U.S. patent application number 14/969107 was filed with the patent office on 2016-04-21 for minimization of torque ripple.
The applicant listed for this patent is Nucleus Scientific, Inc.. Invention is credited to Timothy A. FOFONOFF, Ian W. HUNTER, Serge LAFONTAINE.
Application Number | 20160111987 14/969107 |
Document ID | / |
Family ID | 46888644 |
Filed Date | 2016-04-21 |
United States Patent
Application |
20160111987 |
Kind Code |
A1 |
HUNTER; Ian W. ; et
al. |
April 21, 2016 |
MINIMIZATION OF TORQUE RIPPLE
Abstract
Systems and methods of operating an electric motor including a
first linear actuator including a first coil, a second linear
actuator including a second coil, a rotational shaft, a cam
assembly mounted on said rotational shaft for translating linear
movement of the first and second linear actuators to rotational
movement of the rotational shaft. The first coil is driven with a
first signal that produces a first radially-directed force. The
second coil is simultaneously driven with a second signal that
produces a second radially-directed force, wherein the first
radially-directed force is represented by a sine function and the
second radially-directed force is represented by the sine function
phase shifted by .+-..pi./2 radians.
Inventors: |
HUNTER; Ian W.; (Lincoln,
MA) ; LAFONTAINE; Serge; (Lincoln, MA) ;
FOFONOFF; Timothy A.; (Cambridge, MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Nucleus Scientific, Inc. |
Lincoln |
MA |
US |
|
|
Family ID: |
46888644 |
Appl. No.: |
14/969107 |
Filed: |
December 15, 2015 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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13587467 |
Aug 16, 2012 |
9231462 |
|
|
14969107 |
|
|
|
|
61524089 |
Aug 16, 2011 |
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Current U.S.
Class: |
318/432 |
Current CPC
Class: |
H02P 6/10 20130101; Y02T
10/642 20130101; H02K 41/0354 20130101; B60L 2270/142 20130101;
Y02T 10/64 20130101; H02P 6/34 20160201; H02K 7/14 20130101; H02K
41/0356 20130101; B60L 2220/44 20130101; B60L 2270/145 20130101;
B60L 2240/429 20130101; B60L 2240/425 20130101; Y02T 10/641
20130101; B60L 2240/423 20130101; H02K 7/075 20130101; H02K 7/06
20130101 |
International
Class: |
H02P 6/10 20060101
H02P006/10; H02K 41/035 20060101 H02K041/035; H02K 7/06 20060101
H02K007/06; H02P 6/00 20060101 H02P006/00 |
Claims
1. A method of operating an electric motor including a first linear
actuator including a first coil, a second linear actuator including
a second coil, a rotational shaft, a cam assembly mounted on said
rotational shaft for translating linear movement of the first and
second linear actuators to rotational movement of the rotational
shaft, said method comprising: driving the first coil with a first
drive signal that produces a first torque on the rotational shaft;
simultaneously driving the second coil with a second drive signal
that produces a second torque on the rotational shaft, wherein the
sum of the first torque and the second torque produces a total
torque, and wherein the first drive signal and the second drive
signal are selected to result in the total torque being
substantially ripple free throughout a complete rotation of the
rotational shaft.
2. The method of claim 1, wherein the first drive signal varies
periodically over a complete rotation of the rotational shaft and
the second drive signal varies periodically over the complete
rotation of the rotational shaft.
3. The method of claim 2, wherein the first drive signal and the
second drive signal each have a period of n cycles per a complete
rotation of the rotational shaft, wherein n is an even integer.
4. The method of claim 3, wherein n equals 4.
5. The method of claim 1, wherein the first drive signal is shifted
in phase relative to the second drive signal by .+-. .pi. 2 n
##EQU00011## radians, wherein n is an integer.
