Patent Publication Number: US-11664047-B2

Title: Management of actuator dynamics in a multiple actuator hard disk drive with an unequal number of heads on the two outer arms of each actuator

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of and claims the benefit of priority to commonly-owned pending U.S. patent application Ser. No. 17/353,584 filed on Jun. 21, 2021, the entire content of which is incorporated by reference for all purposes as if fully set forth herein. 
    
    
     FIELD OF EMBODIMENTS 
     Embodiments of the invention may relate generally to data storage devices such as hard disk drives and particularly to approaches for improving the structural dynamics of the actuators in a multi-actuator hard disk drive. 
     BACKGROUND 
     A hard disk drive (HDD) is a non-volatile storage device that is housed in a protective enclosure and stores digitally encoded data on one or more circular disks having magnetic surfaces. When an HDD is in operation, each magnetic-recording disk is rapidly rotated by a spindle system. Data is read from and written to a magnetic-recording disk using a read-write transducer (or read-write “head”) that is positioned over a specific location of a disk by an actuator. A read-write head makes use of magnetic fields to write data to, and read data from, the surface of a magnetic-recording disk. A write head works by using the current flowing through its coil to produce a magnetic field. Electrical pulses are sent to the write head, with different patterns of positive and negative currents. The current in the coil of the write head produces a localized magnetic field across the gap between the head and the magnetic disk, which in turn magnetizes a small area on the recording medium. 
     Increasing areal density (a measure of the quantity of information bits that can be stored on a given area of disk surface) is one of the on-going goals of hard disk drive technology evolution. In one form, this goal manifests in the type of high-capacity HDDs that are especially attractive in the context of enterprise, cloud computing/storage, and data center environments. However, the performance of high-capacity HDDs has not necessarily scaled up commensurately with the increases in capacity. This has led to the need to develop and implement various means to increase high-capacity HDD performance. 
     In recent years the growth in areal density in HDDs has not kept pace with the trends of years past. This has shifted the burden on the mechanics to boost capacity increases by increasing the number of disks within the prescribed form factor. As these HDDs are primarily used for near line storage in data centers in hyper-scale environments, the performance of these high-capacity drives also has to satisfy the IOPs (Input/Output Operations Per Second) density requirements (in some instances, similarly referred to as IOPs/TB) to minimize latency. This demand has led to a shift to multiple actuators for providing parallel access to data. 
     Any approaches that may be described in this section are approaches that could be pursued, but not necessarily approaches that have been previously conceived or pursued. Therefore, unless otherwise indicated, it should not be assumed that any of the approaches described in this section qualify as prior art merely by virtue of their inclusion in this section. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments are illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings and in which like reference numerals refer to similar elements and in which: 
         FIG.  1    is a plan view illustrating a hard disk drive (HDD), according to an embodiment; 
         FIG.  2    is a perspective view illustrating a dual-actuator configuration, according to an embodiment; 
         FIG.  3 A  is a perspective view illustrating a dual-actuator configuration having dynamics optimization features, according to an embodiment; 
         FIG.  3 B  is a top view illustrating a portion of the single-HGA (head-gimbal assembly) end-arm of the HSA (head-stack assembly) of  FIG.  3 A , according to an embodiment; 
         FIG.  3 C  is a bottom view illustrating a portion of the single-HGA end-arm of the HSA of  FIG.  3 A , according to an embodiment; 
         FIG.  4 A  is a top view illustrating a single-HGA end-arm of an HSA of a dual-actuator configuration, according to an embodiment; 
         FIG.  4 B  is a bottom view illustrating the dual-HGA end-arm of the HSA of  FIG.  4 A , according to an embodiment; 
         FIG.  5 A  is a top view illustrating a single-HGA end-arm of an HSA of a dual-actuator configuration, according to an embodiment; 
         FIG.  5 B  is a bottom view illustrating the dual-HGA end-arm of the HSA of  FIG.  5 A , according to an embodiment; 
         FIG.  6 A  is a top view illustrating a single-HGA end-arm of an HSA of a dual-actuator configuration, according to an embodiment; 
         FIG.  6 B  is a bottom view illustrating the dual-HGA end-arm of the HSA of  FIG.  6 A , according to an embodiment; 
         FIG.  7 A  is a top view illustrating a single-HGA end-arm of an HSA of a dual-actuator configuration, according to an embodiment; 
         FIG.  7 B  is a bottom view illustrating the dual-HGA end-arm of the HSA of  FIG.  7 A , according to an embodiment; 
         FIG.  8 A  is a top view illustrating a single-HGA end-arm of an HSA of a dual-actuator configuration, according to an embodiment; and 
         FIG.  8 B  is a bottom view illustrating the dual-HGA end-arm of the HSA of  FIG.  8 A , according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Generally, approaches to improving the structural dynamics of an actuator system in a multi-actuator hard disk drive are described. In the following description, for the purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the embodiments of the invention described herein. It will be apparent, however, that the embodiments of the invention described herein may be practiced without these specific details. In other instances, well-known structures and devices may be shown in block diagram form in order to avoid unnecessarily obscuring the embodiments of the invention described herein. 
     INTRODUCTION 
     Terminology 
     References herein to “an embodiment”, “one embodiment”, and the like, are intended to mean that the particular feature, structure, or characteristic being described is included in at least one embodiment of the invention. However, instances of such phrases do not necessarily all refer to the same embodiment, 
     The term “substantially” will be understood to describe a feature that is largely or nearly structured, configured, dimensioned, etc., but with which manufacturing tolerances and the like may in practice result in a situation in which the structure, configuration, dimension, etc. is not always or necessarily precisely as stated. For example, describing a structure as “substantially vertical” would assign that term its plain meaning, such that the sidewall is vertical for all practical purposes but may not be precisely at 90 degrees throughout. 
