CN103089616A - Internal engaged tooth profile pair - Google Patents
Internal engaged tooth profile pair Download PDFInfo
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- CN103089616A CN103089616A CN2013100312367A CN201310031236A CN103089616A CN 103089616 A CN103089616 A CN 103089616A CN 2013100312367 A CN2013100312367 A CN 2013100312367A CN 201310031236 A CN201310031236 A CN 201310031236A CN 103089616 A CN103089616 A CN 103089616A
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- flank profil
- internal gear
- curve
- coefficient
- cosine
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Abstract
The invention discloses an internal engaged tooth profile pair. A single tooth profile of an internal gear comprises a cosine-based composite curve of a straight line section I, a cosine curve I, a straight line section II and a cosine curve II which meet the first-order continuation in a polar coordinate; a single conjugated tooth profile, which corresponds to the single tooth profile of the internal gear, of an external gear is obtained through a engagement theory, so as to form a conjugated tooth profile pair; and a complete conjugated tooth profile pair is obtained by uniformly distributing the single tooth profiles of the internal gear and the external gear respectively around the centers of the internal gear and the external gear according to the gear numbers. The complete conjugated tooth profile pair is obtained by firstly sequentially determining the straight line section I, the cosine curve I, the straight line section II and the cosine curve II which meet the first-order continuation and form the single tooth profile of the internal gear, subsequently converting into a rectangular coordinate system, obtaining the single tooth profile corresponding to the external gear conjugated with the internal gear through the single tooth profile according to the engagement theory so as to form the single conjugated tooth profile pair, and finally uniformly distributing the single tooth profiles of the internal gear and the external gear respectively around the centers of the internal gear and the external gear according to the gear numbers.
Description
Technical field
This invention belongs to mechanical engineering field, and the interior contacting profile that relates in particular to a kind of field of fluid machinery is secondary.
Background technique
Gear pump mainly contains two kinds of external gear pump and crescent gear pumps, and crescent gear pump has compact structure, relative slippage is little, the life-span is long, and flow pulsation is little, noise is low, at a high speed lower volumetric efficiency advantages of higher and obtain extensive use.The core component of internally engaging pump is a pair of inside and outside engaging tooth wheel set with conjugate profiles, and whether reasonable in design its flank profil is secondary will directly affect pump performance.Crescent gear pump mainly contains involute class internally engaging pump, cycloidal type internally engaging pump and linear conjugated flank profil internally engaging pump etc. at present.Its common design method is generally that directly the design flank profil is secondary in rectangular coordinate system, and this flank profil pair designing method can only be designed to the internally engaging pump of symmetrical flank profil usually because design parameter is few.
Summary of the invention
The object of the invention is to provide a kind of interior contacting profile secondary, and the design parameter that solves existing internal gear pair existence is few, usually can only be designed to the problem of the internally engaging pump of symmetrical flank profil.
Another object of the present invention is to provide the design method of above-mentioned interior contacting profile pair.
Technical solution of the present invention is as follows:
A kind of interior contacting profile is secondary, the single flank profil of internal gear consists of by satisfying the cosine base compound curve that the continuous straightway I of single order, cosine curve I, straightway II and cosine curve II form in polar coordinates successively, the single conjugate profiles of the external gear corresponding with the single flank profil of internal gear obtains by the theory of engagement, forms conjugate profiles secondary; The secondary single flank profil for internal gear, external gear of complete conjugate profiles obtains according to its number of teeth is uniform around its center respectively.
The design method of above-mentioned interior contacting profile pair is first to determine to consist of the cosine base compound curve that is comprised of straightway I, cosine curve I, straightway II and cosine curve II successively that single order requires continuously that satisfies of the single flank profil of internal gear in polar coordinates; Then it is transformed in rectangular coordinate system, the single flank profil of corresponding internal gear is made of tooth root circular arc, cosine curve I conversion curve, tooth top circular arc, cosine curve II conversion curve successively; Obtain corresponding single flank profil on external gear with its conjugation by the single flank profil in rectangular coordinate system according to the theory of engagement again, form single conjugate profiles secondary; At last the single flank profil of inside and outside gear is carried out the uniform complete conjugate profiles that is comprised of internal gear tooth and external gear flank profil of obtaining around its center according to its number of teeth respectively secondary.
