JPH0215743B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to gears, and particularly to gears having a small relative curvature at the contact points and a slip ratio of substantially zero.

〔Definition of terms〕

Definitions of technical terms used in this specification are as follows.

(1) Relative curvature 1/K Tooth profile curve F ₁ of gear O ₁ and tooth profile curve of gear O ₂
When F ₂ is in contact with point C, the centers of curvature g ₁ and g ₂ of both tooth profile curves at point C are on the common tangent line of both tooth profile curves.

Assuming that the radii of curvature of both tooth profile curves are ρ ₁ and ρ ₂ respectively, ρ ₁ = g ₁ ρ ₂ = g ₂ Then, the relative curvature 1/K is: 1/K = 1/ρ ₁ + 1/ρ ₂ It is. However, when g ₁ and g ₂ are on opposite sides of C, ρ ₁ and ρ ₂ have the same sign, and when they are on the same side, ρ ₁ and ρ ₂ have different signs.

(2) Slip rate When a small angle rotation is performed and the engagement point moves from the above point C to points C ₁ and C ₂ on F ₁ and F ₂ ,
If the lengths of arcs CC ₁ and CC ₂ are dS ₁ and dS ₂ , the slip rates δ ₁ and δ ₂ are respectively δ ₁ = dS ₁ − dS ₂ /dS ₁ δ ₂ = dS ₁ − dS ₂ /dS ₂ It is.

(3) Mesh ratio ε The angle through which both gears O ₁ and O ₂ rotated between the mesh start point (point C _A ) and the mesh end point (point C _B ) of the above pair of tooth profile curves F ₁ and F ₂ . When φ ₁ and φ ₂ are respectively, the number of teeth is Z ₁ and Z ₂ , and φ ₁ = 2π/Z ₁ φ ₂ = 2π/Z ₂ , the contact ratio ε is as follows: ε=φ ₁ /φ ₁ = _φ2 / _φ2 .

[Conventional technology]

The typical tooth profile of a power transmission gear is an involute tooth profile, but cycloid tooth profiles, circular arc tooth profiles, and combinations thereof are also known.

Looking at the radius of curvature of each of the above tooth profiles, for gears other than circular gears, the radius of curvature of the tooth profile changes monotonically and continuously in the direction of the tooth digits, and at the meshing point, both gears contact each other with their convex surfaces. It is not possible to maintain the relative curvature between the tooth profile curves during meshing to a small value, preferably substantially zero.

The strength of a tooth profile has a limit determined by the bending stress of the tooth and a limit determined by the surface pressure between the tooth surfaces. However, in the commonly used involute gears, the limit due to bending stress is higher than the limit due to tooth surface pressure, so it is necessary to increase the limit due to tooth surface pressure stress, the so-called K value.

This K value is determined by the so-called Hertzian stress that acts between the tooth surfaces, and the Hertzian stress is determined by the relative curvature between the tooth surfaces and the tooth surface pressure.
In order to increase the above K value, it is necessary to make the relative curvature at the meshing point as small as possible, preferably zero.

A tooth profile with a small relative curvature is the Wildhaber Novikov tooth profile, which consists of a circular arc tooth profile.
This tooth profile is a point contact tooth profile that only meshes at one point of the tooth profile (meshing ratio = 0), so in order to use the above Wildhaber Novikov tooth profile as a power transmission gear, it must be made into a wide screw gear. However, there were problems in that it was difficult to manufacture and the cost was high.

Furthermore, even if this is a wide screw gear, actual meshing always occurs only at one point on a cross section perpendicular to the axis, and the meshing point changes from one end of the teeth [meshing start point] as the gear rotates. Because it moves in the face width direction from one end to the other end (meshing end point), this gear system tends to generate vibrations, and therefore cannot be driven at high speeds, so it has not been widely put into practical use.

[Problem that the invention seeks to solve]

The present invention has been made based on the above-mentioned viewpoints, and its purpose is to reduce the relative curvature and increase the K value, that is, the strength limit of the tooth due to tooth surface pressure stress, and to The objective is to provide a gear having a ratio of 1 or more and a relatively small meshing pressure angle to prevent surface pressure and bearing stress from increasing and having overall high strength.

[Means for solving problems]

The above object is thus achieved by a gear in which the curvature of the tooth profile is a continuous and differentiable function that does not vary monotonically along the tooth profile.