6. The method of claim 1, wherein the cam assembly presents to the
first linear actuator a first cam surface having a first profile
and presents to the second linear actuator a second cam surface
having a second profile, wherein a first derivative of the first
profile is represented by .PSI.(n.sub.c.theta.) and a first
derivative of the second profile is represented by
.PSI.(n.sub.c.theta.+.DELTA.), wherein .theta. is an angle of
rotation of the rotational shaft, n, is an even integer
representing a number of cycles of the first profile the and second
profile over a complete rotation of the rotational shaft, and
.DELTA. is a phase shift between the first profile and the second
profile, wherein the first drive signal causes the first linear
actuator to generate a force represented by F.sub.c(n.sub.c.theta.)
and the second drive signal causes the second linear actuator to
generate a force represented by F.sub.c(n.sub.c.theta.+.DELTA.),
and wherein the first drive signal and the second drive signal are
selected to cause
F.sub.c(n.sub.c.theta.).PSI.(n.sub.c.theta.)+F.sub.c(n.sub.c.theta.+.DELT-
A.).PSI.(n.sub.c.theta.+.DELTA.) to be constant as a function of
.theta..
7. The method of claim 1, wherein the cam assembly presents to the
first linear actuator a first cam surface having a first profile
and presents to the second linear actuator a second cam surface
having a second profile, wherein the first profile, the second
profile, the first drive signal and the second drive signal are
selected to result in the total torque being substantially ripple
free throughout the complete rotation of the rotational shaft.
8. The method of claim 7, wherein the first profile is described by
n cycles of a trigonometric function, wherein n is an even
integer.
9. The method of claim 8, wherein the second profile is described
by n cycles of said trigonometric function.
10. The method of claim 9, wherein n equals 4.
11. The method of claim 9, wherein said trigonometric function is a
sine function.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a divisional of prior U.S. patent
application Ser. No. 13/587,467, filed Aug. 16, 2012 which claims
benefit or priority to U.S. Provisional Application No. 61/524,089,
filed Aug. 16, 2011, the entire disclosures of which are hereby
incorporated by reference in their entirety.
TECHNICAL FIELD
[0002] This invention relates generally to the control of electric
motors and more specifically to the control of linear Lorentz-Type
actuator motors.
BACKGROUND OF THE INVENTION
[0003] Lorentz-type motors exploit the basic principle that a
charged particle moving in a magnetic field experiences a force in
a direction perpendicular to the direction of movement. Stated
mathematically: F=qvXB, where F is force, q is the charge of the
charged particle, v is the instantaneous velocity of the particle,
and B is the magnetic field. So, if a current is flowing through a
wire and a magnetic field is applied in perpendicular direction,
the wire experiences a force trying to move it sideways.
[0004] A simple configuration that harnesses this principle is a
coil encircling a magnetic core made of permanent magnets. The
coil, referred to as the actuator, is arranged to be capable of
sliding back and forth along the length of the magnetic core or
magnetic stator. In that configuration, flowing a current though
the coil results in a force on the coil pushing it in one direction
along the length of the magnetic core. Reversing the direction of
current flow causes the coil to move in the opposite direction. The
magnitude of the current determines the strength of the force. And
the shape of the current waveform determines how the force changes
over time. With such an arrangement, by applying an appropriate
current waveform to the coil, one can make the coil move back and
forth along the magnetic core in a controlled manner. The
controlled movement of the actuator can, in turn, be used to
perform work.
BRIEF DESCRIPTION OF THE DRAWINGS
[0005] FIGS. 1A-1B illustrate a rotary motor in a wheel.
[0006] FIG. 1C illustrates a magnetic stator assembly.
[0007] FIGS. 2A-2C illustrate components of the rotary motor of
FIG. 1 in various stages of motion.
[0008] FIG. 2D illustrates an exemplary shape of a cam.
[0009] FIG. 3 is a cam profile based on an Archimedes Spiral
[0010] FIG. 4 is a plot of cam radial position as a function of
angle.
[0011] FIG. 5 is a sinusoidal cam profile.
[0012] FIG. 6 is a plot of cam radial position as a function of
angle for the cam shown in FIG. 5.
[0013] FIGS. 7A-7B illustrate an arrangement of two hub motors for
one wheel.
[0014] FIGS. 8A-8B illustrate views of two rotationally offset
cams.
[0015] FIGS. 9A-9B illustrate a disc of an example rotary device
coupled to a rim of a wheel.
[0016] FIG. 10 illustrate two cam profiles in quadrature.
[0017] FIG. 11 illustrate the symmetry features of a torque
function.
[0018] FIG. 12 illustrates a piecewise quadratic torque
function.
[0019] FIG. 13 illustrates a piecewise quadratic profile for the
first derivative of the cam profile.
