The present invention relates to a linear motor, and more
particularly, to a linear motor in which a gap portion is defined by magnetic poles
or teeth having characteristic shapes.

In a linear motor, magnetic poles on a stator (or moving
element) and teeth on a moving element (or stator) face one another to form a gap.
The cogging force of the linear motor is settled depending on the shapes of the
magnetic poles and the teeth that are opposed to the poles. In order to lower the
cogging force, therefore, various magnetic poles or teeth having special shapes
have been proposed.

FIG. 11 shows a prior art example of a stator or moving
element (slider) of which the magnetic poles are formed of permanent magnets. The
stator or slider is constructed in a manner such that a plurality of permanent magnets
1 are arranged parallel to one another on a plate 10 that is formed of a magnetic
material such as iron. If each permanent magnet 1 is cut in a direction parallel
to the direction of relative movement of the slider with respect to the stator,
in the example shown in FIG. 11, the gap-side external shape of its cross section
is a straight line 31. Thus, the gap-side surface (the surface opposite the plate
10) of each magnet 1 is flat.

FIGS. 12 to 14 show alternative prior art examples of the
stator or moving element of which the magnetic poles are formed of permanent magnets.
If each of permanent magnets 1 that are arranged side by side on a plate 10 is cut
in a direction parallel to the direction of relative movement of the slider with
respect to the stator, in the example shown in FIG. 12, the gap-side external shape
of its cross section is a circular arc 32. Likewise, in the example shown in FIG.
13, the gap-side external shape of the cross section of each permanent magnet 1
is a parabola 33. In the example shown in FIG. 14, the gap-side external shape of
the cross section of each permanent magnet 1 is a hyperbola 34. Such pole shapes
are disclosed in JP(A)03207256.

As described above with reference to FIGS. 11 to 14, many
attempts have been made to vary the shapes of the magnetic poles to lower the cogging
force. Pole shape variation for other purposes is found in EP-A-1164684 and DE-C-19829052.

The object of the present invention is to provide a linear
motor of which the cogging force is reduced.

According to the present invention there is provided a
linear motor having two members which are to move relatively to one another in a
linear manner with a gap between the two members and on at least one of the two
members the gap-side surface of each magnetic pole and/or tooth forming a gap portion
comprises a curred shape the whole of which is represented by a reciprocal function
of cosine in trigonometric function, whereby cogging force of the linear motor is
reduced owing to said curred shape function of said gap-side surface.

The reciprocal function of cosine in trigonometric function
may be given by
$$\mathrm{R}=\mathrm{A}-\mathrm{B}/\mathrm{cos}\left(\mathrm{C}\mathrm{\&thgr;}\right),$$
where R is the distance from a certain point on the center line of each magnetic
pole or each tooth opposite thereto, &thgr; is the angle to the center line, and
A, B and C are constants. Alternatively, furthermore, the reciprocal function of
cosine in trigonometric function, in an XY coordinate system in which the central
axis of each magnetic pole or each tooth opposite thereto is the X-axis and an axis
perpendicular to the X-axis is the Y-axis, and the point of intersection of the
X- and Y-axes is the origin, may be given by
$$\mathrm{X}=\mathrm{A}-\mathrm{B}/\mathrm{cos}\left(\mathrm{C}\mathrm{Y}\right),$$
where A, B and C are constants.

With the above construction, the cogging force of a motor
according to the present invention can be made lower than that of a conventional
motor.

BRIEF DESCRIPTION OF THE DRAWINGS

- FIG. 1 is a view illustrating a stator or slider according to an embodiment
which is not part of the invention, of which the magnetic poles are formed of permanent
magnets;
- FIG. 2 is a view illustrating a stator or slider according to another embodiment
which is not part of the invention, of which the magnetic poles are formed of permanent
magnets ;
- FIG. 3 is a view illustrating a stator or slider according to a further embodiment
which is not part of the invention, of which the magnetic poles are formed of permanent
magnets;
- FIG. 4 is a view illustrating a stator or slider on the non-exciting side according
to yet another embodiment which is not part of the invention, in which a linear
motor is formed of a reluctance-type motor;
- FIG. 5 is a view illustrating a stator or slider according to a first embodiment
of the invention, of which the magnetic poles are formed of permanent magnets;
- FIG. 6 is a view illustrating a stator or slider according to a second embodiment
of the invention, of which the magnetic poles are formed of permanent magnets;
- FIG. 7 is a view illustrating a stator or slider according to a third embodiment
of the invention, of which the magnetic poles are formed of permanent magnets;
- FIG. 8 is a view illustrating a stator or slider on the non-exciting side according
to a fourth embodiment of the invention, in which a linear motor is formed of a
reluctance-type motor;
- FIG. 9 is a view showing a model configuration for linear motors for the comparison
of cogging forces generated in a linear motor of the invention and a conventional
linear motor;
- FIG. 10 is a diagram showing external shapes of magnetic poles for comparison;
- FIG. 11 is a view illustrating a stator or slider of a conventional linear motor
of which the cross section of each magnetic pole has a straight external shape;
- FIG. 12 is a view illustrating a stator or slider of a conventional linear motor
of which the cross section of each magnetic pole has a circular external shape;
- FIG. 13 is a view illustrating a stator or slider of a conventional linear motor
of which the cross section of each magnetic pole has a parabolic external shape;
and
- FIG. 14 is a view illustrating a stator or slider of a conventional linear motor
of which the cross section of each magnetic pole has a hyperbolic external shape.