Characteristics of the present invention also are:
The design parameter of single flank profil comprises internal gear number of teeth z
2, external gear number of teeth z
1, modulus m, flank profil half tooth depth coefficient k
1, tooth root circular arc arc length coefficient k
2, flank profil symmetry coefficient k
3, cosine curve translation coefficient k
4With tooth top circular arc arc length coefficient k
5
The angular range of the single flank profil of internal gear is
Wherein, the start-stop angle of straightway I is respectively θ
1, θ
2, its equation is: r=r
b+ H (θ
1≤ θ≤θ
2), in formula: r
bBe the mean value of cosine curve, H is the amplitude of longitudinal cosine type curve;
Definition flank profil half tooth depth coefficient
Definition tooth root circular arc arc length coefficient k
2Terminal by straightway I obtains:
The terminal angle of cosine curve I is respectively θ
2, θ
3, the equation of cosine curve I is:
Definition flank profil symmetry coefficient
Definition cosine curve translation coefficient
The start-stop angle of straightway II is respectively θ
3, θ
4, its equation is: r=r
b-H (θ
3≤ θ≤θ
4),
Tooth top circular arc arc length coefficient k
5Terminal by straightway II obtains:
The terminal angle of cosine curve II is respectively θ
4, θ
5, the equation of cosine curve II is:
Preferably, flank profil half tooth depth coefficient k
1Span be 0≤k
1≤ 1.5; Tooth root circular arc coefficient k
2Span be 0≤k
2≤ 0.8; Flank profil symmetry coefficient k
3Span be 0.2≤k
3≤ 0.8; Cosine curve translation coefficient k
4Span be 0.5≤k
4≤ 2; Tooth top circular arc arc length coefficient k
5Span be 0≤k
5≤ 0.8; Internal gear number of teeth z
2With external gear number of teeth z
1Be positive integer and satisfy: z
2-z
1〉=1, z
1〉=2; θ in polar coordinate system
1Can be the arbitrary real number, the single flank profil angular extensions alpha of internal gear satisfies: θ
5-θ
1=α=360/z
2
The present invention has following beneficial effect:
1) the present invention by adjusting the flank profil symmetry coefficient, can obtain asymmetrical gear pump flank profil,
In two of gear flanks, long limit is more suitable for transmission like this, and minor face is more suitable for sealing, is conducive to separating of transmission and sealing function, has strengthened transmission performance and sealing function;
2) the present invention is in the situation that the constant main flow that changes pump by changing flank profil half tooth depth coefficient of modulus and the number of teeth;
3) the present invention by the setting of tooth top circular arc and tooth root circular arc, is of value to processing and detects; By
Adjust tooth top circular arc arc length coefficient and tooth root circular arc arc length coefficient capable of regulating gear pump intensity;
4) to reach single order continuous for the fairness between flank profil pair of the present invention;
5) the present invention is by adjusting cosine curve translation coefficient k
4Can reduce entrap phenomenon;
6) design method of the present invention is that mathematical model has been set up in the polynary optimization of flank profil pair.
Description of drawings
Fig. 1 is the internal gear polar coordinate system cosine base composite curve chart of contacting profile pair in the present invention;
Fig. 2 is the secondary figure of the flank profil of the embodiment of the present invention 1 in rectangular coordinate system;
Fig. 3 is the embodiment of the present invention 2, embodiment 3 flank profil pair and the comparison diagram thereof in rectangular coordinate system;
Fig. 4 is the embodiment of the present invention 4, embodiment 5 flank profil pair and the comparison diagram thereof in rectangular coordinate system;
Fig. 5 is the secondary figure of the flank profil of the embodiment of the present invention 6 in rectangular coordinate system.
Embodiment
The present invention is described in further detail below in conjunction with the drawings and specific embodiments.
In the present invention, contacting profile is secondary, the single flank profil of internal gear is made of the cosine base compound curve that satisfies successively the continuous straightway I of single order, cosine curve I, straightway II and cosine curve II in polar coordinates, the single conjugate profiles of the external gear corresponding with the single flank profil of internal gear obtains by the theory of engagement, forms conjugate profiles secondary; The secondary single flank profil for internal gear, external gear of complete conjugate profiles obtains according to its number of teeth is uniform around its center respectively.