[0020] FIG. 14 illustrates a non-trigonometric force function
compared to a trigonometric force function.
[0021] FIG. 15 illustrates a non-trigonometric cam profile compared
to a trigonometric cam profile.
[0022] FIG. 16 is an exemplary control system for providing
constant torque.
[0023] FIG. 17 shows a load cell for directly measuring the Lorentz
force.
[0024] FIG. 18 is an exemplary control system which employs
feedback for force profile generation.
DETAILED DESCRIPTION
[0025] The subject of this application is the design and operation
of a hub-mounted motor assembly so as to minimize torque ripple.
The hub-mounted motor is a linear Lorentz-type actuator motor.
Before discussing the design and operation of the hub-mounted motor
assembly, a brief review of the linear Lorentz-type actuator motor
will be presented. A more detailed discussion can be found in U.S.
Ser. No. 12/590,495, entitled "Electric Motor," and incorporated
herein in its entirety by reference.
The Linear Lorentz-Type Actuator Motor
[0026] The linear Lorentz-type actuator motor is a rotary device
100 that is mounted inside a wheel on a vehicle, as illustrated in
FIG. 1A. Rotary device 100 includes a magnetic stator assembly 120,
opposed electromagnetic actuators 110a, 110b, and a
linear-to-rotary converter (e.g., oval-shaped cam) 105. Rotary
device 100 is attached to the chassis of a vehicle, for example, at
a point on the far side of the wheel (not shown). Rotary device 100
is attached to the wheel via cam 105 using a circular support
plate, for example, which has been removed to show the inside of
the wheel. Such a plate is attached to both the rim of the wheel
and cam 105 using fasteners, such as bolts. The wheel and cam
support plate rotate relative to a hub 145 about a bearing 150.
[0027] FIG. 1B shows rotary device 100 from the side of the wheel
140 with the tire and some other components removed. The core of
rotary device 100 includes cam 105, two opposed electromagnetic
actuators 110a, 110b, and a magnetic stator assembly 120.
Electromagnetic actuators 110a, 110b each house a coil 115a, 115b
that encircles magnetic stator assembly 120. Magnetic actuators
110a, 110b is arranged to reciprocate relative to magnetic stator
assembly 120 when an appropriate drive signal is applied to coils
115a, 115b. One electromagnetic actuator 110a is shown having a
housing 155a surrounding its coil 115a and the other
electromagnetic actuator 110b is shown with its housing removed to
show its coil 115b.
[0028] Magnetic stator assembly 120 depicted in FIG. 1B is oriented
vertically and includes a plurality of magnetic stators 125a, 125b,
each of which includes multiple individual permanent magnets
oriented so that their magnetic moments are perpendicular to the
axis of magnetic stator assembly 120. When current is applied to
coils 115a, 115b of the electromagnetic actuators 110a, 110b (e.g.,
alternating current), actuators 110a, 110b are forced to move
vertically along magnetic stator assembly 120 due to the resulting
electromagnetic forces (i.e., the Lorentz forces). As is well
known, when a coil carrying an electrical current is placed in a
magnetic field, each of the moving charges of that current
experiences what is known as the Lorentz force, and collectively
they create a net force on the coil. The direction of movement and
force generated is controlled by the polarity and amplitude of the
current induced in the coil.
[0029] Rotary device 100 also includes a plurality of shafts 130a,
130b, coupled to a bearing support structure 165. Electromagnetic
actuators 110a, 110b slide along the shafts using, for example,
linear bearings. Attached to each electromagnetic actuator 110a,
110b is a pair of followers 135a-d that interface with cam 105 to
convert their linear motion to rotary motion of the cam. To reduce
friction, followers 135a-d freely rotate so as to roll over the
surfaces of cam 105 during the operating cycle. Followers 135a-d
are attached to electromagnetic actuators 110a, 110b via, for
example, the actuators' housings. As electromagnetic actuators
110a, 110b reciprocate, the force exerted by followers 135a-d on
cam 105 drives cam 105 in rotary motion.
[0030] FIG. 1C illustrates magnetic stator assembly 120 with two
magnetic stators 125a, 125b. Magnetic stators 125a, 125b each
include multiple magnets. For example, magnetic stator 125a
includes, on one end surface portion, eight magnets 160a-h. All of
the magnets 160 have their magnetic moments oriented perpendicular
to the surface on which they are mounted and in the same
direction.