Figs 1 to 4 show embodiments which are not in accordance
with the present invention, and which are included merely for completeness.

FIG. 1 is a view illustrating a stator or slider (moving
element) according to an embodiment of which the field poles are formed of permanent
magnets.

The stator or slider is constructed in a manner such that
a plurality of permanent magnets 1 to form the magnetic poles are arranged parallel
to one another on a plate 10 that is formed of a magnetic material such as iron.
An external shape 20 of the cross section of each permanent magnet 1 on the gap
side (the side opposite the plate 10) can be represented by a hyperbolic function
according to this embodiment.

Thus, when the permanent magnets 1 are cut in the direction
of their arrangement, that is, in the direction parallel to the relative movement
of the slider with respect to the stator (horizontal direction of FIG. 1), the gap-side
external shape 20 of the cross section of each permanent magnet 1 can be represented
by a hyperbolic function.

A center line indicated by dashed line in FIG. 1 is supposed
to be the X-axis. This line passes through the center of the cross section of each
permanent magnet 1 and extends in the vertical direction (direction in which the
magnetic poles face teeth across a gap). Thereupon, the hyperbolic function can
be given by
$$\mathrm{R}=\mathrm{A}-\mathrm{B}\ast \left({\mathrm{e}}^{\mathrm{C}\mathrm{\&thgr;}}+{\mathrm{e}}^{-\mathrm{C}\mathrm{\&thgr;}}\right),$$
where R is the distance from a certain point on the X-axis, &thgr; is the angle
to the X-axis, A, B and C are constants, and e is the base of a natural logarithm
or a constant.

If an axis that horizontally extends at right angles to
the X-axis (in the direction of relative movement of the slider with respect to
the stator) is the Y-axis, FIG. 1 shows the respective cross sections of the permanent
magnets 1 on the XY-plane. In this XY coordinate system, the aforesaid hyperbolic
function is given by
$$\mathrm{X}=\mathrm{A}-\mathrm{B}\ast \left({\mathrm{e}}^{\mathrm{C}\mathrm{Y}}+{\mathrm{e}}^{-\mathrm{C}\mathrm{Y}}\right),$$
where A, B and C are constants, and e is the base of a natural logarithm or a constant.

As seen from equation (2), X has its maximum when Y is
zero. In other words, X = A - 2B is obtained when Y = 0 is given. Thus, the vertex
of each permanent magnet 1 shown in FIG. 1 is on the X-axis, and the origin (0,
0) of the XY coordinate system is in a position on the X-axis that is lower than
the vertex by (A - 2B).

The cogging force can be lessened by creating the shape
20 represented by the hyperbolic function given by equation (1) or (2) over the
whole surface of each permanent magnet 1 that faces the gap. Alternatively, the
cogging force can be lessened by creating the same shape only over the region near
the vertex of each permanent magnet 1 (central region covering the X-axis).

FIG. 2 is a view illustrating a stator or slider according
to another embodiment not of the invention, of which the field poles are formed
of permanent magnets. In this embodiment, a core 2 is bonded to the top of each
permanent magnet 1, as shown in FIG. 2. The combined cross section of the magnet
1 and the core 2 has the same shape with the cross section of each permanent magnet
1 shown in FIG. 1. Thus, the gap-side external shape 20 of the cross section of
the core 2 can be represented by the aforesaid hyperbolic function. This embodiment
has the same construction with the first embodiment shown in FIG. 1 except for the
shape of the cross section of each permanent magnet 1.

FIG. 3 is a view illustrating a stator or slider according
to a further embodiment not of the invention, of which the field poles are formed
of permanent magnets. In this embodiment, a core 2 covers each permanent magnet
1, as shown in FIG. 3. The cross section of the covered magnet 1 has the same shape
with that of each permanent magnet 1 shown in FIG. 1. Thus, the gap-side external
shape 20 of the cross section of the core 2 can be represented by the aforesaid
hyperbolic function. This embodiment has the same construction with the first embodiment
shown in FIG. 1 except for the shape of the cross section of each permanent magnet
1.