The design method of contacting profile pair in the present invention: first determine the single flank profil of internal gear in polar coordinates, it consists of by satisfying the cosine base compound curve that the continuous straightway I of single order, cosine curve I, straightway II and cosine curve II form successively; Then it is transformed in rectangular coordinate system, the single flank profil of corresponding internal gear is made of tooth root circular arc, cosine curve I conversion curve, tooth top circular arc, cosine curve II conversion curve successively; Obtain corresponding single flank profil on external gear with its conjugation by the single flank profil in rectangular coordinate system according to the theory of engagement again, form single conjugate profiles secondary; At last the single flank profil of inside and outside gear is carried out the uniform complete conjugate profiles that is comprised of internal gear tooth and external gear flank profil of obtaining around its center according to its number of teeth respectively secondary.
The design parameter of single flank profil mainly contains: internal gear number of teeth z
2, external gear number of teeth z
1, module m; The Pitch radius r of internal gear
2=m * z
2/ 2, the Pitch radius r of external gear
1=m * z
1/ 2, the centre distance d=r of gear
2-r
1Referring to Fig. 2, and the coordinate that internal gear connects firmly is x
2o
2y
2, its initial point is that the gyration center of internal gear is o
2, and the coordinate that external gear connects firmly is x
1o
1y
1, the gyration center of its initial point external gear is o
1
Referring to Fig. 1, the single flank profil of internal gear is respectively by straightway I in polar coordinate system, and cosine curve I, straightway II, cosine curve II form, and the angular range of single flank profil is
Wherein, the start-stop angle of straightway 1 is respectively θ
1, θ
2, its equation is:
r=r
b+H(θ
1≤θ≤θ
2)
In formula: r
bBe the mean value of cosine curve, i.e. the central diameter of internal gear; H is the amplitude of longitudinal cosine type curve.
Claim
Be half tooth depth coefficient, H=k
1* m.
Terminal by straightway 1 obtains:
Claim k
2Be tooth root circular arc arc length coefficient.
The terminal angle of cosine curve 1 is respectively θ
2, θ
3The equation of cosine curve 1 is:
Claim
Be the flank profil symmetry coefficient;
Claim
Be the cosine curve translation coefficient.
The start-stop angle of straightway 2 is respectively θ
3, θ
4, its equation is:
r=r
b-H(θ
3≤θ≤θ
4)
The terminal of straightway 2 satisfies:
Claim k
5Be tooth top circular arc arc length coefficient;
The terminal angle of cosine curve 2 is respectively and is θ
4, θ
5, the equation of cosine curve 2 is:
In formula: θ
5Satisfy θ
5-θ
1=α.
Corresponding flank profil is root circular arc, polar coordinate system cosine curve I conversion curve, tooth top circular arc, polar coordinate system cosine curve II conversion curve composition in rectangular coordinate system.
Carry out according to the following formula conversion by polar coordinates to rectangular coordinate system:
x=r·cos(θ)
y=r·sin(θ)
So far, parameter k
1, k
2, k
3, k
4, k
5Become the independent parameter of controlling the single flank profil of internal gear, parameter θ
1The initial phase of controlling flank profil does not exert an influence to the shape of flank profil, makes the conjugate profiles of internal gear tooth have and not produce any interference by selecting suitable parameter.
Usually the parameter value scope satisfies following constraint conditio:
θ
1Without any restriction, can be any real number;
Module m satisfies: m〉0;
Flank profil half tooth depth coefficient k
1, its span is 0≤k
1≤ 1.5;
Tooth root circular arc arc length coefficient k
2, its span is 0≤k
2≤ 0.8;
Flank profil symmetry coefficient k
3, its span is 0.2≤k
3≤ 0.8;
Cosine curve translation coefficient k
4, its span is 0.5≤k
4≤ 2;
Tooth top circular arc arc length coefficient k
5, its span is 0≤k
5≤ 0.8;
Internal gear number of teeth z
2With external gear number of teeth z
1Be positive integer and satisfy: z
2-z
1〉=1; z
1〉=2;
Whole profile on internal gear is with its center o
2Centered by according to number of teeth z
2Single flank profil to internal gear is carried out uniform obtaining.