     While terms such as “optimal”, “optimize”, “minimal”, “minimize”, “maximal”, “maximize”, and the like may not have certain values associated therewith, if such terms are used herein the intent is that one of ordinary skill in the art would understand such terms to include affecting a value, parameter, metric, and the like in a beneficial direction consistent with the totality of this disclosure. For example, describing a value of something as “minimal” does not require that the value actually be equal to some theoretical minimum (e.g., zero), but should be understood in a practical sense in that a corresponding goal would be to move the value in a beneficial direction toward a theoretical minimum. 
     Context 
     Recall the observation that the performance of high-capacity HDDs has not scaled up commensurately with increases in storage capacity. This IOPS density deficit stands in the way of widespread adoption of such HDDs. In other words, the high latencies of large capacity HDDs in a clustered environment, such as in data centers with multiple clustered nodes, results in a bottleneck due to slower access to stored data. The pressure to increase the performance (e.g., IOPS) by reducing the latencies for data operations of high-capacity HDDs has become even stronger as capacities of HDDs continue to increase. 
     One possible approach to increasing HDD performance is the implementation of multi-actuator systems, in which multiple independently operating actuators are assembled onto a single shared pivot shaft in order to independently and concurrently read from and/or write to multiple recording disks of a disk stack. Since the available z-space (vertical height) within the drive is optimized to maximize the number of disks, the disk pitch would ideally be constant through the entire stack. However, due to additional space needed for the flex circuit and to allow the upper and lower actuators to rotate independently without interference, this becomes a challenging task. The endeavor to achieve constant disk pitch nevertheless continues. 
     For a dual-actuator drive, each actuator has two end-arms (or outer arms), i.e., a cover or base facing end-arm and another end-arm that faces the complementary actuator. If the number of disks in the disk stack is even, the adjacent end-arms (i.e., one from each of the two actuators (actuator-facing end-arms)) need to have one head-gimbal assembly (HGA) each to ensure an even split in capacity between the two actuators. Thus, the z-space required to fit two actuator arms (one actuator-facing end-arm each, from the upper and lower actuators) between the disks and have them adequately separated from each other is increased. This configuration, while being inefficient from the standpoint of achieving the highest possible capacity, also comes with a penalty to actuator inertia since an extra end-arm per actuator which carries just one HGA instead of two is an inefficient use of inertia/TB (terabyte). Further, there is an increase in TMR (track mis-registration) with having end-arms from two different actuators in the shared space between co-rotating disks. This necessitates the use of an odd number of disks, with the center disk of the stack being shared by the upper and lower actuators. In such a configuration, the actuator-facing end-arms of the upper and lower actuators that are serving the shared center disk have two HGAs each, while the cover/base facing end-arms have just one HGA each. Further, the arm-tip of the end-arm carrying two HGAs is thicker than the arm-tips of the other inner arms in the same head-stack assembly (HSA) with two HGAs. This increase in end-arm tip thickness is dictated by the larger disk spacing needed to accommodate the flexible cable assembly (FCA) traces for the HGA on the shared disk while precluding the need for a unique HGA. This increase in the dual-HGA end-arm tip thickness also mandates the end-arm root thickness to be higher than the other inner arms. 
     Under the foregoing scenario, the geometry (thickness) of the end-arm servicing the shared disk is quite different from any of the inner arms. This leads to a dynamic asymmetry in the actuator since there are now HSAs with (a) identical inner arms with two HGAs each, (b) a unique end-arm with two HGAs, and (c) a cover/base facing end-arm with one HGA. As a result of this mismatch, the actuator dynamics (as characterized by the plant transfer function) varies between the end-arm with one HGA and all the other arms with two HGAs (also referred to as dual-HGA arms), resulting in high gains in differing frequency ranges. The end-arm with a single HGA exhibits unusually high gains (significantly higher than the other arms with two HGAs) at certain frequencies. These high gains seen in the plant transfer function are associated with arm torsion, arm sway, and higher order system modes that are detrimental to the performance of the actuator. 
     In the context of a dual-actuator system, the dynamics of the two actuators are strongly coupled. This means that exciting one (primary) actuator (i.e., by way of seeking) causes resonance modes on the other (secondary) actuator to be excited as well. Here too, the secondary actuator dynamics differ between the end-arm with one HGA and all the other arms with two HGAs, resulting in high gains in different frequency ranges that are associated with arm modes. This coupling of dynamics negatively affects the ability of the active read-write head on the secondary actuator to stay on-track, or to efficiently seek to a track, due to excessive TMR. The performance of the HDD is thus reduced, in that an inordinate amount of time is expended trying to position and maintain the head centered over a data track (e.g., via servoing). The corresponding read and write operations are effectively delayed, thus reducing overall I/O performance. Furthermore, in scenarios in which a multitude of such HDDs populate a customer enclosure, acoustic excitation caused by air pressure fluctuations from cooling fans as well as structurally transmitted external vibration can excite arm and system resonance modes. The high gain of the end-arm with a single HGA for instance, clearly stands out in the acoustic transfer functions. It is these high gain arm and system modes that are either excited directly by the primary actuator or are coupled to the secondary actuator, or are excited by external vibration or acoustic pressure, that the embodiments described herein seek to mitigate. 
     Dual-Actuator System with Structural Dynamics Optimization Features 
     Embodiments described herein relate to approaches to managing actuator structural dynamics in dual-actuator HDDs with an odd number of HGAs, where the number of HGAs between the two end-arms of each actuator is different. In particular, the embodiments pertain to reducing the gain differences in the arm modes (torsion, sway) and system modes (Butterfly-3, Butterfly-4) seen in the plant transfer functions between arms with two HGAs and an arm with a single HGA. This is achieved by introducing an intentional mismatch of structural stiffness between the end-arm with a single HGA and the dual-HGA arms, which ensures that the gains for the problematic modes of interest (arm sway, arm torsion, and higher order system modes) are better matched between all the HGAs, and at the same time are also significantly reduced. Note that the number of actuators that may be assembled onto a shared pivot shaft may vary from implementation to implementation, however, an exemplary dual-actuator arrangement is described throughout herein. 
