CN103075493A - Bevel gear based on conjugate curves and meshing pair thereof - Google Patents

Abstract

The invention discloses a bevel gear based on conjugate curves and a meshing pair thereof. The meshing pair comprises a bevel gear I and a bevel gear II which are mutually in point meshing and have arc tooth profile curves, and a contact curve gamma1 consisting of meshing points on the tooth profile curve of the bevel gear I and a contact curve gamma2 consisting of meshing points on the tooth profile curve of the bevel gear II are conjugate curves. According to the bevel gear transmission meshing pair based on the conjugate curves, the tooth profile curves of the mutually meshed bevel gear I and bevel gear II are respectively in an arc shape, the meshed tooth surfaces of the bevel gear I and the bevel gear II move along the conjugate curves, the meshing characteristics of the contact curves are succeeded, and the meshing of the contact curves between the tooth surfaces is high in contact strength; a contact transmission process is close to pure rolling along an axial direction, and the transmission efficiency is high; the tooth surfaces are easy to process and manufacture, transmission errors are small, and the service life is long; under the conditions of equivalent transmission ratio and center distance, the selection and determination of a small tooth number and a large modulus can be realized; and the transmission requirements of high speed, heavy load, large power and high efficiency can be met.

Description

Bevel gear and engagement pair thereof based on conjugate curve

Technical field

The invention belongs to the gear transmission technology field, concrete is a kind of bevel gear based on conjugate curve and engagement pair thereof.

Background technique

Gear transmission is one of principal mode in the mechanical transmission, because it has the advantages such as ratio coverage is large, power range is wide, compact structure is reliable, be widely used in various machinery and the instrument and apparatus, become a kind of transmission that accounts for the largest percentage in the existing machinery product.

At present, bevel gear drive mainly contains concurrent aces transmission and two kinds of type of belt drive of alternating axis transmission both at home and abroad, and adopts the secondary transmission that realizes power for Research foundation of involute beveloid gear more.Contact performance between the engaging tooth wheel set is very large on bearing capacity and the life-span impact of gear train, all can cause early stage gear spot corrosion or the failure phenomenon such as peel off such as flank of tooth stress raisers and EDGE CONTACT etc., can cause break of gear tooth etc. when serious, then so that the paralysis of whole transmission system has had a strong impact on gear-driven reliability.Profile modification is adopted in correlative study, the modes such as processing and drive characteristic analysis of making are improved the problems such as gear capacity is low, driving error is large, working life is short although have successively, to improve contact bearing capacity and the reliability of gear pair, still still can not fundamentally solve the transmission shortcoming of such transmission.

In view of this, the present invention is intended to explore a kind of bevel gear based on conjugate curve and engagement pair thereof, this bevel gear engagement pair has advantages of that sliding ratio is little between the flank of tooth, contact strength is large and bearing capacity is high, transmission accuracy is high and long service life, can satisfy high speed, heavily loaded, high-power and high efficiency transmission requirement.

Summary of the invention

The technical problem to be solved in the present invention is to propose a kind of bevel gear and engagement pair thereof based on conjugate curve, this bevel gear engagement pair has advantages of that sliding ratio is little between the flank of tooth, contact strength is large and bearing capacity is high, transmission accuracy is high and long service life, can satisfy high speed, heavily loaded, high-power and high efficiency transmission requirement.

Realize above-mentioned technical purpose, the present invention has at first proposed a kind of bevel gear based on conjugate curve, and the tooth curve of this bevel gear is circular arc, and the curvilinear equation of the inter_curve that is made of contact points on the flank profil curved surface of this gear is:

$\left\{\begin{array}{c}x=X\left(\mathrm{\θ}\right)\\ y=Y\left(\mathrm{\θ}\right)\\ z=f\left(\mathrm{\θ}\right)\end{array}\right.,{\mathrm{\θ}}_1\≤\mathrm{\θ}\≤{\mathrm{\θ}}_2$

Wherein, θ is the parameter of curve angle; θ ₁, θ ₂Be the Line of contact span, namely a corresponding parameter of curve angle is located to nibbling out in parameter of curve angle corresponding to the engaging-in point of flank profil place;

The centre-point curve that the center of circle of the flank profil curved surface of this bevel gear consists of be inter_curve along the equidistant curve of flank profil curved surface common normal line direction, and the curvilinear equation of centre-point curve is:

$\left\{\begin{array}{c}{x}_h=x\&PlusMinus;\mathrm{\&rho;}\&CenterDot;\frac{n_x}{\sqrt{n_x^2+{\mathrm{<figure-callout\; id="2"\; label="n\; y"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^{}+n_z^2}}\\ y_h=y\&PlusMinus;\mathrm{\&rho;}\&CenterDot;\frac{n_{y1}}{\sqrt{n_x^2+{\mathrm{<figure-callout\; id="2"\; label="n\; y"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^{}+{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2^2}}\\ z_h=z\&PlusMinus;\mathrm{\&rho;}\&CenterDot;\frac{n_z}{\sqrt{n_x^2+{\mathrm{<figure-callout\; id="2"\; label="n\; y"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^{}+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^{}}}\end{array}\right.$

In the formula, ρ is the radius of curvature of the dome curved tooth contour curved surface of bevel gear I; n _x, n _y, n _zRespectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates.

Further, the flank profil curved surface of described bevel gear be the centre of sphere along the ball family tubulose envelope surface that described centre-point curve moves, its surface equation is respectively:

In the formula,

Be the ball family parameter, and satisfy

The invention allows for a kind of bevel gear engagement pair based on conjugate curve, comprise that mutual point gearing and tooth curve are bevel gear I and the bevel gear II of circular arc, the inter_curve Γ that is made of contact points on the flank profil curved surface of described bevel gear I ₁With the inter_curve Γ that is consisted of by contact points on the flank profil curved surface of described bevel gear II ₂Be conjugate curve;

The inter_curve Γ of described bevel gear I ₁Curvilinear equation be:

$\left\{\begin{array}{c}{x}_1=X\left(\mathrm{\&theta;}\right)\\ y_1=Y\left(\mathrm{\&theta;}\right)\\ {\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1=f\left(\mathrm{\&theta;}\right)\end{array}\right.,{\mathrm{\&theta;}}_1\&le;\mathrm{\&theta;}\&le;{\mathrm{\&theta;}}_2$

In the formula, θ is the parameter of curve angle; θ ₁, θ ₂Be the Line of contact span, namely a corresponding parameter of curve angle is located to nibbling out in parameter of curve angle corresponding to the engaging-in point of flank profil place;

When the axis Plane intersects of the axis of described bevel gear I and bevel gear II, by the conjugate curve principle, the inter_curve Γ of described bevel gear II ₂Curvilinear equation be:

$\left\{\begin{array}{c}{x}_2=x_1(-\sin {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2+\cos {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})+y_1(\cos {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2+\sin {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})\\ +{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\cos {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}-{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">l</figure-callout>}}_1\cos {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}\\ {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">y</figure-callout>}}_2=x_1(-\sin {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2-\cos {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})+y_1(\cos \mathrm{\&phi;}\cos {\mathrm{\&phi;}}_2-\sin {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})\\ -{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\sin {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}+{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">l</figure-callout>}}_1\sin {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}\\ z_2=x_1(-\cos {\mathrm{\&phi;}}_1\sin \mathrm{\&Sigma;})+y_1(-\sin {\mathrm{\&phi;}}_1\sin \mathrm{\&Sigma;})+{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\cos \mathrm{\&Sigma;}-{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">l</figure-callout>}}_1\cos \mathrm{\&Sigma;}+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">l</figure-callout>}}_2\\ \mathrm{\&Phi;}(\mathrm{\&theta;},{\mathrm{\&phi;}}_1)=n\&CenterDot;{\mathrm{\&upsi;}}^{\left(12\right)}=0\end{array}\right.$

Wherein, φ ₁, φ ₂Be respectively bevel gear I, bevel gear II around the rotating angle of axis separately, satisfy and concern φ ₂=i ₂₁φ ₁, i ₂₁Be gear ratio; ∑ is the crossed axis angle between bevel gear I and the bevel gear II; l ₁, l ₂Be respectively bevel gear I, the bevel gear II conical point the distance round end of on its axial direction; N is inter_curve Γ ₂Method at the contact points place along given wrapping angle direction is vowed; υ ⁽¹²⁾Be illustrated in the speed of related movement at contact points place;

