JP2010216518A - Gear without transmission error and backlash - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a gear that a well-known transmission error and play can be processed to be zero. <P>SOLUTION: The gear without transmission error and backlash, wherein: when a profile of a gear is set to be circle, tip engagement becomes zero in play; when a ratio of diameter is set to be one-to-one, a correct transmission angle exists in a range of play in the other angle; when the same engagement is set to be one period, and a plane gear is processed to be helical gear by differential lamination, an engagement with phase shift exists on the lamination at a pitch point, and a behavior of a gear is limited within a section with zero play; the helical gear with a lamination phase width of 1/2 period or more can be processed to be zero in the transmission error and play; a margin of a gear can be set by eliminating an overlap section in a collision direction of the tip engagement; the gear with a different gear ratio can be constructed on a spherical surface in such a way that the transmission error and play are set to be zero by eliminating the overlap of engagement; and in a spiral bevel gear with a concentric lamination of sphere, a gear of the previous application is constructed with crossing angles of all shafts, a gear of the present application, however, can be extended in a definition of obtainable profile. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a gear device in which a helical gear having a tooth shape based on an arc is combined, and more particularly to a gear device including a helical gear and a spiral bevel gear that can extremely reduce transmission errors and backlash.

  Conventionally, with spur gears, gears with round teeth, which tend to increase transmission error and play, are rarely used, but there are some exceptions for gears with round teeth. Gears are known. One of them is a gear using an arc tooth profile, and at least a part of the tooth profile curve from the contact start point to the point where the engagement rate is 1 is on the pitch circle. There are known ones that have a center and are smoothly connected to the tooth profile curves on both sides thereof (see, for example, Patent Document 1).

Japanese Patent Laid-Open No. 11-94052 Japanese Patent Laid-Open No. 49-9524 JP 50-152146 A Japanese Patent Laid-Open No. 51-13047 JP-A-53-22294 JP 2008-138874 A PCT / JP2008 / 066053 Japanese Patent Application No. 2009-26732

In the conventional round spur gear, the gear size is mainly determined by the size of the tooth profile reference circle and the number of teeth, and there is no deviation margin in the collision direction. There wasn't. For this reason, the design based on the conventional ellipse is used, and the tooth shape is applied as it is to a helical gear having a helical tooth row.
For this reason, it has not been possible to design a gear that eliminates backlash, which is a gap between the pitch circles between meshing gears, and that has zero transmission error.
Therefore, in view of the above technical problem, an object of the present invention is to provide a gear device that extremely reduces backlash and transmission error.
The above is the subject of PCT / JP2008 / 066053 of application previously.

  In the previously filed PCT / JP2008 / 066053, gears having a transmission error and a backlash close to zero can be configured only when their rotational axes are parallel to each other. Therefore, in Japanese Patent Application No. 2009-26732, the mutual rotational axes are This is to construct a gear that can mesh at all angles other than parallel and has transmission error and backlash close to zero.

  In the present application, a shape that can constitute a gear having transmission error and backlash close to zero will be deeply examined, and the embodiments of PCT / JP2008 / 066053 and Japanese Patent Application No. 2009-26732 of the earlier application will be deepened. .

  In order to solve the above-described problems, the gear device of the present invention is a first outer shape on which a spur gear is planarly laminated in the axial direction and is shifted by a predetermined angle to form an envelope of the outer shape of the gear. A helical gear having a line as an outer shape, and a gear device combined so that the helical gears mesh with each other, and a spherical surface gear is axially concentrically stacked on a spherical surface as a second form. A spiral bevel gear whose outer shape is an envelope of a gear outer shape formed around the axis by shifting by a predetermined angle, and a gear device combined so as to mesh the spiral bevel gears, on the plane and on the spherical surface In the above, one or a plurality of tooth profile reference circles, the center is located on the circumference of the gear reference circle, the gear reference circle outer peripheral side or the gear reference circle inner peripheral side of the tooth reference reference circle, The shape along the circumference of the vehicle reference circle is the outer shape, and the outer shape is configured on a flat surface or a spherical surface. The outer shape on the tooth reference circle on the outer circumference side of the gear reference circle and the inner circumference side of the gear reference circle The tooth tip and root set is a tooth shape that is part of the sliding contact portion and the surface sliding contact portion on one of the sliding contact side portions on the tooth profile reference circle, and is transmitted correctly. In the angle, the part overlapping with the part sliding contact part is deleted, and the other meshing overlapping part is to delete one of the overlapping parts of the meshing. The tooth shape of the part is configured, and all the meshes of the gear device laminated in plane and concentric spheres have meshing phase widths constituting the transmission sliding contact part, and all meshing is a correct transmission angle. It is characterized by that.

In order to solve the above-described problems, the gear device of the present invention is configured such that the tooth profile reference circle is a double concentric and different in diameter, and one of the sliding contact side portions is configured with a small diameter tooth profile reference circle, The other is composed of a large-diameter tooth reference circle.

  In the gear device of the present invention, in the configuration of the tooth profile reference circle, the tooth profile reference circle whose center is located on the circumference of the gear reference circle is continuously disposed, and the tooth profile reference on the outer periphery side of the gear reference circle is provided. A circle and a tooth reference circle on the inner circumference side of the gear reference circle are alternately formed as outer shapes, the part other than the meshing reference point is set as the partly sliding part, and the meshing overlapping part overlapping the partly sliding part is provided. It deletes, and the other meshing overlap part is characterized by deleting either one of the meshing overlapping parts.

  The gear device of the present invention will be described by the following terms in the present specification and claims. First, the “gear reference circle” is a reference circle centered on the rotation axis of the gear. In the present invention, the center of the tooth profile reference circle described below is arranged on the circumference. The “tooth profile reference circle” is a circle used as a reference for forming the tooth tip, the tooth bottom, and the tooth surface of the gear of the present invention. They are in contact with each other. These “Gear Reference Circle” and “Tooth Profile Reference Circle” are not actual gear outlines, but are virtual diagrams to be considered at the design stage, and are cross sections perpendicular to the gear rotation axis. The technical idea is to form a helical gear by superimposing a planar spur gear (spar gear) in the axial direction and shifting it by a predetermined angle to make the outer contour of the gear outer shape formed around the shaft. It is said. The “gear plane shape” indicates a cross section of the gear perpendicular to the rotation axis, and refers to the shape of the spur gear that is the basis for forming the envelope of the gear outer shape.

"Spherical surface gear" is a gear configured on the surface of a perfect sphere, and the above-mentioned gear plane shape is replaced with a spherical surface, and the rotation axis of the spherical surface gear extends through the center of the sphere. It has a thickness in the radial direction from the center of the sphere, and is a unique expression of the present invention.
“Concentric sphere stack” is a structure in which the surfaces of a plurality of spheres having the same center can form a plurality of sphere surfaces by the difference in the diameters of the spheres. The surface gears can mesh with each other and rotate on each spherical surface, and the size of the spherical surface gear on each sphere surface changes in proportion to the diameter of each sphere, so that the same meshing on each sphere surface. The spherical surface gears on the surface of each sphere are continuously laminated according to the conditions described in the present invention, and a smooth spiral is obtained by making the spherical surface gears as thin as possible. It can be a bevel gear and is an expression unique to the present invention.
In addition, when the definition on the plane in the present invention is changed to the definition on the spherical surface, the definition on the plane and the definition on the sphere surface are replaced. The definition of distance indicates the distance on the surface of the sphere, and the definition of straight line replaces the definition of a line on the surface of the sphere that looks straight from the center of the sphere.

“Gear reference circle outer circumference side” and “Gear reference circle inner circumference side” are the outer circumference side and the inner circumference side as seen from the gear reference circle, and distinguish the outer circumference side and the inner circumference side of the tooth profile reference circle. .
“Planar stacking” corresponds to concentric sphere stacking in which spur gears (spar gears) are stacked in the axial direction and shifted by a predetermined angle within a cross section perpendicular to the rotation axis of the gear. Further, a smooth helical gear can be obtained by making the spur gear (spar gear) as thin as possible.
The “helical gear” is a flat gear in which plane gears are stacked in stages.
The “spiral bevel gear” is a concentric sphere laminated with spherical surface gears.
The “sliding contact side portion” branches the meshing of the gear at the center line of the meshing apex, and shows one sliding contact portion and the other sliding contact portion separately.
“Transmission slidable contact portion” means the slidable contact side portions on both sides of the gear meshing at the correct transmission angle, and in the case of a stacked gear, any one of the multiple slidable contact side portions stacked. The sliding contact side portions on both sides of the correct transmission angle are shown.
The “partly slidable contact portion” indicates a portion on the circumference of the tooth profile reference circle of the tooth profile having a part of the tooth profile reference circle as an outer shape. The “surface sliding contact portion” is a portion on the circumference of the tooth profile reference circle of the tooth profile having the curved surface of the tooth profile reference circle as an outer shape, and indicates a surface in which a part of the slide contact portion is slidably engaged. .