       FIG.  2    is a perspective view illustrating a dual-actuator configuration, according to an embodiment.  FIG.  2    depicts a conventional configuration of a dual-actuator  200  with an unequal number of heads on the end-arms  204   a - 1 ,  204   a - 2  of the upper actuator  202   a  and, likewise, on the end-arms  204   b - 1 ,  204   b - 2  of the lower actuator  202   b , without incorporating dynamics optimization features of the present embodiments.  FIG.  2    specifically illustrates a configuration having two actuators  202   a ,  202   b  in an HDD comprising nine recording disks (not shown here; see, e.g., recording medium  120  of  FIG.  1   ), where the upper and lower actuators  202   a ,  202   b  each comprises nine (9) heads. Each actuator  202   a ,  202   b  has (i) a single end-arm with a single HGA, i.e., end-arm  204   a - 1  and end-arm  204   b - 1 , (ii) a single end-arm with two HGAs, i.e., end-arm  204   a - 2  and end-arm  204   b - 2 , and (iii) one or more inner-arms with two HGAs, i.e., inner-arms  206   a  and inner-arms  206   b . As discussed, the uppermost end-arm  204   a - 1  adjacent to an HDD cover would have a single HGA facing the upper or top surface of a corresponding disk, whereas the lowermost end-arm  204   b - 1  adjacent to an HDD base would have a single HGA facing the lower or bottom surface of a corresponding disk. Furthermore, the end-arms  204   a - 2 ,  204   b - 2  that are adjacent to each other and belong to separate actuators comprise two HGAs each, where one of the HGAs on end-arm  204   a - 2  and one of the HGAs on end-arm  204   b - 2  are configured to service a center shared disk of the disk stack. Generally, each arm  204   a - 1 ,  204   a - 2 ,  206   a ,  204   b - 1 ,  204   b - 2 ,  206   b  of each actuator  202   a ,  202   b  could have either a single arm damper  208   a ,  208   b  (applied to one surface of the arm) or could have two arm dampers  208   a ,  208   b  (applied to both surfaces of the arm). In the instance depicted in  FIG.  2   , the top actuator  202   a  has dampers (not visible here) applied on the under-side of the inner-arms  206   a  and the bottom actuator  202   b  has dampers  208   b  applied on the upper surface of the inner-arms  206   b , whereas the end-arm  204   a - 2  has a damper  208   a  applied to the upper surface of the arm and the end-arm  204   b - 2  has a damper (not visible here) applied to the underside of the arm. Each of the end-arms  204   a - 1 ,  204   a - 2 ,  204   b - 1 ,  204   b - 2  and the inner arms  206   a ,  206   b  may have an arm core hole  205   a ,  205   b . Here, the core hole  205   a ,  205   b  geometries have the same configuration or shape on all of the arms. 
       FIG.  3 A  is a perspective view illustrating a dual-actuator configuration having dynamics optimization features, according to embodiments.  FIG.  3 A  depicts a generally similar dual-actuator configuration such as with  FIG.  2   , while incorporating elements of various embodiments described in more detail elsewhere herein. That is,  FIG.  3 A  depicts an improved configuration of a dual-actuator  300  with an unequal number of heads on the end-arm  304   a - 1  (e.g., one head) and on the end- and inner-arms  304   a - 2 ,  306   a  (e.g., two heads per arm) of the upper actuator  302   a . Likewise, there is an unequal number of heads on the end-arm  304   b - 1  (e.g., one head) and on the end- and inner-arms  304   b - 2 ,  306   b  (e.g., two heads per arm) of the lower actuator  302   b . This is done, for example, in a configuration having two actuators  302   a ,  302   b  in an HDD comprising nine recording disks (not shown here; see, e.g., recording medium  120  of  FIG.  1   ), where the upper and lower actuators  302   a ,  302   b  each comprises nine (9) heads. Each actuator  302   a ,  302   b  has a single end-arm with a single HGA, i.e., end-arm  304   a - 1  and end-arm  304   b - 1 , whereas all other arms of that actuator carry two HGAs, i.e., end arms  304   a - 2 ,  304   b - 2  and inner-arms  306   a ,  306   b . As discussed, the uppermost end-arm  304   a - 1  adjacent to an HDD cover would have a single HGA facing the upper or top surface of a corresponding disk, whereas the lowermost end-arm  304   b - 1  adjacent to an HDD base would have a single HGA facing the lower or bottom surface of a corresponding disk. The end-arms  304   a - 2 ,  304   b - 2  that are adjacent to each other and that belong to separate actuators comprise two HGAs each, where one of the HGAs on end-arm  304   a - 2  and one of the HGAs on end-arm  304   b - 2  are configured to service a center shared disk of the disk stack. According to embodiments, each arm  304   a - 1 ,  304   a - 2 ,  306   a ,  304   b - 1 ,  304   b - 2 ,  306   b  of each actuator  302   a ,  302   b  may have differing arm damper  308   a ,  308   b  configurations, as discussed in more detail elsewhere herein (see, e.g.,  FIGS.  3 B- 3 C ). Similarly, each of the end-arms  304   a - 1 ,  304   a - 2  carrying a single HGA and the other end-arms  304   b - 1 ,  304   b - 2  and the inner arms  306   a ,  306   b  carrying two HGAs may have differing arm core holes  305   a ,  305   b  configurations, according to embodiments, as discussed in more detail elsewhere herein. Here, the end-arms  304   a - 1 ,  304   b - 1  carrying a single HGA (one each for the top and bottom actuators  302   a ,  302   b ) have relevant distinguishing features. 