When the axial space of the axis of described bevel gear I and bevel gear II is staggered, by the conjugate curve principle, described inter_curve Γ ₂Curvilinear equation be:

$\left\{\begin{array}{c}{x}_2=x_1(\cos {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2-\sin {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})+y_1(-\sin {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2-\cos {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})\\ +{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\sin {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}-(D_1-b_1)\sin {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}-a\cos {\mathrm{\&phi;}}_2\\ y_2=x_1(\cos {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2+\sin {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})+y_1(-\sin {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2+\cos {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})\\ -{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\cos {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}+(D_1-b_1)\cos {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}-a\sin {\mathrm{\&phi;}}_2\\ {\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">z</figure-callout>}}_2=x_1\left(\sin {\mathrm{\&phi;}}_1\sin \mathrm{\&Sigma;}\right)+y_1\left(\cos {\mathrm{\&phi;}}_1\sin \mathrm{\&Sigma;}\right)+{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\cos \mathrm{\&Sigma;}-(D_1-b_1)\cos \mathrm{\&Sigma;}+(D_2-b_2)\\ \mathrm{\&Phi;}(\mathrm{\&theta;},{\mathrm{\&phi;}}_1)=n\&CenterDot;{\mathrm{\&upsi;}}^{\left(12\right)}=0\end{array}\right.$

Wherein, φ ₁, φ ₂Be respectively bevel gear I, bevel gear II around the rotating angle of axis separately, satisfy and concern φ ₂=i ₂₁φ ₁, i ₂₁Be gear ratio; ∑ is the crossed axis angle between bevel gear I and the bevel gear II; Distance between the benchmark pitch circle of bevel gear I and bevel gear II and work pitch circle is used respectively b ₁, b ₂Expression, D ₁, D ₂Be respectively the work pitch cylinder of bevel gear I, bevel gear II along the distance of axial direction; A is the beeline between bevel gear I axis and the bevel gear II axis; N is inter_curve Γ ₂Method at the contact points place along given wrapping angle direction is vowed; υ ⁽¹²⁾Be illustrated in the speed of related movement at contact points place.

Further, the centre-point curve Γ ' of the center of circle of described bevel gear I flank profil curved surface formation ₁Be inter_curve Γ ₁Equidistant curve along the engagement of wrapping angle direction; The centre-point curve Γ ' that the center of circle of described bevel gear II flank profil curved surface consists of ₂Be inter_curve Γ ₂Equidistant curve along the engagement of wrapping angle direction.

Further, the tooth curve of described bevel gear I and bevel gear II is respectively dome arc and concave circular arc;

And the centre-point curve Γ ' of described bevel gear I ₁Curvilinear equation be:

${{\mathrm{\&Gamma;}}^{\&prime;}}_1:\left\{\begin{array}{c}{x}_{1h}=x_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{x1}}{\sqrt{n_{x1}^2+{\mathrm{<figure-callout\; id="1"\; label="n\; y"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^1+{\mathrm{<figure-callout\; id="1"\; label="n\; z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^1}}\\ y_{1h}={\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{y1}}{\sqrt{n_{x1}^2+{\mathrm{<figure-callout\; id="1"\; label="n\; y"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^1+{\mathrm{<figure-callout\; id="1"\; label="n\; z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^1}}\\ z_{1h}=z_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{z1}}{\sqrt{n_{x1}^2+{\mathrm{<figure-callout\; id="1"\; label="n\; y"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^1+{\mathrm{<figure-callout\; id="1"\; label="n\; z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^1}}\end{array}\right.$

The centre-point curve Γ ' of described bevel gear II ₂Curvilinear equation be:

${{\mathrm{\&Gamma;}}^{\&prime;}}_2:\left\{\begin{array}{c}{x}_{2h}=x_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{x2}}{\sqrt{n_{x2}^2+{\mathrm{<figure-callout\; id="2"\; label="n\; y"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^2}}\\ y_{2h}=y_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{y2}}{\sqrt{n_{x2}^2+{\mathrm{<figure-callout\; id="2"\; label="n\; y"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^2}}\\ z_{2h}=z_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{z2}}{\sqrt{n_{x2}^2+{\mathrm{<figure-callout\; id="2"\; label="n\; y"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^2}}\end{array}\right.$

In the formula, ρ ₁Radius of curvature for the dome curved tooth contour curved surface of bevel gear I; ρ ₂Radius of curvature for the concave circular arc flank profil curved surface of bevel gear II; n _X1, n _Y1, n _Z1, n _X2, n _Y2, n _Z2Respectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates.

Further, the flank profil curved surface ∑ of described bevel gear I ₁For the centre of sphere along described centre-point curve Γ ' ₁The ball family tubulose envelope surface of motion, its equation is:

The flank profil curved surface ∑ of described bevel gear II ₂For the centre of sphere along described centre-point curve Γ ' ₂The ball family tubulose envelope surface of motion, its equation is:

In the formula, ρ ₁Radius of curvature for the dome curved tooth contour curved surface of bevel gear I; ρ ₂Radius of curvature for the concave circular arc flank profil curved surface of bevel gear II; n _X1, n _Y1, n _Z1, n _X2, n _Y2, n _Z2Respectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates;

Represent respectively the envelope requirement of bevel gear I, bevel gear II ball family tubulose envelope surface, wherein parameter item represents that tooth surface equation is to the differentiate of each autoregressive parameter;

Be the ball family parameter, and satisfy

Further, the crossed axis angle between described bevel gear I and the bevel gear II is 0 °＜∑≤90 °.

Further, described inter_curve Γ ₁With inter_curve Γ ₂Be smoothed curve.

Beneficial effect of the present invention is:

The present invention is based on the bevel gear engagement pair of conjugate curve, the tooth curve of intermeshing bevel gear I and bevel gear II is circular arc, be that one of them is protruding circular arc profile among bevel gear I and the bevel gear II, another is the concave circular arc flank profil, and the mesh tooth face of bevel gear I and bevel gear II moves along conjugate curve; This bevel gear pair has been inherited the engagement characteristics of inter_curve, and the engagement of the inter_curve between dome arc and the concave circular arc flank of tooth has high contact strength; The Contact Transmission process is rolled near pure vertically, and transmission efficiency is high; The flank of tooth is easy to manufacturing, and driving error is little, long service life; At same velocity ratio, concentricityly can realize that the selection of the little number of teeth, large modulus determines under the condition; And can satisfy high speed, heavily loaded, high-power and high efficiency transmission requirement, therefore, the bevel gear engagement pair based on conjugate curve of the present invention is a kind of high-performance gear driving pair that has a extensive future.

Description of drawings

Fig. 1 is the first example structure schematic diagram that the present invention is based on the bevel gear engagement pair of conjugate curve;

Fig. 2 is that the present embodiment is based on the space coordinates schematic diagram of the bevel gear engagement pair of conjugate curve;

Fig. 3 is the present embodiment based on the bevel gear engagement pair of conjugate curve along wrapping angle direction theory of engagement figure;

Fig. 4 is for being flank profil Surface forming principle schematic;

Fig. 5 is that the present embodiment is based on the normal tooth profile engagement pair schematic diagram of the bevel gear engagement pair of conjugate curve;

Fig. 6 is that the present embodiment is based on the flank profil curved surface mesh schematic representation of the bevel gear engagement pair of conjugate curve;

Fig. 7 is the second example structure schematic diagram that the present invention is based on the bevel gear engagement pair of conjugate curve;

Fig. 8 is the 3rd example structure schematic diagram that the present invention is based on the bevel gear engagement pair of conjugate curve;

Fig. 9 is that the present embodiment is based on the space coordinates schematic diagram of the bevel gear engagement pair of conjugate curve.

Embodiment

Below in conjunction with accompanying drawing the specific embodiment of the present invention is elaborated.