In such a tooth profile, the curvature increases and decreases periodically,
In addition, the locus of the center of curvature usually becomes a series of sawtooth curves that approach the pitch circle and straddle one or both sides of the pitch circle.

Note that it is desirable that the center of curvature corresponding to the point where the curvature becomes minimum is located on the pitch line.

[Effect]

By configuring as described above, the relative curvature of the mutually meshing tooth surfaces can be made substantially 0 at the point where the curvature is minimum, and on the other hand, the meshing ratio of the mutually meshing gears can be maintained at 1 or more. In addition, the meshing pressure angle can be made relatively small to prevent surface pressure and bearing stress from increasing, and as mentioned above, the relative curvature between the tooth surfaces of the gear can be reduced compared to conventional gears. Since the tooth profile can be kept small, the overall strength of the tooth profile can be greatly increased.
The face width and module can be made smaller than conventional gears.

Further, since the gear according to the present invention has a slip ratio of substantially 0, the transmission efficiency is high and wear is low.

Furthermore, the gear according to the present invention can of course be used as a screw gear, but it can also normally be used as a spur gear, and even when used as a spur gear, contact occurs over the entire face width. Compared to arc gears that mesh only at one point, the strength per unit tooth width is much higher.

〔Example〕

Hereinafter, the details of the present invention will be specifically explained with reference to the drawings.

1 and 2 are partially enlarged fragmentary views showing examples of gear teeth according to the present invention, FIG. 3 is an explanatory view showing the meshing state of the gears, and FIG. 4 is a reference rack tooth profile curve. FIG. 5 is an explanatory diagram showing the entire reference rack tooth profile.

1 to 3, 1 is the tooth profile curve of a gear with 15 teeth, 2 is its pitch circle, 3 is the tooth profile curve of a gear with 5 teeth, and 4 is its pitch circle.

Therefore, the tooth profiles 1 and 3 of the gear according to the present invention are directed from the pitch line toward the tooth tip and the tooth root,
The radius of curvature is configured to change periodically by repeating increases and decreases, and at the point where the radius of curvature becomes minimum, the centers of the radii of curvature of both gears are both on the pitch line, and one The addendum and dedendum of the gear mesh with the dedendum and addendum of the other gear, respectively, and since the addendum of both gears is convex and the dedendum is concave, meshing is always performed between the concave surface and the convex surface, and therefore, As mentioned above, at the meshing point where the radius of curvature is minimum, the relative curvature between tooth profiles 1 and 3 becomes 0, and therefore the slip rate also becomes 0.

Therefore, in the gear according to the present invention, such preferable meshing points appear many times periodically during one pitch.

In the middle of the points where the relative curvature and sliding rate are 0, the relative curvature and sliding rate are not completely 0, but even at those points, meshing always takes place between the convex surface and the concave surface, and the difference in curvature Since the value of the relative curvature is not very large, the relative curvature is also kept at a relatively small value, and the slip rate is also kept at substantially zero. Therefore, the difference in relative curvature and slip rate between conventional involute gears is
This is particularly severe at engagement points far from the pitch line.

Next, an example of the tooth profile curve of the gear according to the present invention will be explained with reference to FIG. The X axis in the figure is a pitch line, and the curve C ₀ C ₁ C ₂ C ₃ is a part of the standard rack tooth profile curve.

Therefore, the arc C ₀ C ₁ has the center of curvature A ₀ on the addendum side.
is an involute of a small arc g ₀ g ₁ with
C ₁ C ₂ has the center of curvature A ₁ on the dedendum side and is an involute of the small arc g 1 _{g 2} that shares the normal with the above small arc g ₀ g ₁ at point g ₁ , and the arc C ₂ C ₃ is It is an involute of the small arc g 2 g ₃ which has the center of curvature A 2 on the addendum side and shares _the normal line at point _{g 2 with} the above small arc g ₁ g ₂ .

Therefore, the end points g ₀ and g ₂ of one of these arcs are on the pitch line, and the radius of curvature is minimal at this point, and the other part is near the pitch line and on the opposite side of the tooth profile 5, that is, the tooth profile is If it is an addendum, the end points g ₁ and g ₃ are at the addendum or vice versa.

From this figure, the radius of curvature is C ₀ C ₁ in the arc C 0 C ₁
It increases monotonically from r ₀ = _{C 0} g ₀ to r ₁ = C ₁ g 1 from C 1 to C ₁ , but in the arc C ₁ C ₂ , from C ₁ to C ₂
It decreases monotonically from r _{1 =} C ₁ g _{1 to} r ₂ = _{C 2 g 2 toward}
It is known that _the value increases monotonically from r ₂ = C ₂ g ₂ to r 3 = C ₃ g ₃ .

