CN110206866B

CN110206866B - Gear and method for manufacturing same

Info

Publication number: CN110206866B
Application number: CN201810923593.7A
Authority: CN
Inventors: 近江宪仕
Original assignee: Enplas Corp
Current assignee: Enplas Corp
Priority date: 2012-09-21
Filing date: 2013-09-17
Publication date: 2022-07-22
Anticipated expiration: 2033-09-17
Also published as: CN110206866A; WO2014046090A1

Abstract

The present invention is a gear having a plurality of teeth (3) and transmitting a rotational motion by meshing with the teeth of a counterpart gear, wherein a shape (b) of each tooth (3) on the tooth root side is formed by including a 1 st curve (c) and a 2 nd curve (d), the 1 st curve (c) is a curved surface smoothly connected to a tooth surface (a) of an involute curve and is represented by a curve protruding in the opposite direction with respect to the tooth surface (a) of the involute curve, and the 2 nd curve (d) is smoothly connected to the 1 st curved surface (c) and is defined by a hyperbolic function protruding in the same direction with respect to the 1 st curved surface (c). This reduces stress generated on the tooth root side when meshing with the teeth of the mating gear, and increases the strength of the teeth.

Description

Gear and method for manufacturing same

The present application is a divisional application of the following patent applications:

application No.: 201380049049.X

Application date: 09 and 17 days 2013

The invention name is as follows: gear and method for manufacturing same

Technical Field

The present invention relates to a gear having a plurality of teeth and transmitting rotational motion between two shafts by meshing with the teeth of a mating gear, and more particularly, to a gear having a tooth profile in which stress generated on the tooth root side is reduced when meshing with the teeth of the mating gear, thereby increasing the strength of the teeth, and a method for manufacturing the gear.

Background

Conventionally, various designs for improving tooth strength have been implemented for gears used in power transmission mechanisms of automobiles, precision machines, and the like.

As such a gear, there is a gear of a type in which teeth of a disc gear having teeth and tooth grooves are engaged with a counter gear (pinion gear) that is interlocked with a tooth surface, and the gear has a structure in which: the tooth surface is drawn by the pinion from the tooth crest toward the tooth bottom after the last engagement point of the pinion, and is close to a trochoid projected on a vertical section with respect to the reference tooth surface, and the tooth groove is formed in a sharp arch shape in a region of the tooth bottom when viewed in a cross section (for example, see patent document 1).

Patent document 1: japanese Kokai publication Hei-2004-519644

However, in the gear described in patent document 1, since the tooth spaces between adjacent teeth are formed in a sharp arch shape in the region of the tooth bottom when viewed in cross section, a sharp triangular concave point is formed in the tooth bottom. In such a gear, when meshing with the teeth of the partner gear, stress tends to concentrate on the concave points of the tooth bottom, and there is a possibility that the stress increases and the gear is broken. Therefore, the entire tooth including the tooth bottom is required to have high strength.

Disclosure of Invention

Problems to be solved by the invention

In view of the above problems, it is an object of the present invention to provide a gear having a tooth profile shape and a method of manufacturing the same, which can reduce stress generated on the tooth root side when meshing with the teeth of a mating gear and can increase the strength of the teeth.

Means for solving the problems

In order to achieve the above-described object, a gear according to embodiment 1 is a gear having a plurality of teeth and transmitting a rotational motion by meshing with a tooth of a partner gear, wherein a shape of a tooth root side of each tooth includes a 1 st curved surface and a 2 nd curved surface, the 1 st curved surface is a curved surface smoothly connected to a tooth surface of an involute curve and is represented by a curved surface projecting in an opposite direction with respect to the tooth surface of the involute curve, and the 2 nd curved surface smoothly connected to the 1 st curved surface and is defined by a hyperbolic function projecting in the same direction with respect to the 1 st curved surface.

The 2 nd curved surface may have a shape of a tooth right-angle cross section having a curvature radius that does not interfere with a movement locus of a tooth of the meshing partner gear.

