Measuring stiction and friction between the heads and discs of a hard disc drive

Apparatus and method for measuring the maximum static friction force and the kinetic friction force between the heads of a disc drive and discs adjacent the heads. The disc drive is rotated by a computer controlled spin-up motor which provides constant angular acceleration of the disc drive. Voltages at the ends of the windings of a spindle motor of the disc drive are sampled to detect the angular acceleration at which disc rotation relative to the heads begins, from which the static friction force and the kinetic friction force are determined. The angular acceleration of the disc drive is monitored through the sampling of velocity commands used to control the angular acceleration of the disc drive, or through the use of an accelerometer mounted with respect to the disc drive.

FIELD OF THE INVENTION 
The present invention relates generally to hard disc drives and more 
particularly, but not by way of limitation, to improvements in the 
measurement of static and kinetic frictional forces between the heads and 
discs of a disc drive. 
BACKGROUND 
Modern hard disc drives comprise one or more rigid discs that are coated 
with a magnetizable medium and mounted on the hub of a spindle motor for 
rotation at a constant high speed. Information is stored on the discs in a 
plurality of concentric circular tracks by an array of transducers 
("heads") mounted to a radial actuator for movement of the heads relative 
to the discs. 
Typically, such radial actuators employ a voice coil motor to position the 
heads with respect to the disc surfaces. The heads are mounted via 
flexures at the ends of a plurality of arms which project radially outward 
from an actuator body. The actuator body pivots about a shaft mounted to 
the disc drive housing at a position closely adjacent the outer extreme of 
the discs. The pivot shaft is parallel with the axis of rotation of the 
spindle motor and the discs, so that the heads move in a plane parallel 
with the surfaces of the discs. 
The actuator voice coil motor includes a coil mounted on the side of the 
actuator body opposite the head arms so as to be immersed in the magnetic 
field of a magnetic circuit comprising one or more permanent magnets and 
magnetically permeable pole pieces. When current is passed through the 
coil, an electromagnetic field is set up which interacts with the magnetic 
field of the magnetic circuit to cause the coil to move in accordance with 
the well-known Lorentz relationship. As the coil moves, the actuator body 
pivots about the pivot shaft and the heads move across the disc surfaces. 
The heads are typically provided with aerodynamically shaped slider 
assemblies which cause the heads to fly over the surfaces of the discs as 
a result of air currents established by the rotation of the discs. To 
limit wear and damage to the heads and the discs, contact between the 
heads and discs is generally minimized except at such time that the discs 
are not rotated at a speed sufficient to support the heads, during which 
time the heads are generally moved to and secured over landing zones of 
the discs, which are typically located near the innermost radii of the 
discs. 
As part of quality control and ongoing research and development efforts, 
manufacturers of disc drives continually engage in test programs in which, 
among other things, the wear of the heads and of the discs in the landing 
zones is monitored as a function of the number of start ups of a disc 
drive. One manner of monitoring this wear is to measure the maximum static 
friction force, generally referred to as "stiction", that is exerted on 
the discs by the heads just prior to the onset of slippage of the discs 
along the heads and to measure the kinetic friction force, generally 
referred to as, simply, "friction", that exists after slippage occurs. 
These forces generally increase as the heads and disc surfaces are eroded 
so that the magnitudes of these forces provide an indication of the extent 
to which wear has occurred. 
A problem with using stiction and friction as indicators of disc and head 
wear is that these effects have been difficult to measure accurately 
without the removal of a disc drive top cover, which is bolted to a 
corresponding disc drive base deck, or case. As will be recognized, the 
case and the top cover cooperate to provide an internally sealed 
environment for the disc drive necessary to minimize the introduction of 
contaminants which can adversely affect the performance of the drive. 
While removal of the top cover has generally permitted accurate stiction 
and friction measurements, such methodology has also had a number of 
associated drawbacks. First, removal of the top cover requires a clean 
environment if the drive is to be reassembled and reoperated. Further, the 
disassembly and reassembly steps required to facilitate direct stiction 
and friction measurements with the top cover removed will invariably lead 
to damage of at least some of the drives subjected to such methodology. 
More significantly, however, disassembly and reassembly of a disc drive 
will typically lead to changes in the mechanical interrelationship between 
the heads and the discs sufficient to introduce inconsistency in 
subsequent measurements. This lack of consistency in stiction and friction 
measurements therefore inherently limits the uses that can be made of the 
measurements. 
While problems that are occasioned by disassembly can be overcome by using 
the spindle motor upon which the discs are mounted to rotate the discs and 
measuring motor current and back emf (electromotive force) to determine 
stiction and friction, such measurements tend to have relatively large 
experimental errors. For example, such an approach will generally yield 
stiction measurements having tolerances of the order of +20%; friction 
measurements are even less precise. 
Consequently, while stiction and friction measurements have provided disc 
drive manufacturers with a useful diagnostic tool, the value of this tool 
has been limited by practical difficulties that are inherent in making the 
measurements. Accordingly, there is a need for an improved approach to 
measuring stiction and friction in a disc drive that overcomes such 
limitations in the prior art. 
SUMMARY OF THE INVENTION 
The present invention provides an apparatus and method for accurately 
measuring stiction and friction between the heads and discs of a disc 
drive without the need for disassembly of the disc drive. 
Generally, in accordance with the preferred embodiments of the present 
invention, the case of the disc drive is angularly accelerated about an 
axis that is parallel to the axis of the disc stack so that frictional 
forces between the heads and discs will cause an angular acceleration of 
the disc stack about its axis. During a measurement, the angular 
acceleration of the case is steadily increased while the voltages at the 
ends of the windings of the spindle motor upon which the discs are mounted 
are monitored to first detect and, subsequently, to measure emfs 
(voltages) that might be induced in the windings by relative motion of the 
rotor of the spindle motor with respect to the disc drive case. 
At the point at which a voltage is first detected in the spindle motor 
windings (indicative of the onset of relative motion between the heads and 
discs), the frictional forces the heads are exerting on the discs will be 
at a maximum value. Accordingly, the stiction is determined by first 
multiplying the angular acceleration of the case when the voltage is 
detected by the moment of inertia of the disc stack about its symmetry 
axis. The resulting value is the torque exerted on the disc stack by the 
stiction. Next, the torque value is divided by the radius of the landing 
zone to determine a total stiction value. The total stiction value can 
then be divided by the number of heads to determine the stiction per head, 
which is the common quantity of interest. 
Moreover, during subsequent acceleration of the case (during which 
continued slippage between the disc stack and the heads will occur), the 
voltages induced in the windings of the spindle motor are sampled and the 
samples are used to generate a table of disc stack orientations for a 
sequence of sample times. This table is then used to generate, 
successively, tables of the angular velocity and angular acceleration of 
the disc stack relative to the disc drive case. 
Concurrently, the acceleration of the case is determined at the sample 
times so that the angular acceleration of the disc stack can be determined 
by subtracting the relative angular acceleration between the disc stack 
and case from the angular acceleration of the case. The total friction can 
then be determined by multiplying the angular acceleration of the disc 
stack by the moment of inertia of the stack about its symmetry axis and 
dividing by the radius of the landing zone. As in the case of stiction, 
the friction per head can then be determined by dividing by the number of 
heads in the disc drive. 