According to PCT / JP2008 / 066053 previously filed, helical gears can be combined to reduce transmission errors and to set backlash close to zero. A new tooth-shaped gear design method makes gear transmission error and backlash close to zero, and can accurately transmit the rotation angle. As a secondary effect, vibration and driving sound can be reduced. Furthermore, since the transmission error is extremely small, it is possible to perform smooth high-speed rotation with less stress at high-speed rotation. Further, since the transmission error is extremely small, energy loss is small and energy is saved.
The above-mentioned PCT / JP2008 / 066053 was a meshing of gears only when the mutual rotation axes were parallel, but according to Japanese Patent Application No. 2009-26732 of the next application, all the rotation axes other than the parallel rotations. Engagement at an angle is possible.
This application deepens the definition of the shape of the above-mentioned application that makes transmission error and backlash zero.

It is a top view of the single tooth tip gear and single tooth bottom gear of the present invention. It is a top view of the gear of a circular tooth. It is a schematic diagram which shows the rotational movement of the circular tooth (tooth profile reference | standard circle) of the apparatus which makes diameter ratio 1: 1. It is a schematic diagram which shows the rotational movement of the gear whose tooth profile reference | standard circle of an apparatus which makes diameter ratio 1: 1 is an ellipse. It is a schematic diagram which shows the mode of engagement of -25.71 degree | times of the circular teeth of 7 teeth and diameter ratio of 1: 1. It is a schematic diagram which shows the mode of engagement of -12 degree | times of the circular tooth of 7 teeth and diameter ratio 1: 1. It is a schematic diagram which shows the mode of a 0 degree mesh | engagement of the circular tooth whose diameter ratio is 1: 1 with 7 teeth. It is a schematic diagram which shows the mode of 7 degree | times meshing of the circular tooth whose diameter ratio is 1: 1 with 7 teeth. It is a schematic diagram which shows the mode of 12 degree | times meshing of the circular tooth whose diameter ratio is 1: 1 with 7 teeth. It is a schematic diagram which shows the mode of engagement of 25.71 degree | times of the circular tooth whose diameter ratio is 1: 1 with 7 teeth. It is a schematic diagram which shows the mode of 0 degree mesh | engagement of the conventional tooth of 7 teeth and diameter ratio 1: 1. It is a schematic diagram which shows the mode of 7 degree | times meshing of the conventional tooth with a diameter ratio of 1: 1 with 7 teeth. It is a schematic diagram which shows the mode of 13 degree | times meshing of the conventional tooth of 7 teeth and the diameter ratio of 1: 1. It is a graph which shows the backlash of the meshing phase of a circular tooth. It is a graph which shows the backlash of the meshing phase of the conventional tooth. It is a perspective view of the helical gear of the conventional tooth and a circular tooth. FIG. 3 is a schematic view of a helical gear configured by laminating gear plane shapes of circular spur gears. It is a schematic diagram at the time of seeing the helical gear of a circular tooth from the side. It is a schematic diagram which shows the gear apparatus in the place where the tooth tip and the tooth base which do not affect the meshing of the circular teeth are cut off. It is a schematic diagram which shows the gear apparatus in which a circular tooth overlaps in the center line direction. It is a schematic diagram which shows the gear apparatus in which the deviation tolerance of a circular tooth was included. It is a schematic diagram of the meshing of the tooth profile reference circle of 30 teeth to 3 teeth. It is an enlarged view of the meshing overlapping part shown in FIG. It is a figure of the locus | trajectory of a movement of the tooth profile standard circle of 30 teeth versus 3 teeth. It is a figure of comparison of the movement locus | trajectory of the tooth tip shown in FIG. It is a comparison figure of the tooth profile of 30 teeth versus 3 teeth. It is a comparison figure of the depth of the tooth base of 30 teeth versus 3 teeth. It is a figure of the tooth profile reference | standard circle | round | yen of engagement, and a circular-tooth centerline. It is a whole view of the tooth profile standard circle which constitutes a gear. It is a figure which leads the calculation of the length of the circle tooth center line of meshing pattern 1 (CASE1). It is a figure which leads the calculation of the length of the circle tooth center line of meshing pattern 2 (CASE2). It is a figure which leads the calculation of the distance of the meshing reference point of meshing pattern 3 (CASE3), and the center of a tooth profile standard circle. It is a calculation table | surface of the change of the distance of the circle tooth | gear centerline of the meshing pattern 1 and 2 of 6 teeth 6 teeth. It is a calculation table | surface of the change of the distance of the meshing reference point of the meshing pattern 3 of 6 teeth versus 6 teeth, and the center of a tooth profile reference circle. It is a calculation table | surface of the change of the distance of the circle tooth | gear centerline of the meshing pattern 1 of 2 teeth | gears 30 teeth. It is a calculation table | surface of the change of the distance of the meshing reference point of the meshing pattern 3 of 3 teeth pair 30 teeth, and the center of a tooth profile standard circle. It is a figure of the meshing phase 0 degree | times shape | molded by the 4th condition of 3 teeth versus 30 teeth. It is a figure of the meshing phase 30 degree | times shape | molded by the 4th condition of 3 teeth versus 30 teeth. It is a figure of the meshing | locking phase 10 degree | times shape | molded by the 4th condition of 3 teeth versus 30 teeth. It is an enlarged view of the contact surface of the gear apparatus shown in FIG. It is a figure of meshing phase 2 degree | times shape | molded of the 4th condition of 3 teeth versus 30 teeth. It is an enlarged view of the contact surface of the gear apparatus shown in FIG. It is a figure of the meshing phase -55 degree | times shape | molded of the 4th condition of 3 teeth versus 30 teeth with a meshing phase width of 1/2 period. It is an enlarged view of the contact surface of the gear apparatus shown in FIG. It is a figure of meshing phase -55 degree | times shape | molded of the 4th condition of 3 teeth versus 30 teeth of meshing phase width of 1 period. It is an enlarged view of the contact surface of the gear apparatus shown in FIG. It is the perspective view which has arranged the gear standard circle and the tooth profile standard circle on the sphere surface. It is sectional drawing for the design concept which concentrically laminated | stacked the spherical surface gear on the intermittent 4 layers. FIG. 6 is a perspective view in which gear reference circles on the sphere surface are stacked concentrically to the center of the sphere. It is a perspective view which shows the spiral bevel gear which a rotation axis intersects. It is a schematic diagram which shows a mode that a single-tooth tip gear meshes at −46.6 degrees. It is a schematic diagram which shows a mode that a single-tooth tip gear meshes at −30 degrees. It is a schematic diagram which shows a mode that a single tooth tip gear meshes with 0 degree. It is a graph which shows the backlash of the meshing phase of a single-tooth tip gear and a single-tooth bottom gear. It is a top view of the single-tooth tip double-tooth shape reference circular gear and the single-tooth bottom double-tooth shape reference circular gear with the tooth tip deleted. It is a schematic diagram which shows a mode that the single tooth tip double-tooth profile reference circular gear meshes at −42.81 degrees. It is a schematic diagram which shows a mode that a single-tooth tip double tooth profile reference circular gear meshes at -20 degrees. It is a schematic diagram which shows a mode that the single-tooth tip double-tooth shape reference circular gear meshes with 0 degree. It is a schematic diagram which shows a mode that the single-tooth tip double tooth profile reference circular gear meshes 10 degrees. It is a schematic diagram which shows a mode that the single-tooth tip double tooth profile reference circular gear meshes 30 degrees. It is a schematic diagram which shows a mode that the single-tooth tip double tooth profile reference circular gear meshes at 38.37 degrees. It is a graph which shows the backlash of the meshing phase of the single-tooth tip double-tooth shape reference circular gear and the single-tooth bottom double-tooth shape reference circular gear in which the tooth tip is deleted. It is a top view of the single-tooth tip double-tooth shape reference circular gear and the single-tooth bottom double-tooth shape reference circular gear in which the root is deleted. It is a model which shows a mode that the single-tooth tip double-tooth profile circular gear meshes at −46.58 degrees. It is a schematic diagram which shows the mode of mesh | engagement of a single tooth tip double tooth profile standard circular gear of -19.5 degree | times. It is a schematic diagram which shows the mode of mesh | engagement of a single tooth tip double tooth shape standard circular gear of -16.7 degree | times. It is a schematic diagram which shows a mode that a single-tooth tip double tooth profile reference circular gear meshes by -10 degrees. It is a schematic diagram which shows a mode that the single-tooth tip double-tooth shape reference circular gear meshes with 0 degree. It is a schematic diagram which shows a mode that the single-tooth tip double tooth profile reference circular gear meshes 10 degrees. It is a schematic diagram which shows a mode that the single tooth tip double tooth profile standard circular gear meshes 17.98 degrees. It is a schematic diagram which shows a mode that a single-tooth tip double-tooth profile reference circular gear meshes at 18 degrees. It is a schematic diagram which shows a mode that the single tooth tip double tooth profile reference circular gear meshes at 40.55 degrees. It is a graph which shows the backlash of the meshing phase of the single-tooth tip double-tooth shape reference circular gear and the single-tooth bottom double-tooth shape reference circular gear in which the root is deleted.