The shape of the tooth right-angle cross section of the 1 st curved surface may be an arc having a radius of curvature that does not interfere with the motion trajectory of the tooth of the meshing partner gear, or a spline shape along an interference region of the motion trajectory.

The gear according to embodiment 2 is a gear having a plurality of teeth and transmitting a rotational motion by meshing with the teeth of a counter gear, wherein the shape of the tooth bottom side of each tooth has the same shape as the shape after generating and cutting the teeth by a rack cutter having a circular portion of a curve defined by a hyperbolic function at the cutting edge.

The method of manufacturing a gear according to embodiment 2 is a method of manufacturing a gear having a plurality of teeth and transmitting a rotational motion by meshing with the teeth of a counter gear, and the shape of the tooth bottom side of each tooth is formed to be the same as the shape after generating and cutting the teeth by a rack cutter having a circular portion of a curve defined by a hyperbolic function at the cutting edge.

In the above method of manufacturing a gear, the gear may be made of metal, and the shape of the tooth root side of each tooth may be generated into a cut tooth by a rack cutter having a circular portion of a curve defined by a hyperbolic function at a cutting edge.

In the method for manufacturing the gear, the material of the gear is resin, and the shape of the tooth root side of each tooth is injection molded using a gear mold which is manufactured based on the gear subjected to generating and cutting by a rack cutter having a circular portion of a curve defined by a hyperbolic function at a cutting edge.

ADVANTAGEOUS EFFECTS OF INVENTION

According to the gear of embodiment 1, the shape of the tooth root side of each tooth includes the 1 st curved surface and the 2 nd curved surface, the 1 st curved surface is a curved surface smoothly connected to the tooth surface of the involute curve and is expressed by a curved surface projecting in the opposite direction with respect to the tooth surface of the involute curve, and the 2 nd curved surface is smoothly connected to the 1 st curved surface and is defined by a hyperbolic function projecting in the same direction with respect to the 1 st curved surface, whereby the tooth bottom surface can form a curved surface defined by the hyperbolic function without forming a concave point of a sharp triangle. Therefore, stress concentration is less likely to occur on the tooth root side, and the stress generated on the tooth root side is reduced when the tooth is meshed with the tooth of the mating gear, thereby achieving high strength of the tooth. Thereby, the long-term durability characteristics of the teeth can be improved.

According to the gear of embodiment 2, the shape of each tooth on the tooth root side does not form a sharp triangular concave point on the tooth bottom surface, and the tooth can have a curved surface similar to the shape after generating and cutting the tooth with the rack cutter having a circular portion of a curve defined by a hyperbolic function at the cutting edge. Therefore, stress concentration is less likely to occur on the tooth root side, and the stress generated on the tooth root side is reduced when the tooth is meshed with the tooth of the mating gear, thereby achieving high strength of the tooth. Thereby, the long-term durability characteristics of the teeth can be improved.

According to the method of manufacturing a gear of embodiment 2, the shape of each tooth on the tooth root side does not form a sharp triangular concave point on the tooth bottom surface, and can be formed into a curved surface similar to the shape after generating and cutting teeth by the rack cutter having a circular portion of a curve defined by a hyperbolic function at the cutting edge. Therefore, stress concentration is less likely to occur on the tooth root side, and the stress generated on the tooth root side is reduced when meshing with the teeth of the mating gear, thereby achieving higher strength of the teeth. Thereby, the long-term durability characteristics of the teeth can be improved.

Drawings

Fig. 1 is a front view showing the overall shape of a gear according to the present invention.

Fig. 2 is a perspective view showing a tooth profile of a standard gear.

Fig. 3 is an enlarged explanatory view showing the tooth shape of the gear in embodiment 1.

Fig. 4 is an explanatory diagram showing a tooth surface motion locus of the tooth top side of the tooth of the partner gear with which the teeth of the gear of embodiment 1 come into contact at the time of meshing.

Fig. 5 is an explanatory diagram showing a detailed shape of a portion a in fig. 4.