       FIG.  4 A  is a top view illustrating a single-HGA (head-gimbal assembly) end-arm of an HSA (head-stack assembly) of a dual-actuator configuration, and  FIG.  4 B  is a bottom view illustrating the dual-HGA end-arm of the HSA of  FIG.  4 A , both according to embodiments.  FIG.  4 A  depicts an embodiment of an end-arm  304   a - 1  ( FIG.  3 A- 3 C ), referred to here as end-arm  404   a - 1 . As such, end-arm  404   a - 1  is configured for implementation as an end-arm with a single HGA, in a dual-actuator configuration  300  ( FIG.  3 A ) in which there are an unequal number of heads on the end-arms  304   a - 1 ,  304   b - 1  ( FIG.  3 A ) and the other end- and inner-arms  304   a - 2 ,  306   a ,  304   b - 2 ,  306   b  ( FIG.  3 A ) of each actuator  302   a ,  302   b  ( FIG.  3 A ), such as in a configuration having two actuators  302   a ,  302   b  in an HDD comprising an odd number of recording disks and a central shared disk, where the upper and lower actuators  302   a ,  302   b  each comprises an odd number of heads. In one instance, the end-arm  404   a - 1  would be positioned adjacent to an HDD cover and would have a single HGA facing down onto the top surface of a corresponding top disk, and the end-arm  404   a - 2  of  FIG.  4 B  corresponding to the same actuator (e.g., actuator  302   a  of  FIG.  3 A ) would be positioned adjacent to the other actuator (e.g., actuator  302   b  of  FIG.  3 A ) of a dual-actuator configuration  300  and would have two HGAs, one facing the bottom surface of an inner disk and one facing the top surface of a central shared disk. In another instance, the end-arm  404   a - 1  would be positioned adjacent to an HDD base and would have a single HGA facing up onto the bottom surface of a corresponding bottom disk, and the end-arm  404   a - 2  corresponding to the same actuator (e.g., actuator  302   b ) would be positioned adjacent to the other actuator (e.g., actuator  302   a ) of a dual-actuator configuration  300  and would have two HGAs, one facing the top surface of an inner disk and one facing the bottom surface of the central shared disk. 
     According to an embodiment, end-arm  404   a - 1  comprises a side notch  410 , having a depth (d). According to a related embodiment, this side notch  410  is present only on each of the end-arms housing a single HGA (e.g., end-arms  304   a - 1 ,  304   b - 1 ), to manage the structural dynamics among the end-arms  304   a - 1 ,  304   b - 1  and all the other end- and inner-arms  304   a - 2 ,  304   b - 2 ,  306   a ,  306   b . Here, the notch  410  is positioned on the inner side of the end-arm  404   a - 1 , which would be on the side closest to a disk stack when implemented within an HDD. The notch  410  may be configured generally as depicted, i.e., with a first radius (R 1 ) and a second radius (R 2 ) to taper down from its maximum depth (d), for example, where R 1  and R 2  may be the same or may be different. According to an embodiment, the depth (d) of notch  410  is equal to or greater than 0.5 millimeters (mm) for example. However, this notch depth may vary from implementation to implementation, based on other design goals and constraints, and the like. Further, according to an embodiment, the notch  410  extends from a corresponding root  409  of the arm portion of the end-arm  404   a - 1  (or from +1 mm away from the root  409 ) to a corresponding swage pad  411  (or up to −1 mm from the swage pad  411 ). Likewise, the lead-in and lead-out radii (R 1  and R 2 ) may also vary from implementation to implementation based on other design goals and constraints, and the like. 
     According to an embodiment, end-arm  404   a - 1  comprises an arm core hole  405   a  at or near the root  409  (e.g., at the root-side) of the end-arm  404   a - 1 , larger than the arm core hole  205   a  of the conventional dual-actuator  200  ( FIG.  2   ), and having a triangular or quadrilateral shape. The core hole  405   a  may be configured generally as depicted, shown here having a substantially quadrilateral shape (here, with rounded corners, for simplicity of manufacturing purposes for example) with the side (with length L 1 ) closest to the root  409  end larger than the side (with length L 2 ) farthest from the root  409  (i.e., L 1 &gt;L 2 ), for structural dynamics purposes for example. According to a related embodiment, this core hole  405   a  is present only on each of the end-arms housing a single HGA (e.g., end-arms  304   a - 1 ,  304   b - 1 ), not on the other end- or inner-arms  304   a - 2 ,  304   b - 2 ,  306   a ,  306   b , to manage the structural dynamics among all of the arms. 
     The embodiment employing the notch  410  and the embodiment employing the arm core hole  405   a  may each be implemented alone, or may preferably be implemented in combination, to manage and improve the structural dynamics of the dual-actuator system, such as to improve the arm torsion and sway mode dynamics and higher order system mode dynamics of each actuator  302   a ,  302   b . Each of these features contributes to reducing and matching gains across all the HGAs for these undesirable modes. The gain reduction is achieved at least in part by introducing a mismatch of sway stiffness between the end-arms  304   a - 1 ,  304   b - 1  having one HGA and the other end- and inner-arms  304   a - 2 ,  306   a ,  304   b - 2 ,  306   b  having two HGAs, which is enabled by the foregoing described features. Additionally, employing end-arms  304   a - 2 ,  304   b - 2  and inner-arms  306   a ,  306   b  which carry two HGAs, having no arm core holes, further improves actuator system dynamics. 