The apparatus used in the preferred embodiment of the present invention to 
carry out these measurements generally comprises a disc drive mount that 
is secured to one end of the shaft of a spin-up motor to permit rotation 
of the case of a disc drive by mounting it in the disc drive mount and 
operating the spin-up motor. The disc drive mount is constructed to 
position the axis of the disc stack in a parallel relation to the axis of 
the spin-up motor shaft and connections to the ends of the disc drive 
spindle motor windings are made via a slip ring assembly that is mounted 
on the opposite end of the spin-up motor shaft. 
Rotation of the spin-up motor is effected by a motor driver that is of the 
type that adjusts the current passed through the windings of the spin-up 
motor in relation to the difference between the angular velocity of the 
motor shaft, which the motor driver determines from current and back emf 
measurements, and a command velocity received by the motor driver. 
A sequence of velocity commands, selected to cause a steady increase in 
spin-up motor acceleration, are sequentially transmitted to the motor 
driver from a computer system comprising a personal computer having an 
input/output card in an expansion slot and the computer system 
repetitively samples voltages at the ends of the disc drive spindle motor 
windings via the slip ring assembly to permit construction of a table of 
disc drive spindle motor emfs against sample index. From this table, the 
computer constructs a table of relative angular velocity of the disc stack 
relative to the disc drive case. 
Concurrently with the sampling of voltages at the ends of the disc drive 
spindle motor windings, signals in the motor driver that express the 
angular velocity of the spin up motor shaft are sampled in one embodiment 
of the invention and the computer is programmed to construct a table of 
disc drive case angular accelerations from these samples. The computer is 
further programmed to determine the sample count at which a voltage is 
first induced in the windings of the disc drive spindle motor and, from 
the angular acceleration of the case for this sample count, determine the 
stiction in the manner described above. 
In a further preferred embodiment of the present invention, the apparatus 
further comprises an accelerometer mounted on the disc drive mount to 
provide a direct measure of the angular acceleration of the disc drive 
case and this measure of angular acceleration of the case is sampled by 
the computer system via the slip ring assembly for generation of the table 
of case angular acceleration for use in determining stiction as described 
above. 
These and various other features as well as advantages which characterize 
the present invention will be apparent from a reading of the following 
detailed description and a review of the associated drawings.

DETAILED DESCRIPTION OF THE FIRST PREFERRED EMBODIMENT 
Referring now to the drawings, and particularly to FIG. 1, shown therein is 
a prior art hard disc drive 100 for which stiction and friction 
measurements can be advantageously measured in accordance with the 
preferred embodiments of the present invention. 
The disc drive 100 generally comprises a disc stack 102 which, in turn, 
comprises a plurality of discs 104, 106 and 108 upon which computer files 
are magnetically stored. To this end, the discs are mounted on the rotor 
110 of a spindle motor 112 for rotation in the case 114 of the disc drive 
about an axis that extends through the centers of the discs so that the 
files can be stored as patterns of magnetization of a surface medium along 
circular tracks that are defined on the discs. The magnetization of the 
discs is effected by read/write heads, such as the head 116 in FIG. 1, 
that are mounted on the ends of flexures 118 of an actuator 120 and the 
flexures extend into the disc stack to support the heads adjacent the disc 
surfaces and position them in radial alignment with a track to be written 
or, subsequently, to be read. 
The flexures are constructed to bias the heads against the disc surfaces so 
that, when the discs are not rotating, the heads will be in contact with 
the disc surfaces; the heads are aerodynamically shaped so as to be 
supported over the disc surfaces by air currents generated by the rotation 
of the discs. As a result, the heads generally contact the disc surfaces 
only when the disc drive is not operating. 
To minimize wear of the disc surfaces and the heads caused by frictional 
forces between the heads and surfaces when the heads move in contact with 
the discs, during non-operation the heads are typically located at landing 
zones, such as indicated at 122. More particularly, the heads 116 are 
moved by the actuator 120 to a position that will cause the heads to be 
radially aligned with the landing zones 122 during start up of the disc 
drive and at the end of operation. A latch assembly 124 is provided to 
secure the actuator in this position. 
Referring now to FIGS. 2 and 3, shown therein is an apparatus 150 
constructed in accordance with the first preferred embodiment of the 
present invention for measuring the maximum static friction force, or 
"stiction", and the kinetic friction force, or "friction", between the 
discs and heads of a disc drive, such as the disc drive 100 of FIG. 1. As 
will be recognized, FIGS. 2 and 3 are complementary drawings, so that FIG. 
2 generally illustrates the mechanical configuration of the apparatus 150 
and FIG. 3 provides a functional block diagram for the electrical 
configuration of the apparatus 150. Accordingly, the apparatus has 
generally been designated with the same reference numeral 150 in both 
drawings and common reference numerals will be used for components of the 
apparatus 150 that are common to both figures without regard to the form 
in which a component is illustrated in these drawings. 
As shown in FIG. 2, the apparatus 150 generally comprises a disc drive spin 
assembly 152 which spins the disc drive 100 (not shown in FIG. 2) at an 
increasing rate during the measurement of stiction and friction and a 
computer 154, which controls the operation of the spin assembly 152 and 
determines the stiction and friction from signals generated by the spin 
assembly 152 during spin up of the disc drive. Referring specifically to 
FIG. 2, the disc drive spin assembly 152 preferably comprises a cabinet 
156 constructed of plate aluminum and includes a support plate 158 which 
forms the top of the cabinet 156, side walls 160 and 162, a floor 164 and 
front and rear walls, 166 and 168 respectively. Thus, the interior of the 
cabinet 156 is entirely enclosed and shielded by the electrically 
conductive aluminum plate. As will be noted below, such construction 
permits the suppression of electrical noise during stiction and friction 
measurements. 
A spin-up motor 170 is mounted on the support plate 158 and a hole 172 is 
formed through the support plate for passage of the shaft 174 of the motor 
170. The spin-up motor 170 is a conventional direct current (dc) motor so 
that the construction thereof need not be further considered for purposes 
of the present disclosure other than to note that the shaft 174 is 
constructed in the form of a tube (see FIGS. 5 and 7) that extends from 
both the upper and lower ends of the case (not numerically designated in 
the drawings) of the spin-up motor 170 for purposes to be discussed below. 
During operation of the apparatus 150, electrical currents are passed 
through the spin-up motor 170 by a motor driver 175 (FIG. 3) that is 
constructed in a conventional manner to sense the rotational velocity of 
the motor 170 and to adjust the current passed through the windings of the 
motor 170. The current will be proportional to the difference between 
motor rotational velocity and a velocity command that is received by the 
motor driver 175. In the preferred embodiment, the velocity command is 
received from the computer 154 as will be discussed below. 
Continuing with FIG. 2 and with reference to FIGS. 4 through 7, the disc 
drive spin assembly 152 further comprises a disc drive mount 176 that, 
during measurement of stiction and friction of a disc drive, is secured to 
the upper end of the spin-up motor shaft 174. More particularly, as shown 
in FIG. 7, the disc drive mount 176 comprises a coupler 178 which has a 
body portion 180 through which a bore 182 is axially formed on a diameter 
to fit the spin-up motor shaft 174. The disc drive mount 176 is secured to 
the shaft 174 via a set screw 184 in a threaded hole 186 formed 
transversely through the wall of the body portion 180. The purpose 
underlying this manner of securing the disc drive mount 176 to the shaft 
174 will become apparent below. 