Fig. 6 is a graph showing the stress distribution of the result of the simulation experiment analysis of the 1 st comparative gear.

Fig. 7 is a graph showing a stress distribution obtained by a simulation experiment analysis of the gear according to embodiment 1.

Fig. 8 is a table illustrating the durability test results of the gear of embodiment 1 and the comparative gear of embodiment 1.

Fig. 9 is an enlarged explanatory view showing a tooth shape of the modified gear of embodiment 1.

Fig. 10 is a table illustrating the results of the durability test of the deformed gear of embodiment 1 and the comparative gear of embodiment 1.

Fig. 11 is an enlarged explanatory view showing the tooth shape of the gear in embodiment 2.

Fig. 12 is an explanatory view showing a rack cutter having a cutting edge with a circular portion of a curve defined by a hyperbolic function.

Fig. 13 is an explanatory diagram showing a detailed shape of the portion B in fig. 12.

Fig. 14 is an explanatory view showing a movement locus of the cutting edge when generating cutting teeth by the rack cutter shown in fig. 12.

Fig. 15 is a graph showing a stress distribution obtained by analyzing a simulation experiment for the 2 nd comparative gear.

Fig. 16 is a graph showing a stress distribution obtained by a simulation experiment analysis of the gear according to embodiment 2.

Description of the symbols

1 … Gear

3 … tooth

6 … tooth crest

7 … tooth bottom surface

10 … rack cutter

11 … rack cutter knife

12 … knife point detected by rack

a … tooth surface

b … tooth flank on tooth root side

c … curved surface No. 1

d … curved surface No.2

g … arc of conventional example

h … curve defined by a hyperbolic function

p … pitch circle

T … trochoid curve

Curve of U …

Detailed Description

Embodiments of the present invention will be described below with reference to the drawings.

Fig. 1 is a front view showing the overall shape of a gear according to the present invention. The gear has a plurality of teeth and transmits a rotational motion between two shafts by meshing with the teeth of a counter gear, and is widely used in a power transmission mechanism of an automobile, a precision machine, an industrial machine, a component thereof, or the like.

In fig. 1, a gear 1 has a substantially disc-shaped web 2 on the outer peripheral side of which a plurality of

teeth

3, 3 … are formed, and a boss 5 is formed in the center of the web 2, and a shaft hole 4 for fixing a rotating shaft is bored in the boss 5, and rotational motion is transmitted between the two shafts. The symbol P indicates a pitch circle of the gear 1.

As shown in fig. 2, the teeth 3 of the gear 1 are formed into a tooth profile of a standard gear having a tooth surface of an involute curve and being bilaterally symmetrical. That is, the tooth width W of the crest 6 of each tooth 3₁A face width W of the tooth bottom face 7 (which means the lowest bottom face of the tooth spaces between the adjacent teeth 3, 3)₂Are formed to have the same size, and the tooth full height H is formed to be constant in the tooth width direction.

Fig. 3 is an enlarged explanatory view showing the shape of the teeth 3 of the gear 1 according to embodiment 1. In fig. 3, the side surface of the tooth 3 is referred to as a tooth surface a, and the shape of the tooth root side of the tooth surface a is referred to as a tooth surface b. The tooth 3 of the gear 1 according to embodiment 1 is designed to have a tooth flank b shape on the tooth root side, and as shown in fig. 3, the tooth flank b shape on the tooth root side of each tooth 3 is formed to include a 1 st curved surface c and a 2 nd curved surface d.

That is, the 1 st curved surface c is a curved surface smoothly connected to the tooth surface a of the involute curve, and is formed in a shape represented by a curve protruding in an opposite direction with respect to the tooth surface a of the involute curve.

The 2 nd curved surface d is smoothly connected to the 1 st curved surface c and has a shape defined by a hyperbolic function that protrudes in the same direction as the 1 st curved surface c. The hyperbolic function is expressed as y ═ cosh (x), and is called a hyperbolic cosine function. Or as a part of a hyperbolic function, expressed as y kXcosh (x/k) (here, k is a coefficient), called a catenary curve.

