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 torque 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 torque, 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.

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
torque.

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

According to the present invention there is provided a
linear motor or a member therefor, designed so that the external shape of the gap-side
surface of each magnetic pole and/or tooth forming a gap portion consists mainly
of a shape represented by a hyperbolic function or a reciprocal function of cosine
in trigonometric function. More specifically, the whole or a part of the external
shape of the gap-side surface or its central portion may be a shape represented
by a hyperbolic function or a reciprocal function of cosine in trigonometric function.

The hyperbolic function may be given by
$$\mathrm{R}=\mathrm{A}-\mathrm{B}*({\mathrm{e}}^{\mathrm{C\&thgr;}}+{\mathrm{e}}^{-\mathrm{C\&thgr;}}),$$

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, A,
B and C are constants, and e is the base of a natural logarithm or a constant. Alternatively,
the hyperbolic function, in an XY coordinate system in which the central axis of
each magnetic pole or each tooth opposite thereto is the X-axis, 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
$$\mathrm{X}=\mathrm{A}-\mathrm{B}*({\mathrm{e}}^{\mathrm{CY}}+{\mathrm{e}}^{-\mathrm{CY}}),$$

where A, B and C are constants, and e is the base of a natural logarithm or a constant.

Alternatively, moreover, the reciprocal function of cosine
in trigonometric function may be given by
$$\mathrm{R}=\mathrm{A}-\mathrm{B}/\mathrm{cos}\left(\mathrm{C\&thgr;}\right),$$

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
$$\mathrm{X}=\mathrm{A}-\mathrm{B}/\mathrm{cos}\left(\mathrm{CY}\right),$$

where A, B and C are constants.

Further, rows of points on the external shape represented
by the aforesaid function may be connected by means of a straight or curved line.

With the above construction, the cogging torque 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 a first embodiment
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 a second embodiment
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 third embodiment
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 a fourth embodiment 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 fifth 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 sixth 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 seventh 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 an eighth 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 torques 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.

FIG. 1 is a view illustrating a stator or slider (moving
element) according to a first embodiment of the present invention, 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
$$\mathrm{R}=\mathrm{A}-\mathrm{B}*({\mathrm{e}}^{\mathrm{C\&thgr;}}+{\mathrm{e}}^{-\mathrm{C\&thgr;}}),$$

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
$$\mathrm{X}=\mathrm{A}-\mathrm{B}*({\mathrm{e}}^{\mathrm{CY}}+{\mathrm{e}}^{-\mathrm{CY}}),$$

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 torque 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 torque 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 a second embodiment 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 third embodiment 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 a fourth embodiment 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 the fourth embodiment,
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 torque 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. Alternatively, the cogging torque
can be lessened by creating the same shape only over the region near the vertex
of the aforesaid surface (central region covering the X-axis).

FIGS. 5 to 8 are views illustrating stators or sliders
according to fifth to eighth embodiments of the invention, respectively, of which
the magnetic poles are formed of permanent magnets. In the first to fourth embodiments
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 fifth to eighth embodiments, 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 fifth 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 first 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:
$$\mathrm{R}=\mathrm{A}-\mathrm{B}/\mathrm{cos}\left(\mathrm{C\&thgr;}\right),$$

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:
$$\mathrm{X}=\mathrm{A}-\mathrm{B}/\mathrm{cos}\left(\mathrm{CY}\right),$$
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 sixth embodiment shown in FIG. 6 has the same construction
with the fifth 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 seventh embodiment shown in FIG. 7 has the same construction
with the fifth 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 eighth embodiment shown in FIG. 8, as in the fourth
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 fourth
embodiment 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 embodiments shown in FIGS. 5 to 8, the cogging
torque can be 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. Alternatively, the cogging torque
can be lessened by creating the same shape only over the central region of each
permanent magnet 1 or tooth 4 that covers the X-axis.

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 embodiment of the invention shown in FIG. 1 in which the external shape
of each magnetic pole or tooth can be represented by a hyperbolic function, and
the alternative 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 torque. The cogging torque 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 torque:
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 torque 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 torque is obtained with use of
an external shape represented by the hyperbolic function.

As mentioned before, 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, may be
the shape represented by the reciprocal function of cosine in trigonometric function
or the hyperbolic function throughout the area. Since the peripheral region of each
magnetic pole or tooth has a small influence, however, the same effect can be obtained
by only using the shape represented by the reciprocal function of cosine in trigonometric
function or the hyperbolic function for the central region near the vertex of each
magnetic pole or tooth.

According to the 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 or the hyperbolic function. However,
the same effect can be obtained by using the shape represented by the reciprocal
function of cosine in trigonometric function or the hyperbolic 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, 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 or the hyperbolic function.