CN103089963A - Inner meshing tooth profile pair - Google Patents

Inner meshing tooth profile pair Download PDF

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CN103089963A
CN103089963A CN2013100311951A CN201310031195A CN103089963A CN 103089963 A CN103089963 A CN 103089963A CN 2013100311951 A CN2013100311951 A CN 2013100311951A CN 201310031195 A CN201310031195 A CN 201310031195A CN 103089963 A CN103089963 A CN 103089963A
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flank profil
tooth profile
cosine curve
curve
coefficient
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CN103089963B (en
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张广鹏
魏伟锋
康宁
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Xian University of Technology
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Xian University of Technology
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Abstract

Provided is an inner meshing tooth profile pair. An outer gear single tooth profile is composed of cosine matrix composite curves of a straight-line segment I, a cosine curve I, a straight-line segment II and a cosine curve II sequentially meeting first order continuing in polar coordinates, an inner gear single conjugate tooth profile corresponding to the outer gear single tooth profile is obtained through the meshing principle, and thus a conjugate tooth profile pair is formed. The complete conjugate tooth profile pair is obtained due to the fact that an outer gear single tooth profile and the inner gear single tooth profile are respectively and uniformly distributed around the centers of the outer gear single tooth profile and the inner gear single tooth profile according to the number of teeth. Firstly, the straight-line segment I, the cosine curve I, the straight-line segment II and the cosine curve II forming the outer gear single tooth profile and meeting the first order continuing in the polar coordinates are sequentially determined; then the straight-line segment I, the cosine curve I, the straight-line segment II and the cosine curve II are converted to a rectangular coordinate system, a corresponding single tooth profile conjugate to a single tooth profile and located on an inner gear is obtained through the ingle tooth profile according to the meshing principle, and thus a single conjugate tooth profile pair is formed; and finally, the complete conjugate tooth profile pair is obtained due to the fact that an outer gear single tooth profile and the inner gear single tooth profile are respectively and uniformly distributed around centers of the outer gear single tooth profile and the inner gear single tooth profile according to the number of teeth.

Description

Interior contacting profile is secondary
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, solves existing internal gear pair and exists because design parameter 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:
Interior contacting profile is secondary, the single flank profil of external 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 internal gear corresponding with the single flank profil of external 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 external gear in polar coordinates; Then it is transformed in rectangular coordinate system, the single flank profil of corresponding external 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 internal 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 z2, external gear number of teeth z1, 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 external gear is
Figure BDA00002784010100021
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
Figure BDA00002784010100022
Definition tooth root circular arc arc length coefficient k 2Terminal by straightway I obtains:
k 2 = ( θ 2 - θ 1 ) α ;
The terminal angle of cosine curve I is respectively θ 2, θ 3, the equation of cosine curve I is:
r = H × cos ( θ - θ 2 θ 3 - θ 2 × 180 ) + r b ;
Definition flank profil symmetry coefficient
Figure BDA00002784010100033
Definition cosine curve translation coefficient
Figure BDA00002784010100034
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:
Figure BDA00002784010100035
The terminal angle of cosine curve II is respectively θ 4, θ 5, the equation of cosine curve II is:
r = H × cos ( θ - θ 4 θ 5 - θ 4 × 180 + 180 ) + r b , In formula, θ 5Satisfy θ 5-θ 1=α.
Preferably, flank profil half tooth depth coefficient k 1Span be 0≤k 1≤ 1.5; Tooth root circular arc arc length 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 external gear satisfies: θ 5-θ 1=α=360/z 1
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 external 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 external 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 internal gear corresponding with the single flank profil of external 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 external 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 external 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 internal 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 external 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
Figure BDA00002784010100061
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
Figure BDA00002784010100062
Be half tooth depth coefficient, H=k 1* m.
Terminal by straightway 1 obtains:
Figure BDA00002784010100063
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:
r = H × cos ( θ - θ 2 θ 3 - θ 2 × 180 ) + r b
Claim
Figure BDA00002784010100065
Be the flank profil symmetry coefficient;
Claim
Figure BDA00002784010100066
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:
Figure BDA00002784010100067
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:
r = H × cos ( θ - θ 4 θ 5 - θ 4 × 180 + 180 ) + r b
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 external 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 external gear is with its center o 1Centered by according to number of teeth z 1Single flank profil to internal gear is carried out uniform obtaining.
Single flank profil on internal gear obtains according to the single flank profil of the theory of engagement by internal gear, and in like manner, the whole profile on internal gear can its center o 2Centered by according to number of teeth z 2Carry 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 wheel tooth
Number 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
Figure BDA00002784010100091
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 external 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 external 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 external 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 external gear in polar coordinates after, it is transformed into rectangular coordinate system x 1o 1y 1In, and obtain a complete single flank profil corresponding on its conjugation internal 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. interior contacting profile is secondary, it is characterized in that, the single flank profil of external 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 internal gear corresponding with the single flank profil of external 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 external 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 external 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 internal 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 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 machine;
The angular range of the single flank profil of external gear is
Figure FDA00002784010000011
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
Figure FDA00002784010000021
Definition tooth root circular arc arc length coefficient k 2Terminal by straightway I obtains:
k 2 = ( θ 2 - θ 1 ) α ;
The terminal angle of cosine curve I is respectively θ 2, θ 3, the equation of cosine curve I is:
r = H × cos ( θ - θ 2 θ 3 - θ 2 × 180 ) + r b ;
Definition flank profil symmetry coefficient
Definition cosine curve translation coefficient
Figure FDA00002784010000025
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:
Figure FDA00002784010000026
The terminal angle of cosine curve II is respectively θ 4, θ 5, the equation of cosine curve II is:
r = H × cos ( θ - θ 4 θ 5 - θ 4 × 180 + 180 ) + r b , In formula, θ 5Satisfy θ 5-8 1=α.
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 root 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 top 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 external gear satisfies: θ 5-θ 1=α=360/z 1
CN201310031195.1A 2013-01-28 2013-01-28 Internal messing flank profil is secondary Expired - Fee Related CN103089963B (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107905997A (en) * 2017-10-19 2018-04-13 浙江大学 A kind of gear ring structure of anti abrasive Internal Gear Pump Used in Water Hydraulics
WO2020133650A1 (en) * 2018-12-27 2020-07-02 重庆大学 Line-surface conjugation-based paired gear meshing pair and design method therefor
CN112228529A (en) * 2020-10-12 2021-01-15 燕山大学 Novel full-series string gear and gear set thereof