At first the embodiment of the bevel gear that the present invention is based on conjugate curve elaborated.The present embodiment is circular arc based on the tooth curve of the bevel gear of conjugate curve, and the curvilinear equation of the inter_curve that is made of contact points on the flank profil curved surface of this gear is:

$\left\{\begin{array}{c}x=X\left(\mathrm{\&theta;}\right)\\ y=Y\left(\mathrm{\&theta;}\right)\\ z=f\left(\mathrm{\&theta;}\right)\end{array}\right.,{\mathrm{\&theta;}}_1\&le;\mathrm{\&theta;}\&le;{\mathrm{\&theta;}}_2$

Wherein, θ is the parameter of curve angle; θ ₁, θ ₂Be the Line of contact span, namely a corresponding parameter of curve angle is located to nibbling out in parameter of curve angle corresponding to the engaging-in point of flank profil place;

The centre-point curve that the center of circle of the flank profil curved surface of this bevel gear consists of be inter_curve along the equidistant curve of flank profil curved surface common normal line direction, and the curvilinear equation of centre-point curve is:

$\left\{\begin{array}{c}{x}_h=x\&PlusMinus;\mathrm{\&rho;}\&CenterDot;\frac{n_x}{\sqrt{n_x^2+{\mathrm{<figure-callout\; id="2"\; label="n\; y"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^{}+n_z^2}}\\ y_h=y\&PlusMinus;\mathrm{\&rho;}\&CenterDot;\frac{n_{y1}}{\sqrt{n_x^2+{\mathrm{<figure-callout\; id="2"\; label="n\; y"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^{}+{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2^2}}\\ z_h=z\&PlusMinus;\mathrm{\&rho;}\&CenterDot;\frac{n_z}{\sqrt{n_x^2+{\mathrm{<figure-callout\; id="2"\; label="n\; y"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_y^{}+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^{}}}\end{array}\right.$

In the formula, ρ is the radius of curvature of the dome curved tooth contour curved surface of bevel gear I; n _x, n _y, n _zRespectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates.

The flank profil curved surface of the present embodiment bevel gear be the centre of sphere along the ball family tubulose envelope surface that described centre-point curve moves, its surface equation is respectively:

In the formula,

Be the ball family parameter, and satisfy

The inter_curve of setting the present embodiment bevel gear is space circular cone equidistant helix:

$\left\{\begin{array}{c}x=(R_f-\mathrm{c\&theta;})\cos \mathrm{\&theta;}\\ y=(R_f-\mathrm{c\&theta;})\sin \mathrm{\&theta;}\\ z=\mathrm{p\&theta;}\\ c=p\tan \mathrm{\&delta;}\end{array}\right.,{\mathrm{\&theta;}}_1\&le;\mathrm{\&theta;}\&le;{\mathrm{\&theta;}}_2$

Wherein, R _fIt is the end circle radius of bevel gear I; θ is the helical curve parameter, and θ ₁, θ ₂Be the Line of contact span, namely a corresponding parameter of curve angle is located to nibbling out in parameter of curve angle corresponding to the engaging-in point of flank profil place; P is helix parameter; δ represents the joint angle of bevel gear.

The curvilinear equation of centre-point curve is:

$\left\{\begin{array}{c}{x}_h=(R_f-\mathrm{c\&theta;})\cos \mathrm{\&theta;}\&PlusMinus;\mathrm{\&rho;}\&CenterDot;\frac{n_x}{\sqrt{n_x^2+n_y^2+n_z^2}}\\ y_h=(R_f-\mathrm{c\&theta;})\sin \mathrm{\&theta;}\&PlusMinus;\mathrm{\&rho;}\&CenterDot;\frac{n_{y1}}{\sqrt{n_x^2+n_y^2+{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_2^2}}\\ z_h=\mathrm{p\&theta;}\&PlusMinus;\mathrm{\&rho;}\&CenterDot;\frac{n_z}{\sqrt{n_x^2+n_y^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^{}}}\end{array}\right.$

The surface equation of flank profil curved surface is:

Wherein, R _fIt is the end circle radius of bevel gear; θ is the helical curve parameter; P is helix parameter; δ represents the joint angle of bevel gear, and c=ptan δ; φ is respectively that bevel gear is around the rotating angle of its axis and relation is arranged; ρ is the radius of curvature of the flank profil curved surface of bevel gear; n _x, n _y, n _zRespectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates; Be the envelope requirement of bevel gear I ball family tubulose envelope surface, wherein parameter item represents that tooth surface equation is to the differentiate of each autoregressive parameter;

Be the ball family parameter, and satisfy

The below elaborates to the embodiment of the bevel gear engagement pair that the present invention is based on conjugate curve.

The first embodiment

As shown in Figure 1, be the first example structure schematic diagram of the bevel gear engagement pair that the present invention is based on conjugate curve.The present embodiment is based on the bevel gear engagement pair of conjugate curve, comprise that intermeshing and tooth curve is bevel gear I and the bevel gear II of circular arc, and the crossed axis angle between bevel gear I and the bevel gear II is 0 °＜∑≤90 °, the crossed axis angle of the present embodiment bevel gear I and bevel gear II is 10 °, and Plane intersects between the axis of the axis of the bevel gear I of the present embodiment and bevel gear II.

Further, be some contact engagement, the flank profil curved surface ∑ of bevel gear I between bevel gear I and the bevel gear II ₁The upper inter_curve Γ that is consisted of by contact points ₁Flank profil curved surface ∑ with bevel gear II ₂The upper inter_curve Γ that is consisted of by contact points ₂Be conjugate curve.Preferably, inter_curve Γ ₁With inter_curve Γ ₂Be smoothed curve, guarantee the engagement stationary performance of gear pair.

As shown in Figure 2, be the space coordinates schematic diagram of the present embodiment based on the bevel gear engagement pair of conjugate curve, wherein, S (O-x, y, z) and S _p(O _p-x _p, y _p, z _p) be the fixing system of coordinates in two spaces, the axis of bevel gear I overlaps with the z axle, the axis of bevel gear II and z _pAxle overlaps, and the angle between the two axial lines is ∑=10 °.System of coordinates S ₁(O ₁-x ₁, y ₁, z ₁) be arranged on the bevel gear I system of coordinates S ₂(O ₂-x ₂, y ₂, z ₂) be arranged on the bevel gear II, initial position they respectively with S and S _pOverlap, bevel gear I is with uniform angular velocity ω ⁽¹⁾Rotate around the z axle, bevel gear II is with uniform angular velocity ω ⁽²⁾Around z _pAxle rotates, and the regulation angular velocity omega ⁽¹⁾, ω ⁽²⁾Forward respectively with z and z _pForward identical; From initial position after after a while, S ₁And S ₂Two system of coordinates move to shown position, φ ₁And φ ₂Be respectively the angle that bevel gear I and bevel gear II turn over, the angle between Gear axis and pitch cone bus is called the joint angle, represents δ with δ ₁And δ ₂The joint angle that represents respectively bevel gear I and bevel gear II, R _1fAnd R _2fBe respectively the Pitch radius of bevel gear I and bevel gear II, l among the figure ₁=R _1f/ tan δ ₁, l ₂=R _2f/ tan δ ₂

Inter_curve Γ on the bevel gear I ₁Curvilinear equation be:

$\left\{\begin{array}{c}{x}_1=X\left(\mathrm{\&theta;}\right)\\ {\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1=Y\left(\mathrm{\&theta;}\right)\\ {\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1=f\left(\mathrm{\&theta;}\right)\end{array}\right.,{\mathrm{\&theta;}}_1\&le;\mathrm{\&theta;}\&le;{\mathrm{\&theta;}}_2$

In the formula, θ is the parameter of curve angle; θ ₁, θ ₂Be the Line of contact span, namely a corresponding parameter of curve angle is located to nibbling out in parameter of curve angle corresponding to the engaging-in point of flank profil place.