  FIGS. 2 to 46 show the contents of the previously filed PCT / JP2008 / 066053, and FIGS. 47 to 50 show the contents of the previously filed Japanese Patent Application No. 2009-26732. Is defined in more detail, and will be described with reference to the drawings. FIG. 1 is a cross-sectional view of an embodiment in which the present invention can be implemented.

  In FIG. 2, the cross-sectional shape of the gears (7, 8) of each circular tooth will now be described. A plurality of tooth shapes whose centers are located on the circumference of the gear reference circle (3) and are arranged in contact with each other A reference circle (4) is provided, and of the circumferential portion of the tooth profile reference circle (4), circumferential portions positioned on the inner peripheral side and the outer peripheral side of the gear reference circle (3) are defined as the tooth profile reference circle (4 ) Are alternately formed as part of the tooth shape, have a convex portion (62) along the outside of the tooth profile reference circle (4) on the tooth tip side, and a tooth profile reference circle ( 4) It has a shape having a concave portion (61) along the inside, and the convex portion (62) and the concave portion (61) are formed so as to be continuous by drawing an S-shape spreading between the tooth tip and the tooth bottom. Yes.

  Further, in particular, the gear device of the present embodiment, as will be described later, from a meshing position where the apex of the tooth tip of one spur gear and the apex of the bottom of the other spur gear overlap with the center line connecting the rotation axes. The spur gear has a tooth profile that is obtained by rotating the gear plane shape of each spur gear at the correct transmission angle and eliminating the overlapping portion of the gear plane shape. Even if it is a quantity, it is desirable to have a shape in which overlapping portions are cut, and ideally such cutting can make gear transmission errors and backlash very close to zero, Transmission loss and the like can be suppressed.

  Next, the design technical contents of the gear device will be described in detail. In the gear device, the following terms are used within the scope of the present specification. First, these terms will be described.

  In this specification, the “starting point of the meshing period” refers to the top of the tooth tip of one gear and the bottom of the other gear on the center line connecting the rotation shafts of the two gears. It shows the origin of the phase where the vertex overlaps. A section where the meshing state is the same is defined as one cycle.

  In the present specification, the "meshing vertex" means that the top of the tooth tip overlaps with the top of the tooth bottom at the starting point of the above-mentioned meshing cycle, and the tooth top and the tooth bottom are interchanged at the half cycle from the starting point of the meshing cycle. In this state, the vertices overlap each other, and the overlapping vertices are indicated.

  In the present specification, the “meshing tangent” has a pitch point in a straight line state on the z-axis, assuming that the rotational state of the helical gear is on the xy-axis. This straight line is shown.

  In the present specification, the “meshing phase” represents an angle with the meshing phase starting point being 0 degree and the clockwise rotation being the “+” direction.

  In this specification, “meshing phase width” means that a helical gear is formed when an outer envelope is formed by laminating a gear plane shape, that is, a spur gear, in the direction of the rotation axis and shifting the spur gear slightly in the rotation direction. However, since the meshing tangent of the helical gear has continuous meshing that is out of phase, this indicates the phase width of the meshing of the helical gear.

  In this specification, the “meshing overlap portion” and the “gear plane shape overlap portion” are collision portions (overlap portions) formed by meshing at the correct transmission angle in the gear plane shape. However, when the overlapping portion is cut by cutting or the like, the overlapping portion disappears and functions as gears that perform ideal transmission.

  “Deviation tolerance” means shaping that removes parts that have little impact on performance so that performance can be guaranteed in response to variations in size, temperature environment, and deformation due to aging. This is an expression specific to the gear device of the present invention. The “deviation margin” indicates the amount of shaping corresponding to the above-described size variation and possible deformation, and indicates the degree of deviation tolerance, and is an expression specific to the gear device of the present invention. is there.

  The “circular tooth center line” is a line connecting the centers of the tooth profile reference circles of the meshing gears, and the length of the circle tooth center line is the same as the diameter of the tooth profile reference circle at the mesh apex. The "meshing reference point" is the contact point of the gear at the starting point of the meshing cycle (the intersection of the circle tooth center line and the tooth profile reference circle), and the position depending on the gear (the part used as the standard for tooth profile shaping). This is an expression specific to the present invention.

  The “limit gap” indicates a minimum gap between gears functioning as a gear, and is an expression specific to the present invention.

  The “overlapping part in the center line direction” is a part that is deleted for shaping the deviation tolerance of the spur gear of the present invention, and the part of the deviation margin is overlapped in the direction of the center line at the meshing vertex and the part is deleted. Say the overlapping parts to do.

  “Rotation axis” is an extension of a line passing through the center of the rotation axis. This is an expression specific to the present invention.

  “Axial angle” indicates the angle at which the rotational axes of the meshing gears intersect. This is an expression specific to the present invention.

  Based on such definitions of terms, the gear device according to the present embodiment will be described with reference to the drawings from the theoretical design shape to the design shape with allowance for deviation. Also, in this specification, the definition on the sphere replaces the definition on the plane with the definition on the sphere, and the definition of the straight line is the definition of the line on the sphere that looks straight when viewed from the center of the sphere. To replace. First, referring to FIGS. 2 to 18, a theoretical design shape that does not take into account deviation tolerance will be described.

  FIG. 2 is a view showing circular gears (7, 8). In this gear device, circular teeth formed by a gear reference circle (3) and a tooth profile reference circle (4) having a speed transmission ratio of 1: 1. Gears (7, 8). The drawing is drawn with a gear having a small number of teeth, which is easily affected by the shape of the teeth (the meshing angle is large). The center of the tooth profile reference circle (4) is on the circumference of the gear reference circle (3), and the tooth profile reference circles (4) are arranged in contact with each other. In the gear device shown in FIG. 2, of the circumferential portion of the tooth profile reference circle (4), the circumferential portions positioned inside and outside the gear reference circle (3) are arranged around the circumference of the gear reference circle (3). The teeth are alternately shaped along the direction, and no conspicuous straight portions are formed on the outer periphery. In the figure, the pitch point (9) is located on the center line (10) connecting the shaft centers of the gears (7, 8).

Next, using FIG. 3 and FIG. 4, the tooth profile tries to compare a circle and an ellipse. First, FIG. 3 is a diagram showing a state of meshing of the gears having a one-to-one diameter of the circular teeth shown in FIG. 2 with a tooth profile reference circle (4). When rotated by a predetermined angle indicated by a straight line (17) from the center of the gear reference circle, the tooth moves about the gear (7) as in the rotational movement locus (11) of the tooth shape reference circle, and the gear (8) When the tooth moves as shown in the rotational movement locus (12) of the tooth profile reference circle and further moves, the gear (7) moves to the position of the rotational movement position (13) of the tooth profile reference circle. About (8), it moves to the position of the rotational movement position (14) of the tooth profile reference circle.
As is apparent from comparing the rotational movement amount of the tooth tip of the tooth profile reference circle (15) and the rotational movement amount of the tooth root of the tooth profile reference circle (16), the rotational speed of the tooth tip and the tooth root is increased by the rotation of the gear. The difference comes out. If the tooth profile is a circle, both the tooth tip and the root are on the circumference, so even if the gear tip and root angles of the gears change, the shape is the same and does not affect the meshing. . In other words, because the movement speed in the x-axis direction (right direction of the drawing) of the center of the tooth profile reference circle is the same, if the tooth shape is a circle, the teeth will not collide at the correct transmission angle. is there.

