JP5700743B2 - A pair of non-pitch involute tooth profile gears that increase the root width and reduce the relative curvature of the tooth profile at the meshing point. - Google Patents

Description

In the present invention, by combining the involute tooth profile and the cycloid tooth profile, the portion outside the reference circle of the low reference pressure angle involute tooth profile curve is used as the tooth profile in the parallel shaft involute internal gear pair in which the number of teeth and the module are determined. The following features are given to improve strength and reduce friction loss.
1) The sign of the slip rate does not change.
2) Increase the root width by making the root circle larger than the reference circle.
3) Increase the relative radius of curvature of the tooth profile at the meshing point.
In this specification, the parallel-shaft involute internal gear pair whose number of teeth and modules are determined is targeted.
The top and back gaps are the same as before. Therefore, only the top gap is shown in the figure, and the back gap is touched when placing the teeth.

  The present invention improves the performance of an involute tooth profile by fusing involute and cycloid, which are typical spur gear tooth profiles in practical use. First, an outline of these tooth profiles will be described.

FIG. 1 shows a tooth profile of a cycloid tooth profile gear. As shown in the figure, the cycloid tooth profile curve is a portion of the inside and outside cycloid curves HC and EC drawn on the reference circle by points on the circles RH and RE rolling inside and outside the reference circle of radius rO. Connected above, part of it is used as a tooth profile.
The advantages of the cycloid gear are summarized as follows.
1) Since the slip ratio of the tooth surface is constant, tooth surface wear can be made uniform.
2) There is no lowering, the minimum number of teeth of the pinion can be reduced, and the tooth base can be thickened, so that the strength and rigidity can be increased.
The shortcomings of cycloid tooth profile gears are summarized as follows.
1) An error in the center distance impairs tooth meshing and reduces transmission performance.
2) Since the slip ratio of the tooth surface changes in a positive or negative manner at the pitch point, pitching damage and large friction loss are likely to occur.
3) Standardization and high-precision tooth profile production are difficult.
4) The same pitch as the rolling circle is a necessary condition for gear compatibility.
(See Non-Patent Documents 1 to 3)

FIG. 2 shows the tooth profile of the involute tooth gear. Here, as shown in the figure, the involute tooth profile curve is an involute curve drawn on the basic circle by a point on the straight line GL rolling on the basic circle having the radius rG, and inside and outside the reference circle having the radius rO as indicated by a bold line. Part of it is used as a tooth profile.
The advantages of involute tooth gears are summarized as follows.
1) The tooth engagement is not impaired by the error of the center distance.
2) Since the tooth surface can be manufactured with a straight cutting edge, a highly accurate tooth profile can be manufactured.
3) Using the reference rack, it is possible to design a shift gear with high practical standardization and design flexibility.
4) The same gear with the module m and the reference pressure angle αO is interchangeable.
The disadvantages of the involute tooth gear are summarized as follows.
1) The slip ratio of the tooth surface is large between the tooth tip and the tooth root, and changes continuously during this time, and changes between positive and negative at the pitch point. Therefore, uneven tooth surface wear, large friction loss and pitching damage are likely to occur.
2) The minimum number of teeth of the pinion is constrained by the lowering, and the strength and rigidity of the teeth decrease with a gear having a small number of teeth.
(See Non-Patent Documents 1 to 3)

As a combination of an involute and a cycloid tooth profile, an involute / cycloid synthetic tooth profile spur gear pair has been proposed. (Refer to Non-Patent Documents 4 to 7) This is because the contact stress is low in the cycloid, so that the contact stress can be kept low, the tooth root can be thickened without being cut down, and the transmission torque can be increased with high strength and high rigidity. Since the slip of the tooth surface is small, the transmission efficiency is high, and the tooth profile is maintained with a constant slip rate. However, there are drawbacks in that high stress is generated at the pitch point. Therefore, it is a proposal to obtain a high-performance gear by avoiding this defect by connecting the vicinity of the pitch point with an involute curve.
In this way, it is an attempt to obtain a high-performance tooth profile by synthesizing both tooth forms, but the features of the involute are not fully utilized, and there remains a disadvantage that the slip rate changes the sign at the pitch point.