This tooth shape is determined as follows. First, in fig. 4, the 2 nd curved surface d has a shape of a tooth right-angle cross section of the tooth 3 having a curvature radius not interfering with a motion trajectory of a tooth of the meshing partner gear, and is formed in a curved shape contacting a tooth bottom surface 7 (see fig. 2) of the standard gear. That is, the locus of motion of the tooth surface on the tooth flank side of the counter gear (not shown) which is brought into contact when the teeth 3 of the gear mesh can be obtained from a trochoid T as shown in fig. 4. The trochoid curve T is limited to the region: the tooth base 7 is not reached in the tooth gap between the

teeth

3, 3 of the standard gear. In this state, the tooth of the mating gear may have a curvature radius that does not interfere with the trochoid curve T, which is the trajectory of motion of the tooth of the mating gear, and may be determined to have a shape defined by a hyperbolic function that is a curve in contact with the tooth bottom surface 7 of the standard gear. In this case, the 2 nd curved surface d has a shape protruding inward from the side surface on the tooth root side of the standard gear shown by the broken line f in fig. 4, and therefore the tooth thickness on the tooth root side is larger than that in the conventional art. Further, the tooth bottom surface 7 of the gear is not formed with the sharp triangular concave points described in patent document 1. In fig. 4, the 2 nd curved surface of the hyperbolic function is formed in a curved shape contacting the tooth bottom surface 7 of the standard gear, but the present invention is not limited to this, and any position may be set as long as it does not interfere with the movement locus of the tooth of the partner gear. For example, if the tooth is set to a position above the tooth bottom surface 7 of the standard gear, the strength of the tooth can be further increased.

Next, in fig. 4, the 1 st curved surface c has a shape of a tooth right-angle cross section of the tooth 3 formed in an arc of a radius of curvature that does not interfere with the movement locus of the tooth of the meshing partner gear or a spline curve shape along the interference region of the movement locus. Here, fig. 5 shows a detailed shape of the portion a in fig. 4. In fig. 5, at the point where the tooth face a intersects the curved face d, an edge e where the curved shape of the tooth face a forming an involute curve and the curved shape of the 2 nd curved face d defined by a hyperbolic function (the direction opposite to the curved shape of the tooth face a) meet. As such, when the tooth surface has an edge, stress is easily concentrated therein. Therefore, in order to eliminate the edge e, the shape of the 1 st curved surface c may be determined as an arc along a curvature radius that does not interfere with the trochoid curve T, which is the motion locus of the tooth of the mating gear, or as a spline curve along an interference region of the trochoid curve T as described above. In this case, the 1 st curved surface c is a smooth tooth surface having no edge e, and is a curved surface smoothly continuing to the tooth surface a of the involute curve, that is, a curved surface represented by a curve protruding in the opposite direction with respect to the tooth surface a of the involute curve. Therefore, a tooth shape in which stress concentration due to the edge does not occur can be realized.

The gear 1 of embodiment 1 having the tooth profile shape determined as described above is explained by obtaining and analyzing (CAE) the stress generated on the tooth root side at the time of meshing by a computer-aided simulation experiment. In this case, as a gear to be compared, a gear having a standard gear tooth profile in which teeth are generated and cut by a rack having a cutting edge with a circular portion defined by an arc is formed (hereinafter, referred to as "1 st comparative gear").

First, a calculation model and analysis conditions for root stress calculation in a simulation experiment will be described. The gear of embodiment 1 and the 1 st comparison gear used in this analysis are spur gears, the module (m) is 1, and the number of teeth is 30. The material is a resin (POM) having a Young's modulus of 2800MPa and a Poisson ratio of about 0.38. The mating gears to be engaged are formed to have the same specifications as those of the gear of embodiment 1 and comparative gear 1. The load condition is that a load of 10N is applied to the tooth surface normal direction at the worst load point position. As the analysis model, a mesh shell model in which only one tooth is extracted is used for analysis. As the calculation software for root stress calculation, "SolidWorks" was used.

