. 18  is a graph of the error sensitivity function of the original servo controller and the modified servo controller as derived from  FIG. 17 ; 
       FIG. 19  is a graph of the mechanical disturbance spectra of the in-plane torque disturbance spectrum and out-of-plane disk disturbance spectrum; and 
       FIGS. 20 and 21  are graphs of the results regarding a conventional disk-head gimbal assembly interface, compared to a head-gimbal assembly, with a two degree roll bias angle, operated with the modified servo-controller. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   The following description is provided to enable any person skilled in the art to make and use the invention and sets forth the best modes presently contemplated by the inventors of carrying out the invention. Various modifications, however, will remain readily apparent to those skilled in the art, since the generic principles of the present invention have been defined herein. 
   Disclosed are improved head gimbal assemblies addressing Track Mis-Registration (TMR). These head gimbal assemblies may be as mechanically simple as contemporary head gimbal assemblies, support parallel flying sliders over flat disk surfaces, and reduce TMR induced by disk vibration. They are easier to build, more reliable, and cost less to make, than other known approaches at comparable track densities and rotational rates. The improved head gimbal assemblies include improved suspensions or mechanisms for moving the slider parallel to the disk surface, when the disk surface is flat, and radially moving the slider toward the track, when the disk surface is bent. 
   Referring to the drawings, more particularly by reference numbers,  FIG. 1  shows an example actuator arm assembly pivoting about the actuator axis  40 , changing the angle between the radial vector  112  and the actuator principal axis  110 . The actuator arm assembly includes the actuator arm  50  coupled to head gimbal assembly  60 , which is coupled to slider  100 . Typically, the actuator arm assembly will rotate through various angles between a furthest inside position of the disk and the furthest outside position on the disk. Test data and analyses are provided for three regions of the disk. These are designated ID (corresponding to the furthest inside position), MD (a middle position where radial vector  112  is approximately at a right angle with  110 ), and OD (the furthest outside position). 
   In  FIG. 1 , an X axis extends along the principal axis  110  of the actuator arm, and a Y axis intersects the X axis at essentially actuator pivot  40 . When the actuator arm  50  positions the slider  100  so that the read-write head is at MD, the radial vector  112  is nearly parallel to the Y axis. Track  18  is shown near MD, but tracks exist from ID to OD, across the disk surface  12 . 
   The hard disk drive may include a plurality of actuator arms and head sliders located adjacent to the disks all controlled by the same voice coil motor. The heads may have separate write and read elements, that magnetize and sense the magnetic field of the disks. 
     FIG. 2  shows a schematic of an example controller system for a disk drive. The controller system includes a voice coil  32  coupled to a magnet assembly to create a voice coil motor. Providing a current to the voice coil  32  creates a torque that swings the actuator arm  50 , contained in the actuator assembly  30 . Moving the actuator arm  50  moves the actuator arm assembly, which moves the heads across the surfaces of the disk  12 . 
   The hard disk drive may further include a disk drive controller  1000 . In  FIG. 2 , disk drive controller  1000  communicates with an analog read-write interface  220 , which in turn communicates the resistivity R_rd found in the spin valve within read-write head  200  to controller  1000 . The disk drive controller may include a computer  1100  coupled  1122  to a memory  1120  including a program system  2000 . The disk drive controller may provide signals Read_bias, Write_bias, and TA_threshold and also receive signals such as TAD. 