At its upper end, the coupler 178 is provided with a flange 188 through 
which, as also shown in FIG. 7, four slots 190, 192, 194 and 196 are 
formed to extend in a direction parallel to a longitudinal axis 198 of the 
coupler 178 which defines a longitudinal axis for the disc drive mount 
176. Screws 200, 202, 204 and 206 are passed through the slots 190, 192, 
194 and 196 respectively into threaded holes 208, 210, 212 and 214 
respectively of a base plate 216. As will be clear from such connection of 
the coupler 178 to the base plate 216, major portions of the disc drive 
mount 176 can be positioned longitudinally on the coupling 178. The 
purpose and significance of this positioning capability will be discussed 
below. 
As more particularly shown in FIGS. 4 and 6, the disc drive mount 176 
further comprises end plates 218 and 220 that are bolted to opposite ends 
of the base plate 216 to extend upwardly therefrom in a parallel relation 
and a U-shaped disc drive mounting plate 222 that is bolted to the tops of 
the end plates 218 and 220. As shown in FIG. 5, slots 224, 226, 228 and 
230 extend parallel to an axis 232 that is transverse to the longitudinal 
axis 198 and are formed through the disc drive mounting plate 222 for 
attachment of the disc drive mounting plate 222 to the upper ends of the 
end plates 218 and 220. In particular, the disc drive mounting plate 222 
is attached to the end plates 218 and 220 via screws 234, 236, 238 and 240 
that pass through the slots 224, 226, 228 and 230 respectively and into 
threaded holes, 242, 244 and 246, for the screws 234, 236 and 238 
respectively, formed in the upper ends of the end plates 218 and 220 and a 
threaded hole (not shown) formed in the upper end of the end plate 220 for 
the screw 240. The slots 224, 226, 228 and 230 provide the disc drive 
mounting plate 222 with a transverse positioning capability that 
complements the longitudinal positioning capability provided by the slots 
190, 192, 194 and 196 of the coupler flange 188. Thus, the disc drive 
mounting plate can be positioned in any direction atop the spin-up motor 
shaft 174 for a purpose that will be discussed below. 
During the measurement of the stiction and friction between the heads and 
discs of the disc drive 100, the disc drive is mounted in the disc drive 
mount 176 to extend through the space between the end walls 218, 220 and 
between the base and mounting plates 216 and 222 respectively as shown in 
phantom line in FIGS. 4 through 7. Such mounting of the disc drive can be 
conveniently effected via threaded holes (not shown) formed in the bottom 
of the case of a disc drive for mounting of the disc drive in a computer 
housing. Thus, as shown in FIG. 5, holes 248, 250, 252 and 254 are formed 
through the disc drive mounting plate 220 so that the disc dive can be 
attached to the underside of the plate 220 by way of screws 256, 258, 260 
and 262. As also indicated in FIG. 5, such mounting of the disc drive 100 
will generally not result in the disc stack 102 being coaxial with the 
spin-up motor shaft 174. This point will be further discussed below. 
Referring again to FIG. 2, the disc drive spin assembly 152 further 
comprises a balance shaft 264 that is mounted on the sidewalls 160, 162 of 
the cabinet 156 by way of bearings 266 and 268 for free rotation of the 
shaft 264 about a horizontal axis. A stub axle 270 is formed on one end of 
the balance shaft 264 on a diameter that is substantially equal to the 
diameter of the spin-up motor shaft 174 to permit balancing of the disc 
drive mount 176 and a disc drive mounted thereon about the spin-up motor 
shaft 174 prior to measuring the stiction and friction between the heads 
and discs of the disc drive. In particular, such balancing is effected by 
using the set screw 184 in the coupler 178 to mount the disc drive mount 
176 on the stub axle 270 and adjusting the position of the disc drive 
mount 176 along the longitudinal and transverse axes, 198 and 232 
respectively, by way of the slots 190, 192, 194 and 196 formed through the 
flange 188 of the coupler 178 and the slots 224, 226, 228 and 230 formed 
through the disc drive mounting plate 222 that pass screws that attach the 
base plate 214 and disc drive mounting plate 222 to the coupler 178 and 
end walls 218 and 220 respectively. Fine balancing can then be effected 
using small weights that are attached to the upper surface of the disc 
drive mounting plate 222, as indicated at 272 in FIGS. 4 and 5. 
The balancing of the disc drive mount 176 and disc drive 100 prior to 
measurement of the stiction and friction between the heads and discs of 
the disc drive prevents excessive vibration of the disc drive spin 
assembly 152 that would not only give rise to electrical noise but could 
cause damage both to the assembly 152, the disc drive 100, or both. 
Further, such vibration could loosen screws that are used to connect parts 
thereof together to present a hazard when the spin-up motor 170 is 
operated during a measurement as discussed below. As a further safeguard 
against the possible dislodgment of parts during a stiction/friction 
measurement, the disc drive spin assembly 152 is preferably further 
comprised of an aluminum hood 274 that is hingedly connected to the 
cabinet 156 for rotation between open and closed positions in which the 
disc drive mount 176 is alternatively accessible and fully enclosed, as 
indicated in FIG. 2. 
As noted above, the disc stack 102 of a disc drive 100 will generally not 
be coaxial with the spin-up motor shaft 174 when the disc drive is mounted 
in the disc drive mount 176 and the disc drive mount is, in turn, mounted 
on the spin-up motor shaft 174. That is, as particularly shown in FIG. 6, 
an offset will typically exist between the axes 276 of the disc stack 102 
and the spin-up motor shaft 174 when the disc drive and disc drive mount 
have been balanced so that the center of mass of the combination is along 
the axis of the spin-up motor shaft 174. Further, as will become clear 
from the discussion of the measurement of stiction and friction to be 
presented below, this offset will, at least in theory, introduce an 
experimental error into the measurements. Consequently, it would at first 
glance appear desirable to eliminate the offsets by positioning the disc 
drive on the disc drive mount so as to coextensively align the disc stack 
102 with the spin-up motor shaft 174 and to use weights mounted on the 
disc drive mount to balance the combined disc drive and disc drive mount 
about the spin-up motor shaft. While such measures could be taken, they 
are not necessary. Particularly, the experimental error introduced into 
the measurements by an offset between the axes of the disc stack and the 
spin-up motor shaft depends upon an imbalance of the disc stack 102 on the 
disc drive case 114 and, as is known in the art, the disc stack of a disc 
drive is very carefully balanced at the time the disc drive is 
manufactured. Consequently, experimental error that might be introduced 
into the stiction and friction measurements by offsets between the axes of 
the disc stack 102 and spin-up motor shaft 174 has been found, as a 
practical matter, to be negligible. Thus, the apparatus 150 can be 
advantageously configured to accommodate a variety of disc drive model 
types. 