FIG. 4 is a view illustrating yet another embodiment not
of the invention, in which a linear motor is formed of a reluctance-type motor,
and shows the configuration of teeth of a stator or slider on the no-coil side (secondary
side) to which no power is supplied. For the stator or slider that constitutes the
linear motor, the side to which power is supplied is referred to as the primary
side, and the side to which no power is supplied is referred to as the secondary
side, hereinafter.

In the case of the reluctance-type motor, teeth 3 on the
secondary side are formed of cores. In the linear motor of FIG. 4, the gap-side
external shape 20 of the cross section of each tooth 3 that is formed of a core
is represented by the aforesaid hyperbolic function. Thus, the cross section of
each tooth 3 shown in FIG. 4 resembles that of each permanent magnet 1 shown in
FIG. 1 (first embodiment).

In the first to fourth embodiments described above, the
cogging force can be lessened by creating the shape 20 represented by the hyperbolic
function given by equation (1) or (2) over the whole surface of each magnetic pole
(permanent magnet 1) or tooth 3 that faces the gap.

FIGS. 5 to 8 are, views illustrating stators or sliders
according to first to fourth embodiments of the invention, respectively, of which
the magnetic poles are formed of permanent magnets. In the embodiments of FIGS 1
to 4 described above, the external shape of the cross section of each magnetic pole
or tooth that faces the gap of the motor can be represented by the hyperbolic function
given by equation (1) or (2). In the first to fourth embodiment of the invention,
on the other hand, the cross section has an external shape represented by a reciprocal
function of cosine in trigonometric function in place of the hyperbolic function.

In the first inventive embodiment shown in FIG. 5, an external
shape 21 of the cross section of each permanent magnet 1 that constitutes a magnetic
pole can be represented by a reciprocal function of cosine. This embodiment has
the same construction with the embodiment shown in FIG. 1 except for the shape of
the cross section of each permanent magnet 1.

As in the case of FIG. 1, a center line that passes through
the center of the cross section of each permanent magnet 1 and extends in the vertical
direction (direction in which the magnetic poles face teeth across a gap) is supposed
to be the X-axis. Further, a line that horizontally extends at right angles to the
X-axis (in the direction of relative movement of the slider with respect to the
stator) is supposed to be the Y-axis. Thereupon, FIG. 5 shows the respective cross
sections of the permanent magnets 1 on the XY-plane. The gap-side external shape
of the cross section of each permanent magnet 1 can be represented by a reciprocal
function of cosine in trigonometric function of the following equation:
$$\mathrm{R}=\mathrm{A}-\mathrm{B}/\mathrm{cos}\left(\mathrm{C}\mathrm{\&thgr;}\right),$$
where R is the distance from a certain point on the X-axis, &thgr; is the angle
to the X-axis, and A, B and C are constants.

Using the XY coordinate system, moreover, the gap-side
external shape of the cross section of each permanent magnet 1 can be represented
by a reciprocal function of cosine in trigonometric function of the following equation:
$$\mathrm{X}=\mathrm{A}-\mathrm{B}/\mathrm{cos}\left(\mathrm{C}\mathrm{Y}\right),$$
Where A, B and C are constants. In equation (4), X has its maximum when Y is zero.
In other words, X = A - B is obtained when Y = 0 is given. Thus, the vertex of each
permanent magnet 1 shown in FIG. 5 is on the X-axis, and the origin (0, 0) of the
XY coordinate system is in a position on the X-axis that is lower than the vertex
by (A - B).

The second inventive embodiment shown in FIG. 6 has the
same construction with the first inventive embodiment shown in FIG. 5 except that
a core 2 is bonded to the top of each permanent magnet 1. The combined cross section
of the magnet 1 and the core 2 has the same shape with the cross section of each
permanent magnet 1 shown in FIG. 5. Thus, the gap-side external shape of the cross
section of the core 2 can be represented by the reciprocal function of cosine in
trigonometric function given by equation (3) or (4).

The third inventive embodiment shown in FIG. 7 has the
same construction with the first inventive embodiment shown in FIG. 5 except that
a core 2 covers each permanent magnet 1. The cross section of the covered magnet
1 has the same shape with that of each permanent magnet 1 shown in FIG. 5. Thus,
the gap-side external shape 21 of the cross section of the core 2 can be represented
by the reciprocal function of cosine in trigonometric function given by equation
(3) or (4).

In the fourth inventive embodiment shown in FIG. 8, as
in the non-inventive embodiment shown in FIG. 4, a reluctance-type linear motor
has a stator or slider on its secondary side. This embodiment has the same construction
with the embodiment of FIG. 4 except for the shape of the cross section of each
tooth 4. A gap-side external shape 21 of the cross section of each tooth 4 shown
in FIG. 8 can be represented by the reciprocal function of cosine in trigonometric
function given by equation (3) or (4).