  On the other hand, FIG. 4 is a diagram showing how the rotational trajectories (18, 19) of the one-to-one diameter elliptical gears mesh with each other. When the oval gear rotates from the position of the tooth profile reference ellipse (20) with a phase of 0 degrees, there is a difference in movement speed between the tooth tip and the tooth bottom, and a portion (21) where the tooth profile reference ellipses overlap is generated. Will do. As shown in FIG. 3, this does not occur if the tooth shape is a circle, but it occurs in an ellipse. Because of this phenomenon, even if the tooth profile is formed based on the ellipse, it causes a transmission error. That is, as shown in FIG. 4, since a portion (21) where the ellipses of the tooth profile reference overlap is generated, the backlash is zero even if it is shaped based on the tooth shape of the ellipse for the purpose of improving the backlash. Even if it can be close to, it is impossible to make a gear with zero transmission error and backlash.

  Here, a circular tooth shape is adopted instead of an ellipse, and a gear having a speed transmission ratio of 1: 1 and a transmission error and a backlash of zero will be examined in detail. In other words, it tries to prove that the helical gear of the circular tooth eliminates transmission error and backlash.

  FIGS. 5 to 10 illustrate the meshing states of a seven-tooth spur gear having a one-to-one diameter. First, the meshing period between FIGS. 5 to 10 is defined with the meshing phase starting point being 0 ° meshing phase, the clockwise reverse rotation being the “+” angle, and the clockwise direction being the “−” angle. The phase is changed at −25.71 degrees, −12 degrees, 0 degrees, 7 degrees, 12 degrees, and 25.71 degrees. It is shown that the backlash is zero at the meshing phase of -25.71 degrees (1/2 period) in FIG. In the meshing phase of -12 degrees in FIG. 6, the backlash is shown to be 1.7 degrees. It is shown that the backlash is zero at the meshing phase of 0 degree in FIG. In FIG. 8, the meshing phase of 7 degrees indicates that the backlash is 0.4 degrees. FIG. 9 shows that the backlash is 1.7 degrees at the meshing phase of 12 degrees. It is shown that the backlash is zero at the phase of 25.71 degrees (1/2 period) in FIG. In each of FIGS. 5 to 13, the left gear is at a specified angle, and the right gear is closer to the “+” side.

  On the other hand, FIG. 11 thru | or 13 has shown each state of mesh | engagement of the 7-tooth gear (22, 23) of the diameter of 1: 1 conventional tooth shape. FIG. 11 is a view showing a state in which the conventional tooth-shaped gears (22, 23) are engaged at 0 degree. FIG. 12 is a view showing a state where the conventional tooth-shaped gears (22, 23) are meshed at 7 degrees. FIG. 13 is a view showing a state where the conventional tooth-shaped gears (22, 23) are engaged at 13 degrees.

  Next, with reference to FIGS. 14 and 15, the backlash of these gears is analyzed. 14 and 15 represent the angle of backlash of the right gear at an arbitrary phase angle of the left gear. The waveform of FIG. 14 is the waveform of the backlash of the circular gear of FIGS. 5 to 10, and the waveform of FIG. 15 is the waveform of the backlash of the conventional tooth-shaped gear of FIGS. The upper limit angle of backlash in the “+” direction of the right gear is graphed by a solid line, and the upper limit angle of backlash in the “−” direction of the right gear is graphed by a dotted line. The right gear is free to rotate at an angle between the solid and dotted waveforms. The values in FIGS. 14 and 15 are obtained by measuring the backlash of a circular gear with 7 teeth by actual measurement of CAD (computer drawing). In the case of the conventional tooth shape, the conventional tooth shape of FIGS. It is what was actually measured. In the case of the conventional tooth shape, the difference in the value of the graph increases due to the difference in the tooth shape, but it is a reference value for observing the tendency of the waveform.

  Since the rotating directions of the meshing gears are opposite, the right and left gears on the drawing have a correct transmission angle with the opposite values of ±. If the engagement of the circular gears (7, 8) in FIGS. 5 to 10 is judged from the waveform in FIG. 14, it can be seen that there is a correct transmission angle within the backlash range at all phases. On the other hand, when the engagement of the conventional tooth-shaped gear in FIGS. 11 to 13 is judged by the waveform in FIG. 15, the distribution of backlash like a sine wave is shown as a whole, and the correct transmission angle is within the backlash range. It has been found that there are many phases that do not exist. That is, from the analysis of the data shown in FIGS. 14 and 15, it is proved that the circular teeth (7, 8) are superior to the conventional shape gear with respect to the correct transmission angle.

  Next, technical considerations regarding the spur gears for the circular teeth up to here are overlapped in the axial direction and shifted by a predetermined angle, and the envelope of the gear outer shape formed around the shaft is defined as the outer shape. Consider the helical gear that can be assumed. In conclusion, both transmission error and backlash can be very close to zero.

  FIG. 16 is a perspective view in which a conventional gear and a circular gear are helical gears, and shows a conventional helical gear (28) and a circular helical gear (29). When the helical gear is viewed from the side, it is as shown in FIG. 18, and the apex (30) of the tip of the circular tooth and the apex (31) of the root of the circular tooth are formed obliquely with respect to the rotation axis. The As shown in FIG. 17, the helical gear (29) has a spur gear overlapped in the axial direction and shifted by a predetermined angle (for example, 5 degrees) to form an outer envelope of the gear outer shape formed around the shaft, As shown in FIG. 18, there is a composite of meshing gears out of phase in the direction of the meshing tangent (9).

  To summarize the conditions for zero transmission error and backlash, first, in the gear plan shape of a one-to-one circular tooth, that is, a spur gear (spur gear), as shown in FIG. The correct transmission angle is included, and the transmission error and the backlash are zero at a point where the meshing phase is shifted from the zero degree point by a half cycle. In helical gears with spur gears overlapped in the axial direction and shifted by a predetermined angle to make the outer shape of the gear outer envelope formed around the shaft, a meshing phase width of 1/2 cycle or more is provided in the rotational axis direction. Is the premise. By providing a mesh phase width of 1/2 cycle or more in the rotation axis direction, the transmission angle at the meshing vertex of the spur gear virtually stacked in the rotation axis direction is the correct transmission angle, and therefore the behavior of the helical gear As a whole, the backlash is limited to zero, and if the above stack is subdivided, all the meshing angles are the correct transmission angles, and a gear device with zero backlash can be obtained. Become.

  When the conditions for establishing the above-described gear device with zero transmission error and zero backlash are defined when the speed transmission ratio is 1: 1, the first condition is that the spur gear (spur gear) has backlash at all meshing phases. This is a shape in which the correct transmission angle is included in the range. In order to satisfy this condition, it is necessary that the tooth profile reference circle is centered on the circumference of the gear reference circle and the tooth profile reference circles are arranged in contact with each other. The second condition is to form a helical gear whose outer shape is an envelope of a gear outer shape formed around the shaft by overlapping the spur gear of the first condition in the axial direction and shifting by a predetermined angle. In all of the stacked spur gears, the meshing vertex is the correct transmission angle, and the meshing backlash at the meshing vertex is zero. The third condition is that the meshing phase width of the helical gear is 1/2 cycle or more. With a gear that satisfies these first to third conditions, a gear device with zero transmission error and backlash can be established.

  In the case of an actual gear, each gear is formed into a shape that includes some errors from the design value depending on the machining accuracy, and in order to obtain a deviation allowance for the gear with zero transmission error and backlash described above. It becomes necessary to perform shaping. In other words, the previous gear device seems to be a gear with perfect performance, zero transmission error and backlash, but in the case of mass production, there are product variations, and due to changes due to temperature and aging, Since an error occurs and it is a perfect shape, the deformation in the collision direction of the gear leads to a rotation failure or a rotation stop. Therefore, unless tolerance is given to a production error, it is not practical as a gear.