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US3555922A (en) * 1968-02-21 1971-01-19 Hsg Spa High efficiency,reversible or irreversible gear pairs with parallel axes suitable to provide high gear ratios,with small center distance
US4643654A (en) * 1985-09-12 1987-02-17 American Standard Inc. Screw rotor profile and method for generating
SU1751367A1 (en) * 1990-08-14 1992-07-30 Харьковский Институт Инженеров Железнодорожного Транспорта Им.С.М.Кирова Internal combustion engine distributor cam
CN101821510A (en) * 2008-08-08 2010-09-01 住友电工烧结合金株式会社 Internal gear pump rotor, and internal gear pump using the rotor
JP2011017318A (en) * 2009-07-10 2011-01-27 Sumitomo Electric Sintered Alloy Ltd Rotor for pumps and internal gear pump using the same
CN201851630U (en) * 2010-10-31 2011-06-01 李钊刚 Asymmetric long-tooth profile evolvent planetary gear box

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3555922A (en) * 1968-02-21 1971-01-19 Hsg Spa High efficiency,reversible or irreversible gear pairs with parallel axes suitable to provide high gear ratios,with small center distance
US4643654A (en) * 1985-09-12 1987-02-17 American Standard Inc. Screw rotor profile and method for generating
SU1751367A1 (en) * 1990-08-14 1992-07-30 Харьковский Институт Инженеров Железнодорожного Транспорта Им.С.М.Кирова Internal combustion engine distributor cam
CN101821510A (en) * 2008-08-08 2010-09-01 住友电工烧结合金株式会社 Internal gear pump rotor, and internal gear pump using the rotor
JP2011017318A (en) * 2009-07-10 2011-01-27 Sumitomo Electric Sintered Alloy Ltd Rotor for pumps and internal gear pump using the same
CN201851630U (en) * 2010-10-31 2011-06-01 李钊刚 Asymmetric long-tooth profile evolvent planetary gear box

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107905997A (en) * 2017-10-19 2018-04-13 浙江大学 A kind of gear ring structure of anti abrasive Internal Gear Pump Used in Water Hydraulics
CN107905997B (en) * 2017-10-19 2019-03-08 浙江大学 A kind of gear ring structure of anti abrasive Internal Gear Pump Used in Water Hydraulics
WO2020133650A1 (en) * 2018-12-27 2020-07-02 重庆大学 Line-surface conjugation-based paired gear meshing pair and design method therefor
CN112228529A (en) * 2020-10-12 2021-01-15 燕山大学 Novel full-series string gear and gear set thereof
CN112228529B (en) * 2020-10-12 2021-09-28 燕山大学 Full-series string gear and gear set thereof

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