   The analog read-write interface  220  frequently includes a channel interface  222  communicating with a pre-amplifier  224 . The channel interface  222  receives commands from the embedded disk controller  1000 , setting the read_bias and write_bias. The analog read-write interfaces  220  may employ either a read current bias or a read voltage bias. For example, the resistance of the read head is determined by measuring the voltage drop across the read differential signal pair (r+ and r−), based upon the read bias current setting read_bias, using Ohm&#39;s Law. 
   In  FIG. 2 , the channel interface  222  provides a Position Error Signal (PES) to the servo controller  240 , which controls voice coil  32  to keep the read-write head close enough to access a data track (such as track  18  of  FIG. 1 ). 
   The invention includes three approaches for addressing the TMR problem by moving the slider face parallel to the disk surface with respect to the track when the disk surface is flat, and a moving the slider toward the track when the disk surface is bent. Each of these approaches for reducing TMR may be used individually or in combination with other approaches discussed herein or elsewhere. 
   Actuator assemblies using example mechanisms employing the first approach are seen in  FIGS. 4A to 6A  and  7 A. In these example mechanisms the actuator arm moves by lever action through a principal axis, with the slider aligned at a bias angle and the slider face parallel to the flat disk surface. The lever action causes the slider to move radially toward the track, when the disk surface is bent. 
   In addition to the example mechanisms employing the first approach,  FIGS. 4A to 6A  also show actuators with example mechanisms employing the second approach.  FIGS. 6B to 6E  show actuator assemblies which use only the second approach to reducing TMR. As will be explained further below, the example mechanisms employing the second approach include two fingers coupling the actuator arm to the load beam, where the fingers flex differently from each other when the disk surface is bent. The difference in the response of each finger to the bending of the disk surface is designed to cause the slider to move radially toward the track when the disk surface bends. 
     FIGS. 7B to 8D  show example mechanisms employing the third approach to reducing TMR. In these mechanisms, the slider is mounted by a flexure at a second bias angle to the principal axis. The actuator holds the slider parallel to the disk surface, when it is flat. The flexure responds as the disk surface bends through the second bias angle, causing the slider to move radially toward the track. 
   In operation, these mechanisms provide a suspension with a roll center movable slider which allows the read-head to follow a track  16  as the disc surface bends down as  16 -A and up as  16 -B. The read head  100  when disk is bent down is labeled  100 -A and when bent up is labeled  100 -B. This process is seen more clearly in reference to  FIGS. 3A to 3D  which show schematically the head-disk interface dynamics.  FIGS. 3A and 3B  show cross section and radial-directional views through the disk  14  of the inventive mechanisms discussed above operating when the disk surface  12  bends down  14 -A, and  FIGS. 3C and 3D  show cross section and radial-directional views through the disk  14  of a first inventive mechanism operating when the disk surface  12  bends up  14 -B. 
   Throughout this document, the read-write head position when the disk surface is flat is denoted A 0 , and when bent is denoted A 1 . The track position when the disk surface is flat is denoted B 0 , and when bent, is denoted B 1 . δ refers to the amount of this off-track movement, or the distance between A 1  and B 1 . δ 1  refers to the distance between A 0  and A 1 . δ 2  refers to the distance between B 0  and B 1 . 
   This head-disk surface interface allows the use of the formula δ=δ 1 +δ 2 , for the motion of  FIGS. 3A and 3C , given that A 0 -B 0  and A 1 -B 1  are essentially 0, because 
   
