CN103089963B - Internal messing flank profil is secondary - Google Patents

Abstract

A kind of internal messing flank profil is secondary, the single flank profil of external gear by meeting single order continuous print straightway I in polar coordinates successively, the cosine basis compound curve of cosine curve I, straightway II and cosine curve II forms, the single conjugate profiles of the internal gear corresponding with the single flank profil of external gear is obtained by the theory of engagement, forms conjugate profiles secondary; Complete conjugate profiles pair is internal gear, the single flank profil of external gear obtains according to its number of teeth is uniform around its center respectively.The present invention adopts and first determines successively to meet straightway I, cosine curve I, the straightway II and cosine curve II that single order forms the single flank profil of external gear continuously in polar coordinates; Then be transformed in rectangular coordinate system, more single flank profil corresponding on obtaining with its conjugation internal gear by single flank profil according to the theory of engagement, form single conjugate profiles secondary; Finally the single flank profil of inside and outside gear is carried out according to its number of teeth around its center respectively that uniform to obtain complete conjugate profiles secondary.

Description

Internal messing flank profil is secondary

Technical field

This invention belongs to mechanical engineering field, and the internal messing flank profil particularly relating to a kind of field of fluid machinery is secondary.

Background technique

Gear pump mainly contains external gear pump and crescent gear pump two kinds, and crescent gear pump has compact structure, relative slippage is little, the life-span is long, and flow pulsation is little, noise is low, high speed is descended volumetric efficiency advantages of higher and obtains extensive use.The core component of internally engaging pump is the inside and outside engaging tooth wheel set a pair with conjugate profiles, and whether reasonable in design its flank profil is secondary directly will affect pump performance.Current crescent gear pump mainly contains involute class internally engaging pump, cycloidal type internally engaging pump and linear conjugated flank profil internally engaging pump etc.Its common design method is generally that directly design flank profil is secondary in rectangular coordinate system, and this flank profil pair designing method is few due to design parameter, usually can only be designed to the internally engaging pump of symmetrical flank profil.

Summary of the invention

It is secondary that the object of the invention is to provide a kind of internal messing flank profil, solves existing internal gear pair and exist 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 the design method providing above-mentioned internal messing flank profil pair.

Technical solution of the present invention is as follows:

Internal messing flank profil is secondary, the single flank profil of external gear is formed by meeting the cosine basis compound curve that single order continuous print straightway I, cosine curve I, straightway II and cosine curve II form successively in polar coordinates, the single conjugate profiles of the internal gear corresponding with the single flank profil of external gear is obtained by the theory of engagement, forms conjugate profiles secondary; Complete conjugate profiles pair is internal gear, the single flank profil of external gear obtains according to its number of teeth is uniform around its center respectively.

The design method of above-mentioned internal messing flank profil pair is, that in polar coordinates, first determines to form the single flank profil of external gear meets the cosine basis compound curve be made up of straightway I, cosine curve I, straightway II and cosine curve II successively that single order requires continuously; Then be transformed in rectangular coordinate system, the single flank profil of corresponding external gear is made up of tooth root circular arc, cosine curve I conversion curve, tooth top circular arc, cosine curve II conversion curve successively; Single flank profil corresponding on obtaining with its conjugation internal gear by the single flank profil in rectangular coordinate system according to the theory of engagement again, forms single conjugate profiles secondary; Finally the single flank profil of inside and outside gear is carried out the uniform complete conjugate profiles pair obtaining being made up of internal gear tooth and external gear flank profil around its center according to its number of teeth respectively.

Feature of the present invention is also:

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 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 _bfor 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 ₂obtained by the terminal of straightway I:

$k_2=\frac{({\mathrm{\θ}}_2-{\mathrm{\θ}}_1)}{\mathrm{\α}};$

The terminal angle of cosine curve I is respectively θ ₂, θ ₃, the equation of cosine curve I is:

$r=H\×\cos (\frac{{\mathrm{\θ}-\mathrm{\θ}}_2}{{\mathrm{\θ}}_3-{\mathrm{\θ}}_2}\×180)+r_b;$

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 ₅obtained by the terminal of straightway II:

The terminal angle of cosine curve II is respectively θ ₄, θ ₅, the equation of cosine curve II is:

$r=H\×\cos (\frac{{\mathrm{\θ}-\mathrm{\θ}}_4}{{\mathrm{\θ}}_5-{\mathrm{\θ}}_4}\×180+180)+r_b,$ In formula, θ ₅meet 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 meet: z ₂-z ₁>=1, z ₁>=2; θ in polar coordinate system ₁can be arbitrary real number, the single flank profil angular extensions alpha of external gear meets: θ ₅-θ ₁=α=360/z ₁.