  Considering the concept of a gear plane shape, that is, a spur gear (spur gear), the gap of the gear meshing with the tooth profile reference circle, if the tooth profile is shaped so as not to exceed the tooth profile reference circle, the backlash increases, but the backlash increases. There is no change that the correct transmission angle exists within the range. Tooth profile shaping that satisfies the three conditions of the previous transmission error and the establishment of a gear device with zero backlash is possible if the meshing vertex and the meshing with zero backlash are realized. This condition is satisfied.

  As shown in FIG. 19, it is possible to cut a portion where the backlash is zero at the meshing apex and does not affect the meshing, near the tooth tip of the tooth shape or near the tooth bottom. In this shaping, the first to third conditions are satisfied. The tooth shape of the gear shown in FIG. 19 is similar to the shape of the gear shown in FIG. 2, and is centered on the circumference of the gear reference circle, and a plurality of teeth arranged in contact with each other. Tooth profile reference circles (35, 36) are provided, and of the circumferential portions of the tooth profile reference circles (35, 36), the circumferential portions positioned inside and outside the tooth profile reference circles are arranged in the circumferential direction of the tooth profile reference circles. Are alternately formed as part of the tooth shape, have convex portions along the outside of the tooth profile reference circle (35, 36) on the tooth tip side, and the tooth profile reference circle (35, 36) on the tooth bottom side. It is set as the shape which has a recessed part along an inner side, and a convex part and a recessed part are formed so that the S-character spreading between the tooth tip and the tooth bottom may be drawn and continued. The bottom of each gear (33, 34) is formed with a flat bottom portion (6) cut toward the center of the shaft, and the top of each gear (33, 34) has a top portion. A machined flat tip portion (5) is formed, and the flat bottom portion (6) and the flat tip portion (5) have a plane parallel to the tangential direction of the circle centering on the gear axis. It is configured. The contact surface (32) is formed with zero backlash on the tooth surface at an angle close to the center line.

  FIG. 20 shows gears (33, 34) overlapped in the center line direction. It can be seen that the tooth surfaces at angles close to the center line do not overlap. As a measure for deviation tolerance, the overlapping portion (37) in the center line direction is cut. In this shaping, the contact surface of the tooth surface at an angle close to the center line is hardly shaved, and the “meshing vertex” of the second condition of the conditions for establishment of meshing with zero backlash described above. The meshing backlash at zero is zero. It can be assumed that it is true in the sense that it is not perfect, but nearly zero.

  In addition, in the cutting of the overlapping portion (37), regarding which of the tooth tip side and the tooth bottom side should be cut, priority is given to the meshing at an angle close to the center line. The root side will be shaved.

  The gear shaped as described above is the gear shown in FIG. With the above design method, gears with little transmission error and backlash can be realized even with materials that cause large deformation of the gear. A gear having a backlash close to zero can be formed.

  Next, “gears with zero transmission error and backlash” when the speed transmission ratio is other than 1: 1 will be described. If the speed transmission ratio of the gears is different, the meshing overlap portion is generated on the assumption of a spur gear shape.

  The condition of the meshing phase Sθ = 10 ° in the speed transmission ratio of 10: 1 (30 teeth vs. 3 teeth) shown in FIGS. 22 and 23 is an angle at which the meshing overlapping portion (21) becomes large. This meshing overlap portion does not occur in gears having the same diameter, but occurs more greatly in gears having a large difference in speed transmission ratio. 22 and 23, the tooth profile reference circle (39) of the three-tooth gear and the tooth profile reference circle (40) of the 30-tooth gear are shown under the condition of the meshing phase Sθ = 10 °. It can be seen that the meshing overlap portion (21) occurs on the reference circle (41). FIG. 23 is an enlarged view of the main part of the meshing portion of the gear of FIG.

  Considering the locus of the tip of the tooth profile reference circle shown in FIG. 24, the movement amount of the tooth profile reference circle (39) of the three-tooth gear and the tooth profile reference circle (40) of the 30-tooth gear is indicated by an arrow. As shown in FIG. 25, the locus of movement of the tooth tip of the tooth profile reference circle of three teeth (42) and the locus of movement of the tooth tip of the tooth profile reference circle of 30 teeth (43) are illustrated. As shown in FIG. 25, a difference (Δy) occurs in the movement of the tooth tip of the tooth profile reference circle in the y-axis direction. Further, as shown in FIGS. 26 and 27, when the three-tooth gear (44) and the 30-tooth gear (45) are meshed, the overlapping position (46 ), It can be seen that the depth of the root becomes deeper in a gear having a large number of teeth.

  Furthermore, when considering the mesh overlapping portion of the speed transmission ratio of 10: 1 (30 teeth vs. 3 teeth), as shown in FIG. 28, the meshing state with the gear is the coordinates of the center of the tooth profile reference circle. Can be represented by rectangles (73, 74) with corners. In FIG. 28, a tooth profile reference circle (47) at the meshing apex of a large gear (for example, 30 teeth) and a tooth profile standard circle (48) at the meshing apex of a small gear (for example, 3 teeth) are drawn. As shown, the tooth shape reference circle (49) to which the large gear is moved and the tooth shape reference circle (50) to which the small gear is moved are depicted. At the meshing apex, the circle tooth center line (51) is centered on the meshing reference point (52) and is the same as the diameter of the tooth profile reference circle. The rectangle (74) indicating the meshing state of the movement destination is a rectangle close to a thin band shape, and is a rectangle having a long side of θy and a short side of θx. On the other hand, the rectangle (73) indicating the meshing state of the meshing vertices is a rectangle having a larger area than the rectangle (74), and has a long side y0 and a short side x0.

  As shown in FIG. 29, the tooth profile reference circle has a right triangle. The tooth profile reference circle (4) has a radius “r”, a tooth profile reference circle number “n”, and a gear reference circle radius “R”. "Is r = R × sin (360 / 2n). Since the positional relationship of the tooth profile reference circle is composed of right triangles, the respective coordinates and distances can be obtained by trigonometric functions. In FIG. 29, the gear reference circle of the large gear has a radius LR, and the gear reference circle of the small gear has a radius SR.

  Next, it is calculated whether or not a meshing overlap portion occurs in each meshing situation of CASE1 to CASE3. First, in the meshes (CASE 1 and CASE 2) of FIGS. 30 and 31, in order to calculate whether or not the mesh overlap portion occurs, if the length of the center line of the circular tooth is shorter than the diameter of the tooth profile reference circle, the mesh is engaged. This means that there is an overlapping part. The center of the large gear (gear reference circle) is the coordinate (Lx, Ly) and the center of the small diameter gear (gear reference circle) is the coordinate (Sx, Sy). The length of is calculated. In the drawing, the movement destination of the tooth profile reference circle (47) at the meshing apex of the large gear is the tooth profile reference circle (49), and the tip of the tooth profile reference circle (48) at the meshing apex of the small gear is the tooth profile reference circle. (50). In this case, if the difference between the circle tooth center line and the diameter of the tooth profile reference circle is Δr, the condition for the occurrence of the overlapping portion is Δr <0.

  Similarly, in CASE 3 shown in FIG. 32, the overlapping portion between the meshing reference point of the small-diameter gear and the outer periphery of the tooth profile reference circle of the large-diameter gear is calculated for each angle at the correct transmission angle. In the drawing, the movement destination of the tooth profile reference circle (47) at the meshing apex of the large gear is the tooth profile reference circle (49), and the tip of the tooth profile reference circle (48) at the meshing apex of the small gear is the tooth profile reference circle. (50). If the distance between the coordinates (SPx, SPy) of the meshing reference point of the small diameter gear and the coordinates (Lx, Ly) of the center of the tooth profile reference circle (49) of the large gear is smaller than the radius of the tooth profile reference circle, The meshing overlap portion is generated. Assuming that the difference between the mesh reference point of the small-diameter gear and the center of the tooth profile reference circle of the large-diameter gear and the radius of the tooth profile reference circle is ΔPr, the condition for the overlapping portion to be generated is ΔPr <0.