[0031] FIGS. 2A-C illustrate components of rotary device 100 in
action, including the rotary device's electromagnetic actuators
110a, 110b (with associated coils 115a, 115b and followers 135a-d)
and cam 105 moving relative to the magnetic stator assembly 120
(including associated magnetic stators 125a, 125b). The rim, the
wheel, and the housings by which the followers are attached to the
coils are not shown in these figures. As illustrated by FIGS. 2A-C,
the reciprocal movement of the coils 115a, 115b in opposition
drives cam 105 to rotate, which, in turn, causes a wheel attached
to cam 105 to rotate. Coils 115a, 115b are shown in FIG. 2A as
being at almost their furthest distance apart. FIG. 2B shows that
as coils 115a, 115b move closer to each other, coils 115a, 115b
drive cam 105 to rotate in a clockwise direction, thereby causing
any attached wheel to also rotate clockwise. In the example device,
the force exerted on cam 105 is caused by the outer followers 135a,
135c squeezing-in on cam 105. FIG. 2C shows that coils 115a, 115b
are even closer together causing further clockwise movement of cam
105.
[0032] After coils 115a, 115b have reached their closest distance
to each other and cam 105, in this case, has rotated ninety
degrees, coils 115a, 115b begin to move away from each other and
drive cam 105 to continue to rotate clockwise. As coils 115a, 115b
move away from each other, inner followers 135b, 135d exert force
on cam 105 by pushing outward on cam 105.
[0033] It is noted that cam 105 is shown in the figures as an oval
shape, but it may have a more complex shape, such as, for example,
a shape having an even number of lobes, as illustrated in FIG. 2D.
The sides of each lobe may be shaped in the form of a sine wave, a
portion of an Archimedes spiral, or some other curve, for example.
The number of lobes determines how many cycles the coils must
complete to cause the cam to rotate full circle. A cam with two
lobes will rotate full circle upon two coil cycles. A cam with four
lobes will rotate full circle upon four coil cycles. Additionally,
more lobes in a cam results in a higher torque.
Analysis of Torque
[0034] The motor consists of circular disk with an outer cam and
inner cam. Two cam followers linked to a coil can create a radial
force on the cam. The force exerted by the cam followers in turn
creates a torque on the disk.
[0035] The idealized equation for the Torque T.sub.c(.theta.)
generated by the cam follower is given by the following
equation:
T c ( .theta. ) = F c ( .theta. ) R c ( .theta. ) .theta. Eq . 1
##EQU00001##
where F.sub.c(.theta.) is the radial force generated by the cam
follower, and R.sub.c(.theta.) is the distance of the cam follower
from the center of the disk. As noted above, in the motor, the
force is generated from a current running in a coil and interacting
with a magnetic field.
[0036] If the force is constant throughout a half stroke and the
slope defining the position of the cam follower as a function of
the wheel angle is also constant, that produces a torque that is
constant throughout the cycle. The two dimensional shape of the cam
would then be as depicted in FIG. 3.
[0037] In FIG. (1), .theta. is the position (rotation) of the wheel
in radians and the disk has four lobes. The cam follower exerts a
vertical force as indicated by the arrow. The position of the cam
in polar coordinates is given by the curve shown in FIG. 4.
[0038] Although this cam profile easily lends itself to a drive
signal that yields a constant torque, it presents two major
drawbacks: the need to instantaneously change the coil velocity at
the end of the cam motion and the need to instantaneously change
the current that generates the force exerted by the cam.
[0039] The approximate equation giving the force required to
accelerate and decelerate the coil is:
F r = M c [ 2 .theta. 2 R c ( .theta. ) ( t .theta. ) 2 + .theta. R
c ( .theta. ) 2 t 2 .theta. ] Eq . 2 ##EQU00002##
where M.sub.c is the mass of the coil. At the extremes of the
stroke motion, the term
2 R c ( .theta. ) .theta. 2 ##EQU00003##
is theoretically infinite, which means in practice that the coil
would undergo an unacceptably high shock due to the abrupt
deceleration and acceleration.