Referring now to FIG. 3, an input/output (I/O) card 280 is mounted in an 
expansion slot of the computer 154 to permit control of the spin-up motor 
170 by the computer 154 and to make measurements from which the stiction 
and friction between heads and discs of a computer are determined. While 
substantially any commercially available I/O card could generally be used 
for the card 280, a particularly suitable I/O card is the Model AT-M10-16F 
Multipurpose Analog Card, manufactured by National Instruments of Austin, 
Tex. Such card can take and store numerous samples of several analog 
signals, each with respect to its own reference signal and, additionally, 
can receive from a computer in which it is mounted a large number of 
commands which it can store for output, upon command, to an external 
device. In the present invention, these commands are velocity commands 
that are outputted to the motor driver 175 on a bus that has been 
indicated by the arrow 282 in FIG. 3. Signals that are sampled and stored 
by the I/O card 280 for transfer to the computer 154 memory include a 
motor speed signal, indicated by the arrow 284 in FIG. 3, that is 
generated for speed control by the motor driver 175. The motor speed 
signal is proportional to the angular velocity of the shaft 174 of the 
spin-up motor and the proportionality constant can be readily determined 
using a stroboscope to determine the rotational speed of the spin-up motor 
while measuring the motor speed signal at appropriate terminals in the 
motor driver. 
The signals sampled by the I/O card 280 also include the voltages at the 
ends of all but one of the windings of the disc drive spindle motor 112 
relative to the voltage at the end of the remaining winding. Thus, where 
the disc drive spindle motor is a three phase motor as illustrated in FIG. 
3, the I/O card 280 samples voltages at the ends of windings 286 and 288 
relative to the voltage at the end of winding 290 by way of a slip ring 
assembly 292 and conducting paths 294, 296 and 298. A suitable slip ring 
assembly 294 for use in the present invention is the model MX-6/ST slip 
ring assembly available from Meridian Laboratories of Middleton, Wis. Such 
slip ring assembly has a tubular, rotating shaft from which conductors 
leading from internal slip rings extend to the lower end of the spin-up 
motor shaft 174 via a tubular coupling 302 as shown in FIG. 2. More 
particularly, these conductors extend upwardly from the slip ring assembly 
292, through the spin-up motor shaft 174 and to a connector assembly 304 
(FIGS. 4-7) so that electrical connections are made to the ends of the 
windings of the spindle motor 112. 
As shown in FIGS. 4-6, the connector assembly 304 comprises a support 
member 306 that is attached to one leg of the "U" of the disc drive 
mounting plate 222 by screws 308, 310 and has an L-shaped arm 312 that 
extends over the opening between the legs of the mounting plate 222. As 
will be clear to those skilled in the art, the end of the arm 312 can be 
caused to overlay any portion of a disc drive 100 that is mounted in the 
disc drive mount 176 by appropriate dimensioning of the arm 312 and a 
suitable location is a location adjacent the electrical connector (not 
shown) by way of which the disc drive 100 is electrically connected to a 
computer. More particularly, the end of the arm 312 overlays a location 
adjacent portions of the disc drive connector by way of which electrical 
power is supplied to the spindle motor. The connector assembly 304 further 
comprises a plastic pin block 314 to which is attached a plastic pin cap 
316 in which are embedded pins 318 that pass through the block 314 and 
protrude from the pin cap 316. The upper end of the pin block 314 is 
secured to the distal end of the arm 312 by way of screws, one of which is 
shown at 320 in FIG. 4, and a rubber pad 322 is sandwiched between the arm 
312 and the block 314. 
The thickness of the pad 322 and the lengths of the pins 318 are selected 
so that the pins will be forced against pins of the electrical connector 
of a disc drive 100 that supply power to the spindle motor when the disc 
drive 100 is mounted in the disc drive mount 176. Thus, electrical contact 
between the slip rings of the slip ring assembly 292 and the windings of 
the spindle motor can be made by forcing a jack 324 on the ends of the 
wires leading from the slip rings onto the upper ends of the pins 318. 
Referring again to FIG. 3, the connections between the slip rings of the 
slip ring assembly 292 and the spindle motor windings includes a 
connection to the common point of the windings. This point is connected to 
the computer ground and the cabinet 156 to suppress electrical noise. 
Operation 
To more fully describe the manner in which the apparatus 150 measures the 
stiction and friction between the heads and discs of the disc drive 100, 
it will be useful to first present an overview of the measurement 
methodology before considering preferred programming of the computer by 
way of which the measurements are preferably implemented. FIGS. 8 and 9, 
which are portions of a top view of the disc drive 100 with the cover 
removed, have been presented for this purpose. 
Initially, as has been noted above, the disc drive 100 for which a 
stiction/ friction measurement is to be made is conveniently mounted in 
the disc drive mount 176 by way of threaded mounting holes formed in the 
underside of the case 114 of the disc drive 100 so that the disc drive 
will be inverted while the measurement is made. Not only does this 
facilitate the mounting of the disc drive in the mount 176 but, further, 
it makes the disc drive electrical connector (which is generally located 
on a printed circuit board attached to the underside of the disc drive 
case), readily accessible to the connector assembly 304 mounted on the 
mounting plate 222 of the disc drive mount 176, as described above. 
Accordingly, while FIGS. 8 and 9 are top views insofar as the disc drive 
100 is concerned, FIGS. 8 and 9 provide views looking upwardly from the 
base plate 214 insofar as the disc drive mount 176 is concerned. Thus, 
directions illustrated in FIGS. 8 and 9 (that is, directions to which 
reference will be made in describing the stiction/friction measurement), 
will be mirror images of the directions as they would be seen looking 
directly down upon the stiction/friction measurement apparatus 150. 
Referring first to FIG. 8, for purposes of clarity the dashed, arcuate 
arrow 350 illustrates the direction in which the disc stack 102 normally 
rotates during the operation of the disc drive 100. In the preferred 
practice of the invention, the disc drive 100 is rotated in the opposite 
direction as indicated by the arrow 352 that has been marked .alpha..sub.C 
to indicate the angular acceleration of the case 114 of the disc drive. 
Thus, if the discs of a disc drive normally rotate in a counterclockwise 
direction as viewed from above the disc drive, the case is operated in a 
clockwise direction, as the case would be viewed from above. In view of 
the inversion of the disc drive in the disc drive mount 176, this 
translates into a counterclockwise rotation of the disc drive mount as 
seen from above the stiction/friction measurement apparatus 150. Thus, for 
the case in which the disc drive is mounted up side down in the disc drive 
mount 176, the mount 176 is turned, as viewed from above, in the same 
direction during a stiction/friction measurement that the disc stack 102 
rotates, as viewed from above, during normal operation. If the disc drive 
is mounted right side up, these rotation directions are opposites of each 
other. 
To carry out the stiction/friction measurement, the spin-up motor 170 (FIG. 
2) is operated so as to cause its shaft 174 and, consequently, the disc 
drive mount 176 and disc drive case 114 to angularly accelerate at a rate 
that steadily increases from zero. To this end, a series of velocity 
commands are outputted to the motor driver 175 and such commands are 
predetermined so that, preferably, they increase from zero at a rate that 
is proportional to time. That is, the rate of change of the angular 
acceleration ("jerk") of the motor shaft 174, the disc drive mount 176 and 
the case 114 of the disc drive 100 about the axis of the shaft 174 will be 
substantially constant. During the measurement, the actuator 120 is 
latched in place so that the heads 116 will rotate with the case to exert 
a frictional force on the discs as indicated by the arrows 354 and 356 in 
FIGS. 8 and 9 respectively. This frictional force will, of course, cause 
the disc stack 102 to undergo an angular acceleration that is in the same 
direction as the angular acceleration .alpha..sub.C of the case 114. 