  FIG. 33 is a table showing the result of calculating the meshing state of CASE 1 in FIG. 30 and CASE 2 in FIG. 31 with a gear having a speed transmission ratio of 1: 1 (6 teeth to 6 teeth). FIG. 34 is a table showing the results of calculation in the case 3 meshing state. The values of Δr and ΔPr are values with the radius of the tooth profile reference circle being 1, Sn and Ln are 12, and FIG. 33 is calculated by shifting the angle by 2.5 degrees between 0 and 30 degrees. Yes. In a gear having a speed transmission ratio of 1: 1 (6 teeth vs. 6 teeth), there is no meshing overlap due to the calculation result. If negative values appear in Δr and ΔPr of the calculation result, a meshing overlap portion has occurred. 14 and 15 described above are graphs of the angle of backlash on the CAD drawing, but the tables in FIGS. 33 and 34 show the overlapping distance (gap) of the tooth profile reference circle at the correct transmission angle. It is derived by calculation.

  Next, the tables of FIGS. 35 and 36 are obtained by calculating gears having a speed transmission ratio of 1 to 10 (3 teeth to 30 teeth). In FIG. 35, the angle θ is shifted by 5 degrees on the small diameter side and at the same time by 0.5 degrees on the large diameter side, and is calculated for the meshing patterns CASE1, CASE2, and CASE3. The values of Δr and ΔPr are values assuming that the diameter of the tooth profile reference circle is 1. From the calculation results, although they are very small values, negative values of Δr and ΔPr (indicated by reference numerals 54, 55, and 56 in the figure) have come out, and meshing overlapping portions are generated. Is.

  Based on such a calculation, a gear overlap with zero transmission error and backlash can be formed by removing the meshing overlap portion where negative values of Δr and ΔPr are generated. If it is defined to remove the meshing overlap where negative values of Δr and ΔPr occur, the fourth condition is that if the speed transmission ratio is other than 1: 1, all phases of meshing at the correct transmission angle In the above, it is a condition that the meshing reference point of the gear plane shape is left and the meshing overlapping portion is cut and the tooth surface is shaped. 30 to 32, at the meshing apex, the backlash is zero and there is no meshing overlapping portion and meshing is performed. Since the meshing reference point of both gears rotates around the center of the gear reference circle, if the meshing overlapping point is removed leaving the meshing reference point, it is possible to shape the tooth profile without collision at the correct transmission angle It is.

  If the speed transmission ratio is other than 1: 1, the second condition ("the spur gear of the first condition is overlapped in the axial direction and shifted by a predetermined angle to form an envelope of the outer shape of the gear formed around the axis". A helical gear having an outer shape is formed, and in all of the stacked spur gears, the meshing vertex is the correct transmission angle, and the meshing backlash at the meshing vertex is zero. ”) Therefore, shaping of the fourth condition (“gear plane shape, ie, in all phases of meshing of the spur gear”, the meshing overlapping portion is removed leaving the meshing reference point and the tooth surface is shaped ”) By doing so, a gear device is configured.

  FIG. 37 to FIG. 46 show the meshing of the gear with the tooth surface and the tooth tip shaped under the contents of the fourth condition. The size of the meshing overlap portion is very small even for a gear having a large difference in speed transmission ratio, and it is in a range where a gear made of a material having a large deviation allowance falls within the allowance for deviation.

  By shaping the tooth profile described above, the first condition described above, “in the gear plane shape (spur gear), is a shape in which the correct transmission angle is included in the backlash range in all meshing phases”. Realized.

  The method of deleting the overlapping portions (54, 55, 56) in FIGS. 43 and 44 is to reduce transmission error and backlash to zero at all rotation angles with a meshing phase width of 1/2 cycle. Since the valley of the three-tooth gear (57) is shallow, the meshing strength is weakened. Therefore, when the number of teeth of such a gear is small, the valley of the deeply meshed ten-tooth gear (58) is backed. As the mesh reference point with zero rush, the mesh phase width is set to one cycle, and the method of deleting the overlapping portions (54, 55, 56) is as shown in FIGS.

  As shown in FIGS. 39 to 46, the gear is formed around the shaft by shaping the surface contacting with the correct transmission angle other than the meshing apex in the gear plane shape, overlapping the spur gear in the axial direction and shifting it by a predetermined angle. If a helical gear with an outer envelope is used as an outer shape, there is a surface that is in contact with the tooth surface on the opposite side of the mesh at the correct transmission angle on any of the mesh tangents. In order to construct a configuration in which backlash is zero at a correct transmission angle, the above-mentioned third condition “helical gear meshing phase width is ½ period or more” is ½ period. The meshing phase width can be reduced. The phase width that can be reduced varies depending on the difference in gear speed transmission ratio and tooth surface shaping.

  The design method of the gear device can be summarized as follows. First, in the case of a gear device having a one-to-one speed transmission ratio, tooth profile reference circles having centers on the circumference of the gear reference circle are continuously in contact with each other. There is an overlapping part which is formed on the inner circumference side slightly with respect to the reference circle, the tooth bottom is formed slightly on the outer circumference side, and the estimated distance of the deviation estimated in the gear structure is moved in the center line direction between the gears at the meshing apex. A spur gear is overlapped in the axial direction and shifted by a predetermined angle to form a helical gear having an outer envelope of the gear formed around the shaft. The design method is to set the meshing apex of the spur gear to the correct transmission angle and provide a meshing phase width of 1/2 cycle or more on the meshing tangent.

  In the case of a gear device having a speed transmission ratio other than 1: 1, it will be described as follows. The tooth profile reference circles with the center on the circumference of the gear reference circle are continuously in contact with each other, and the tip of the tooth is slightly inside the tooth profile reference circle and the tooth bottom is slightly It is formed on the outer peripheral side, and is scraped off in the shape of a spur gear, leaving the meshing reference points of the meshing overlapping portions of all phases. Also, for the meshing part, the tooth shape of the shaping part is scraped with the width of the limit gap, and at the meshing apex, the overlapping distance where the estimated distance of the deviation estimated for the gear structure is moved in the direction of the center line between the gears Sharpen. A spur gear is overlapped in the axial direction and shifted by a predetermined angle to form a helical gear with the outer contour of the gear formed around the shaft as the outer shape. The design method is to make the angle and provide a mesh phase width of about ½ period on the mesh tangent.

  Assuming a thick gear plane shape (spur gear) in FIG. 17, the backlash shown in FIG. 14 has a width in the phase close to zero, so the phase of the spur gear is not subdivided and shifted by a certain angle. Even gears stacked in the axial direction can constitute a gear with almost zero transmission error and backlash.

  The contents described above are the contents of PCT / JP2008 / 066053 submitted before this case. By applying the above contents, gears in which the transmission error and backlash are close to zero when the rotating shafts of the meshing gears are not parallel will be described below.

Thus, the content is replaced with the definition of a spherical surface from the definition of a plane.
As shown in FIG. 47, when the sphere surface gear is configured on the sphere surface, the rotation axis (76) of the meshing sphere surface gear passes through the center of the sphere, and depending on the size of the sphere and the size of the gear, The gears can be engaged at any shaft angle (Aθ) where the rotation axes are not parallel to each other. Similar to the content of the design method of the gear of the gear plane shape meshing on the plane, a plurality of tooth profile reference circles (4) having centers on the circumference of the gear reference circle (3) are contacted on the sphere surface. Deploy. The shape of the spherical surface gear is formed on the spherical surface in the same manner as the content of the gear plane shape. Even if the spherical surface gear rotates about the rotation axis (76) on the surface of the sphere (77), the spherical surface gear does not protrude from the surface of the sphere (77) and meshes only on the surface of the sphere (77). Is.

  The rotational axes (76) of the mutual spherical surface gears that mesh on the surface of the sphere (77) intersect at the center of the sphere (77). As shown in FIG. 48, the spherical surface gears on the surfaces of a plurality of spheres having the same center and different radii can be rotated while satisfying the first to fourth conditions on the plane. It is possible to construct a spiral bevel gear that has concentric spheres stacked in the direction and is shifted by a predetermined angle so that the outer shape of the envelope of the outer shape of the gear formed around the axis. FIG. 48 shows intermittent four layers in which the design concept is easy to understand. However, when the layers are continuously subdivided to include the first to third conditions, FIG. 50 is obtained.