     
       
         
           
             
               
                 
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   In  FIGS. 3A and 3C , δ 2 =td/2*θ=−δ 1 . 
   Each of the previously mentioned approaches will be discussed in more detail below. 
     FIGS. 4A to 6A , and  7 A, show several means for moving the slider parallel to a disk surface. Including moving the actuator arm by a lever action through the principal axis with the slider aligned at a bias angle  710 , when the slider face is essentially parallel to the disk surface. 
   With respect to the track when the disk surface is flat,  FIGS. 4A to 6A , and  7 A, show the means for radially moving the slider. Each of which includes a means for the lever action to cause the slider to move radially bent. More specifically, the lever action through the principal axis at the bias angle  710 , causes the radial motion of the slider. In these Figures, the dynamics of the head-disk interface determine the bias angle  710 , which is preferably between plus and minus 10 degrees from zero. 
   In  FIG. 4A , a head gimbal assembly includes a suspension having bias angle  710 , attached by connection beam  82  to extended base plate  84 . The suspension mounts on the actuator arm, at bent edge  700  of extended base plate  84  and at bent edge  702  of load beam  80 . 
   In  FIG. 4B , a head gimbal assembly includes a suspension having bias angle  710 , attached to base plate  70 . It mounts on the actuator arm, at bent edge  704  of base plate  70  and at bent edge  700  of load beam  80 . 
   In  FIG. 4C , a head gimbal assembly includes a suspension having bias angle  710 , attached by connection beam  82  to extended base plate  84 . This is mounted on the actuator arm, at the bent edge  700  of the extended base plate  84 . 
   In  FIG. 4D , a head gimbal assembly includes a suspension having bias angle  710 , attached to base plate  70 , which is mounted on the actuator arm, at bent edge  704  of base plate  70 . 
     FIGS. 4A to 6B , and  7 A, show the second inventive mechanism for reducing TMR. This includes the means for moving the actuator arm coupled to the load beam via two fingers. The first finger flexes differently from the second finger when the disk surface is bent. The first finger flexes differently from the second finger, causing the slider to move radially with respect to the track when the disk surface is bent. 
   In particular,  FIGS. 6B to 6E  show embodiment of the second mechanism, which do not involve a bias angle  710  as shown in  FIGS. 4A to 6A  and  7 A.  FIG. 6B  shows a top view of a head gimbal assembly, based upon the difference in the connection beam fingers  82 -A and  82 -B connecting up  83 -A and down  83 -B, respectively. Finger  82 -A flexes differently from finger  82 -B, causing slider  100  to move radially with respect to the track, as disk surface  12  is bent.  FIG. 6C  shows fingers  82 -A and  82 -B connecting up and down on the upper connection beam  86  and lower connection beam, as in  FIG. 6E .  FIGS. 6D and 6E  show side views of the head gimbal assembly of  FIG. 6B  when the thickness of the base plate  70  and load beam  80  differ, or are the same, respectively. Extended base plate  84 , finger  82 -A, and upper connection beam  86  are preferably made from one sheet of metal, preferably stainless steel. 
     FIG. 7A  shows a top view of suspension  80  attached to base plate  70  using a cutout  720  to create fingers  80 -A and  80 -B, which together form bias angle  710 . The bias angle  710  can be determined by the dynamics of the head-disk interface, the shape of cut-out  720 , and the stiffness of load beam  80 . 
     FIGS. 7B to 8D  show examples of a third inventive mechanisms for reducing TMR. This includes moving the actuator arm by the lever action through the principal axis when the slider is parallel to the disk surface. The slider is mounted on a flexure at a second bias angle  712  to the principal axis. The means for radially moving the slider includes the flexure  94  responding as the disk surface bends through the second bias angle, causing the slider to move radially toward the track. 
     FIG. 7B  shows a top view of the suspension attached to base plate  70 , with two points  722  and  724  welding flexure  90  to load beam  80 , providing bias angle  710 . Flexure  90  attaches to both slider  100  and to load beam  80 . The number of welding points close to the slider is preferably at least two. If the line between welding points is not perpendicular to the principal axis  110 , then the trajectory of bending motion of the flexure induced by disk axial vibration will be on a tilted bending line. It is sometimes preferred that the line, between the welding points  722  and  724 , is not perpendicular to the principal axis  110 . 
     FIGS. 9A to 9F  show radial head motions for the head gimbal assembly of  FIG. 8D , due to the bending motion of the flexure gimbal  92  induced by disk axial vibration. In  FIGS. 9B ,  9 D, and  9 F, the trajectory of head, moves about the tilted bending line  740 . This line is preferably in a range of plus or minus 10 degrees of arc from zero labeled as  730 . 
     FIGS. 10A to 10F  show radial head motions for the head gimbal assembly of  FIG. 7B , according to the bending motion of the flexure gimbal induced by the disk axial vibration. In  FIGS. 10B ,  10 D, and  10 F, the trajectory of head, moves about the tilted bending line  740  from line  750 . This line is again, preferably, in a range of plus or minus 10 degrees of arc from zero as shown by g 0 , g 1  and g 2 . 