Because the angular acceleration of the disc drive case is initially zero, 
the force required to cause the disc stack 102 to accelerate with the case 
114 will initially be less than the maximum static friction force that can 
be exerted on the discs by the heads with the result that the frictional 
force F.sub.S exerted on the discs by the heads will be just the value 
necessary to prevent slippage of the discs across the heads. Accordingly, 
the discs 104 will also angularly accelerate with the case 114 at the rate 
.alpha..sub.C. However, because the angular acceleration of the case 114 
increases with time, the force required to maintain angular acceleration 
of the disc stack 102 with the case 114 can eventually reach the maximum 
static friction force the heads 116 can exert on the discs 104. Beyond the 
angular acceleration of the case for which this occurs, the disc stack 102 
will slip with respect to the heads so that a relative angular 
acceleration .alpha..sub.REL of the disc stack 102 with respect to the 
case 114, in a direction opposite the angular acceleration .alpha..sub.C 
of the case 114, will occur as illustrated by the arrows 358 and 360 in 
FIG. 9. 
When relative motion of the disc stack 102 with respect to the case 114 
occurs, the disc drive motor 112 will operate as a generator so that the 
onset of the relative motion will be marked by the appearance of voltages 
across the pairs of windings 286 and 288 and 286 and 290. At the point at 
which the relative motion between the disc stack 102 and case 114 begins, 
the angular acceleration of the disc stack 102 will be the same as the 
angular acceleration of the case. Thus, a total stiction value, 
corresponding to the total static friction force exerted by the heads on 
the discs, can be determined by multiplying the angular acceleration of 
the case by the moment of inertia of the disc stack and dividing by the 
radius of the landing zone. The stiction per head can then be found by 
dividing by the number of heads. 
Thus, in accordance with the preferred embodiment of the present invention, 
the angular velocity of the disc drive case 114 is repetitively sampled, 
through the sampling of the angular velocity of the spin-up motor shaft 
174 developed by the motor driver 175, so that the angular acceleration of 
the case can be determined for an ith sample period in accordance with the 
following relationship: 
##EQU1## 
where f.sub.S is the sampling frequency and .omega..sub.C i+1 and 
.omega..sub.C i-1 are the angular velocity samples for the (i+1)th and 
(i-1)th samples respectively. 
Further, the voltages at the ends of the windings 286, 288 and 290 of the 
disc drive spindle motor 112 are concurrently sampled to detect the sample 
period in which slippage between the heads and discs of the disc drive 100 
occurs. The stiction is then determined from the angular acceleration 
determined for the sample period in which slippage is detected as 
described above. 
By continuing to sample the angular velocity of the case, the friction 
between the heads and discs can also be measured. Following the onset of 
slippage between the heads 116 and discs 104, the kinetic friction force 
F.sub.K will be constant and will cause the disc stack 102 to undergo 
angular acceleration at a rate .alpha..sub.D, as represented by the arrow 
362 in FIG. 9. The angular acceleration .alpha..sub.D will be related to 
the angular .alpha..sub.C in accordance with the following relationship: 
EQU .alpha..sub.D =.alpha..sub.C -.alpha..sub.REL (2) 
where .alpha..sub.REL is the relative angular acceleration of the disc 
stack 102 with respect to the case 114. 
During the continuation of spin-up of the motor 170, the angular 
acceleration of the case 114 is determined for each sample time, other 
than the first, from the samples of the spin up motor angular velocity as 
described above and the relative angular acceleration of the disc stack 
102 with respect to the case 114 is determined from samples of the 
voltages at the ends of the windings 286, 288 and 290 of the disc drive 
spindle motor 112. To this end, the orientation of the disc stack 102 with 
respect to the disc drive case 114, as measured by the angle 
.theta..sub.REL indicated at 364 in FIG. 9 between a reference line 366 
defined below and an arbitrary radius 368, can be shown to be given by the 
following relationship: 
##EQU2## 
where .DELTA..epsilon..sub.1 is the emf induced across the windings 286 
and 290, .DELTA..epsilon..sub.2 is the emf induced across the windings 286 
and 288 and K is a conversion factor that converts electrical degrees to 
mechanical degrees. As is known in the art, the emfs induced in the 
windings of a polyphase motor during rotation of the rotor is a periodic 
signal that passes through several periods for each period of rotation of 
the rotor, the number of such periods depending upon the structure of the 
motor in a known way. From this relationship, the reference line 366 is 
defined to be any position of the line 368 for which the angle 
.theta..sub.REL determined from equation (3) is zero. Equation (3) can be 
numerically differentiated twice to yield the relative angular 
acceleration of the disc stack 102 with respect to the case 114. Thus, for 
the ith sample time after the onset of slippage between the heads 116 and 
discs 104: 
##EQU3## 
where .theta..sub.REL i is the value of .theta..sub.REL determined from 
equation (3) at the ith sample time, .omega..sub.REL i is the angular 
velocity of the disc stack 103 relative to the case 114 at the ith sample 
time, .alpha..sub.REL i is the relative angular acceleration in the ith 
sample time and f.sub.S is again the sampling frequency. In the preferred 
practice of the invention, the relative angular acceleration between the 
disc stack 102 and the case 114 and the angular acceleration of the disc 
drive case are determined for a plurality of sample times, the angular 
acceleration of the disc stack 102 at those sample times is determined 
using equation (2) and averaged, and the kinetic friction force (friction) 
is determined by multiplying the average disc stack acceleration by the 
moment of inertia of the disc stack 102 and dividing by the radius of the 
landing zone. As in the case of stiction, the friction per head can then 
be determined by dividing by the number of heads. 
Before proceeding to the programming of the computer 154, two points about 
the above description of the inventive method should be noted. First, 
equation (3) for the angle .theta..sub.REL that describes the orientation 
of the disc stack 102 with respect to the case 114 of the disc drive 100 
is derived on the assumption that the emf induced in a winding of a DC 
motor by rotation of its rotor has the general form of a sine function at 
a multiple of the rotation frequency. As is known in the art, this emf 
will also include harmonics of such sine function. The effect of the 
harmonics in the emfs induced in the windings is eliminated by filtering 
winding voltage sample tables as will be discussed below. Such filtering 
is also used to suppress noise in the measurements and thereby enhance the 
accuracy of the measurements. 
Secondly, equation (3) describes the orientation of the rotor of a three 
phase spindle motor. It is readily extendable to DC motors that operate in 
a different number of phases, however, by replacing the angle of 120 in 
the equation with 360/n, where n is the number of phases of the motor, and 
using voltages at the ends of three consecutive windings to determine the 
emfs .DELTA..epsilon..sub.1 and .DELTA..epsilon..sub.2. 