Since the axis of bevel gear I and the axis Plane intersects of bevel gear II, by the conjugate curve principle, inter_curve Γ ₂Curvilinear equation be:

$\left\{\begin{array}{c}{x}_2=x_1(-\sin {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2+\cos {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})+y_1(\cos {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2+\sin {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})\\ +{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\cos {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}-{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">l</figure-callout>}}_1\cos {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}\\ {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">y</figure-callout>}}_2=x_1(-\sin {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2-\cos {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})+y_1(\cos \mathrm{\&phi;}\cos {\mathrm{\&phi;}}_2-\sin {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})\\ -{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\sin {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}+{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">l</figure-callout>}}_1\sin {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}\\ {\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">z</figure-callout>}}_2=x_1(-\cos {\mathrm{\&phi;}}_1\sin \mathrm{\&Sigma;})+y_1(-\sin {\mathrm{\&phi;}}_1\sin \mathrm{\&Sigma;})+{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\cos \mathrm{\&Sigma;}-{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">l</figure-callout>}}_1\cos \mathrm{\&Sigma;}+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">l</figure-callout>}}_2\\ \mathrm{\&Phi;}(\mathrm{\&theta;},{\mathrm{\&phi;}}_1)=n\&CenterDot;{\mathrm{\&upsi;}}^{\left(12\right)}=0\end{array}\right.$

Wherein, φ ₁, φ ₂Be respectively bevel gear I, bevel gear II around the rotating angle of axis separately, satisfy and concern φ ₂=i ₂₁φ ₁, i ₂₁Be gear ratio; ∑ is the crossed axis angle between bevel gear I and the bevel gear II; l ₁, l ₂Be respectively bevel gear I, the bevel gear II conical point the distance round end of on its axial direction; N is inter_curve Γ ₂Method at the contact points place along given wrapping angle direction is vowed; υ ⁽¹²⁾Be illustrated in the speed of related movement at contact points place.

The present embodiment is set the inter_curve Γ on the bevel gear I ₁Be space circular cone equidistant helix:

$\left\{\begin{array}{c}{x}_1=(R_f-\mathrm{c\&theta;})\cos \mathrm{\&theta;}\\ {\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1=(R_f-\mathrm{c\&theta;})\sin \mathrm{\&theta;}\\ {\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1=\mathrm{p\&theta;}\\ c=p\tan {\mathrm{\&delta;}}_1\end{array}\right.,{\mathrm{\&theta;}}_1\&le;\mathrm{\&theta;}\&le;{\mathrm{\&theta;}}_2$

Wherein, R _fIt is the end circle radius of bevel gear I; θ is the helical curve parameter, and θ ₁, θ ₂Be the Line of contact span, namely a corresponding parameter of curve angle is located to nibbling out in parameter of curve angle corresponding to the engaging-in point of flank profil place; P is helix parameter; δ ₁The joint angle of expression bevel gear I.

Obtain inter_curve Γ according to the conjugate curve principle ₂Curvilinear equation be:

Wherein,

In the formula, R _fIt is the end circle radius of bevel gear I; θ is the helical curve parameter; P is helix parameter; δ ₁The joint angle of expression bevel gear I, and c=ptan δ ₁l ₁, l ₂Be respectively bevel gear I, the bevel gear II conical point the distance round end of on its axial direction; n _x, n _y, n _zThe expression conjugate curve are along the component of given wrapping angle direction method vector in each coordinate axes; i ₂₁Be gear ratio, φ ₁, φ ₂Be respectively bevel gear I, bevel gear II around the angle of revolution of axis separately, and the φ of relation is arranged ₂=i ₂₁φ ₁

Further, as shown in Figure 4, the centre-point curve Γ ' that the center of circle of bevel gear I flank profil curved surface consists of ₁Be inter_curve Γ ₁Equidistant curve along the engagement of wrapping angle direction; The centre-point curve Γ ' that the center of circle of bevel gear II flank profil curved surface consists of ₂Be inter_curve Γ ₂Equidistant curve along the engagement of wrapping angle direction.The bevel gear I of the present embodiment and the tooth curve of bevel gear II are respectively dome arc and concave circular arc, and the double wedge exterior feature of setting bevel gear I is equidistant along wrapping angle direction forward, and distance is ρ ₁The recessed flank profil of bevel gear II is oppositely equidistant along the wrapping angle direction, and distance is ρ ₂, and actual equidistant distance has ρ ₂＞ρ ₁, the distance between curve and the inter_curve centered by the radius of a ball of spheroid in the ball family.

As can be known, the centre-point curve Γ ' of bevel gear I ₁Curvilinear equation be:

${{\mathrm{\&Gamma;}}^{\&prime;}}_1:\left\{\begin{array}{c}{x}_{1h}=x_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{x1}}{\sqrt{n_{x1}^2+n_{y1}^2+{\mathrm{<figure-callout\; id="1"\; label="n\; z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^1}}\\ y_{1h}={\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{y1}}{\sqrt{n_{x1}^2+n_{y1}^2+{\mathrm{<figure-callout\; id="1"\; label="n\; z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^1}}\\ z_{1h}={\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{z1}}{\sqrt{n_{x1}^2+n_{y1}^2+{\mathrm{<figure-callout\; id="1"\; label="n\; z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^1}}\end{array}\right.$

The centre-point curve Γ ' of bevel gear II ₂Curvilinear equation be:

${{\mathrm{\&Gamma;}}^{\&prime;}}_2:\left\{\begin{array}{c}{x}_{2h}=x_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{x2}}{\sqrt{n_{x2}^2+n_{y2}^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^2}}\\ y_{2h}=y_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{y2}}{\sqrt{n_{x2}^2+n_{y2}^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^2}}\\ z_{2h}=z_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{z2}}{\sqrt{n_{x2}^2+n_{y2}^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^2}}\end{array}\right.$

In the formula, ρ ₁Radius of curvature for the dome curved tooth contour curved surface of bevel gear I; ρ ₂Radius of curvature for the concave circular arc flank profil curved surface of bevel gear II; n _X1, n _Y1, n _Z1, n _X2, n _Y2, n _Z2Respectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates.

Further, the flank profil curved surface ∑ of bevel gear I ₁For the centre of sphere along centre-point curve Γ ' ₁The ball family tubulose envelope surface of motion, its equation is:

The flank profil curved surface ∑ of bevel gear II ₂For the centre of sphere along centre-point curve Γ ' ₂The ball family tubulose envelope surface of motion, its equation is:

In the formula, ρ ₁Radius of curvature for the dome curved tooth contour curved surface of bevel gear I; ρ ₂Radius of curvature for the concave circular arc flank profil curved surface of bevel gear II; n _X1, n _Y1, n _Z1, n _X2, n _Y2, n _Z2Respectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates;

The envelope requirement that represents respectively the ball family tubulose envelope surface of bevel gear I, bevel gear II, wherein parameter item represents that tooth surface equation is to the differentiate of each autoregressive parameter; Be the ball family parameter, and satisfy

Concrete, the inter_curve Γ of the present embodiment ₁With inter_curve Γ ₂Be the space circular cone equidistant helix of conjugation, as can be known:

The flank profil surface equation of bevel gear I is:

The flank profil surface equation of bevel gear II is:

Wherein, R _fIt is the end circle radius of bevel gear I; θ is the helical curve parameter; P is helix parameter; δ ₁The joint angle of expression bevel gear I, and c=ptan δ ₁i ₂₁Be velocity ratio, φ ₁, φ ₂Be respectively bevel gear I, bevel gear II around the rotating angle of axis separately and the φ of relation is arranged ₂=i ₂₁φ ₁l ₁, l ₂Be respectively bevel gear I, the bevel gear II conical point the distance round end of on its axial direction; ρ ₁Radius of curvature for the dome curved tooth contour curved surface of bevel gear I; ρ ₂Radius of curvature for the concave circular arc flank profil curved surface of bevel gear II; n _X1, n _Y1, n _Z1, n _X2, n _Y2, n _Z2Respectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates;

The envelope requirement that represents respectively the ball family tubulose envelope surface of bevel gear I, bevel gear II, wherein parameter item represents that tooth surface equation is to the differentiate of each autoregressive parameter;

Be the ball family parameter, and satisfy

Along with the present embodiment rotates with certain angular velocity based on the bevel gear engagement pair of conjugate curve, at a time contact points moves a distance along separately inter_curve, the flank profil of bevel gear I and bevel gear II moves simultaneously vertically a distance and enters the participation engagement of next contact points place, the tooth curve radius of arc of bevel gear II is greater than the tooth curve radius of arc of bevel gear I, according to reality engagement situation, the former the relative latter forms local the containing, makes it have higher engagement driving intensity.