[0040] Instantaneously changing the current also presents technical
challenges, given that the current flows through a coil with a
significant inductance. A linear approximation of the voltage
required to change the current in the coil is given by:
V c ( t ) = R c I c ( t ) + L c t I ( t ) + V emf ( t ) Eq . 3
##EQU00004##
where V.sub.c(t) is the voltage required across the coil as a
function of the required change in coil current I.sub.c(t), R.sub.c
is the coil resistance, L.sub.c is the coil inductance and
V.sub.emf(t) is the back electromotive force generated by the coil
as it moves through a changing magnetic field. Here again, given
the discontinuity in the current the voltage across the coil would
tend to infinity.
[0041] One partial solution is to change the cam profile such that
its second derivative is finite and continuous at all points, i.e.,
it has a third order derivative. One example of such a cam profile
would be a sinusoidal shape. In such a case, the cam profile would
be given by the equation:
R.sub.c(.theta.)=R.sub.0+A.sub.csin(n.sub.1.theta.) Eq. 4
where R.sub.0 is the circle around which the cam evolves (mean
position), A.sub.c is the cam amplitude and n.sub.1 is the number
of lobes or number of strokes per revolution. The cam profile then
looks like what is shown in FIG. 5. And in polar coordinates, the
cam profile is shown in FIG. 6.
[0042] In this case the force to be generated by the coil is given
by:
F c ( .theta. ) = T c ( .theta. ) .theta. R c ( .theta. ) Eq . 5
##EQU00005##
[0043] However, the derivative of the cam position R.sub.c(.theta.)
is null at the end of the strokes, hence the required force would
also diverge to infinity. This remains true for any cam profile. If
there is only one cam, the corollary is that it would not be
self-starting if the initial position occurs when the cam follower
is at the end of a stroke.
[0044] Using multiple cams such that their null points are spaced
apart circumvents the problem. In the simplest example, there would
be two cams on a disk, each on opposite side.
An Exemplary Embodiment
[0045] A wheel which implements this approach is shown in FIGS.
7A-B. In this case the tire of the wheel, and some other
components, have been removed for clarity. There are two rotary
devices 1500 and 1600, one mounted on each side of a central disc
1635. The rotary devices are similar to the rotary devices
described above. Rotary device 1500 includes a pair of
electromagnetic actuators 1510a, 1510b, and a magnetic stator
assembly 1520. Similarly, rotary device 1600 includes a pair of
electromagnetic actuators 1610a, 1610b, and a magnetic stator
assembly 1620. Each of magnetic stator assemblies 1520, 1620
includes two magnetic stators 1515a, 1515b, 1615a, 1615b, which
include magnetic flux return paths 1640a-d and magnets (e.g.,
1630a, 1630b). The housings surrounding the coils of the
electromagnetic actuators 1510a, 1510b, 1610a, 1610b are not shown.
Each coil reciprocates along four arrays of magnets, which, as
described above, may include multiple magnets. Two of the magnet
arrays are located inside the coil (e.g., inner magnetic stator
component 1630b) and two are located outside the coil (e.g., outer
magnetic stator component 1630a). Each set of magnets are mounted
to a magnetic flux return path 1640a-d.
[0046] The disc 1635 includes two cams, one on either side of the
disc 1635. In this example, each cam of the device is in the form
of a grove that includes an inner surface 1605a and an outer
surface 1605b. Coupled to electromagnetic actuators 1510a and 1510b
are two pairs of followers 1625a, 1625b, the different followers of
each pair interfacing with a respective surface 1605a, 1605b of the
cam. Electromagnetic actuators 1610a and 1610b are similarly
coupled to followers. As the coils move towards each other, one of
the followers of each electromagnetic actuator 1510a, 1510b exerts
force on the inner surface 1605a of the cam. As the coils move away
from each other, the other follower exerts force on the outer
surface 1605b of the cam.
[0047] FIG. 7B illustrates a different view of the rotary devices.
It should be apparent that each pair of electromagnetic actuators
(pair 1510a, 1510b and pair 1610a, 1610b) are at different phases
of reciprocation. This is because, in the example device, the cams
on either side of the disc 1635 are rotationally offset from each
other by, for example, forty-five degrees. This helps to prevent
the actuators from stopping at a point on the cams from which it
would be difficult to again start. Thus, if one pair of actuators
stops on a "dead-spot" of its respective cam, the other pair of
actuators would not be at a dead-spot. FIG. 7B also illustrates an
arrangement of the coils and magnetic stator components. For
example, magnetic stators components 1630b and 1630c are located
inside the coil of actuator 1610a, and magnetic stators components
1630a and 1630d are located outside the coil.