Single flank profil on external gear obtains according to the single flank profil of the theory of engagement by internal gear, and in like manner, the whole profile on external gear can its center o
1Centered by according to number of teeth z
1Carry out uniform obtaining.
Above-mentioned is the complete design process of interior contacting profile pair, and interior contacting profile pair provided by the present invention consists of by the flank profil of internal gear with the external gear flank profil of its conjugation, and the flank profil of inside and outside gear is an organic indivisible integral body.
Can obtain difform cosine base crescent gear pump flank profil by the combination that changes parameter, because different parameters combination can obtain different design results, because the combination of parameter has infinite a plurality of can not all enumerating, only provide the design embodiment under the different parameters state, as shown in hereinafter embodiment.
Fig. 2 to Fig. 5 is the design embodiment under the different parameters combination, and its parameter is as shown in table 1.
Fig. 2 and Fig. 5 are respectively an embodiment, and in figure, main curve implication is seen on figure and illustrated;
Embodiment illustrated in fig. 21 is minimum number of teeth combination, and its number of teeth is poor is 1, inside and outside gear ratio: z
2: z
1=3:2.
Figure 3 shows that embodiment 2,3 two embodiments of embodiment, inside and outside gear ratio: z
2: z
1=7:5 contrasts symmetrical flank profil and asymmetric flank profil, simultaneously to the flank profil that includes circular arc with do not have the flank profil of circular arc to contrast.
Figure 4 shows that embodiment 4,5 two embodiments of embodiment, inside and outside gear ratio: z
2: z
1=8:5 is mainly to cosine curve translation coefficient k
4Contrast.
Embodiment illustrated in fig. 56, inside and outside gear ratio: z
2: z
1=13:10, tooth is poor is 3.
Table 1 Fig. 2 is to design parameter embodiment illustrated in fig. 5
The present invention provides a kind of parameterized original tooth profile design method in polar coordinate system, then the polar coordinates flank profil is transformed to and ask its common flank profil to obtain a pair of conjugate profiles in right angled coordinates.
Design principle of the present invention is: the single flank profil of internal gear is made of straight line I, cosine curve I, straight line II, cosine curve II successively in polar coordinates, and the corresponding single flank profil of internal gear in rectangular coordinate system is made of tooth root circular arc, cosine curve I conversion curve, tooth top circular arc, cosine curve II conversion curve successively.The single tooth Profile Design of internal gear adopts parameterized mode to carry out, except internal gear number of teeth z
2, external gear number of teeth z
1, outside modulus m, parameter also has: flank profil half tooth depth coefficient k
1, tooth root circular arc arc length coefficient k
2, flank profil symmetry coefficient k
3, cosine curve translation coefficient k
4, tooth top circular arc arc length coefficient k
5, these parameters finally jointly control the secondary shape of the flank profil of gear.When build the single flank profil of completing internal gear in polar coordinates after, it is transformed into rectangular coordinate system x
2o
2y
2In, and obtain a complete single flank profil corresponding on its conjugation external gear according to the theory of engagement, the single flank profil of interior external gear is carried out uniform complete conjugation internal gear tooth and the conjugation external gear flank profil of obtaining around its center according to its number of teeth respectively.
Claims (4)
1. contacting profile is secondary in one kind, it is characterized in that, the single flank profil of internal gear consists of by satisfying the cosine base compound curve that the continuous straightway I of single order, cosine curve I, straightway II and cosine curve II form in polar coordinates successively, the single conjugate profiles of the external gear corresponding with the single flank profil of internal gear obtains by the theory of engagement, forms conjugate profiles secondary; The secondary single flank profil for internal gear, external gear of complete conjugate profiles obtains according to its number of teeth is uniform around its center respectively.
As claimed in claim 1 in the design method of contacting profile pair, it is characterized in that, first determine the single flank profil of internal gear in polar coordinates, it consists of by satisfying the cosine base compound curve that the continuous straightway I of single order, cosine curve I, straightway II and cosine curve II form successively; Then it is transformed in rectangular coordinate system, the single flank profil of corresponding internal gear is made of tooth root circular arc, cosine curve I conversion curve, tooth top circular arc, cosine curve II conversion curve successively; Obtain corresponding single flank profil on external gear with its conjugation by the single flank profil in rectangular coordinate system according to the theory of engagement again, form single conjugate profiles secondary; At last the single flank profil of inside and outside gear is carried out the uniform complete conjugate profiles that is comprised of internal gear tooth and external gear flank profil of obtaining around its center according to its number of teeth respectively secondary.