In these inventive embodiments shown in FIGS. 5 to 8, the
cogging force is lessened by creating the shape 21 represented by the reciprocal
function of cosine given by equation (3) or (4) over the whole surface of each magnetic
pole (permanent magnet 1) or tooth 4 that faces the gap.

Each permanent magnet 1 shown in FIG. 1 or each tooth 3
shown in FIG. 4 is worked so that its cross section has the gap-side external shape
20 represented by the hyperbolic function. Alternatively each permanent magnet 1
shown in FIG. 5 or each tooth 4 shown in FIG. 8 is worked so that its cross section
has the gap-side external shape 21 represented by the reciprocal function of cosine
in trigonometric function. In doing this, a plurality of points set on the shape
20 or 21 are connected by means of a straight or curved line. If the cross section
of each core 2 has the gap-side external shape 20 represented by the hyperbolic
function or the shape 21 represented by the reciprocal function of cosine in trigonometric
function, as in the embodiment shown in FIG. 2, 3, 6 or 7, the shape 20 or 21 is
created by successively laminating thin steel sheets to one another.

To examine the advantageous effect of the present invention,
a test was conducted to compare a prior art example in which the external shape
of each magnetic pole or tooth is a straight line circular arc; parabola, or hyperbola,
the first non-inventive embodiment shown in FIG. 1 in which the external shape of
each magnetic pole or tooth can be represented by a hyperbolic function, and the
first inventive embodiment shown in FIG. 5 in which the external shape of each magnetic
pole or tooth can be represented by a reciprocal function of cosine in trigonometric
function.

FIG. 9 shows a common configuration for tested linear motors.
In FIG. 9, a slider 60 is on the primary side (power supply side), and a stator
50 is on the secondary side. The stator 50 is formed of a plurality of permanent
magnets 1 arranged side by side on the plate 10. The slider 60 is provided with
core teeth 40 wound with a coil. The coil to be wound on the teeth 40 is not shown
in FIG. 9.

The depth of each permanent magnet (magnetic pole) 1 (in
the direction perpendicular to the drawing plane in FIGS. 1, 5, 11, 12 and 13) is
fixed, and the gap between the stator 50 and the slider 60 (gap between the vertex
of each permanent magnet 1 and the distal end of each corresponding tooth 40 in
FIG. 9) is also fixed. Further, the maximum height of each permanent magnet 1 (distance
from the upper surface of the plate 10 to the vertex of each magnet 1) and its volume
are fixed. However, only the gap is fixed for each permanent magnet 1 of which the
cross section has a straight gap-side external shape, as shown in FIG. 11.

FIG. 10 shows the gap-side external shapes of the respective
cross sections of these magnetic poles (permanent magnets) for comparison. In FIG.
10, shapes represented by a reciprocal function of cosine in trigonometric function,
hyperbolic function, circular arc, parabola (broken line), and hyperbola are drawn
ranging from outside to inside in the order named. The shapes represented by the
circular arc and the parabola (broken line) are substantially coincident with each
other.

The following table shows the result of measurement of
cogging force. The cogging force is given in Newton (N), a unit of force, and the
ratio is based on the shape represented by the hyperbolic function.
External shape of
magnetic pole:
Cogging force:
Ratio

Reciprocal
function of cosine
25.0
N
-16.2%

Hyperbolic function
29.8
N
0

Circular arc
31.0
N
+3.9%

Parabola
31.7
N
+6.5%

Hyperbola
35.2
N
+18.0%

Straight line
89.6
N
201.0%

Thus, the cogging force has its minimum when the magnetic
poles have an external shape represented by the reciprocal function of cosine in
trigonometric function. The second lowest cogging force is obtained with use of
an external shape represented by the hyperbolic function.

As mentioned before, according to the invention the gap-side
external shape of the cross section of each magnetic pole or tooth, cut in a direction
parallel to the direction of relative movement of the slider with respect to the
stator, is the shape represented by the reciprocal function of cosine in trigonometric
function throughout its area.

According to the inventive embodiments described above,
each magnetic pole or tooth on the secondary side has an external shape represented
by the reciprocal function of cosine in trigonometric function. However, the same
effect can be obtained by using the shape represented by the reciprocal function
of cosine in trigonometric function for the external shape of each tooth or magnetic
pole on the primary side. In this case, each magnetic pole or tooth on the secondary
side may be formed having the straight shape shown in FIG. 11. Alternatively, in
an inventive embodiment each magnetic pole or tooth on each of the primary and secondary
sides may be formed having an external shape represented by the reciprocal function
of cosine in trigonometric function.