Gears Volume 1 New Edition, Masanori Senba, Nikkan Kogyo Shimbun, p. 44 & 54-55 (1971). Gear Basics and Measurement 1st edition, Muneharu Ryokaku, Seibundo Shinkosha, p. 8-68 (1962). Gear and hobbing machine work, Satoshi Koizumi, Kouda Printing Co., Ltd., p. 14-16 (1994). Design and performance of involute-cycloid synthetic tooth gear, Yoshio Terauchi, Kazuteru Nagamura, Hiromitsu Saijo, Transactions of the Japan Society of Mechanical Engineers (C) Vol. 47, no. 417, 663-674 (1981). Regarding the tooth surface strength of involute and cycloid synthetic tooth profile gears, Yoshio Terauchi, Kazuteru Nagamura, Hiromitsu Saijo, JSME Proceedings (C) Vol. 47. No. 420, p. 1082-1093 (1981). Friction Loss of Involute-Cycloid Synthetic Tooth Shape Gear, Kazuteru Nagamura, Takashi Ikegami, Aoi Saito, JSME Annual Meeting 2001 (01-1), p. 155-156 (2001) 2001-08-22. Strength and performance of involute-cycloid synthetic tooth profile spur gear, Kazuteru Nagamura, Takashi Ikegami, Koichi Isaki, Proceedings of the 2004 Annual Meeting of the Japan Society of Mechanical Engineers, p. 13-14 (2004) 2004-09-04.

We propose a new involute tooth profile that eliminates the disadvantages of the involute internal gear pair without detracting from the advantages of the involute, except for the design and manufacture using the reference rack, and further increases the strength of the number of teeth and modules compared to the same involute gear. These issues are organized as follows.
1) The tooth engagement is not impaired by the error of the center distance.
2) Since the tooth surface can be manufactured with a straight cutting edge, a highly accurate tooth profile can be manufactured.
3) The slip rate of the tooth surface does not change the sign, and the lubrication state is improved to reduce pitching and friction loss.
4) During the meshing, the sliding rate of the tooth surface is reduced and the tooth surface wear is made uniform.
5) Preventing the lowering and reducing the minimum number of teeth of the pinion.
6) Increase the pinion root width and increase the bending strength.
7) Reduce the relative curvature of the tooth profile at the meshing point and increase the surface pressure strength.

As is clear from the paragraphs 0003 and 0004, the point on the straight line rolling around the reference circle is the basis.
The involute tooth profile curve with zero reference pressure angle, which is the involute curve drawn on the quasi-circle, is
Epicycloidal tooth profile with an infinite radius of rolling circle around the reference circle
It can be regarded as a line.
Therefore, the portion outside the reference circle of the low reference pressure angle involute tooth profile curve is the tooth profile curve ( hereinafter referred to as the tooth profile curve ).
After, the standard of the circle outside the involute tooth profile), approximates the tooth profile involute tooth profile curve of the reference pressure angle zero having the same features and epicycloid tooth profile, tooth
By making a part of the shape curve into a tooth profile (hereinafter referred to as a non-standard circle involute tooth profile )
From the beginning to the end of the tooth engagement, the sign of the slip rate does not change and the number of teeth and
Compared to conventional involute gears, the pinion has a larger tooth root width,
Respond to the problem by reducing the relative curvature of the tooth profile at the point .
Note that this is the tooth profile on one side of the tooth, but as with conventional gears, the tooth profile on both sides of the tooth takes into account the tooth pitch, tip width and root gap width, and the center radius of the tooth. Place symmetrically with respect to the line. And in this tooth profile arrangement, a back space is given.