       FIG.  5 A  is a top view illustrating a single-HGA end-arm of an HSA of a dual-actuator configuration, and  FIG.  5 B  is a bottom view illustrating the dual-HGA end-arm of the HSA of  FIG.  5 A , both according to embodiments.  FIG.  5 A  depicts an embodiment of the end-arm  304   a - 1  ( FIG.  3 A- 3 C ), which again is embodied in the end-arm  404   a - 1  of  FIG.  4 A . Here again, end-arm  404   a - 1  is configured for implementation as an end-arm with a single HGA, in a dual-actuator configuration  300  ( FIG.  3 A ) in which there are an unequal number of heads on the end-arms  304   a - 1 ,  304   b - 1  ( FIG.  3 A ) and the other end- and inner-arms  304   a - 2 ,  306   a ,  304   b - 2 ,  306   b  ( FIG.  3 A ) of each actuator  302   a ,  302   b  ( FIG.  3 A ), such as in a configuration having two actuators  302   a ,  302   b  in an HDD comprising an odd number of recording disks and a central shared disk, where the upper and lower actuators  302   a ,  302   b  each comprises an odd number of heads. Note that this end-arm  404   a - 1  is configured with the side notch  410  and the arm core hole  405   a , just as described in reference to the similarly-labeled end-arm  404   a - 1  of  FIG.  4 A , to which reference is made for the detailed description of those respective features. According to a related embodiment, this side notch  410  is present only on each of the end-arms (e.g., end-arms  304   a - 1 ,  304   b - 1 ) housing a single HGA, to manage the structural dynamics among all of the arms. 
     The difference between the embodiments of  FIGS.  5 A- 5 B  and the embodiments of  FIGS.  4 A- 4 B  resides in the dual-HGA end-arm  504   a - 2  of the HSA, shown in  FIG.  5 B . Here, rather than having no arm core hole, such as with end-arm  404   a - 2  ( FIG.  4 B ), end-arm  504   a - 2  comprises an arm core hole  505   b  between the root  509  of the end-arm  504   a - 2  (e.g., at the root-side of the end-arm  504   a - 2 ) and the corresponding swage pad  511 . According to an embodiment, arm core hole  505   b  of end-arm  504   a - 2  is smaller in area than the arm core hole  405   a  of end-arm  404   a - 1 , and is entirely contained within the footprint of the larger arm core hole  405   a . Furthermore, according to an embodiment, the smaller arm core hole  505   b  is implemented in all of the arms that carry two HGAs, such as end-arms  304   a - 2 ,  304   b - 2  and inner-arms  306   a ,  306   b  of  FIG.  3   . This embodiment of an actuator such as actuator  302   a  of dual-actuator  300  can also contribute to reducing and matching gains across all the HGAs for the undesirable structural dynamics modes such as the actuator torsion and sway modes and the system modes. 
     With reference now to  FIGS.  3 B- 3 C ,  FIG.  3 B  is a top view illustrating a portion of the single-HGA end-arm of the HSA of  FIG.  3 A , and  FIG.  3 C  is a bottom view illustrating the single-HGA end-arm of the HSA of  FIG.  3 A , according to an embodiment. For example,  FIG.  3 B  illustrates the top view and  FIG.  3 C  illustrates the bottom view of an end-arm housing a single HSA such as end-arms  304   a - 1 ,  304   b - 1  ( FIG.  3 A ),  404   a - 1  ( FIG.  4 A ). Here, end-arm  304   a - 1  further comprises arm damper  308   a  coupled with the top, outer (non-disk side) surface of the base arm structure. Damper  308   a  comprises a through-hole (or cut-out) that is coincident with the through hole  305   a  of the end-arm  304   a - 1 , such that the top of the through-hole  305   a  of the end-arm  304   a - 1  is not covered by the top damper  308   a  and thus the through-hole  305   a  is exposed, as depicted in  FIG.  3 B . According to an embodiment, the through-hole of the top damper  308   a  is shaped similarly to or preferably the same as the through-hole  305   a  of the end-arm  304   a - 1 , such that the through-hole of the top damper  308   a  substantially overlays the through-hole  305   a  of the end-arm  304   a - 1 . 
     According to a related embodiment, end-arm  304   a - 1  further comprises arm damper  308   b  coupled with the bottom, inner (disk side), or underside surface of the base arm structure. Unlike the top damper  308   a , the bottom damper  308   b  does not comprise a through-hole coincident with the through hole  305   a  of the end-arm  304   a - 1  so that, here, the bottom or underside of the through-hole  305   a  of the end-arm  304   a - 1  is covered by the bottom damper  308   b , as depicted in  FIG.  3 C . The dampers  308   a ,  308   b  coupled with the end-arm  304   a - 1  and/or  404   a - 1  contribute to reducing and matching gains across all the HGAs for the undesirable dynamics modes and, therefore, improve the actuator torsion and sway modes. According to an embodiment, the dampers  308   a ,  308   b  are composed of metal (e.g., stainless steel) with a viscoelastic adhesive (VEA). 
     Summarily, each of the foregoing embodiments characterizes an approach pertaining to reducing the gain differences in the arm modes (torsion, sway) and system modes (Butterfly-3, Butterfly-4) seen in the plant transfer functions between arms with two HGAs and an end-arm with a single HGA. This is achieved at least in part by introducing a structural stiffness mismatch between the arms with two HGAs and an end-arm with one HGA, such that the gains for the problematic modes of interest (e.g., arm sway, arm torsion, and higher order system modes) are better matched among all the HGAs, and at the same time are also beneficially reduced. Such approaches are equally applicable to scenarios in which the end-arm with two HGAs have different thicknesses for the arm root and the arm tip from the other inner arms. 