First, fig. 6 shows the stress distribution of the tooth root stress obtained by analyzing the 1 st comparative gear. In fig. 6, the horizontal axis represents the X coordinate (mm) in the direction of the full height of the tooth, the right side of the coordinate represents the tooth top side, and the left side represents the tooth bottom side. The origin of the horizontal axis is the gear center (the center of the shaft hole 4). The vertical axis represents the magnitude of the generated principal stress (MPa). In the 1 st comparative gear, as shown in fig. 6, the principal stress gradually increases from the tooth crest side to the tooth bottom side, and the principal stress sharply increases from the position where the X coordinate is 14.3mm, and the maximum principal stress σ max reaches 5.39 MPa.

Next, fig. 7 shows a stress distribution of the tooth root stress obtained by analyzing the gear according to embodiment 1. In fig. 7, the horizontal axis and the vertical axis represent the X coordinate (mm) in the tooth full height direction and the magnitude of the generated principal stress (MPa), as in fig. 6. In the gear according to embodiment 1, as shown in fig. 7, the principal stress also gradually increases from the tooth tip to the tooth bottom, and the maximum principal stress σ max is 4.7MPa, which is reduced by about 13% as compared with the gear according to comparative example 1. In addition, even in the case of a change in stress from the tooth tip to the tooth bottom, the abrupt change in stress as in comparative gear No. 1 is small.

As is clear from the analysis results of the above-described simulation experiments, according to the tooth profile of the gear of embodiment 1, the generated stress on the tooth root side can be reduced and the tooth can be strengthened when meshing with the tooth of the mating gear as compared with the gear of comparative example 1. Thus, the long-term durability characteristics of the teeth are improved.

In addition, according to the gear according to embodiment 1, since the shape of the tooth root side is formed as a curved surface defined by a hyperbolic function, stress concentration is less likely to occur on the tooth root side as compared with the conventional gear in which the tooth bottom forms a sharp triangular concave point.

Next, the results of the durability test performed on the gear of embodiment 1 will be described in comparison with the results of the durability test performed on the comparative gear.

Fig. 8 is a table illustrating the durability test results of the gear of embodiment 1 and the comparative gear of embodiment 1. In this durability test, the gear of embodiment 1 shown in fig. 3 was used with the following gears: in a catenary curve, which is a part of a hyperbolic function defining the 2 nd curved surface d, y is kXcosh (x/k), the coefficient k is 0.343. The comparative gear 1 is a gear in which a tooth profile of a standard gear is generated into a cut tooth by a rack having a cutting edge with a circular portion defined by an arc, as in the case of the gear analyzed by a computer aided simulation (CAE). Each specification of the gear according to embodiment 1 and the gear according to comparative gear 1 as a sample is a spur gear, and the module (m) is 1, the pressure angle is 20 °, the number of teeth is 30, and the tooth width is 5 mm. The material is a resin (POM) having a young's modulus of 2800MPa and a poisson ratio of 0.38, and is, for example, a resin called "polyoxymethylene M90-44" (japanese: ジュラコン M90-44) manufactured by polyplastic materials corporation (japanese: ポリプラスチックス).

The conditions of the durability test were, rotational speed: 1000rpm, lubricant: grease manufactured by Country oil & fat company ("Country oil & fat Co., Ltd." TA No.2 for fractional quenching "" (Japanese: マルテンプ TA No.2), ambient temperature: 60 °, load torque: 2.00 Nm. The test method was carried out by meshing the same gears with each other and rotating them in the same direction together with the gear of embodiment 1 and the gear of comparison 1, and comparing the elapsed time (hr) until breakage and the number of meshing times (times) of any of the gears that were meshed.

The durability test results are shown in fig. 8, and the 1 st comparative gear was destroyed after 8.9 hours from the start of rotation and the number of meshing reached 534000. On the other hand, in the gear of embodiment 1, destruction occurred after the number of meshing reached 798000 times after 13.3 hours from the start of rotation. It is understood from this that the durability characteristics are improved by increasing the strength of the gear of embodiment 1 when the life ratio of the gear of embodiment 1 to the 1 st comparative gear is 149%.