Programming 
Flow charts outlining programming steps in accordance with the 
considerations discussed above are presented in FIGS. 10, 11 and 12 to 
which attention is now invited. As shown in FIG. 10, the program begins 
with standard programming, indicated at step 370, in which the user of the 
apparatus 150 is afforded an opportunity to adjust any parameters, such as 
the moment of inertia of the disc stack 102 or the radius of the landing 
zone, that are used in determining the stiction and friction. The 
parameters, of course, are related to the specific to the model of the 
disc drive being tested and will consequently be adjusted whenever the 
need arises because of a change in the disc drive for which the stiction 
and friction are to be measured. Other parameters that might be adjusted 
include any parameter that enters into the discussion to follow. 
Preferably, this verification step is carried out using standard 
programming that displays parameters which might be adjusted for 
identification of those to be adjusted and entry of new values for the 
identified parameters. 
Following the verification of parameters, the computer outputs to the I/O 
card 280, at step 372, the rate at which velocity commands are to be 
outputted to the motor driver 175 and the rate at which the angular 
velocity of the spin-up motor and the voltages at the ends of the windings 
288 and 290, relative to the voltage at the end of the winding 286, of the 
disc drive spindle motor are to be sampled. Preferably, both rates are the 
same and a typical command and sample rate is 2 kilohertz. 
A range of stiction and friction values is then selected at step 374. As 
will be clear to those skilled in the art, a practical maximum value for 
the stiction is a value that the disc drive spindle motor 112 cannot 
overcome and, as will be discussed below, the measurements are 
discontinued if the stiction attains this value. The disc drive, in that 
case, is no longer operable. In the preferred practice of the invention, 
the range from zero to this practical maximum is further divided into 
smaller ranges, typically three, and the measurements are made using the 
least of these smaller ranges for which results can be obtained to 
maximize the precision of the measurements. In particular, because the 
angular acceleration of the disc drive mount 176 is increased uniformly to 
a maximum value that is proportional to the stiction at the top of a 
range, each change in sample count corresponds to a change in acceleration 
that is proportional to the maximum stiction. Consequently, limiting the 
stiction range limits the uncertainty in the acceleration of the case 114 
at which slippage begins. 
Following the selection of a test range, the velocity commands that are to 
be outputted to the motor driver 175 by the I/O card 280 are calculated, 
step 376, and transferred to memory in the I/O card, step 378. These 
commands can be suitably calculated as follows. Initially, the maximum 
angular acceleration the disc drive mount 176 and case 114 of the disc 
drive being tested are to reach is calculated using the criterion that the 
maximum force that will be exerted by the heads 116 on the discs 104, if 
no slippage occurs, is to be 110% of the maximum stiction selected at step 
374. If this maximum value, per head, is F.sub.MAX, the maximum 
acceleration will be: 
##EQU4## 
A selected maximum index for spin-up is then selected to cause the disc 
drive mount 176 to have a selected maximum angular velocity 
.omega..sub.MAX when the mount attains the maximum angular acceleration. 
This maximum spin-up index will be given by: 
##EQU5## 
where f.sub.s is the sampling and command rate outputted to the I/O card 
at step 372. For other indices, the angular velocity commands during spin 
up of the disc drive mount will be given by: 
##EQU6## 
Insofar as only the measurement of the stiction and friction are concerned, 
no further angular velocity commands are needed in the operation of the 
apparatus 150. However, at the conclusion of a measurement in which 
slippage between the heads and discs does occur (that is, a measurement 
necessary to measure friction), the disc stack 102 will be rotating in the 
same direction as the disc drive mount 176 and case 114 of the disc drive 
100. Consequently, if the disc drive mount 176 is halted too rapidly, the 
disc stack 102 can undergo relative rotation with respect to the case 114 
that is in the direction opposite the direction 350 in which the disc 
stack normally rotates. As will be recognized, such reverse rotation can 
result in damage to the discs and heads. To avoid this damage, the disc 
drive mount is brought to rest by way of a sequence of angular velocity 
commands for indices n.sub.MAX +1 through 11 n.sub.MAX that are given by: 
##EQU7## 
Such relation decreases the angular acceleration to zero at a rate that is 
a tenth the rate of increase of acceleration used during spin up and will 
prevent reverse rotation of the disc stack from occurring. 
Once the angular velocity commands have been calculated and transferred to 
memory in the I/O card 280, the computer 154 issues a command to the I/O 
card to begin sampling the angular velocity of the shaft 174 of the 
spin-up motor 170 and the voltage differences .DELTA..epsilon..sub.1 and 
.DELTA..epsilon..sub.2 across the pairs of windings 286, 288 and 286, 290 
respectively (as indicated by step 380), and a command to begin outputting 
the velocity commands to the motor driver 175, step 382. The computer 154 
then repetitively polls the I/O card 280, step 384, to determine the index 
of the most recent velocity command outputted to the motor driver 175 and 
when this index reaches the maximum index for spin-up (i.e., n.sub.MAX) a 
command is issued to the I/O card 280 to terminate sampling, step 386, and 
inputs the samples that have been taken by the I/O card at step 388. As 
will be clear form the above, these samples will form tables that list 
values that the angular velocity .omega..sub.C of the disc drive mount 176 
and emfs .DELTA..epsilon..sub.1 and .DELTA..epsilon..sub.2 induced in the 
pairs of windings will have at the times the samples are taken. These 
tables are then filtered, step 390, to suppress noise in all of the 
measurements and to limit harmonics in the emf tables. A suitable filter 
program for this purpose is LABWINDOWS/CVI available from National 
Instruments of Austin, Tex., a program that has fifth order Butterworth 
characteristics with a selectable cut off frequency. A suitable criterion 
for selecting the cut off frequency, which can be selected for each of the 
tables independently of the others, is the lowest cut off frequency that 
will not vary the general shape of a display of the tabulated data. 
The filtering of the disc drive mount angular velocity table and the emf 
tables is followed by a test of whether the disc drive mount 176 and disc 
drive case 114 attained an angular velocity of at least 90% of the maximum 
angular velocity .omega..sub.MAX used to determine the velocity commands 
outputted to the motor driver 175 during spin up of the disc drive mount 
176. More particularly, an index i is initialized to zero, step 392, after 
which the angular velocity .omega..sub.C i for ith sample time is compared 
to 90% of the angular velocity .omega..sub.MAX, step 394. For those values 
of the index i for which .omega..sub.C i is less than 90% of 
.omega..sub.MAX, the index i is compared to the index n.sub.MAX that 
corresponds to the largest angular velocity command issued to the motor 
driver 175, step 396, and, if the index has reached such maximum spin up 
index, the computer 154 outputs an indication to its monitor that the case 
114 and mount 176 did not attain an angular velocity that is at least 90% 
of the maximum velocity command, step 398, and the program ends. If the 
index i is less than n.sub.MAX, it is incremented, step 400, and the 
program returns to step 394 to compare the next sample of the angular 
velocity of the case 114 and disc drive mount 176 to 90% of the maximum 
angular velocity .omega..sub.MAX. Because the incrementing of the index i 
will cause the index to eventually reach the maximum index n.sub.MAX that 
will terminate the program if the angular velocity of the disc drive case 
114 and the disc drive mount 176 have not reached at least 90% of the 
maximum angular velocity .omega..sub.MAX, the program will be terminated 
unless the 90% value was attained during spin up of the disc drive case 
114 and mount 176. The purpose of this test will become clear below. 