[0048] FIG. 8A illustrates two rotationally offset cams 1505, 1606.
The cams 1505, 1606 are part of or are mounted on a disc 1635. One
cam 1505 is on one side of the disc 1635, and the other cam 1606 is
on the opposite side, as indicated by the dashed line. In some
devices the cam may be offset by forty-five degrees, for example.
The cams 1505, 1606 have an even number of lobes, e.g. 2, 4, 6
etc.. Cams having two lobes are offset by 45 degrees. Cams having
four lobes are offset by 22.5 degrees.
[0049] FIG. 8B illustrates a vertical cross-section of a disc 1635
with two rotationally offset cams, each having in inner surface
1605a, 1605c and an outer surface 1605b, 1605d. Due to the offset,
the inner surfaces 1605a, 1605c are not in line with each other.
Likewise, the outer surfaces 1605b, 1605d are also not in line with
each other.
[0050] FIG. 9A illustrates how the disc 1635 of the example rotary
device is coupled to the rim 1705 of a wheel. The rim 1705 consists
of one piece to which the disc 1635 is affixed using fasteners,
such as bolts, along an inner ring 1715. Alternatively, the rim
1705 may include two parts 1710a, 1710b that bolt together along
ring 1715. When fastened together, the two parts 1710a, 1710b form
a full rim 1705 with inner ring 1715. A tire is then be mounted to
the rim 1705. FIG. 9B shows how the disc 1635 is fastened to the
inner ring 1715 of the disc 1635.
Minimizing Torque Ripple
[0051] Returning to the description of the technique for minimizing
torque ripple, we direct the reader's attention to an example using
two four lobe cams, which is illustrated in FIG. 10.
[0052] Note that the profiles are not mirror images but are in
quadrature and that they consist of the same basic profile
R.sub.c(x) but "shifted" with respect to each other. Assuming that
n.sub.c is the number of lobes in the cam, i.e. the number of times
that a basic function R.sub.c(x) is repeated within one full
circle, and that the derivative of the cam profile is given by
.PSI..sub.c(n.sub.c.theta.), the equation for the torque provided
by the summation of the torques .PHI.(.theta.) of the individual
cams would be:
T=.PHI.(n.sub.c.theta.)+.PHI.(n.sub.c.theta.+.DELTA.) Eq. 6
T=F.sub.c(n.sub.c.theta.).PSI.(n.sub.c.theta.)+F.sub.c(n.sub.c.theta.+.D-
ELTA.).PSI.(n.sub.c.theta.+.DELTA.) Eq. 7
And typically .DELTA. corresponds to one quarter of a lobe,
i.e.
.DELTA. = .pi. 2 . ##EQU00006##
[0053] This leads to the following question: what is the family of
functions .PHI.(.theta.)=F.sub.c(.theta.).PSI..sub.c(.theta.) such
that total torque is constant (i.e., ripple free) when at least two
out-of-phase cams and actuators are used. This equation implies
that the function .PHI.(.theta.) has a periodicity of 2.DELTA.:
.PHI.(.theta.)=T-.PHI.(.theta.+.DELTA.) Eq. 8
.PHI.(.theta.+.DELTA.)=T-.PHI.(.theta.+2.DELTA.) Eq. 9
Substituting:
.PHI.(.theta.)=T-(T-.PHI.(.theta.+2.DELTA.))=.PHI.(.theta.+2.DELTA.)
Eq. 10
Which is as required, i.e. the function .PHI.(.theta.) is periodic,
with a period that is double that of the period of one full cam
cycle. This still leaves the ensemble of functions quite large. For
reasons of symmetry, it is reasonable to require that:
.PHI.(.theta.)=.PHI.(-.theta.) Eq. 11
And we can also assume that the cam reaches its extremum at
.theta.=0 and .theta.=.DELTA.. Hence, the class of functions
.PHI.(.theta.) that we are seeking has the following properties:
[0054] 1. .PHI.(.theta.)=0 [0055] 2. .PHI.(.DELTA.)=Tmax where Tmax
is the maximum torque [0056] 3. .PHI.(.theta.) is symmetrical with
respect to the .theta.=0 vertical axis [0057] 4. .PHI.(.theta.) is
symmetrical with respect to the point (.DELTA./2, Tmax/2). [0058]
5. .PHI.(.theta.) is continuous. The general shape of this function
is given in FIG. 11.