The second embodiment

As shown in Figure 7, be the second example structure schematic diagram of the bevel gear engagement pair that the present invention is based on conjugate curve.The bevel gear engagement pair based on conjugate curve of the present embodiment, comprise that intermeshing and tooth curve is bevel gear I and the bevel gear II of circular arc, and the crossed axis angle between bevel gear I and the bevel gear II is 0 °＜∑≤90 °, the crossed axis angle of the present embodiment bevel gear I and bevel gear II is 90 °, and Plane intersects between the axis of the axis of the bevel gear I of the present embodiment and bevel gear II.

Further, be some contact engagement, the flank profil curved surface ∑ of bevel gear I between bevel gear I and the bevel gear II ₁The upper inter_curve Γ that is consisted of by contact points ₁Flank profil curved surface ∑ with bevel gear II ₂The upper inter_curve Γ that is consisted of by contact points ₂Be conjugate curve.Preferably, inter_curve Γ ₁With inter_curve Γ ₂Be smoothed curve, guarantee the engagement stationary performance of gear pair.

The present embodiment is identical with the first embodiment based on the space coordinates of the bevel gear engagement pair of conjugate curve, wherein, and S (O-x, y, z) and S _p(O _p-x _p, y _p, z _p) be the fixing system of coordinates in two spaces, the axis of bevel gear I overlaps with the z axle, the axis of bevel gear II and z _pAxle overlaps, and the angle between the two axial lines is ∑=90 °.System of coordinates S ₁(O ₁-x ₁, y ₁, z ₁) be arranged on the bevel gear I system of coordinates S ₂(O ₂-x ₂, y ₂, z ₂) be arranged on the bevel gear II, initial position they respectively with S and S _pOverlap, bevel gear I is with uniform angular velocity ω ⁽¹⁾Rotate around the z axle, bevel gear II is with uniform angular velocity ω ⁽²⁾Around z _pAxle rotates, and the regulation angular velocity omega ⁽¹⁾, ω ⁽²⁾Forward respectively with z and z _pForward identical; From initial position after after a while, S ₁And S ₂Two system of coordinates move to shown position, φ ₁And φ ₂Be respectively the angle that bevel gear I and bevel gear II turn over, the angle between Gear axis and pitch cone bus is called the joint angle, represents δ with δ ₁And δ ₂The joint angle that represents respectively bevel gear I and bevel gear II, R _1fAnd R _2fBe respectively the Pitch radius of bevel gear I and bevel gear II, l among the figure ₁=R _1f/ tan δ ₁, l ₂=R _2f/ tan δ ₂

The present embodiment is set the inter_curve Γ on the bevel gear I ₁Be space circular cone equidistant helix:

$\left\{\begin{array}{c}{x}_1=(R_f-\mathrm{c\&theta;})\cos \mathrm{\&theta;}\\ {\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1=(R_f-\mathrm{c\&theta;})\sin \mathrm{\&theta;}\\ {\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1=\mathrm{p\&theta;}\\ c=p\tan {\mathrm{\&delta;}}_1\end{array}\right.,{\mathrm{\&theta;}}_1\&le;\mathrm{\&theta;}\&le;{\mathrm{\&theta;}}_2$

Wherein, R _fIt is the end circle radius of bevel gear I; θ is the helical curve parameter, and θ ₁, θ ₂Be the Line of contact span, namely a corresponding parameter of curve angle is located to nibbling out in parameter of curve angle corresponding to the engaging-in point of flank profil place, and p is helix parameter, δ ₁The joint angle of expression bevel gear I, and c=ptan δ ₁

Obtain inter_curve Γ according to the conjugate curve principle ₂Curvilinear equation be:

Wherein,

In the formula, R _fIt is the end circle radius of bevel gear I; θ is the helical curve parameter; P is helix parameter; δ ₁The joint angle of expression bevel gear I, and c=ptan δ ₁i ₂₁Be gear ratio, φ ₁, φ ₂Be respectively bevel gear I, bevel gear II around the rotating angle of axis separately, and the φ of relation is arranged ₂=i ₂₁φ ₁l ₁, l ₂Be respectively bevel gear I, the bevel gear II conical point the distance round end of on its axial direction; n _x, n _y, n _zThe expression conjugate curve are along the component of given wrapping angle direction method vector in each coordinate axes; i ₂₁Be gear ratio.

Further, as shown in Figure 4, the centre-point curve Γ ' that the center of circle of bevel gear I flank profil curved surface consists of ₁Be inter_curve Γ ₁Equidistant curve along the engagement of wrapping angle direction; The centre-point curve Γ ' that the center of circle of bevel gear II flank profil curved surface consists of ₂Be inter_curve Γ ₂Equidistant curve along the engagement of wrapping angle direction.The bevel gear I of the present embodiment and the tooth curve of bevel gear II are respectively dome arc and concave circular arc, and the double wedge exterior feature of setting bevel gear I is equidistant along wrapping angle direction forward, and distance is ρ ₁The recessed flank profil of bevel gear II is oppositely equidistant along the wrapping angle direction, and distance is ρ ₂, and actual equidistant distance has ρ ₂＞ρ ₁, the distance between curve and the inter_curve centered by the radius of a ball of spheroid in the ball family.

As can be known, the centre-point curve Γ ' of bevel gear I ₁Curvilinear equation be:

${{\mathrm{\&Gamma;}}^{\&prime;}}_1:\left\{\begin{array}{c}{x}_{1h}=x_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{x1}}{\sqrt{n_{x1}^2+n_{y1}^2+{\mathrm{<figure-callout\; id="1"\; label="n\; z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^1}}\\ y_{1h}={\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{y1}}{\sqrt{n_{x1}^2+n_{y1}^2+{\mathrm{<figure-callout\; id="1"\; label="n\; z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^1}}\\ z_{1h}={\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{z1}}{\sqrt{n_{x1}^2+n_{y1}^2+{\mathrm{<figure-callout\; id="1"\; label="n\; z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^1}}\end{array}\right.$

The centre-point curve Γ ' of bevel gear II ₂Curvilinear equation be:

${{\mathrm{\&Gamma;}}^{\&prime;}}_2:\left\{\begin{array}{c}{x}_{2h}=x_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{x2}}{\sqrt{n_{x2}^2+n_{y2}^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^2}}\\ y_{2h}=y_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{y2}}{\sqrt{n_{x2}^2+n_{y2}^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^2}}\\ z_{2h}=z_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{z2}}{\sqrt{n_{x2}^2+n_{y2}^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^2}}\end{array}\right.$

In the formula, ρ ₁Radius of curvature for the dome curved tooth contour curved surface of bevel gear I; ρ ₂Radius of curvature for the concave circular arc flank profil curved surface of bevel gear II; n _X1, n _Y1, n _Z1, n _X2, n _Y2, n _Z2Respectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates.

Further, the flank profil curved surface ∑ of bevel gear I ₁For the centre of sphere along centre-point curve Γ ' ₁The ball family tubulose envelope surface of motion, the flank profil curved surface ∑ of bevel gear II ₂For the centre of sphere along centre-point curve Γ ' ₂The ball family tubulose envelope surface of motion, and the inter_curve Γ of the present embodiment ₁With inter_curve Γ ₂Be the space circular cone equidistant helix of conjugation, as can be known:

The flank profil surface equation of bevel gear I is:

The flank profil surface equation of bevel gear II is:

Wherein, R _fIt is the end circle radius of bevel gear I; θ is the helical curve parameter; P is helix parameter; δ ₁The joint angle of expression bevel gear I, and c=ptan δ ₁i ₂₁Be gear ratio, φ ₁, φ ₂Be respectively bevel gear I, bevel gear II around the rotating angle of axis separately and the φ of relation is arranged ₂=i ₂₁φ ₁l ₁, l ₂Be respectively bevel gear I, the bevel gear II conical point the distance round end of on its axial direction; ρ ₁Radius of curvature for the dome curved tooth contour curved surface of bevel gear I; ρ ₂Radius of curvature for the concave circular arc flank profil curved surface of bevel gear II; n _X1, n _Y1, n _Z1, n _X2, n _Y2, n _Z2Respectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates;

Represent respectively the envelope requirement of bevel gear I, bevel gear II ball family tubulose envelope surface, wherein parameter item represents that tooth surface equation is to the differentiate of each autoregressive parameter;

Be the ball family parameter, and satisfy

Along with the present embodiment rotates with certain angular velocity based on the bevel gear engagement pair of conjugate curve, at a time contact points moves a distance along separately inter_curve, the flank profil of bevel gear I and bevel gear II moves simultaneously vertically a distance and enters the participation engagement of next contact points place, the tooth curve radius of arc of bevel gear II is greater than the tooth curve radius of arc of bevel gear I, according to reality engagement situation, the former the relative latter forms local the containing, makes it have higher engagement driving intensity.