When, as will generally be the case, the disc drive case 114 and the disc 
drive mount 116 attain an angular velocity of at least 90% of 
.omega..sub.MAX, the computer generates a table of angular accelerations 
of the disc drive case 114 and mount 176, step 402, as a function of 
sample numbers beginning with the second sample, by repetitive application 
of equation (1) above and filters the angular acceleration table, step 
404, again using the aforementioned filter program. Following the 
filtering of the disc drive case 114 and mount 176 angular acceleration 
table, the program turns, as shown in FIG. 11, to the determination of 
whether breakaway (slippage) between the heads 116 and discs 104, occurred 
during the spin-up of the disc drive case 114 and mount 176. 
Referring to FIG. 11, the determination of whether breakaway occurred 
begins with the reinitialization of the index i to zero, step 406, 
followed by a comparison, step 408, of the absolute value of the ith 
sample of the difference between the voltages at the ends of windings 286 
and 288 of the disc drive spindle motor 112 to a minimum value 
.DELTA..epsilon..sub.MIN that is selected to exceed noise in the 
measurement of the voltage difference. If breakaway has not occurred at 
least by the time the ith sample was taken (that is, if no emf has been 
induced in the windings 286 and 288 by relative motion between the disc 
stack 102 and the disc drive case 114), the comparison will indicate that 
the absolute value of the ith voltage difference is less than 
.DELTA..epsilon..sub.MIN and a test is then made, step 410, to determine 
whether the index i has reached the maximum index n.sub.MAX that 
corresponds to the maximum velocity command issued to the motor driver 
175. If not, the index i is incremented, step 412, and the program returns 
to step 408 for testing of the magnitude of the next sample of the voltage 
difference .DELTA..epsilon..sub.1. If the index has reached n.sub.MAX, the 
computer determines whether the measurements were carried out for the 
highest range for which stiction and friction might be measured, step 414, 
and if not, selects the next higher range, step 416, and returns to step 
376 for calculation of a new set of velocity commands and another spin up 
of the disc drive case 114 and mount 176. If the spin up occurred using 
the maximum stiction and friction test values to determine the velocity 
commands, the computer 154 displays a message, step 418, that the stiction 
exceeds the maximum force that can be overcome by the disc drive spindle 
motor 112; that is, the program determines that the disc drive is 
inoperable. 
It should be noted that it is this manner of determining that a disc drive 
is inoperable that underlies the previous test of whether the disc drive 
case 114 and mount 176 reached 90% of the maximum commanded angular 
velocity. When coupled with the determination of the maximum angular 
velocity on the basis that the frictional force between the heads 16 and 
discs 104 is to reach 110% of the stiction at the upper end of the test 
range, the angular velocity test ensures that a lack of occurrence of 
breakaway for the highest test range did not occur because of a failure of 
the apparatus 150 to angularly accelerate the disc drive case 114 and 
mount 176 at a rate that will cause breakaway if the stiction is within 
the test range. 
If the disc drive being tested is operable, the comparison at step 408 will 
eventually result in the detection of a voltage difference at the ends of 
windings 286 and 288 of the disc drive spindle motor 112 and a test is 
then carried out to determine the sample at which breakaway occurred. In 
particular, the sign of the sample of the voltage difference for which 
breakaway was detected is compared, step 420, to the sign of the previous 
sample of the voltage difference and if, these signs are the same, the 
index i is decremented, step 422, for comparison of the signs of the 
preceding two samples of the voltage difference. The sample index for 
which a sign reversal is detected is then selected as a tentative 
breakaway index n.sub.B, step 422. Once the tentative breakaway index has 
been determined, it is verified, step 424, by repeating the steps 
beginning with 420 using the voltage difference .DELTA..epsilon..sub.2 
between the ends of winding 286 and 290. 
It will be noted that such verification is made without reinitializing the 
index i so that, if the breakaway index determined from the voltage 
difference between the ends of the windings 286 and 290 is not the same as 
the voltage difference between the ends of the windings 286 and 288, the 
smaller of the two indices will be determined in the verification step. 
This smaller value is selected in the verification step as the breakaway 
index that is then used for determination of the stiction between the 
heads 116 and discs 104 of the disc drive. Such choice is based on the 
consideration that the voltages at the ends of the disc drive spindle 
motor windings arising from emf induced in the windings by rotation of the 
disc stack 102 relative to the disc drive case 114 is a periodic function 
so that detection of the rise of one of the voltage differences, 
.DELTA..epsilon..sub.1 or .DELTA..epsilon..sub.2, may be delayed by an 
inappropriate orientation of the rotor of the disc drive spindle motor 112 
when breakaway occurs. If this is the case, selection of the earlier of 
two possible indices as the breakaway index ensures that the sample time 
at which breakaway occurred will be properly identified. 
Once the breakaway index has been identified, the stiction is determined, 
step 426, by multiplying the angular acceleration of the disc drive case 
114 and mount 176 at the sample time identified by the breakaway index by 
the moment of inertia of the disc stack 102 and dividing by the radius of 
the landing zone as described above. This value may then be divided by the 
number of heads the disc drive contains to determine the stiction per 
head. The computer 154 then turns to the determination of the friction 
between the heads 116 and discs 104 as illustrated by the flow chart 
presented in FIG. 12. 
Referring to FIG. 12, the determination of the friction between the heads 
and discs begins with the generation, at step 428, of a table of 
orientations of the disc stack 102 when the samples of the voltage 
differences between the ends of the spindle motor windings 286, 288 and 
290 were taken using equation (3) that has been presented above. This 
table is then twice numerically differentiated to generate, steps 430 and 
432, tables of relative angular velocity and relative angular acceleration 
of the disc stack 102 with respect to the disc drive case 114. The latter 
is then filtered, step 434, in the same manner that the tables of voltage 
differences .DELTA..epsilon..sub.1 and .DELTA..epsilon..sub.2 were 
filtered. 
As noted above, the frictional forces between the heads 116 and discs 104 
are substantially constant once breakaway has occurred and the discs are 
slipping along the heads. Consequently, the relative angular acceleration 
.alpha..sub.REL of the disc stack 102 and the angular acceleration 
.alpha..sub.C of the disc drive case 114 for any sample time after 
breakaway occurred can be used to determine the angular acceleration 
.alpha..sub.D of the disc stack 102 from equation (2) for determination of 
the friction between the heads 116 and discs 104. However, any set of 
measurements will be subject to experimental error giving rise to random 
variations in the values of the quantities being measured and it common 
practice to use an average of many measured values as the value of the 
quantity. The computer 154 is thus programmed to generate such an average 
for the angular acceleration of the disc stack 102 from which friction 
between the heads and discs is determined. 
Moreover, in the measurement of friction between the heads and discs of a 
disc drive, a systematic error can exist in values of the relative angular 
acceleration obtained for higher relative velocities of the disc stack 102 
because of aerodynamic forces on the heads 116 arising from the swirling 
of air by the relative motion of the discs. The computer 154 is programmed 
to prevent this systematic error from being significant by, initially, 
limiting the maximum angular velocity .omega..sub.MAX that is attained by 
the disc drive case 114 and mount 176 during spin up of the mount 176. 