[0059] We also know that the function .PHI.(.theta.) is the product
of two other functions, F.sub.c(.theta.) and .PSI.(.theta.), where
.PSI.(.theta.) must have a first order derivative, such that the
cam profile given by:
R.sub.c(.theta.)=.intg..PSI.(.theta.)d.theta. Eq. 12
Intuitively it would also be desirable that the functions
F.sub.c(.theta.), R.sub.c(.theta.) and .PSI.(.theta.) have the same
symmetry. Therefore one reasonable question to ask is would there
be a function such that F.sub.c(.theta.) and .PSI.(.theta.) are the
same function? In this case:
T=.PSI..sup.2(n.sub.c.theta.)+.PSI..sup.2(n.sub.c.theta.+.DELTA.)
Eq. 13
which is the basic equation of a right triangle.
[0060] Here the components in quadrature can be viewed as the sides
of a right triangle, such that one is a sine of an angle and the
other one the cosine of the angle:
cos 2 ( .PHI. ) = .PSI. 2 ( n c .theta. ) Eq . 14 cos ( .PHI. +
.DELTA. ) = cos ( .PHI. + .pi. 2 ) = cos ( .PHI. ) cos ( .pi. 2 ) -
sin ( .PHI. ) sin ( .pi. 2 ) = - sin ( .PHI. ) Eq . 15 .thrfore.
cos 2 ( .PHI. + .DELTA. ) = sin 2 ( .PHI. ) Eq . 16
##EQU00007##
[0061] In conclusion, if the shape of the cam is a sine function,
its derivative is a cosine function, its derivative is a sine
function, and if the current waveform is also a sine function then
the two components in quadrature sum up to a constant torque with
no ripple.
[0062] In principle, there is an infinite number of functions
F.sub.c(.theta.), R.sub.c(.theta.) and .PSI.(.theta.) leading to a
constant torque. In practice, the choice is rather limited, given
that we must have:
F c ( .theta. ) = .PHI. ( .theta. ) .PSI. ( .theta. ) Eq . 17
##EQU00008##
And when both .PHI.(.theta.) and .PSI.(.theta.) tend to zero, the
ratio must also converge to zero. We also require to a first order
derivative. It becomes a non-trivial exercise to find other
functions besides the sinusoidal type function to meet these
criteria, and they typically end up very close to a trigonometric
function. However, in the modern day of microprocessor based
digital control where computation time is a prime consideration
such alternate functions might have a benefit.
[0063] One of the simplest examples of an alternate approach would
be to use piece-wise quadratic functions for .PHI..sub.1(.theta.)
and .PSI..sub.i(.theta.), as given in this MathCAD recursive
representation, omitting for the time being the number of lobes in
the equations:
.PHI. 1 ( .theta. ) := | z .rarw. .theta. z .rarw. mod ( z , .pi. )
y .rarw. 8 .pi. 2 z 2 if z .ltoreq. .pi. 4 otherwise | y .rarw. 1 -
.PHI. 1 ( .pi. 2 - z ) if z .ltoreq. .pi. 2 y .rarw. .PHI. 1 ( .pi.
- z ) otherwise y .rarw. y Eq . ( 18 ) ##EQU00009##
where .theta..sub.1(.theta.) is shown in FIG. 12.
.PSI. 1 ( x ) := | z .rarw. x z .rarw. mod ( z , 2 .pi. ) y .rarw.
1 - 4 .pi. 2 ( .pi. 2 - z ) 2 if z .ltoreq. .pi. 2 otherwise | y
.rarw. .PSI. 1 ( .pi. - z ) if z .ltoreq. .pi. y .rarw. - .PSI. 1 (
z - .pi. ) otherwise y .rarw. y sign ( x ) Eq . ( 19 )
##EQU00010##
where .PSI..sub.1(.theta.) is shown in FIG. 13.