   Embodiments of a third set of example mechanisms built according to the invention are shown in  FIGS. 7B through 8D .  FIGS. 11A to 11D  show various views of this set of mechanisms. 
     FIG. 11A  shows a cross section view, through disk  14  when the disk surface  12  bends down  12 -A.  FIG. 11B  shows a radial-directional view when disk surface  12  bends up  12 -B. 
     FIG. 11C  shows a cross section view when the disk surface  12  bends up  12 -B.  FIG. 11D  shows a radial-directional view when the disk surface  12  bends up  12 -B. 
   It is reasonable to use the formula δ=δ 1 −δ 2 =0, for the motion of  FIGS. 11A and 11C , since A 0 -B 0  and A 1 -B 1  are essentially 0, leading, as in  FIG. 3C , to δ 2 =td/2*θ=−δ 1 . 
     FIG. 12  shows the results of the bending slope per unit axial displacement, for various radial positions for four common bending modes for ID through OD. The horizontal axis indicates radial position in terms of meters. The vertical axis indicates the bending slope per unit axial displacement in terms of 1/meter. Trace  800  indicates the results for bending mode (3, 0). Trace  802  indicates the results in bending mode (2, 0). Trace  804  indicates the results in bending mode (1, 0). Trace  806  indicates the results in bending mode (0, 0). 
     FIGS. 13A ,  13 B, and  13 C summarize results regarding the power spectral density function in terms of axial vibration frequency versus displacement in meters at ID, at MD, and at OD, respectively. 
   In  FIGS. 12 through 13C , the experimental hard disk drive was rotating at 7200 RPM. 
     FIGS. 14A and 14B  show the geometric analysis used for the bias angle  710  formula for the mechanisms of  FIGS. 7B to 8D  when the disk surface bends down as in  FIG. 11A  and bent up as in  FIG. 11C . In these Figures: 
   A refers to the upper center point of slider  100  for the stationary state. 
   C refers to upper center point of slider  100  for the disk spinning state. 
   c refers to a deformed track  18  on the spinning disk surface  12 . 
   ts refers to the thickness of slider  100 . 
   td refers to the thickness of disk  14 . 
   θ refers to the disk bending angle. 
   r refers to the radius of the disk, which is preferably 45 mm. 
   φ refers to the roll bias angle, which is portrayed in  FIGS. 7B to 8D  by reference number  710 . 
   In  FIGS. 14A to 14D , the bending angle per unit of axial vibration at r was experimentally determined to be 
   75/m for bending mode (3, 0), 
   60/m for bending mode (2, 0), 
   50/m for bending mode (1, 0), and 
   40/m for bending mode (0, 0). 
   The bias angle  710  of the earlier Figures is the roll bias angle φ of  FIGS. 14A-16C . In  FIG. 14A , the roll bias angle φ=arc cos((a−b cos θ)/c) for the disk bending down. In  FIG. 14B , the roll bias angle φ=arc cos ((b cos θ−d)/c) for the disk bending up. This leads to φ≈1.2 degrees of arc at the Outside position of Disk OD, with r=45 mm. In  FIGS. 14A and 14B , the radial motion of slider  100  is about h=b*sin θ=(ts+td/2) sin θ. 
     FIG. 14C  shows the geometric analysis of the roll bias angle  710  formula for the roll center mechanisms of  FIGS. 4A to 6A , and  7 A, when the disk surface bends down as in  FIG. 8A . 
     FIG. 14D  shows the geometric analysis of the roll bias angle  710  formula for the roll center mechanisms of  FIGS. 4A to 6A , and  7 A, when the disk surface bends up as in  FIG. 9A . 
   In  FIGS. 14C and 14D : 
   Ar refers to the roll center for the stationary state. 
   Cr refers to roll center for the disk spinning state. 
   c refers to a deformed track  18  on the spinning disk surface  12 . 
   ts refers to the thickness of slider  100 . 
   td refers to the thickness of disk  14 . 
   θ refers to the disk bending angle. 
   r refers to the radius of the disk, which is preferably 45 mm. 
   φ refers to the roll bias angle, which is portrayed in  FIGS. 4A to 6A , and  7 A by reference number  710 . 
   In  FIG. 14C , the roll bias angle φ=arc cos((ar−br cos θ)/cr) for the disk bending down. In  FIG. 14D , the roll bias angle φ=arc cos((br cos θ−dr)/cr) for the disk bending up. This leads to φ≈1.6 degrees of arc at the Outside position of Disk OD, with r=45 mm. 
   Drive level experiments were conducted on two types of production hard disk drives with the roll biased load beam built to move the roll center radially as shown in  FIG. 5A . The hard disk drives operated at 56,000 TPI at 7200 RPM and at 93,000 TPI at 7200 RPM. Both types of hard disk drives were able to move the roll center radially with the biased load beam. 
   Skew angles as used herein refer to the angular difference from the perpendicular of the principal axis  110  of the actuator with respect to the tangent of the track  18 . In the experimental hard disk drives, the skew angle at OD is about 13.1 degrees arc, at MD about −5 degrees arc, and at ID about −18 degrees arc. Please refer to  FIG. 1  for an illustration of these positions. 
     FIGS. 15A and 15B  show the results regarding the bending angle versus the roll bias angle at OD when the disk bends down and up, respectively. The vertical axes represent the roll bias angle φ ( 710 ) in terms of degrees arc. The horizontal axes represent the bending angle in units of 10 −5  degrees of arc. 
   The roll biased load beam acts to attenuate several peaks related to disk modes in the spectrum of the non-repeatable run-out (NRRO) PES signal, shown in  FIGS. 16A-16C . In addition, the repeatable run-out (RRO) level is also attenuated, because of the attenuation of the NRRO in the writing of the servo track. The results in the following table are for tracks near OD. 
   