A method for realizing the internal gear pair according to claim 1 using the means described in the preceding paragraph will be described.
Fig. 3 shows the meshing of the non-reference circle involute internal gear pair.
FIG. 4 shows the basic quantities of the pinion teeth of the noncircular reference involute tooth profile internal gear pair. The range of the tooth profile is between the tip circle with radius rT2 and the root circle with radius rF2. The basic quantities of gear teeth can be explained in Fig. 4 by replacing the symbols T and F in the figure and changing 2 to 1, so the presentation is omitted.
3 and 4, the relational expression of the quantities in the pinion and the gear, the relational expression between the quantities of the pinion and the gear, the requirements for the formation of the teeth, and the geometric characteristics of the teeth in the meshing are shown below.

The relational expression of pinion quantities is given by equation (1).

The relational expression of gear quantities is given by equation (2).

The relational expression between the quantities of the gear and the pinion is given by Expression (3) including the back clearance c.

The conditional expression for preventing trochoidal interference, which is a necessary condition for practical use, is given by Eq. (4). This is the relationship between the pinion and gear tooth tip angular positions ηT2B and ηT1B in the 01-xy coordinate system when the pinion tooth tip comes to the intersection B of the pinion tip circle and the gear tip circle.

The condition for preventing pinion tips is given by Equation (5).

The condition of meshing ratio ε and gear formation is given by equation (6).

The relative curvature (1 / ρ), slip velocity vU and slip rate σ at the pinion root width wF2 and an arbitrary engagement point U are given by equations (7), (8), (9) and (10), respectively. .

A reference for designing a reference non-circular involute internal gear pair will be described below using equations (1) to (6). First, a module m which is a unit of tooth size defined by ISO is used. Then, following the practically used involute gear, the tooth profile reference value is given by equation (11), which is used as the design standard for the new tooth gear.

(Equation 11) c = 0.2, d> 0.2, e> 0.4δ2, g = 0.125, j = 2, r01 = rT1, r02 = rF2 (11)

These reference values can be changed as appropriate according to the application.

When the reference value is given by Expression (11), the radius of the tip, root, and root circle is expressed by the following expression.

  The reference value given by the equation (11) is appropriately modified and used for avoiding trochoidal interference, trimming interference and fillet interference and selecting the engagement rate as in the case of the conventional involute gear. Since this analysis and modification method is well-known in conventional involute gears, a description thereof will be omitted. Further, the k value of the equation (1) can be modified in consideration of the strength of the gear pair and individual gears.

An internal gear pair according to claim 1 is a non-standard-circular involute internal gear that meets a problem by approximating an involute tooth profile with a zero reference pressure angle, with a portion of a low standard pressure-angle involute curve outside the standard circle as a tooth profile. It is a pair.

  According to the first aspect of the present invention, a new involute tooth profile internal gear pair that meets the problem described in [0007] is obtained.

  The shrimp cycloid and hypocycloid curves connected by a reference circle and the teeth of a cycloid gear having a tooth profile as a part thereof are shown.   The involute curve and the gear teeth with a part of it are shown.   The meshing of the non-reference involute tooth profile internal gear pair is shown.   The amount of the pinion teeth of the reference non-circular involute tooth profile internal gear pair is shown.

The invention is disclosed by the following examples. In the implementation, first, the number of teeth and the module of each gear pair are determined, and the reference pressure angle is a variable, and the equation (11)
Whether the originally constructed teeth satisfy the gear tooth requirements shown in equations (1) to (6).
Studied, then out of the teeth of the reference pressure angle requirements are met, in accordance with the use conditions of the gear,
select. In addition, the usage range as the tooth profile of the new tooth profile curve can be appropriately modified and used according to the application based on the matters described in the paragraph 0017. Since these are not the essence of the present invention but are well-known design operations for conventional involute gears, their description is omitted.
Here, a design example with a meshing rate of about 1.5 is shown from the teeth of the reference pressure angle satisfying the above requirements .