Fig. 9 is an enlarged explanatory view showing a tooth shape of the modified gear of embodiment 1. The meanings of the tooth surface a and the tooth surface b, and the 1 st curved surface c and the 2 nd curved surface d in fig. 9 are the same as those in fig. 3. Here, in fig. 9, there are gears: in a catenary curve, which is a part of a hyperbolic function defining the 2 nd curved surface d, y ═ kXcosh (x/k), the coefficient k is 0.428. The tooth surface b on the side root side of the modified gear according to embodiment 1 is formed in a shape close to a semicircular arc shape as compared with the gear according to embodiment 1. The results of the durability test will be described for the deformed gear 1 of embodiment 1 having the tooth profile thus determined.

Fig. 10 is a table illustrating the durability test results of the deformed gear of embodiment 1 and the comparative gear of embodiment 1. This durability test is a durability test comparing the deformed gear of embodiment 1 shown in fig. 9 and the comparative gear 1. In this case, the specifications, materials, conditions of the endurance test, the test method, and the like of the deformed gear of embodiment 1 and the comparative gear of embodiment 1 as samples are the same as those of the endurance test shown in fig. 8.

As shown in fig. 10, the durability test results showed that the 1 st comparative gear was destroyed after 8.9 hours from the start of rotation and the number of meshing reached 534000. On the other hand, in the deformed gear according to embodiment 1, after 23.1 hours from the start of rotation, the number of meshes reached 1386000, and then breakage occurred. It is understood from this that the percentage of life of the deformed gear according to embodiment 1 compared with that of the comparative gear 1 is 260%, and the deformed gear according to embodiment 1 is improved in durability by increasing the strength thereof.

Fig. 11 is an enlarged explanatory view showing the shape of the teeth 3 of the gear 1 according to embodiment 2. In fig. 11, the side surface of the tooth 3 is referred to as a tooth surface a, and the shape of the tooth root side of the tooth surface a is referred to as a tooth surface b. Further, the tooth 3 of the gear 1 according to embodiment 2 is a tooth in which the shape of the tooth root side of the tooth surface a is designed, and as shown in fig. 11, the tooth surface b shape of the tooth root side of each tooth 3 has the same shape as the shape after generating and cutting the tooth with the rack cutter having a circular portion of a curve defined by a hyperbolic function at the edge. In particular, a portion connected to the tooth bottom surface 7 (see fig. 2) is a concave curved surface.

The concave curved surface (b) is a curved surface smoothly connected to the tooth surface a of the involute curve, that is, is formed in a shape represented by a curve protruding in the opposite direction with respect to the tooth surface a of the involute curve. The gear 1 having such a shape on the tooth root side may be a metal gear obtained by cutting a metal material or a resin gear obtained by injection molding a resin.

Here, in order to manufacture the gear 1 having the tooth profile shown in fig. 11, the shape of the tooth root side of each tooth 3 may be formed to be the same as the shape after generating and cutting the tooth by a rack cutter having a circular portion of a curve defined by a hyperbolic function at the cutting edge. The rack cutter 10 used in this case has a circular portion of a curve defined by a hyperbolic function at the cutting edge 12 of the blade 11, as shown in fig. 12. The hyperbolic function is expressed as y ═ cosh (x), and is called a hyperbolic cosine function. Alternatively, the catenary curve is a part of a hyperbolic function expressed as y — kXcosh (x/h) (where k is a coefficient).