3. the design method of interior contacting profile pair as claimed in claim 2, it is characterized in that: the design parameter of described single flank profil comprises internal gear number of teeth z
2, external gear number of teeth z
1, modulus m, flank profil half tooth depth coefficient k x, tooth top circular arc arc length coefficient k
2, flank profil symmetry coefficient k
3, cosine curve translation coefficient k
4With tooth root circular arc arc length coefficient k
5
The angular range of the single flank profil of internal gear is
Wherein, the start-stop angle of straightway I is respectively θ
1, θ
2, its equation is: r=r
b+ H (θ
1≤ θ≤θ
2), in formula: r
bBe the mean value of cosine curve, H is the amplitude of longitudinal cosine type curve;
Definition flank profil half tooth depth coefficient
Definition tooth top circular arc arc length coefficient k
2Terminal by straightway I obtains:
The terminal angle of cosine curve I is respectively θ
2, θ
3, the equation of cosine curve I is:
Definition flank profil symmetry coefficient
Definition cosine curve translation coefficient
The start-stop angle of straightway II is respectively θ
3, θ
4, its equation is: r=r
b-H (θ
3≤ θ≤θ
4);
Tooth root circular arc arc length coefficient k
5Terminal by straightway II obtains:
The terminal angle of cosine curve II is respectively θ
4, θ
5, the equation of cosine curve II is:
4. the design method of interior contacting profile pair as claimed in claim 3, is characterized in that, described flank profil half tooth depth coefficient k
1Span be 0≤k
1≤ 1.5; Described tooth top circular arc arc length coefficient k
2Span be 0≤k
2≤ 0.8; Described flank profil symmetry coefficient k
3Span be 0.2≤k
3≤ 0.8; Described cosine curve translation coefficient k
4Span be 0.5≤k
4≤ 2; Described tooth root circular arc arc length coefficient k
5Span be 0≤k
5≤ 0.8; Described internal gear number of teeth z
2With external gear number of teeth z
1Be positive integer and satisfy: z
2-z
1〉=1, z
1〉=2, θ in polar coordinate system
1Can be the arbitrary real number, the single flank profil angular extensions alpha of internal gear satisfies: θ
5-θ
1=α=360/z
2
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|---|---|---|---|
| CN201310031236.7A CN103089616B (en) | 2013-01-28 | 2013-01-28 | A kind of internal messing flank profil is secondary |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201310031236.7A CN103089616B (en) | 2013-01-28 | 2013-01-28 | A kind of internal messing flank profil is secondary |
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| Publication Number | Publication Date |
|---|---|
| CN103089616A true CN103089616A (en) | 2013-05-08 |
| CN103089616B CN103089616B (en) | 2015-11-18 |
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|---|---|---|---|
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104791244A (en) * | 2015-04-22 | 2015-07-22 | 嘉兴东唐汽车科技有限公司 | Internal gear pump applied to SCR system |
| CN106402327A (en) * | 2016-12-09 | 2017-02-15 | 东华大学 | Robot joint precision transmission gear structure |
| CN116085252B (en) * | 2023-01-18 | 2024-05-14 | 西安理工大学 | Visual double-screw mixed-delivery pump internal flow comprehensive testing device |
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2013
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|---|---|---|---|---|
| CN104791244A (en) * | 2015-04-22 | 2015-07-22 | 嘉兴东唐汽车科技有限公司 | Internal gear pump applied to SCR system |
| CN106402327A (en) * | 2016-12-09 | 2017-02-15 | 东华大学 | Robot joint precision transmission gear structure |
| CN116085252B (en) * | 2023-01-18 | 2024-05-14 | 西安理工大学 | Visual double-screw mixed-delivery pump internal flow comprehensive testing device |
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| Publication number | Publication date |
|---|---|
| CN103089616B (en) | 2015-11-18 |
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