     In the context of a dual actuator HDD with an odd number of disks, these embodiments provide for improvements in the direct plant transfer function (i.e., the response of an actuator to its own actuation) and the coupled plant transfer functions (i.e., the response of the secondary actuator to actuation of the primary actuator). For example, embodiments can provide for a beneficial reduction of the gain of the end arm with a single HGA in the direct plant transfer function at critical frequencies associated with arm sway and higher order system modes. Furthermore, embodiments can provide for minimizing the differences in gain between the end-arm with one HGA and the end- and inner-arms with two HGAs at higher order system modes in the direct plant transfer function, achieved at least in part by way of an optimal mismatch of sway stiffness between end-arm with one HGA and other arms with two HGAs, which ensures that the responses of all the arms are balanced. This in turn enables a robust servo controller design. Embodiments can provide for a beneficial reduction in the gains of the arms with two HGAs in the direct plant transfer function at critical arm torsion frequencies. Still further, embodiments can provide for lower gains in the coupled plant transfer function at critical arm torsion and sway frequencies, and can provide for gain reduction in the acoustic transfer function (e.g., measured as off-track motion per unit sound pressure) at critical arm sway frequencies, leading to a lower cumulative acoustic gain (i.e. characterized by a lower cumulative Non-Repeatable Run-Out (NRRO)). 
     The described embodiments do not rely on the use of counter-weights of any form, which helps lower HDD cost by eliminating both part cost and process cost in internal assembly process, and improves performance by lowering inertia. 
     Additional Approaches to Managing the Structural Dynamics Among Actuator Arms with an Unequal Number of Heads on the Two Outer Arms of Each Actuator 
       FIG.  6 A  is a top view illustrating a single-HGA end-arm of an HSA of a dual-actuator configuration, and  FIG.  6 B  is a bottom view illustrating the dual-HGA end-arm of the HSA of  FIG.  6 A , both according to an embodiment.  FIG.  6 A  depicts an embodiment of the end-arm  304   a - 1  ( FIG.  3 A- 3 C ), which is embodied in the end-arm  604   a - 1  of  FIG.  6 A . Here, end-arm  604   a - 1  is configured for implementation as an end-arm with a single HGA, in a dual-actuator configuration  300  ( FIG.  3 A ) in which there are an unequal number of heads on the end-arms  304   a - 1 ,  304   b - 1  ( FIG.  3 A ) and the other end- and inner-arms  304   a - 2 ,  306   a ,  304   b - 2 ,  306   b  ( FIG.  3 A ) of each actuator  302   a ,  302   b  ( FIG.  3 A ), such as in a configuration having two actuators  302   a ,  302   b  in an HDD comprising an odd number of recording disks and a central shared disk, where the upper and lower actuators  302   a ,  302   b  each comprises an odd number of heads. Note that this end-arm  604   a - 1  is configured with a side notch  610  configured, shaped, positioned the same as or similar to the side notch  410  ( FIGS.  4 A,  5 A ), but with no arm core hole such as the core hole  405   a  of  FIGS.  4 A,  5 A . According to an embodiment, the depth of the side notch  610  of end-arm  604   a - 1  is greater than or equal to the depth of the side notch  410  ( FIGS.  4 A,  5 A ) of the end-arm  404   a - 1 . Furthermore and according to an embodiment, the end-arm  604   a - 2  is similar to the end-arm  404   a - 2  ( FIG.  4 B ) in that it would be positioned adjacent to the other actuator of a dual-actuator configuration  300  and would have two HGAs, and there is no arm core hole on end-arm  604   a - 2  such as there is with arm core hole  505   b  of  FIG.  5 B . Furthermore, in this embodiment this no core hole configuration applies to all of the arms that carry two HGAs, such as end-arms  304   a - 2 ,  304   b - 2  and inner-arms  306   a ,  306   b  of  FIG.  3   . 
       FIG.  7 A  is a top view illustrating a single-HGA end-arm of an HSA of a dual-actuator configuration, and  FIG.  7 B  is a bottom view illustrating the dual-HGA end-arm of the HSA of  FIG.  7 A , both according to an embodiment.  FIG.  7 A  depicts an embodiment of the end-arm  304   a - 1  ( FIG.  3 A- 3 C ), which is embodied in the end-arm  704   a - 1  of  FIG.  7 A . Here, end-arm  704   a - 1  is configured for implementation as an end-arm with a single HGA, in a dual-actuator configuration  300  ( FIG.  3 A ) in which there are an unequal number of heads on the end-arms  304   a - 1 ,  304   b - 1  ( FIG.  3 A ) and the other end- and inner-arms  304   a - 2 ,  306   a ,  304   b - 2 ,  306   b  ( FIG.  3 A ) of each actuator  302   a ,  302   b  ( FIG.  3 A ), such as in a configuration having two actuators  302   a ,  302   b  in an HDD comprising an odd number of recording disks and a central shared disk, where the upper and lower actuators  302   a ,  302   b  each comprises an odd number of heads. Note that this end-arm  704   a - 1  is configured with a side notch  710  configured, shaped, positioned the same as or similar to the side notch  410  ( FIGS.  4 A,  5 A ), but with no arm core hole such as the core hole  405   a  of  FIGS.  4 A,  5 A . According to an embodiment, the depth of the side notch  710  of end-arm  704   a - 1  is greater than or equal to the depth of the side notch  410  ( FIGS.  4 A,  5 A ) of the end-arm  404   a - 1 . Furthermore and according to an embodiment, the end-arm  704   a - 2  is similar to the end-arm  504   a - 2  ( FIG.  5 B ) in that it would be positioned adjacent to the other actuator of a dual-actuator configuration  300  and would have two HGAs, and comprises an arm core hole  705   b  configured, shaped, positioned the same as or similar to the arm core hole  505   b  of  FIG.  5 B . Furthermore, in this embodiment this core hole configuration applies to all of the arms that carry two HGAs, such as end-arms  304   a - 2 ,  304   b - 2  and inner-arms  306   a ,  306   b  of  FIG.  3   . 