The actual tooth profile is obtained by extending the tooth profile curve from side to side in the figure using the same method as above.

Although it is theoretically more advantageous to make the angle that each small circular arc makes with respect to the radius of curvature, there is no particular restriction, and for example, 1 to 5 degrees is sufficient.

Therefore, in the rack tooth profile constructed in this way, the many points g ₀ , g ₂ , ... are the centers of curvature corresponding to the points C ₀ , C ₂ , C ₄ , C ₆ , ... on the tooth profile curve, respectively. , and all of those points are on the pitch line, and all the gears created using the reference rack are located at these points C ₀ , C ₂ , C ₄ , as well as this reference rack and gears 1 and 3 above. The relative curvature becomes 0 at the meshing points corresponding to C ₆ , .

FIG. 5 shows the entire reference rack tooth profile. As is clear from Figs. 4 and 5, the centers of curvature g ₀ , g 2 , ... at points C ₀ , C ₂ , C ₄ , C ₆ , ... on _the tooth profile curve are all on the pitch line. , the radius of curvature at these points becomes a minimum value. That is, at points other than the above C ₀ , C ₂ , ..., for example, in the middle of C ₀ C ₂ , the radius of curvature is larger than C ₀ g ₀ and C ₂ g ₂ , and the center of curvature is located below the pitch line. That's it. Thus, the locus of these centers of curvature becomes a series of sawtooth curves always in the vicinity of the pitch line.

A gear cut with this rack tool has many centers of curvature of the tooth profile on the pitch circle, and when it meshes with another gear manufactured with the same tool, the relative curvature is 0.

Therefore, the gear according to the present invention has the same advantage as the Wildhaber Novikov gear in that it meshes with a relative curvature of 0, and this can be achieved by reducing the angle that each of the small arcs makes with respect to the center of curvature. Although the number of points where the relative curvature becomes 0 increases and the slip ratio decreases, the meshing ratio can still be maintained at 1 or more even in this case, so the gear according to the present invention can be used as a spur gear. In this respect, it has the same advantages as an impolite gear. From this point of view, it is known that the gear of the present invention combines the advantages of an involute gear and a Wildhaber Novikov gear.

If the above-mentioned angle is about 3 degrees, gears as shown in FIGS. 1 and 2, for example, can be obtained. These gears can be designed relatively freely without making the pressure angle too large, and the radius of curvature increases and decreases periodically along the tooth ridge, so that the meshing of the tooth surfaces is always between the concave and convex surfaces. Therefore, according to the present invention, the relative curvature at the meshing point can be made substantially zero.

It should be noted that the present invention is not limited to the embodiments described above. That is, for example, in the embodiment, the arc constituting the tooth profile curve is an involute of a circle, but
The tooth-shaped curve is not necessarily limited to this, and may be an involute of any other appropriate curve, and furthermore, other known curves may be employed.

〔Effect of the invention〕

Since the present invention is configured as described above, according to the present invention, it is possible to reduce the relative curvature of the meshing point and obtain a meshing ratio of 1 or more without increasing the meshing pressure angle too much, Since it is possible to prevent surface pressure and bearing stress from increasing, the strength of the tooth surface can be significantly increased.

[Brief explanation of drawings]

FIGS. 1 and 2 are partially enlarged fragmentary views showing an example of the tooth profile of a gear according to the present invention, FIG. 3 is an explanatory diagram showing the meshing state of the gear, and FIG. 4 is a reference rack tooth profile curve. FIG. 5 is an explanatory diagram showing the entire reference rack tooth profile. 1... Gear with 15 teeth, 2, 4... Pitch circle, 3
...A gear with 5 teeth.

Claims (1)

[Scope of Claims] 1. A gear characterized in that the curvature of the tooth profile curve is a continuous and differentiable function that periodically increases and decreases in the tooth direction. 2. The gear according to claim 1, wherein the locus of the center of curvature of the tooth profile curve is a series of sawtooth curves existing near the pitch line. 3. The gear according to claim 1, wherein the center of curvature corresponding to the point on the tooth profile curve where the curvature is minimum is located on the pitch line. 4. The gear according to claim 1, wherein the relative curvature at the point where the curvature is minimum is substantially 0.