     
       
         
             
             
             
             
           
             
                 
             
             
               Roll bias angle 
               Std-RRO (%) 
               Std-NRRO (%) 
               Std-Total (%) 
             
             
                 
             
           
          
             
               Standard (0) 
               1.582 
               1.855 
               2.441 
             
             
               One degree 
               1.484 
               1.465 
               2.070 
             
             
               Two degrees 
               1.328 
               1.406 
               1.936 
             
             
                 
             
          
         
       
     
   
     FIG. 16A  summarizes the spectral density  820  of NRRO PES/Track pitch measure in percent versus vibrational frequency for a disk-head gimbal assembly with no roll bias angle, which is standard in conventional hard disk drives.  FIGS. 16B and 16C  summarize the spectral densities  822  and  824  of NRRO PES/Track pitch measure in percent versus vibrational frequency for a disk-head gimbal assembly with a roll bias angle of one degree and of two degrees, respectively. 
   In  FIGS. 16A to 16C , the vertical axis represents NRRO per track pitch as a percentage. The horizontal axis represents vibrational frequency in Herz. 
   Reference labels  1 B and  1 F represent the backward frequency and the forward frequency associated with bending mode (1, 0). 
   Reference labels  2 B and  2 F represent the backward frequency and the forward frequency associated with bending mode (2, 0). 
   Reference labels  3 B and  3 F represent the backward frequency and the forward frequency associated with bending mode (3, 0). 
   Reference labels  4 B and  4 F represent the backward frequency and the forward frequency associated with bending mode (4, 0). 
   TMR is further reduced by reconfiguring the servo controller  240  of  FIG. 2  for roll biased head gimbal assemblies, by sacrificing gain in the disk vibration region of the spectrum and increasing suppression in the low frequency region. In conventional hard disk drives, gain in the disk vibration frequency range cannot be sacrificed. 
     FIG. 17  shows a weight function  840 - 848  for PES feedback in the frequency domain. The servo controller gain in disk vibration frequency range  842  to  846  is traded for increased rejection of low frequency disturbances  840 .  FIG. 17  was derived by a random search method with the weighted function for PES in the neighborhood ranges,  840 - 848 . 
     FIG. 18  shows the error sensitivity function of the original servo controller  850  and the modified servo controller  852  as derived from  FIG. 17 . The vertical axis represents the error sensitivity in decibels. The horizontal axis represents the disk vibrational frequency in Herz. 
   F 1  indicates a definition of disk vibration frequency range, from 1K Hz to 3K Hz. F 2  indicates an alternative definition, from 800 Hz to 4K Hz. 
   F 3  indicates a definition of low frequency range from 17 Hz to 800 Hz. F 4  indicates an alternative definition, from 0 Hz to 800 Hz. 
   The preferred definition of disk vibration frequency range may vary among hard disk drives, possibly including higher and/or lower frequencies. 
   The preferred definition of low frequency range may vary among hard disk drives, possibly including higher and/or lower frequencies. 
     FIG. 19  shows the mechanical disturbance spectra. Trace  860  represents the in-plane torque disturbance spectrum. Trace  862  represents the out-of-plane disk disturbance spectrum. References labels  3 B,  3 F,  4 B, and  4 F represent backward and forward resonance of bending modes (3, 0) and (4, 0). The vertical axis represents displacement on a logarithmic scale. The horizontal axis represents mechanical vibration in Herz. 
     FIGS. 20 and 21  show the results regarding a conventional disk-head gimbal assembly interface  870 , compared to a head-gimbal assembly with a two degree roll bias angle, operated with the modified servo-controller  872 . Trace  870  represents a conventional disk and head gimbal assembly interface with a total NRRO PES of 2.578%. Trace  872  represents the experimental hard disk drive with a roll bias angle of two degrees operated by the modified servo-controller, having a total NRRO PES of 1.621%. This is a significant reduction in TMR, as measured by PES. 
   The invention includes applying this servo-controller scheme to any TMR reducing mechanism showing favorable results when trading off gain at the disk vibration frequency range in favor of increased rejection of low frequency disturbances. 
   Those skilled in the art will appreciate that various adaptations and modifications of the just-described preferred embodiments can be configured without departing from the scope and spirit of the invention. Therefore, it is to be understood that, within the scope of the appended claims, the invention may be practiced other than as specifically described herein.