       FIG.  8 A  is a top view illustrating a single-HGA end-arm of an HSA of a dual-actuator configuration, and  FIG.  8 B  is a bottom view illustrating the dual-HGA end-arm of the HSA of  FIG.  8 A , both according to an embodiment. Here, the end-arm  804   a - 2  is similar to the end-arms  504   a - 2  ( FIG.  5 B ),  704   a - 2  ( FIG.  7 B ) in that it would be positioned adjacent to the other actuator of a dual-actuator configuration  300  and would have two HGAs, and comprises an arm core hole  805   b  configured, shaped, positioned the same as or similar to the arm core holes  505   b ,  705   b  ( FIGS.  5 B,  7 B ). Furthermore, in this embodiment this core hole configuration applies to all of the arms that carry two HGAs (such as end arms  304   a - 2 ,  304   b - 2  and inner-arms  306   a ,  306   b  of  FIG.  3   ), as well as the arms that carry a single HGA (such as end-arms  304   a - 1 ,  304   b - 1  of  FIG.  3   ). As such,  FIG.  8 A  depicts an embodiment of the end-arm  304   a - 1  ( FIG.  3 A- 3 C ), which is embodied in the end-arm  804   a - 1  of  FIG.  8 A . Here, end-arm  804   a - 1  is configured for implementation as an end-arm with a single HGA, in a dual-actuator configuration  300  ( FIG.  3 A ) in which there are an unequal number of heads on the end-arms  304   a - 1 ,  304   b - 1  ( FIG.  3 A ) and the other end- and inner-arms  304   a - 2 ,  306   a ,  304   b - 2 ,  306   b  ( FIG.  3 A ) of each actuator  302   a ,  302   b  ( FIG.  3 A ), such as in a configuration having two actuators  302   a ,  302   b  in an HDD comprising an odd number of recording disks and a central shared disk, where the upper and lower actuators  302   a ,  302   b  each comprises an odd number of heads. Note that this end-arm  804   a - 1  is configured with a side notch  810  configured, shaped, positioned the same as or similar to the side notch  410  ( FIGS.  4 A,  5 A ), and with an arm core hole  805   a . However, this core hole  805   a  differs in shape from and is smaller in area than the core hole  405   a  of  FIGS.  4 A,  5 A . Note that this core hole  805   a  has the same geometry (e.g., same shape form and area) as the core hole  805   b , i.e., all the arms have the same arm core hole geometry. According to an embodiment, the depth of the side notch  810  of end-arm  804   a - 1  is greater than or equal to the depth of the side notch  410  ( FIGS.  4 A,  5 A ) of the end-arm  404   a - 1 . 
     The foregoing embodiments illustrated and described in reference to  FIGS.  6 A- 8 B  can provide incremental benefits in relation to reducing and matching gains across all the HGAs for the undesirable structural dynamics modes and, therefore, provide some incremental improvements to various actuator torsion, sway, and system modes. Furthermore, in the context of all the embodiments illustrated and described in reference to  FIGS.  3 A- 8 B , the actuator z-datum may be defined to be on the surface surrounding the comb bore and closest to the end arm with a single HGA, which enables the machining of the larger arm core hole (if applicable) and the notch with a tighter tolerance on that end-arm, resulting in a robust design from a producibility standpoint. 
     While embodiments, techniques and approaches are described herein throughout in the context of a dual-actuator system, it is contemplated and one can appreciate that these embodiments, techniques and approaches may be similarly applied to and implemented in multi-actuator systems, generally. That is, the number of actuators or actuator assemblies in a multi-actuator system in which the described embodiments, techniques and approaches may be implemented is not limited to two. 
     Physical Description of an Illustrative Operating Context 
     Embodiments may be used in the context of a digital data storage device (DSD) such as a hard disk drive (HDD). Thus, in accordance with an embodiment, a plan view illustrating a conventional HDD  100  is shown in  FIG.  1    to aid in describing how a conventional HDD typically operates. 
       FIG.  1    illustrates the functional arrangement of components of the HDD  100  including a slider  110   b  that includes a magnetic read-write head  110   a . Collectively, slider  110   b  and head  110   a  may be referred to as a head slider. The HDD  100  includes at least one head gimbal assembly (HGA)  110  including the head slider, a lead suspension  110   c  attached to the head slider typically via a flexure, and a load beam  110   d  attached to the lead suspension  110   c . The HDD  100  also includes at least one recording medium  120  rotatably mounted on a spindle  124  and a drive motor (not visible) attached to the spindle  124  for rotating the medium  120 . The read-write head  110   a , which may also be referred to as a transducer, includes a write element and a read element for respectively writing and reading information stored on the medium  120  of the HDD  100 . The medium  120  or a plurality of disk media may be affixed to the spindle  124  with a disk clamp  128 . 
     The HDD  100  further includes an arm  132  attached to the HGA  110 , a carriage  134 , a voice-coil motor (VCM) that includes an armature  136  including a voice coil  140  attached to the carriage  134  and a stator  144  including a voice-coil magnet (not visible). The armature  136  of the VCM is attached to the carriage  134  and is configured to move the arm  132  and the HGA  110  to access portions of the medium  120 , all collectively mounted on a pivot shaft  148  with an interposed pivot bearing assembly  152 . In the case of an HDD having multiple disks, the carriage  134  may be referred to as an “E-block,” or comb, because the carriage is arranged to carry a ganged array of arms that gives it the appearance of a comb. 
     An assembly comprising a head gimbal assembly (e.g., HGA  110 ) including a flexure to which the head slider is coupled, an actuator arm (e.g., arm  132 ) and/or load beam to which the flexure is coupled, and an actuator (e.g., the VCM) to which the actuator arm is coupled, may be collectively referred to as a head-stack assembly (HSA). An HSA may, however, include more or fewer components than those described. For example, an HSA may refer to an assembly that further includes electrical interconnection components. Generally, an HSA is the assembly configured to move the head slider to access portions of the medium  120  for read and write operations. 