  When concentric spheres are continuously stacked toward the center of the gear reference circle (3) on the surface of the outermost peripheral sphere (77) shown in FIG. 49, a conical shape having a spherical bottom is formed. Since the axis angle (Aθ) of the intersection of the rotation axes (76) can be arbitrarily set by the sizes of the gear reference circle (3) and the sphere (77), the mutual rotation axes of the meshing gears Even if (76) is other than parallel, it is possible to engage at all shaft angles.

Although the circle on the plane is also a circle on the spherical surface and the outer periphery is not deformed, the influence of replacing the above-described planar gear design method on the sphere surface will be considered.
The effect of replacing a plane with a spherical surface is that the influence of the sphere on the plane increases, and the axial angle (Aθ) increases, that is, the sphere surface gear increases with respect to the sphere (77). That is. If the shaft angle (Aθ) exceeds 90 degrees, it can be turned back to a maximum angle of 90 degrees by moving the rotational force transmission side of the rotating shaft of the spherical surface gear to the target side of the spherical surface gear. The maximum angle of the shaft angle (Aθ) can be 90 degrees.

In the first condition on the plane, the tooth profile reference circles are arranged in contact with each other on the sphere surface, and if the sphere surface gears have the same number of teeth, the movement speeds of the tooth tips are the same in the direction perpendicular to the center line. Thus, there is no change in that the correct transmission angle is in the range of meshing backlash in the waveform of FIG. 14, and there is no influence on the first condition.
In the second condition and the third condition on the plane, even the spherical surface gear can have the same function as that of the plane lamination by the concentric sphere lamination, to the second condition and the third condition. There is no influence of.
The influence of the fourth condition on the plane is that, on the spherical surface, the gear reference circle and the tooth profile reference circle have the same configuration as on the plane, and the tooth profile reference circles are arranged in contact with each other. The backlash is zero at the angle, and the movement of the meshing reference point, focusing on the meshing change from the meshing apex, has no difference in tendency between the plane and the ball surface. Even if there is a difference between the flat surface and the spherical surface to the extent of the overlapping portion, the overlapping overlapping portion is deleted, and there is no effect on configuring the engaging at the correct transmission angle. is there.
By the above, there is no influence on said 1st-4th conditions by replacing the design method of a planar gear with a spherical surface.

  The paragraph numbers [0068] to [0073] are Japanese Patent Application No. 2009-26732 previously filed. In consideration of the above contents, it is considered whether a gear having a transmission error and backlash close to zero is possible with the contents other than the above.

Thus, both the definition on the plane and the definition on the surface of the sphere are explained by the definition on the plane.
1, FIG. 51 to FIG. 53, the tooth profile reference circle (4) of a three-tooth gear is centered on the gear reference circle (3), and one tooth tip is engaged with one gear and the other is engaged. A gear device having one tooth base is assumed.
Similarly to FIGS. 5 to 15, the starting point of the meshing period is the meshing phase of 0 degree, the clockwise reverse rotation is the “+” angle, the clockwise direction is the “−” angle, The single-tooth tip gear (86) is set to a specified angle, and the backlash of the single-tooth bottom gear (87) is obtained.
The meshing of this gear device meshes the object with reference to a rotation angle of 0 degree.
When the single-tooth tip gear (86) in FIG. 51 exceeds −46.6 degrees and 46.6 degrees, the single-tooth bottom gear (87) is in an idling state. At the starting point of the meshing period in FIG. 53, the transmission error and backlash are zero.
The range of backlash due to the meshing angle of this gear device is shown in FIG. 54. The idle rotation of the single-tooth bottom gear (87) is backlash in all angles, and the backlash is not caused in the range where the single-tooth bottom gear (87) does not idle. The correct transmission angle is included in the range. Therefore, the first condition is satisfied, and the third condition is that the gear phase of the helical gear is set to one or more rotations of the gear, thereby enabling a gear device with zero transmission error and backlash. Become.
From the above description, it is possible to use a gear device having a speed transmission ratio other than 1: 1 and a gear device in which the rotating shafts of meshing gears are not parallel to each other according to paragraphs [0015] to [0073] above. Led.

Further, in FIG. 55, the tooth profile reference circle (4) of the three-tooth gear is centered on the gear reference circle (3) and has the same center as the tooth profile reference circle (4) and has a tooth profile reference of 80% in diameter. A double tooth profile reference circle of a circle (90), assuming a gear device having one tooth tip on one gear and one tooth bottom on the other gear to be meshed, One side of the sliding contact side is a large-diameter tooth profile reference circle (4), and one side of the object is a small-diameter tooth profile reference circle (90).
The tooth tip is centered on the tooth reference circle, and the two sliding contacts at the intersection of each tooth reference circle at −45 degrees and 45 degrees from the center line, and the two tooth contact reference circles and the gear reference circle. A single tooth tip double tooth reference circular gear (91) having a deformed trapezoidal shape connecting the intersections is assumed. The single tooth bottom double tooth profile reference circular gear (92) has a shape of each tooth profile reference circle that is sorted at the apex of the tooth tip.
Consider a mesh consisting of two concentric tooth reference circles. This is because the single tooth tip double tooth shape reference circular gear (91) and the single tooth bottom double tooth shape reference circular gear (92) separate the large and small tooth shape reference circles by the center line at the starting point of the meshing cycle, The object side of the slidable contact side portion is constituted by another tooth profile reference circle. The resulting meshing state is depicted in FIGS.
The meshing of the outer tooth profile reference circle (4) is in a state where the single tooth tip double tooth profile reference circular gear (91) is -42.81 degrees and the single tooth bottom double tooth profile reference circular gear (92) can freely rotate. It becomes.
The meshing of the inner tooth profile reference circle (90) is that the single tooth tip double tooth profile reference circular gear (91) is 38.37 degrees, and the single tooth bottom double tooth profile reference circular gear (92) is free to rotate. Become.
FIG. 62 shows the backlash range of this meshing according to the meshing angle. In this case, as in [0075] in the paragraph number above, the idle rotation of the single-tooth bottom double-tooth reference circular gear (92) is backlash at all angles, and in the range where no idle rotation occurs, the correct transmission angle is within the backlash range. It is included. Therefore, the first condition is satisfied, and the third condition is that the gear phase of the helical gear is set to one or more rotations of the gear, thereby enabling a gear device with zero transmission error and backlash. Become.
From the above description, it is possible to use a gear device having a speed transmission ratio other than 1: 1 and a gear device in which the rotating shafts of meshing gears are not parallel to each other according to paragraphs [0015] to [0073] above. Led.

55 to 61, the tooth tip of the single tooth tip double tooth profile reference circular gear (91) is deleted, but in FIGS. 63 to 72, the single tooth bottom double tooth profile reference circular gear (92) is used. ) Of the root of the tooth is removed. The single tooth tip double tooth profile reference circular gear (91) has each tooth profile reference circle as an outer shape, and the positions of the two sliding contacts are the same as those in FIG. In many parts of the single-tooth bottom double-tooth profile circular gear (92), deformations that do not contact the surface of the tooth-tip of the single-tooth double-tooth profile circular gear (91) other than the two sliding contacts. .
The difference between the range of backlash in FIG. 65 and the correct transmission angle is small for the single tooth bottom double tooth reference circular gear (92) of the small diameter tooth reference circle (90) of another tooth reference reference circle. This is because the sliding contact is in contact with the tooth tip of the single tooth tip double tooth reference circle gear (91) of the large-diameter tooth reference circle (4). In the embodiment, shaping is performed so as not to protrude.
FIG. 73 shows a waveform representing the backlash range according to the meshing angle shown in FIGS. That is, the correct transmission angle is included in the backlash range. Therefore, the first condition is satisfied, and the third condition is that the gear phase of the helical gear is set to one or more rotations of the gear, thereby enabling a gear device with zero transmission error and backlash. Become.
From the above description, it is possible to use a gear device having a speed transmission ratio other than 1: 1 and a gear device in which the rotating shafts of meshing gears are not parallel to each other according to paragraphs [0015] to [0073] above. Led.