[0064] The resulting force profile F.sub.1 calculated from the
ratio of .PHI..sub.1 to .PSI..sub.1 is outlined in FIG. 14, and
compared to a trigonometric function.
[0065] Finally, the CAM profile R.sub.1 is computed from the
integral of .PSI..sub.1 and compared to a trigonometric function in
FIG. 15.
[0066] Although difficult to prove, it is to be expected that all
CAM shapes and force profiles that are well behaved in terms of
symmetry and smoothness would all be very close in shape to
trigonometric functions. Only two CAMs in quadrature were analyzed
here, the same approach could be used for other even numbers of
CAMS.
[0067] In actual practice, although it is easy to generate a CAM
with a precise triangular function, it is more difficult to
generate a force profile that is a sinusoidal. For an idealized
Lorentz force actuator assuming a constant magnetic induction B,
this would translate in generating an exact current profile with a
sinusoidal function. However, in practice the magnetic induction B
is not constant and depends on the geometry of the permanent
magnets used to generate the field. Furthermore, the field
generated by magnets depends on the temperature and is also
influenced by the current flowing in the motor coil. All of these
effects must be carefully modeled to generate a current that truly
minimizes ripple.
[0068] A typical control system is depicted in FIG. 16. It includes
switching power electronics 500 which supplies a pulse width
modulated drive signal to the coils in the motor to produce the
desired torque and speed. The operation of switching power
electronics 500 is controlled based on models of the motor
including a model 502 of the magnetic induction of the motor (i.e.,
the magnetic field seen by the coil as a function of the position
of the coil, the current in the coil, and the temperature of the
coil) and a model 504 which enables one to determined the voltage
of a pulse width modulated signal that is necessary to produce the
desired drive current in the coils. Input for the models comes from
a rotary encoder 506 which indicates the angular position of the
cam or wheel, a conversion module 508 that converts the angular
position into a position of the coil or cam follower, and various
sensors in the motor supplying information about the motor's
operating conditions. Note that the model changes depending on
operating conditions and some the model needs to take these into
account. The various sensors include a motor temperature sensor
510, a current sensor 512, a battery voltage sensor 514, and a coil
voltage sensor 516.
[0069] From a wheel rotary encoder 506, the angular and radial
position of the coil and cam follower are calculated. From the cam
follower position, the desired force to be generated by the coil is
calculated from a function F.sub.c(.theta.). The desired current
required to produce this force is equal to the current in the coil
times the magnetic induction. Since the magnetic induction B is not
exactly uniform, it has to be estimated from model 502 using the
motor temperature, coil current, and relative position of the coil
with respect to the permanent magnets.
[0070] The desired current is converted to a pulse modulation
width. This is done in two steps. First from the model of the coil
dynamics, a voltage required across the coil to obtain the desired
current in the coil is calculated. Then, a model of the power
electronics is required to calculate the switching duty cycle based
on the desired voltage, the supply voltage, the actual current in
the coil and the voltage across the coil.
[0071] So far the control is all feed forward model based. However,
the models have a certain level of inaccuracy, so feedback is used
to correct between the desired current and measured current.
[0072] An alternative approach to generating the desired force
profile is by measuring the force that is generated and directly
controlling that force using a feedback control on current, as
summarized in FIGS. 17 and 18.
[0073] FIG. 17 illustrates how the Lorentz force generated by the
coil can be directly measured. A load cell 700 is inserted between
the coil 702 and the cam follower 704. The cam follower itself can
be subject to large off-axis forces from the reaction with the cam.
However, force transducers can be designed to be largely
insensitive to such lateral forces. Therefore, an accurate
measurement of the axial force can be obtained from the load cell
and then used in various control algorithms to adjust the current
such that the required force profile is generated.
[0074] FIG. 18 illustrates one of the many alternative control
strategies that can be used to obtain the required force profile.
The algorithms described above to estimate the current needed to
get the desired force could be used in a feedforward manner. Then,
the error between the desired force and measured coil force would
be feed to some other feedback control system which uses that
measurement to make current corrections in order to obtain the
desired force profile. The advantage of the feedback control
approach is that it will tend to be more stable than a purely feed
forward approach.
[0075] Other embodiments are within the following claims.
* * * * *