The present invention has following beneficial effect:

1) the present invention is by adjustment flank profil symmetry coefficient, can obtain asymmetrical gear pump flank profil,

In two flanks of such gear, long limit is more suitable for transmission, and minor face is more suitable for sealing, is conducive to being separated of transmission and sealing function, enhances transmission performance and sealing function;

2) the present invention when modulus and the number of teeth constant to change the flow of pump mainly through changing flank profil half tooth depth coefficient;

3) the present invention passes through the setting of tooth top circular arc and tooth root circular arc, is of value to processing and detects; Pass through

Adjustment tooth top circular arc arc length coefficient and tooth root circular arc arc length coefficient adjustable gear pump intensity;

4) it is continuous that the fairness between flank profil pair of the present invention reaches single order;

5) the present invention is by adjustment cosine curve translation coefficient k ₄entrap phenomenon can be reduced;

6) design method of the present invention is that the polynary optimization of flank profil pair establishes mathematical model.

Accompanying drawing explanation

Fig. 1 is the external gear polar coordinate system cosine basis composite curve chart of internal messing flank profil pair of the present invention;

Fig. 2 is the flank profil pair figure of the embodiment of the present invention 1 in rectangular coordinate system;

Fig. 3 is the secondary and comparison diagram of flank profil in rectangular coordinate system of the embodiment of the present invention 2, embodiment 3;

Fig. 4 is the secondary and comparison diagram of flank profil in rectangular coordinate system of the embodiment of the present invention 4, embodiment 5;

Fig. 5 is the flank profil pair figure of the embodiment of the present invention 6 in rectangular coordinate system.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.

Internal messing flank profil of the present invention is secondary, the single flank profil of external gear by meeting single order continuous print straightway I in polar coordinates successively, the cosine basis compound curve of cosine curve I, straightway II and cosine curve II forms, the single conjugate profiles of the internal gear corresponding with the single flank profil of external gear is obtained by the theory of engagement, forms conjugate profiles secondary; Complete conjugate profiles pair is internal gear, the single flank profil of external gear obtains according to its number of teeth is uniform around its center respectively.

The design method of internal messing flank profil pair of the present invention: first determine the single flank profil of external gear in polar coordinates, it is formed by meeting the cosine basis compound curve that single order continuous print straightway I, cosine curve I, straightway II and cosine curve II form successively; Then be transformed in rectangular coordinate system, the single flank profil of corresponding external gear is made up of tooth root circular arc, cosine curve I conversion curve, tooth top circular arc, cosine curve II conversion curve successively; Single flank profil corresponding on obtaining with its conjugation internal gear by the single flank profil in rectangular coordinate system according to the theory of engagement again, forms single conjugate profiles secondary; Finally the single flank profil of inside and outside gear is carried out the uniform complete conjugate profiles pair obtaining being made up of internal gear tooth and external gear flank profil around its center according to its number of teeth respectively.

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 ₁; See Fig. 2, and the coordinate that internal gear connects firmly is x ₂o ₂y ₂, its initial point is 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.

See Fig. 1, in polar coordinate system, the single flank profil of external gear is respectively by straightway I, and cosine curve I, straightway II, cosine curve II form, then 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 _bfor 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, then H=k ₁× m.

Obtained by the terminal of straightway 1: claim k ₂for tooth root circular arc arc length coefficient.

The terminal angle of cosine curve 1 is respectively θ ₂, θ ₃then the equation of cosine curve 1 is:

$r=H\×\cos (\frac{{\mathrm{\θ}-\mathrm{\θ}}_2}{{\mathrm{\θ}}_3-{\mathrm{\θ}}_2}\×180)+r_b$

Claim for flank profil symmetry coefficient;

Claim for 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 meets: claim k ₅for tooth top circular arc arc length coefficient;

The terminal angle of cosine curve 2 is respectively as θ ₄, θ ₅, then the equation of cosine curve 2 is:

$r=H\×\cos (\frac{{\mathrm{\θ}-\mathrm{\θ}}_4}{{\mathrm{\θ}}_5-{\mathrm{\θ}}_4}\×180+180)+r_b$

In formula: θ ₅meet θ ₅-θ ₁=α.

Then corresponding in rectangular coordinate system 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.

Converted according to the following formula to rectangular coordinate system by polar coordinates:

x=r·cos(θ)

y=r·sin(θ)

So far, parameter k ₁, k ₂, k ₃, k ₄, k ₅become the independent parameter controlling the single flank profil of external gear, parameter θ ₁the initial phase that control flank profil does not have an impact to the shape of flank profil, makes the conjugate profiles of internal gear tooth exist and not produce any interference by selecting suitable parameter.

Usual parameter value scope meets following constraint conditio:

θ ₁without any restriction, can be any real number;

Module m meets: 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 meet: 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 ₁uniform obtaining is carried out to the single flank profil of internal gear.

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 internal messing flank profil pair, and internal messing flank profil provided by the present invention is secondary by the flank profil of internal gear with form with the external gear flank profil of its conjugation, and the flank profil of inside and outside gear is an organic indivisible entirety.