Typically, this maximum angular velocity is selected to be about 2000 rpm. 
The second technique used to limit the effect of aerodynamic forces on the 
heads 116 is to use a range of relative angular accelerations that occur 
for relative angular velocities that are low enough that aerodynamic 
forces on the heads will be negligible to determine the angular 
acceleration of the disc stack after breakaway has occurred. As described 
in the following paragraph, the preferred technique utilized in the 
programming guarantees a constant and known aerodynamic force upon the 
head. 
Returning to FIG. 12, after initializing an index i, at step 436, that 
counts the values of relative angular acceleration used in determining the 
angular acceleration of the disc stack, the relative angular velocities in 
the table generated at step 430 are compared, step 438, to a test angular 
velocity .omega..sub.TEST that is selected to be high enough only to 
eliminate slip-stick characteristics of motion that takes place 
immediately after slippage between two objects in contact begins. The 
value of the index i for which the angular velocity taken from the table 
generated in step 430 first attains the test angular velocity is selected, 
at step 440, as an index n.sub.1 that identifies the lower end 
.theta..sub.1 of a range of angles of relative orientation between the 
disc stack 102 and the disc drive case 114, step 442, over which the 
angular acceleration of the disc stack 102 is to be averaged. 
Once the lower end of the range has been identified, an accumulation value 
S is initialized to zero, step 444, and an ith difference 
.DELTA..alpha..sub.i between the ith value of the angular acceleration 
.alpha..sub.C i of the case 114 and the ith value of the relative angular 
acceleration .alpha..sub.REL i of the disc stack 102 with respect to the 
case 114 is determined, step 446, and added to the accumulation value S, 
step 448. The angle of orientation of the disc stack 102 for the index i 
is then compared with the sum of the angle .theta..sub.1 at the low end of 
the range, and 360.degree., step 450, to determine whether the 
accumulation has been carried out over a range of orientations of the disc 
stack 102 that make up one revolution of the disc stack 102 on the disc 
drive case 114. If, not, the index i is incremented, step 452, and the 
program returns to the accumulation of angular acceleration differences. 
The index for which the a complete revolution of the discs 104 on the case 
114 is completed is selected, step 454, as the index n.sub.2 that marks 
the upper end of the range over which the angular acceleration of the disc 
stack is determined and the friction is then determined, step 456, in 
accordance with the relation: 
##EQU8## 
where S is the final accumulated acceleration difference, I is the moment 
of inertia of the disc stack about its rotation axis, r is radius of the 
landing zone and n.sub.2 -n.sub.1 is the number of acceleration 
differences that were accumulated to determine the value of S. Following 
the calculation of the friction, both the stiction and friction are 
outputted to the monitor of the computer 154, steps 458 and 460. 
DETAILED DESCRIPTION OF THE SECOND PREFERRED EMBODIMENT 
As will be appreciated by those skilled in the art, the primary limitation 
on the precision with which the apparatus 150 can measure stiction and 
friction between the heads and discs of a disc drive is a result of the 
use of samples of the back emf generated angular velocity of the shaft 174 
of the spin-up motor 170 to determine the angular acceleration of the disc 
drive mount 176 and, consequently, of the case 114 of the disc drive 100. 
In particular, the measurement of the angular velocity of the shaft 174 by 
the motor driver 175 involves the measurement of the current that is 
passed through the windings of the spin-up motor 170 and the current 
measurements are sensitive to, for example, fluctuations in the 
temperature of the motor. More importantly, the differentiation of the 
back emf generated angular velocity to determine acceleration generates 
undesirable error/noise, which can be eliminated through the additional 
use of an accelerometer, as discussed below. 
Referring now to FIG. 13, illustrated therein is a modification of the disc 
drive mount, designated 176', that eliminates motor current measurements 
to provide an embodiment of the invention that is capable of measuring 
stiction and friction with greater precision than will the first 
embodiment of the invention described above, should a need arise for doing 
so. 
As shown in FIG. 13, the disc drive mount 176' differs from the disc drive 
mount 176 of the first embodiment in that a notch 462 is formed in one end 
of the base plate 216 to receive an accelerometer 464 which measures 
accelerations along the direction indicated by the double arrow 466. More 
particularly, the accelerometer 464 is cemented into the notch 462 and 
electrical connection between the I/O card 280 and the accelerometer 464 
is made via an enlarged slip ring assembly that will accommodate a larger 
number of conductors than is necessary for the first embodiment. The 
direction 466 is selected to lie substantially tangentially to a circle 
centered on the shaft 174 of the spin-up motor 170 so that the 
accelerometer 464 can be calibrated to measure the angular acceleration of 
the disc drive mount 176' about the axis of the shaft 174. Accelerometers 
suitable for use as the accelerometer 464 are the EGA series 
accelerometers available from Entram Electronics of Fairfield, N.J. 
FIG. 14 illustrates the modification of initial portions of the programming 
of the computer 154 to adapt the programs described above with respect to 
FIGS. 10, 11 and 12 for use in the second embodiment of the invention. In 
particular, the modification of the program generally comprises: (1) 
including the accelerometer output among the quantities to be sampled a 
step 380 shown in FIG. 10 and carried into FIG. 14; (2) replacing the step 
388 of FIG. 10 with a step 468 which includes the angular acceleration 
table generated by repetitive sampling of the accelerometer 464 by the I/O 
card 280 among the quantities transferred to the memory of the computer 
154 from the I/O card 280; (3) replacing the filtering step 390 of FIG. 10 
with a filtering step 470 that includes filtering of the disc drive case 
angular acceleration table; and (4) deletion of the steps 402 and 404 of 
FIG. 10 that are used in the first embodiment to determine and filter the 
angular acceleration of the case 114 from the case angular velocity table 
inputted at step 388. 
In summary, in accordance with the foregoing description the spin-up motor 
170 is provided with the rotatable shaft 174 which is rotated in 
accordance with motor drive current applied by the motor driver 175. The 
disc drive 100 is mounted relative to the rotatable shaft 174 by way of 
the disc drive spin assembly 152 and electrical contact is established 
with the windings 286, 288 and 290 of the spindle motor 112 by an 
electrical contact assembly, such as the slip ring 294. Measurements of 
static and kinetic friction between the disc drive heads 116 and the discs 
104, 106 and 108 are thus determined by the computer 154 in response to 
the rotation of the disc drive case 114 and voltages induced in the 
windings 286, 288 and 290 of the spindle motor 112. 
It will be clearly understood that the axis of rotation of the discs will 
be aligned to be substantially parallel with the axis of rotation of the 
rotatable shaft of the spin-up motor. The fact that these axes do not have 
to be coextensively aligned is a significant advantage of the present 
invention. However, for purposes of the appended claims, parallel 
alignment of the axes will be read with sufficient breadth to also 
encompass coextensive alignment of the axes. 
It will be clear that the present invention is well adapted to attain the 
ends and advantages mentioned as well as those inherent therein. While 
presently preferred embodiments have been described for purposes of this 
disclosure, numerous changes may be made which will readily suggest 
themselves to those skilled in the art and which are encompassed in the 
spirit of the invention disclosed and as defined in the appended claims.