     With further reference to  FIG.  1   , electrical signals (e.g., current to the voice coil  140  of the VCM) comprising a write signal to and a read signal from the head  110   a , are transmitted by a flexible cable assembly (FCA)  156  (or “flex cable”, or “flexible printed circuit” (FPC)). Interconnection between the flex cable  156  and the head  110   a  may include an arm-electronics (AE) module  160 , which may have an on-board pre-amplifier for the read signal, as well as other read-channel and write-channel electronic components. The AE module  160  may be attached to the carriage  134  as shown. The flex cable  156  may be coupled to an electrical-connector block  164 , which provides electrical communication, in some configurations, through an electrical feed-through provided by an HDD housing  168 . The HDD housing  168  (or “enclosure base” or “baseplate” or simply “base”), in conjunction with an HDD cover, provides a semi-sealed (or hermetically sealed, in some configurations) protective enclosure for the information storage components of the HDD  100 . 
     Other electronic components, including a disk controller and servo electronics including a digital-signal processor (DSP), provide electrical signals to the drive motor, the voice coil  140  of the VCM and the head  110   a  of the HGA  110 . The electrical signal provided to the drive motor enables the drive motor to spin providing a torque to the spindle  124  which is in turn transmitted to the medium  120  that is affixed to the spindle  124 . As a result, the medium  120  spins in a direction  172 . The spinning medium  120  creates a cushion of air that acts as an air-bearing on which the air-bearing surface (ABS) of the slider  110   b  rides so that the slider  110   b  flies above the surface of the medium  120  without making contact with a thin magnetic-recording layer in which information is recorded. Similarly in an HDD in which a lighter-than-air gas is utilized, such as helium for a non-limiting example, the spinning medium  120  creates a cushion of gas that acts as a gas or fluid bearing on which the slider  110   b  rides. 
     The electrical signal provided to the voice coil  140  of the VCM enables the head  110   a  of the HGA  110  to access a track  176  on which information is recorded. Thus, the armature  136  of the VCM swings through an arc  180 , which enables the head  110   a  of the HGA  110  to access various tracks on the medium  120 . Information is stored on the medium  120  in a plurality of radially nested tracks arranged in sectors on the medium  120 , such as sector  184 . Correspondingly, each track is composed of a plurality of sectored track portions (or “track sector”) such as sectored track portion  188 . Each sectored track portion  188  may include recorded information, and a header containing error correction code information and a servo-burst-signal pattern, such as an ABCD-servo-burst-signal pattern, which is information that identifies the track  176 . In accessing the track  176 , the read element of the head  110   a  of the HGA  110  reads the servo-burst-signal pattern, which provides a position-error-signal (PES) to the servo electronics, which controls the electrical signal provided to the voice coil  140  of the VCM, thereby enabling the head  110   a  to follow the track  176 . Upon finding the track  176  and identifying a particular sectored track portion  188 , the head  110   a  either reads information from the track  176  or writes information to the track  176  depending on instructions received by the disk controller from an external agent, for example, a microprocessor of a computer system. 
     An HDD&#39;s electronic architecture comprises numerous electronic components for performing their respective functions for operation of an HDD, such as a hard disk controller (“HDC”), an interface controller, an arm electronics module, a data channel, a motor driver, a servo processor, buffer memory, etc. Two or more of such components may be combined on a single integrated circuit board referred to as a “system on a chip” (“SOC”). Several, if not all, of such electronic components are typically arranged on a printed circuit board that is coupled to the bottom side of an HDD, such as to HDD housing  168 . 
     References herein to a hard disk drive, such as HDD  100  illustrated and described in reference to  FIG.  1   , may encompass an information storage device that is at times referred to as a “hybrid drive”. A hybrid drive refers generally to a storage device having functionality of both a traditional HDD (see, e.g., HDD  100 ) combined with solid-state storage device (SSD) using non-volatile memory, such as flash or other solid-state (e.g., integrated circuits) memory, which is electrically erasable and programmable. As operation, management and control of the different types of storage media typically differ, the solid-state portion of a hybrid drive may include its own corresponding controller functionality, which may be integrated into a single controller along with the HDD functionality. A hybrid drive may be architected and configured to operate and to utilize the solid-state portion in a number of ways, such as, for non-limiting examples, by using the solid-state memory as cache memory, for storing frequently-accessed data, for storing I/O intensive data, and the like. Further, a hybrid drive may be architected and configured essentially as two storage devices in a single enclosure, i.e., a traditional HDD and an SSD, with either one or multiple interfaces for host connection. 
     Extensions and Alternatives 
     In the foregoing description, embodiments of the invention have been described with reference to numerous specific details that may vary from implementation to implementation. Therefore, various modifications and changes may be made thereto without departing from the broader spirit and scope of the embodiments. Thus, the sole and exclusive indicator of what is the invention, and is intended by the applicants to be the invention, is the set of claims that issue from this application, in the specific form in which such claims issue, including any subsequent correction. Any definitions expressly set forth herein for terms contained in such claims shall govern the meaning of such terms as used in the claims. Hence, no limitation, element, property, feature, advantage or attribute that is not expressly recited in a claim should limit the scope of such claim in any way. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. 
     In addition, in this description certain process steps may be set forth in a particular order, and alphabetic and alphanumeric labels may be used to identify certain steps. Unless specifically stated in the description, embodiments are not necessarily limited to any particular order of carrying out such steps. In particular, the labels are used merely for convenient identification of steps, and are not intended to specify or require a particular order of carrying out such steps.