The 3rd embodiment

As shown in Figure 8, be the 3rd example structure schematic diagram of the bevel gear engagement pair that the present invention is based on conjugate curve.The present embodiment is based on the bevel gear engagement pair of conjugate curve, comprise that intermeshing and tooth curve is bevel gear I and the bevel gear II of circular arc, and the crossed axis angle between bevel gear I and the bevel gear II is 0 °＜∑≤90 °,, and spatial intersecting between the axis of the axis of the bevel gear I of the present embodiment and bevel gear II.

Further, be some contact engagement, the flank profil curved surface ∑ of bevel gear I between bevel gear I and the bevel gear II ₁The upper inter_curve Γ that is consisted of by contact points ₁Flank profil curved surface ∑ with bevel gear II ₂The upper inter_curve Γ that is consisted of by contact points ₂Be conjugate curve.Preferably, inter_curve Γ ₁With inter_curve Γ ₂Be smoothed curve, guarantee the engagement stationary performance of gear pair.

As shown in Figure 9, be the space coordinates schematic diagram of the present embodiment based on the bevel gear engagement pair of conjugate curve, S (O-x, y, z), S _p(O _p-x _p, y _p, z _p) be the fixing system of coordinates in two spaces, the axis of bevel gear I overlaps with the z axle, the axis of bevel gear II and z _pAxle overlaps, and the angle between the two axial lines is ∑=10 °.System of coordinates S ₁(O ₁-x ₁, y ₁, z ₁) be arranged on the bevel gear I system of coordinates S ₂(O ₂-x ₂, y ₂, z ₂) be arranged on the bevel gear II, initial position they respectively with S and S _pOverlap, bevel gear I is with uniform angular velocity ω ⁽¹⁾Rotate around the z axle, bevel gear II is with uniform angular velocity ω ⁽²⁾Around z _pAxle rotates, and the regulation angular velocity omega ⁽¹⁾, ω ⁽²⁾Forward respectively with z and z _pForward identical; From initial position after after a while, S ₁And S ₂Two system of coordinates move to shown position, φ ₁And φ ₂Be respectively the angle that bevel gear I and bevel gear II turn over, the angle between Gear axis and pitch cone bus is called the joint angle, represents δ with δ ₁And δ ₂The joint angle that represents respectively bevel gear I and bevel gear II, r ₁And r ₂Be respectively the Pitch radius of bevel gear I and bevel gear II, r _W1And r _W2The radius that represents respectively the work pitch cylinder of bevel gear I and bevel gear II, the distance between the pitch circle of bevel gear I and bevel gear II is used respectively b ₁And b ₂Expression, D ₁And D ₂Then be respectively the work pitch cylinder of bevel gear I and bevel gear II along the distance of axial direction, a is the beeline between bevel gear I axis and the bevel gear II axis, and the P point is any one contact points on the coupling gear.

Inter_curve Γ on the bevel gear I ₁Curvilinear equation be:

$\left\{\begin{array}{c}{x}_1=X\left(\mathrm{\&theta;}\right)\\ {\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1=Y\left(\mathrm{\&theta;}\right)\\ {\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1=f\left(\mathrm{\&theta;}\right)\end{array}\right.,{\mathrm{\&theta;}}_1\&le;\mathrm{\&theta;}\&le;{\mathrm{\&theta;}}_2$

In the formula, θ is the parameter of curve angle; θ ₁, θ ₂Be the Line of contact span, namely a corresponding parameter of curve angle is located to nibbling out in parameter of curve angle corresponding to the engaging-in point of flank profil place.

Because the axis of bevel gear I and the axial space of bevel gear II are staggered, by the conjugate curve principle, inter_curve Γ ₂Curvilinear equation be:

$\left\{\begin{array}{c}{x}_2=x_1(\cos {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2-\sin {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})+y_1(-\sin {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2-\cos {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})\\ +{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\sin {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}-(D_1-b_1)\sin {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}-a\cos {\mathrm{\&phi;}}_2\\ {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">y</figure-callout>}}_2=x_1(\cos {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2+\sin {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})+y_1(-\sin {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2+\cos {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})\\ -{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\cos {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}+(D_1-b_1)\cos {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}-a\sin {\mathrm{\&phi;}}_2\\ {\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">z</figure-callout>}}_2=x_1\left(\sin {\mathrm{\&phi;}}_1\sin \mathrm{\&Sigma;}\right)+y_1\left(\cos {\mathrm{\&phi;}}_1\sin \mathrm{\&Sigma;}\right)+{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1\cos \mathrm{\&Sigma;}-(D_1-b_1)\cos \mathrm{\&Sigma;}+(D_2-b_2)\\ \mathrm{\&Phi;}(\mathrm{\&theta;},{\mathrm{\&phi;}}_1)=n\&CenterDot;{\mathrm{\&upsi;}}^{\left(12\right)}=0\end{array}\right.$

Wherein, φ ₁, φ ₂Be respectively bevel gear I, bevel gear II around the rotating angle of axis separately, satisfy and concern φ ₂=i ₂₁φ ₁, i ₂₁Be gear ratio; ∑ is the crossed axis angle between bevel gear I and the bevel gear II; Distance between the benchmark pitch circle of bevel gear I and bevel gear II and work pitch circle is used respectively b ₁, b ₂Expression, D ₁, D ₂Be respectively the work pitch cylinder of bevel gear I, bevel gear II along the distance of axial direction; A is the beeline between bevel gear I axis and the bevel gear II axis; N is inter_curve Γ ₂Method at the contact points place along given wrapping angle direction is vowed; υ ⁽¹²⁾Be illustrated in the speed of related movement at contact points place.

The present embodiment is set the inter_curve Γ on the bevel gear I ₁Be space circular cone equidistant helix:

$\left\{\begin{array}{c}{x}_1=(R_f-\mathrm{c\&theta;})\cos \mathrm{\&theta;}\\ {\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1=(R_f-\mathrm{c\&theta;})\sin \mathrm{\&theta;}\\ {\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1=\mathrm{p\&theta;}\\ c=p\tan {\mathrm{\&delta;}}_1\end{array}\right.,{\mathrm{\&theta;}}_1\&le;\mathrm{\&theta;}\&le;{\mathrm{\&theta;}}_2$

Wherein, R _fIt is the end circle radius of bevel gear I; θ is the helical curve parameter, and θ ₁, θ ₂Be the Line of contact span, namely a corresponding parameter of curve angle is located to nibbling out in parameter of curve angle corresponding to the engaging-in point of flank profil place, and p is helix parameter, δ ₁The joint angle of expression bevel gear I, and c=ptan δ ₁

Obtain inter_curve Γ according to the conjugate curve principle ₂Curvilinear equation be:

Wherein,

In the formula, R _fIt is the end circle radius of bevel gear I; θ is the helical curve parameter; P is helix parameter; δ ₁The joint angle of expression bevel gear I, and c=ptan δ ₁i ₂₁Be gear ratio, φ ₁, φ ₂Be respectively bevel gear I and bevel gear II around the rotating angle of axis separately, and the φ of relation is arranged ₂=i ₂₁φ ₁Distance between the benchmark pitch circle of bevel gear I and bevel gear II and work pitch circle is used respectively b ₁, b ₂Expression, D ₁, D ₂Be respectively the work pitch cylinder of bevel gear I, bevel gear II along the distance of axial direction; A is the beeline between bevel gear I axis and the bevel gear II axis; n _x, n _y, n _zThe expression conjugate curve are along the component of given wrapping angle direction method vector in each coordinate axes.