Fig. 13 shows a detailed shape of the portion B in fig. 12. In fig. 13, the blade 11 of the rack cutter 10 is generally formed in an arc shape at the cutting edge 12 when a gear having a high strength at the tooth bottom is manufactured by a generating cutting tooth system in a normal gear design. I.e. point C of the cutting edge 12₁、D、C₂The portion (c) is formed as an arc g (conventional example) having a predetermined radius. On the other hand, the point C of the cutting edge 12 shown in fig. 13 is a point C of the blade 11 of the rack tool 10 used for manufacturing the gear 1 of embodiment 2₁、D、C₂Is formed as a circular portion substituted with a curve h defined by a hyperbolic function. In this case, the curve h defined by the hyperbolic function is located inside the arc g of the conventional example, and the cutting edge 12 is slightly thinner. The gear 1 subjected to generating and cutting by the rack tool 10 having the cutting edge 12 has a larger tooth thickness on the tooth root side than the gear subjected to generating and cutting by the rack tool of the conventional example in which the cutting edge 12 is formed into the arc g. In fig. 13, the point C of the cutting edge 12 is replaced by a curve h defined by a hyperbolic function₁、D、C₂For the left and right curve starting points (or connection points) C₁、C₂The position of (2) may be set to any position within a range not interfering with the movement locus of the teeth of the meshing partner gear.

Fig. 14 is an explanatory diagram showing a movement locus of the cutting edge 12 when generating cutting teeth by the rack tool 10 shown in fig. 12. In this case, the gear 1 is made of metal as a raw material, and the gear 1 is manufactured by generating a shape of the tooth root side of each tooth 3 into a cut tooth by the rack cutter 10 having the cutting edge 12 having a circular portion of a curve defined by a hyperbolic function. The movement locus of the cutting edge 12 when the blade 11 of the rack tool 10 contacts the material of the gear 1 to generate the cutting teeth can be obtained from a curve U shown in fig. 14. The curve U has its apex in contact with the tooth bottom surface 7 in the tooth space between the

teeth

3 and 3 of the standard gear. In this case, the concave curved surface (b) shown in fig. 11 has a shape protruding inward of the tooth surface on the tooth root side of the standard gear shown by a broken line i in fig. 14, and therefore the tooth thickness on the tooth root side is larger than that of the conventional example. Further, the bottom face 7 of the gear tooth is not formed with the sharp triangular concave points described in patent document 1. In fig. 14, the concave curved surface (b) is formed in a curved shape contacting the tooth bottom surface 7 of the standard gear, but embodiment 2 is not limited to this, and any position may be set as long as it does not interfere with the trajectory of motion of the tooth of the partner gear. For example, if the tooth is set at a position above the bottom face 7 of the standard gear, the strength of the tooth can be further increased.

In the above description, although the state of manufacturing the metal gear has been described, embodiment 2 is not limited to this, but a resin gear may be manufactured by injection molding using a gear mold (die) made of a gear obtained by generating and cutting teeth with the rack cutter 10 for the shape of the tooth root side of each tooth 3, the cutting edge 12 of the rack cutter 10 having a circular portion of a curve defined by a hyperbolic function. In the production of the gear mold in this case, a metal gear subjected to generating gear cutting by the rack tool 10 may be used as an electrode to produce the gear mold by electric discharge machining. Alternatively, the gear mold is manufactured by a conventionally known method other than electric discharge machining.

The gear 1 of embodiment 2 having the tooth profile shape determined as described above will be described with respect to a result of Calculating and Analyzing (CAE) a stress generated on the tooth root side at the time of meshing by a computer-aided simulation experiment. In this case, as the gear to be compared, a gear having a standard gear tooth profile in which teeth are generated and cut by a rack having a cutting edge with a circular portion defined by an arc is formed (hereinafter, referred to as "comparative gear 2").

First, a calculation model and analysis conditions for root stress calculation in a simulation experiment will be described. The gear of embodiment 2 and the 2 nd comparison gear used in this analysis are spur gears, the module (m) is 1, and the number of teeth is 30. The material was a resin (POM) having a young's modulus of 2800MPa and a poisson's ratio of 0.38. The mating gears to be engaged are formed to have the same specifications as those of the gear of embodiment 2 and the 2 nd comparative gear. The load condition is that a load of 10N is applied to the tooth surface normal direction at the worst load point position. As an analysis model, analysis was performed using a mesh shell model in which only one tooth was extracted. As the calculation software for root stress calculation, "SolidWorks" was used.