An internal gear pair with the following number of teeth, module and center distance is designed. The angular velocities of the gear and pinion are ω1 = 104.72 rad / s and ω2 = 209.44 rad / s.
Z1 = 40, Z2 = 20, m = 3, a = 60 mm
In order to verify the validity of the present invention with a specific example, the design result of the involute internal gear pair outside the reference circle is compared with the design result of the involute internal gear pair having a reference pressure angle of 20 deg.
The latter is a shift gear having a shift coefficient of 0.5 that avoids trochoidal interference.
Here, in order to verify the validity of the invention, the engagement ratio ε of both and the pinion root arc width
wF2 mm, relative radius of curvature of tooth surface at meshing point ρ mm, slip rate σ and slip velocity v
m / s is shown below.
1) Design result of standard out-of-reference involute internal gear pair α0 = 12, ε = 1.586, -0.54 ≦ σ1 <0 , 0 <σ2 ≦ 0.35,
12.48 ≦ ρ ≦ 90.58, 0 <v ≦ 1.53

2) Design result of involute dislocation internal gear pair with reference pressure angle 20 deg and dislocation coefficient 0.5 α0 = 20, ε = 1.643, -0.32 ≦ σ1 ≦ 0.32, -0.46 ≦ σ2 ≦ 0.24,
8.12 ≦ ρ ≦ 58.43, -0.5 ≦ v ≦ 1.01
As in this example, the former has a slightly lower meshing rate and a larger sliding speed than the latter, but the positive or negative slip rate is not reversed, the relative curvature radius of the meshing point,
The root width is large, and the validity of the present invention is verified.

B: intersection point of tooth tip circle of gear pair BJ: tooth tip E of gear J when pinion tooth tip is point B: meshing end FJ: tooth profile root of gear J OJ: center of gear J OJ-xJyJ: gear J Reference coordinate system P: pitch point QJ: involute tooth profile starting point S of gear J: start of meshing TJ: tooth profile tooth tip U of gear J: arbitrary meshing point (including U = E, U = P, U = S)
ZJ: Number of teeth of gear J a: Center distance c: Arc back gap on tooth root circle d: Arc gap of gear pair on gear tip circle when pinion tooth tip is point B mm
e: Sum of center angles formed by pinion tooth gap and tooth tip width deg
g: Apex coefficient h: Tooth length mm
he (= jm): Effective tooth height mm
i: Gear-to-pinion tooth ratio j: Tooth length coefficient k: Pinion tooth tip circle to root circle radius ratio m: Module rOJ: Reference circle radius of gear J mm
rFJ: radius of tooth root of gear J mm
rGJ: Basic circle radius of gear J mm
rRJ: radius of tooth root circle of gear J mm
rTJ: radius of tooth tip circle of gear J mm
vU: Slip velocity at point U m / s
wF2: Pinion tooth arc width mm
αO: Gear reference pressure angle deg
αFJ: Root pressure angle of gear J deg
αTJ: tooth tip pressure angle of gear J deg
ε: Gear pair engagement ratio δJ: Center angle formed by the circular pitch of gear J deg
δFJ: Center angle formed by the tooth gap width of gear J deg
δTJ: Center angle formed by the tooth tip width of gear J deg
θB: angular position of point B in the 02-x2y2 coordinate system deg
θJB: rotation angle of gear J when the tooth tip is point B deg
θJ: A variable indicating the rotation angle of the gear J deg
ρU: relative radius of curvature of tooth profile at point U mm
σU: slip ratio at point U ηTJ _B : angular position of tooth tip of gear J in 01-x1y1 coordinate system when pinion tooth tip is point B deg
ωJ: angular velocity of gear J rad / s
Gear J: J = 1 indicates a gear, J = 2 indicates a pinion

Claims (1)

In an involute internal gear pair consisting of a gear and a pinion, the slip rate is reduced during meshing.
Compared with the conventional involute gear with the same number of teeth and the same module, the sign does not change,
Increase the root width of the pinion and reduce the relative curvature of the tooth profile at the meshing point.
For satisfying the condition of not causing trochoidal interference and pinion tooth tips,
Low standard pressure angle involute out of reference circle involuted tooth profile
Lute internal gear pair.

Images