Further, as shown in Figure 4, the centre-point curve Γ ' that the center of circle of bevel gear I flank profil curved surface consists of ₁Be inter_curve Γ ₁Equidistant curve along the engagement of wrapping angle direction; The centre-point curve Γ ' that the center of circle of bevel gear II flank profil curved surface consists of ₂Be inter_curve Γ ₂Equidistant curve along the engagement of wrapping angle direction.The bevel gear I of the present embodiment and the tooth curve of bevel gear II are respectively dome arc and concave circular arc, and the double wedge exterior feature of setting bevel gear I is equidistant along wrapping angle direction forward, and distance is ρ ₁The recessed flank profil of bevel gear II is oppositely equidistant along the wrapping angle direction, and distance is ρ ₂, and actual equidistant distance has ρ ₂＞ρ ₁, the distance between curve and the inter_curve centered by the radius of a ball of spheroid in the ball family.

As can be known, the centre-point curve Γ ' of bevel gear I ₁Curvilinear equation be:

${{\mathrm{\&Gamma;}}^{\&prime;}}_1:\left\{\begin{array}{c}{x}_{1h}=x_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{x1}}{\sqrt{n_{x1}^2+n_{y1}^2+{\mathrm{<figure-callout\; id="1"\; label="n\; z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^1}}\\ y_{1h}={\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{y1}}{\sqrt{n_{x1}^2+n_{y1}^2+{\mathrm{<figure-callout\; id="1"\; label="n\; z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^1}}\\ z_{1h}={\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">z</figure-callout>}}_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{z1}}{\sqrt{n_{x1}^2+n_{y1}^2+{\mathrm{<figure-callout\; id="1"\; label="n\; z"\; filenames="HDA00002832083800021.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^1}}\end{array}\right.$

The centre-point curve Γ ' of bevel gear II ₂Curvilinear equation be:

${{\mathrm{\&Gamma;}}^{\&prime;}}_2:\left\{\begin{array}{c}{x}_{2h}=x_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{x2}}{\sqrt{n_{x2}^2+n_{y2}^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^2}}\\ y_{2h}=y_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{y2}}{\sqrt{n_{x2}^2+n_{y2}^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^2}}\\ z_{2h}=z_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{z2}}{\sqrt{n_{x2}^2+n_{y2}^2+{\mathrm{<figure-callout\; id="2"\; label="n\; z"\; filenames="HDA00002832083800032.png"\; state="\{\{state\}\}">n</figure-callout>}}_z^2}}\end{array}\right.$

In the formula, ρ ₁Radius of curvature for the dome curved tooth contour curved surface of bevel gear I; ρ ₂Radius of curvature for the concave circular arc flank profil curved surface of bevel gear II; n _X1, n _Y1, n _Z1, n _X2, n _Y2, n _Z2Respectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates.

Further, the flank profil curved surface ∑ of bevel gear I ₁For the centre of sphere along centre-point curve Γ ' ₁The ball family tubulose envelope surface of motion, its equation is:

The flank profil curved surface ∑ of bevel gear II ₂For the centre of sphere along centre-point curve Γ ' ₂The ball family tubulose envelope surface of motion, its equation is:

In the formula, ρ ₁Radius of curvature for the dome curved tooth contour curved surface of bevel gear I; ρ ₂Radius of curvature for the concave circular arc flank profil curved surface of bevel gear II; n _X1, n _Y1, n _Z1, n _X2, n _Y2, n _Z2Respectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates;

The envelope requirement that represents respectively the ball family tubulose envelope surface of bevel gear I, bevel gear II, wherein parameter item represents that tooth surface equation is to the differentiate of each autoregressive parameter; Be the ball family parameter, and satisfy

Concrete, the inter_curve Γ of the present embodiment ₁With inter_curve Γ ₂Be the space circular cone equidistant helix of conjugation, as can be known:

The flank profil surface equation of bevel gear I is:

The flank profil surface equation of bevel gear II is:

Wherein, R _fIt is the end circle radius of bevel gear I; θ is the helical curve parameter; P is helix parameter; δ ₁The joint angle of expression bevel gear I, and c=ptan δ ₁i ₂₁Be gear ratio, φ ₁, φ ₂Be respectively bevel gear I, bevel gear II around the rotating angle of axis separately and the φ of relation is arranged ₂=i ₂₁φ ₁Distance between the benchmark pitch circle of bevel gear I and bevel gear II and work pitch circle is used respectively b ₁, b ₂Expression, D ₁, D ₂Be respectively the work pitch cylinder of bevel gear I, bevel gear II along the distance of axial direction; A is the beeline between bevel gear I axis and the bevel gear II axis; ρ ₁Radius of curvature for the dome curved tooth contour curved surface of bevel gear I; ρ ₂Radius of curvature for the concave circular arc flank profil curved surface of bevel gear II; n _X1, n _Y1, n _Z1, n _X2, n _Y2, n _Z2Respectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates;

The envelope requirement that represents respectively the ball family tubulose envelope surface of bevel gear I, bevel gear II, wherein parameter item represents that tooth surface equation is to the differentiate of each autoregressive parameter; Be the ball family parameter, and satisfy

Along with the present embodiment rotates with certain angular velocity based on the bevel gear engagement pair of conjugate curve, at a time contact points moves a distance along separately inter_curve, the flank profil of bevel gear I and bevel gear II moves simultaneously vertically a distance and enters the participation engagement of next contact points place, the tooth curve radius of arc of bevel gear II is greater than the tooth curve radius of arc of bevel gear I, according to reality engagement situation, the former the relative latter forms local the containing, makes it have higher engagement driving intensity.

Explanation is at last, above embodiment is only unrestricted in order to technological scheme of the present invention to be described, although with reference to preferred embodiment the present invention is had been described in detail, those of ordinary skill in the art is to be understood that, can make amendment or be equal to replacement technological scheme of the present invention, and not breaking away from aim and the scope of technical solution of the present invention, it all should be encompassed in the middle of the claim scope of the present invention.

Claims (8)

1. bevel gear based on conjugate curve, it is characterized in that: the tooth curve of this bevel gear is circular arc, and the curvilinear equation of the inter_curve that is made of contact points on the flank profil curved surface of this gear is:

$\left\{\begin{array}{c}x=X\left(\mathrm{\&theta;}\right)\\ y=Y\left(\mathrm{\&theta;}\right)\\ z=f\left(\mathrm{\&theta;}\right)\end{array}\right.,{\mathrm{\&theta;}}_1\&le;\mathrm{\&theta;}\&le;{\mathrm{\&theta;}}_2$

Wherein, θ is the parameter of curve angle; θ ₁, θ ₂Be the Line of contact span, namely a corresponding parameter of curve angle is located to nibbling out in parameter of curve angle corresponding to the engaging-in point of flank profil place;

The centre-point curve that the center of circle of the flank profil curved surface of this bevel gear consists of be inter_curve along the equidistant curve of flank profil curved surface common normal line direction, and the curvilinear equation of centre-point curve is:

$\left\{\begin{array}{c}{x}_h=x\&PlusMinus;\mathrm{\&rho;}\&CenterDot;\frac{n_x}{\sqrt{n_x^2+n_y^2+n_z^2}}\\ y_h=y\&PlusMinus;\mathrm{\&rho;}\&CenterDot;\frac{n_{y1}}{\sqrt{n_x^2+n_y^2+n_2^2}}\\ z_h=z\&PlusMinus;\mathrm{\&rho;}\&CenterDot;\frac{n_z}{\sqrt{n_x^2+n_y^2+n_z^2}}\end{array}\right.$

In the formula, ρ is the radius of curvature of the dome curved tooth contour curved surface of bevel gear I; n _x, n _y, n _zRespectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates.