First, fig. 15 shows the stress distribution of the tooth root stress obtained by analyzing the comparative gear 2. In fig. 15, the horizontal axis represents an X coordinate (mm) in the tooth full height direction, the right side of the coordinate represents the tooth top side, and the left side represents the tooth bottom side. The origin of the horizontal axis is the gear center (the center of the shaft hole 4). The vertical axis represents the magnitude of the generated principal stress (MPa). In this comparative gear 2, as shown in fig. 15, the principal stress gradually increases from the tooth tip side to the tooth bottom side, and the principal stress sharply increases from a position where the X coordinate is 14.3mm, and the maximum principal stress σ max reaches 5.39 MPa.

Next, fig. 16 shows a stress distribution of the tooth root stress obtained by analyzing the gear according to embodiment 2. In fig. 16, the horizontal axis and the vertical axis represent the X coordinate (mm) in the tooth full height direction and the magnitude of the generated principal stress (MPa), as in fig. 15. In the gear according to embodiment 2, as shown in fig. 16, the principal stress also increases gradually from the tooth tip to the tooth bottom, and although the principal stress increases from the X coordinate of 14.3mm, the maximum principal stress σ max is 5.05 MPa. In this case, the rising position of the principal stress is substantially the same as the 2 nd comparison gear. This rising state is also substantially the same as the 2 nd comparison gear. However, in embodiment 2, the maximum principal stress σ max is lower (by about 6%) than that of comparative gear No. 2. Further, the 2 nd comparative gear has a convex distribution having a peak (maximum value) at one point by observing the stress distribution on the tooth root side, but the gear of embodiment 2 is considered to have a form in which the stress is widely dispersed (flattened), and thus the maximum stress is reduced.

As is clear from the analysis results of the above-described simulation experiments, according to the tooth profile of the gear of embodiment 2, the generated stress on the tooth root side can be reduced and the tooth can be strengthened when meshing with the tooth of the mating gear as compared with the gear of comparative example 2. Thus, the long-term durability characteristics of the teeth are improved.

In the gear according to embodiment 2, the shape of each tooth on the tooth root side is less likely to cause stress concentration on the tooth root side than in the gear according to the related art in which the tooth bottom surface forms a sharp triangular concave point.

In the above embodiment, the example in which the present invention is applied to the standard gear has been described, but the present invention is not limited to this, and for example, it is needless to say that the present invention can also be applied to a modified gear.

The gear of the present invention is not limited to a spur gear, and can be widely applied to tooth shapes of helical gears, herringbone gears, bevel gears, face gears, worm gear devices, double curve gears, and the like. The gear of the present invention is not limited to a gear made of resin, and can be applied to a gear made of metal (for example, alloy steel for machine structural use, carbon steel, stainless steel, brass, phosphor bronze, and the like).

Claims

1. A gear having a plurality of teeth and transmitting a rotational motion by meshing with teeth of a counter gear,

the shape of the tooth root side of each tooth is the same as the shape after generating the cut tooth with a rack cutter having a circular portion of a curve defined by a hyperbolic function at the tip.

2. A method of manufacturing a gear having a plurality of teeth and transmitting a rotational motion by meshing with teeth of a counter gear, the method comprising,

the shape of the tooth root side of each tooth is formed to be the same as the shape after generating and cutting the tooth with a rack cutter having a circular portion of a curve defined by a hyperbolic function at the cutting edge.

3. The method of manufacturing a gear according to claim 2, wherein the gear is made of metal as a raw material, and the shape of the tooth root side of each tooth is generated into a cut tooth by a rack cutter having a circular portion of a curve defined by a hyperbolic function at a cutting edge.

4. The method of manufacturing a gear according to claim 2, wherein the material of the gear is a resin, and the shape of the tooth root side of each tooth is injection molded using a gear mold which is produced on the basis of the gear after generating and cutting the tooth with a rack cutter having a circular portion of a curve defined by a hyperbolic function at a cutting edge.