Difform cosine basis crescent gear pump flank profil can be obtained by the combination changing parameter, because different parameters combination can obtain different design results, combination due to parameter has infinite multiplely can not all to enumerate, only provide the design embodiments under different parameters state, as shown in Examples below.

Fig. 2 to Fig. 5 is the design embodiments under different parameters combination, and its parameter is as shown in table 1.

Fig. 2 and Fig. 5 is respectively an embodiment, and in figure, main graph implication is shown in figure illustrates;

Embodiment illustrated in fig. 21 is minimum number of teeth combination, and its number of teeth difference is 1, inside and outside wheel tooth

Number ratio: z ₂: z ₁=3:2.

Figure 3 shows that embodiment 2, embodiment 3 two embodiments, inside and outside gear ratio: z ₂: z ₁=7:5, contrasts symmetrical flank profil and asymmetric flank profil, simultaneously to including the flank profil of circular arc and not having the flank profil of circular arc to contrast.

Figure 4 shows that embodiment 4, embodiment 5 two embodiments, inside and outside gear ratio: z ₂: z ₁=8:5, 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 difference 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 polar coordinates flank profil is transformed in right angled coordinates and asks its common flank profil to obtain a pair conjugate profiles.

Design principle of the present invention is: in polar coordinates, the single flank profil of external gear is made up of straight line I, cosine curve I, straight line II, cosine curve II successively, and the corresponding single flank profil of external gear in rectangular coordinate system is made up 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 being transformed into rectangular coordinate system x after the single flank profil having built external gear in polar coordinates 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 internal-external gear is carried out uniform around its center according to its number of teeth respectively, obtains complete conjugation internal gear tooth and conjugation external gear flank profil.

Claims (3)

1. internal messing flank profil is secondary, it is characterized in that, the single flank profil of external gear is formed by meeting the cosine basis compound curve that single order continuous print straightway I, cosine curve I, straightway II and cosine curve II form successively in polar coordinates, the single conjugate profiles of the internal gear corresponding with the single flank profil of external gear is obtained by the theory of engagement, forms conjugate profiles secondary; Complete conjugate profiles pair is internal gear, the single flank profil of external gear obtains according to its number of teeth is uniform around its center respectively;

Described straightway I, cosine curve I, straightway II and cosine curve II determine in such a way:

Parameters, internal gear number of teeth z ₂, external gear number of teeth z ₁, module 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,

Then the angular range of the single flank profil of external gear is wherein, the start-stop angle of straightway I is respectively θ ₁and θ ₂, its equation is: r=r _b+ H, now θ ₁≤ θ≤θ ₂, in formula, r is footpath, pole, and θ is polar angle, r _bfor 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 ₂obtained by the terminal of straightway I:

The terminal angle of cosine curve I is respectively θ ₂and θ ₃, the equation of cosine curve I is: $r=H\×cos(\frac{\mathrm{\θ}-{\mathrm{\θ}}_2}{{\mathrm{\θ}}_3-{\mathrm{\θ}}_2}\×180)+r_b,$ Definition flank profil symmetry coefficient $k_3=\frac{{\mathrm{\θ}}_3-{\mathrm{\θ}}_1}{\mathrm{\α}};$

Definition cosine curve translation coefficient r ₁for the Pitch radius of external gear;

Straightway II start-stop angle is respectively θ ₃and θ ₄, its equation is: r=r _b-H, now θ ₃≤ θ≤θ ₄;

Tooth top circular arc arc length coefficient k ₅obtained by the terminal of straightway II:

The terminal angle of cosine curve II is respectively θ ₄and θ ₅, the equation of cosine curve II is:

$r=H\×cos(\frac{\mathrm{\θ}-{\mathrm{\θ}}_4}{{\mathrm{\θ}}_5-{\mathrm{\θ}}_4}\×180+180)+r_b,$ In formula, θ ₅meet θ ₅-θ ₁=α.

2. the design method of internal messing flank profil pair as claimed in claim 1, it is characterized in that, first in polar coordinates, determine the single flank profil of external gear, it is formed by meeting the cosine basis compound curve that single order continuous print straightway I, cosine curve I, straightway II and cosine curve II form successively; Then be transformed in rectangular coordinate system, the single flank profil of corresponding external gear is made up of tooth root circular arc, cosine curve I conversion curve, tooth top circular arc, cosine curve II conversion curve successively; Single flank profil corresponding on obtaining with its conjugation internal gear by the single flank profil in rectangular coordinate system according to the theory of engagement again, forms single conjugate profiles secondary; Finally the single flank profil of inside and outside gear is carried out the uniform complete conjugate profiles pair obtaining being made up of internal gear tooth and external gear flank profil around its center according to its number of teeth respectively.

3. the design method of internal messing flank profil pair as claimed in claim 1, 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 meet: z ₂-z ₁>=1, z ₁>=2, θ in polar coordinate system ₁for any real number,

The single flank profil angular extensions alpha of described external gear meets: θ ₅-θ ₁=α=360/z ₁.