The configuration of the tooth profile reference circle (4) of the gear device with three teeth meshed with the same configuration of the six tooth profile reference circles (4) with the gear reference circle (3) on the left in FIG. It can be determined only by the configuration of the left tooth profile reference circle (4) in the figure.
That is, the angle from the center of the tooth reference circle (4) of the meshing reference point at the meshing apex of the three-tooth gear is 60 degrees from the center line, and FIG. 55 to FIG. According to the contents derived from [0015] to [0077] of FIG. 29, even a gear device configured by continuously contacting tooth profile reference circles as shown in FIG. 29 can slide on the tooth profile reference circles other than the mesh reference points. Even a contact point satisfies the first condition, and a gear device with zero transmission error and backlash becomes possible.

  Accurately rotating gears increase the accuracy of various devices, have low noise, low energy loss, and high-speed rotation, and have high industrial utility value.

1 Spiral bevel gear 1
2 Spiral bevel gear 2
3 Gear Reference Circle 4 Tooth Profile Reference Circle 5 Tooth Flat Flat Part 6 Tooth Flat Flat Part 7 Circular Tooth Gear 8 Circular Tooth Gear 9 Meshing Tangent (Pitch Point)
10 Centerline 11 Tooth profile reference circle rotational movement trajectory (circular gear (7))
12 Tooth profile reference circle rotational movement trajectory (circle gear (8))
13 Rotational movement position of tooth profile reference circle (circular gear (7))
14 Rotational movement position of tooth profile reference circle (circular gear (8))
15 Rotational movement amount of tooth tip of tooth profile reference circle 16 Rotational movement amount of tooth bottom of tooth profile reference circle 17 Straight line from center of gear reference circle 18 Rotation movement position of tooth profile reference being ellipse 19 Rotation movement position of tooth profile reference being ellipse 20 Position at which the tooth profile reference is an ellipse phase 0 degree 21 Duplicated portion 22 Conventional gear 23 Conventional tooth gear 24 Backlash angle waveform of circular tooth “+” direction 25 Back of circular tooth “−” direction Waveform of rush angle 26 Waveform of backlash angle of “+” direction of conventional tooth 27 Waveform of backlash angle of “−” direction of conventional tooth 28 Helical gear of conventional tooth 29 Helical gear of circular tooth 30 Tip of tooth of circular tooth Vertex 31 Vertex of tooth root 32 Contact surface of tooth surface at angle close to center line 33 Shaped gear 34 Shaped gear 35 Tooth shape reference circle of shaped gear (33) 36 Shaped gear (3 4) Tooth profile reference circle 37 Overlapping portion in the center line direction 38 Deviation allowable gap 39 3 tooth profile reference circle 40 30 tooth profile reference circle 41 30 tooth gear reference circle 42 3 tooth profile reference circle Trajectory of movement 43 Trajectory of movement of tooth tip of tooth profile reference circle of 30 teeth 44 Shape of gear of 3 teeth 45 Part of shape of gear of 30 teeth 46 Superposition of shapes of tooth base of 3 teeth and 30 teeth 47 Large Tooth profile reference circle at the meshing apex of the gear 48 Tooth profile reference circle at the meshing vertex of the small gear 49 Tooth profile reference circle at the move destination of the large gear 50 Tooth profile reference circle at the move destination of the small gear 51 Circular tooth center line 52 Engagement reference point 53 Arrow indicating meshing reference point 54 Duplicated portion of CASE1 meshing of 3 teeth vs. 30 teeth 55 Duplicated portion of meshing of CASE2 of 3 teeth vs. 30 teeth 56 Duplicated portion of meshing of CASE3 of 3 teeth vs. 30 teeth 57 Three-tooth gear shaped according to condition 4 5 Conditions of 30 teeth shaping is the fourth gear 61 recess 62 protrusion 71 rotating shaft 1
72 Rotating shaft 2
73 Rectangle 1 with the center of the tooth profile reference circle at the top of the mesh as the corner
74 Rectangle 2 whose corner is the center of the tooth profile reference circle
75 Center of sphere 76 Axis of rotation 77 Sphere 78 Concentric sphere stacked inside sphere (77) 79 Concentric sphere stacked inside sphere (78) 80 Concentric sphere stacked inside sphere (79) Sphere 81 Sphere surface gear 82 Sphere surface gear laminated concentrically on the inside of sphere surface gear (81) 83 Sphere surface gear laminated on the inside of sphere surface gear (82) 84 Inside of ball surface gear (83) Spherical surface gears stacked concentrically on the sphere 85 Gear reference circles stacked concentrically to the center of the sphere 86 Single tooth tip gear 87 Single tooth bottom gear
88 Waveform of backlash angle in the “+” direction of the single-tooth bottom gear 89 Waveform of backlash angle in the “−” direction of the single-tooth bottom gear 90 Inner double tooth reference circle 91 Single tooth tip double tooth reference circular gear 92 Single tooth bottom double tooth profile reference circular gear
LR Radius of gear reference circle for large gear
SR Radius of gear reference circle for small gears
Lθ Large gear rotational movement angle (rotational angle from the starting point of the meshing cycle)
Sθ Rotational movement angle of small gear (rotation angle from the starting point of meshing cycle)
Aθ Axis angle Δx Amount of change in x-axis direction Δy Amount of change in y-axis direction r Radius of tooth profile reference circle n Number of tooth profile reference circles Δr Amount of overlap of tooth profile reference circles ΔPr Engagement reference point of one gear and tooth profile of the other gear Amount of overlap with the reference circle x0 Center distance in the x-axis direction of the tooth profile reference circle meshed at the meshing vertex y0 Center distance in the y-axis direction of the tooth profile reference circle meshed at the meshing vertex θx Engage at the rotational movement destination Center distance in the x-axis direction of the tooth profile reference circle that is in contact with it.
Ln Number of tooth profile reference circles for large gear
Sn Number of tooth profile reference circles for small gears
Sx The x-axis coordinate of the center of the tooth profile reference circle of the small gear
Sy Coordinate of the y-axis at the center of the tooth profile reference circle of the small gear
Lx Coordinate of the x axis of the center of the tooth profile reference circle of the large gear
Ly The coordinate of the y-axis of the center of the tooth profile reference circle of the gear with a large rotational movement destination
SPx The x-axis coordinate of the meshing reference point of the small rotating gear
SPy The y-axis coordinate of the meshing reference point of the small rotating gear

Claims (3)

The first form is a helical gear in which a spur gear is planarly laminated in the axial direction on a plane and is shifted by a predetermined angle to form an outer envelope of a gear outer shape formed around the shaft. A gear device combined to mesh,
A spiral bevel gear having a spherical outer gear as an outer shape on the surface of the sphere as a second form, wherein the spherical surface gears are stacked concentrically in the axial direction and shifted by a predetermined angle to form a gear outer shape envelope around the shaft, A gear device that combines spiral bevel gears to mesh with each other,
On the plane and the sphere surface, one or more tooth profile reference circles are centered on the circumference of the gear reference circle, and the gear reference circle outer periphery side or the gear reference circle inner periphery side of the tooth reference reference circle The outer shape is a shape along the circumference of the gear reference circle, and the outer shape is formed on a flat surface or a spherical surface. On the tooth profile reference circle on the gear reference circle outer periphery side and the gear reference circle inner periphery side. The outer shape is deformed, and the tooth shape in which the pair of the tooth tip and the tooth bottom is a part of the sliding contact portion and the surface sliding contact portion on one of the sliding contact side portions on the tooth profile reference circle. age,
At the correct transmission angle, the part that overlaps with the sliding contact part is deleted, and the other meshing overlapping part deletes one of the overlapping parts. Configure the tooth shape of the sliding contact part,
The meshing phase width that constitutes the transmission sliding contact portion in all the meshing of the gear devices laminated in plane and concentric spheres,
A gear device characterized in that all meshing is at a correct transmission angle.   The tooth profile reference circle according to claim 1 is a concentric double with different diameters, one of the sliding contact side portions is configured with a small diameter tooth profile reference circle, and the other is configured with a large diameter tooth profile reference circle. Gear device.   In the configuration of the tooth profile reference circle according to claim 1, the tooth profile reference circle whose center is located on the circumference of the gear reference circle is continuously disposed, and the tooth profile reference circle on the outer periphery side of the gear reference circle; The tooth reference circle on the inner circumference side of the gear reference circle is made into an outer shape alternately, the part other than the mesh reference point is used as the part sliding contact part, and the mesh overlapping part overlapping the part sliding contact part is deleted. 2. The gear device according to claim 1, wherein the other meshing overlapping portion deletes one of the meshing overlapping portions.