2. described bevel gear based on conjugate curve according to claim 1 is characterized in that: the flank profil curved surface of described bevel gear be the centre of sphere along the ball family tubulose envelope surface that described centre-point curve moves, its surface equation is respectively:

In the formula, Be the ball family parameter, and satisfy

3. the bevel gear engagement pair based on conjugate curve is characterized in that: comprise that mutual point gearing and tooth curve are bevel gear I and the bevel gear II of circular arc, the inter_curve Γ that is made of contact points on the flank profil curved surface of described bevel gear I ₁With the inter_curve Γ that is consisted of by contact points on the flank profil curved surface of described bevel gear II ₂Be conjugate curve;

The inter_curve Γ of described bevel gear I ₁Curvilinear equation be:

$\left\{\begin{array}{c}{x}_1=X\left(\mathrm{\&theta;}\right)\\ y_1=Y\left(\mathrm{\&theta;}\right)\\ z_1=f\left(\mathrm{\&theta;}\right)\end{array}\right.,{\mathrm{\&theta;}}_1\&le;\mathrm{\&theta;}\&le;{\mathrm{\&theta;}}_2$

In the formula, θ is the parameter of curve angle; θ ₁, θ ₂Be the Line of contact span, namely a corresponding parameter of curve angle is located to nibbling out in parameter of curve angle corresponding to the engaging-in point of flank profil place;

When the axis Plane intersects of the axis of described bevel gear I and bevel gear II, by the conjugate curve principle, the inter_curve Γ of described bevel gear II ₂Curvilinear equation be:

$\left\{\begin{array}{c}{x}_2=x_1(-\sin {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2+\cos {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})+y_1(\cos {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2+\sin {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})\\ +z_1\cos {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}-l_1\cos {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}\\ y_2=x_1(-\sin {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2-\cos {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})+y_1(\cos \mathrm{\&phi;}\cos {\mathrm{\&phi;}}_2-\sin {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})\\ -z_1\sin {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}+l_1\sin {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}\\ z_2=x_1(-\cos {\mathrm{\&phi;}}_1\sin \mathrm{\&Sigma;})+y_1(-\sin {\mathrm{\&phi;}}_1\sin \mathrm{\&Sigma;})+z_1\cos \mathrm{\&Sigma;}-l_1\cos \mathrm{\&Sigma;}+l_2\\ \mathrm{\&Phi;}(\mathrm{\&theta;},{\mathrm{\&phi;}}_1)=n\&CenterDot;{\mathrm{\&upsi;}}^{\left(12\right)}=0\end{array}\right.$

Wherein, φ ₁, φ ₂Be respectively bevel gear I, bevel gear II around the rotating angle of axis separately, satisfy and concern φ ₂=i ₂₁φ ₁, i ₂₁Be gear ratio; ∑ is the crossed axis angle between bevel gear I and the bevel gear II; l ₁, l ₂Be respectively bevel gear I, the bevel gear II conical point the distance round end of on its axial direction; N is inter_curve Γ ₂Method at the contact points place along given wrapping angle direction is vowed; υ ⁽¹²⁾Be illustrated in the speed of related movement at contact points place;

When the axial space of the axis of described bevel gear I and bevel gear II is staggered, by the conjugate curve principle, described inter_curve Γ ₂Curvilinear equation be:

$\left\{\begin{array}{c}{x}_2=x_1(\cos {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2-\sin {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})+y_1(-\sin {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2-\cos {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})\\ +z_1\sin {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}-(D_1-b_1)\sin {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}-a\cos {\mathrm{\&phi;}}_2\\ y_2=x_1(\cos {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2+\sin {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})+y_1(-\sin {\mathrm{\&phi;}}_1\sin {\mathrm{\&phi;}}_2+\cos {\mathrm{\&phi;}}_1\cos {\mathrm{\&phi;}}_2\cos \mathrm{\&Sigma;})\\ -z_1\cos {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}+(D_1-b_1)\cos {\mathrm{\&phi;}}_2\sin \mathrm{\&Sigma;}-a\sin {\mathrm{\&phi;}}_2\\ z_2=x_1\left(\sin {\mathrm{\&phi;}}_1\sin \mathrm{\&Sigma;}\right)+y_1\left(\cos {\mathrm{\&phi;}}_1\sin \mathrm{\&Sigma;}\right)+z_1\cos \mathrm{\&Sigma;}-(D_1-b_1)\cos \mathrm{\&Sigma;}+(D_2-b_2)\\ \mathrm{\&Phi;}(\mathrm{\&theta;},{\mathrm{\&phi;}}_1)=n\&CenterDot;{\mathrm{\&upsi;}}^{\left(12\right)}=0\end{array}\right.$

Wherein, φ ₁, φ ₂Be respectively bevel gear I, bevel gear II around the rotating angle of axis separately, satisfy and concern φ ₂=i ₂₁φ ₁, i ₂₁Be gear ratio; ∑ is the crossed axis angle between bevel gear I and the bevel gear II; Distance between the benchmark pitch circle of bevel gear I and bevel gear II and work pitch circle is used respectively b ₁, b ₂Expression, D ₁, D ₂Be respectively the work pitch cylinder of bevel gear I, bevel gear II along the distance of axial direction; A is the beeline between bevel gear I axis and the bevel gear II axis; N is inter_curve Γ ₂Method at the contact points place along given wrapping angle direction is vowed; υ ⁽¹²⁾Be illustrated in the speed of related movement at contact points place.

4. described bevel gear engagement pair based on conjugate curve according to claim 3 is characterized in that: the centre-point curve Γ ' that the center of circle of described bevel gear I flank profil curved surface consists of ₁Be inter_curve Γ ₁Equidistant curve along the engagement of wrapping angle direction; The centre-point curve Γ ' that the center of circle of described bevel gear II flank profil curved surface consists of ₂Be inter_curve Γ ₂Equidistant curve along the engagement of wrapping angle direction.

5. described bevel gear engagement pair based on conjugate curve according to claim 4, it is characterized in that: the tooth curve of described bevel gear I and bevel gear II is respectively dome arc and concave circular arc;

And the centre-point curve Γ ' of described bevel gear I ₁Curvilinear equation be:

${{\mathrm{\&Gamma;}}^{\&prime;}}_1:\left\{\begin{array}{c}{x}_{1h}=x_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{x1}}{\sqrt{n_{x1}^2+n_{y1}^2+n_{z1}^2}}\\ y_{1h}=y_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{y1}}{\sqrt{n_{x1}^2+n_{y1}^2+n_{z1}^2}}\\ z_{1h}=z_1+{\mathrm{\&rho;}}_1\&CenterDot;\frac{n_{z1}}{\sqrt{n_{x1}^2+n_{y1}^2+n_{z1}^2}}\end{array}\right.$

The centre-point curve Γ ' of described bevel gear II ₂Curvilinear equation be:

${{\mathrm{\&Gamma;}}^{\&prime;}}_2:\left\{\begin{array}{c}{x}_{2h}=x_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{x2}}{\sqrt{n_{x2}^2+n_{y2}^2+n_{z2}^2}}\\ y_{2h}=y_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{y2}}{\sqrt{n_{x2}^2+n_{y2}^2+n_{z2}^2}}\\ z_{2h}=z_2-{\mathrm{\&rho;}}_2\&CenterDot;\frac{n_{z2}}{\sqrt{n_{x2}^2+n_{y2}^2+n_{z2}^2}}\end{array}\right.$

In the formula, ρ ₁Radius of curvature for the dome curved tooth contour curved surface of bevel gear I; ρ ₂Radius of curvature for the concave circular arc flank profil curved surface of bevel gear II; n _X1, n _Y1, n _Z1, n _X2, n _Y2, n _Z2Respectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates.

6. described bevel gear engagement pair based on conjugate curve according to claim 5 is characterized in that: the flank profil curved surface ∑ of described bevel gear I ₁For the centre of sphere along described centre-point curve Γ ' ₁The ball family tubulose envelope surface of motion, its equation is:

The flank profil curved surface ∑ of described bevel gear II ₂For the centre of sphere along described centre-point curve Γ ' ₂The ball family tubulose envelope surface of motion, its equation is:

In the formula, ρ ₁Radius of curvature for the dome curved tooth contour curved surface of bevel gear I; ρ ₂Radius of curvature for the concave circular arc flank profil curved surface of bevel gear II; n _X1, n _Y1, n _Z1, n _X2, n _Y2, n _Z2Respectively that method is vowed n decomposition method vector along the reference axis direction under the gear system of coordinates;

Represent respectively the envelope requirement of bevel gear I, bevel gear II ball family tubulose envelope surface, wherein parameter item represents that tooth surface equation is to the differentiate of each autoregressive parameter; Be the ball family parameter, and satisfy

7. each described bevel gear engagement pair based on conjugate curve according to claim 3-6 is characterized in that: the crossed axis angle between described bevel gear I and the bevel gear II is 0 °＜∑≤90 °.

8. described bevel gear engagement pair based on conjugate curve according to claim 7 is characterized in that: described inter_curve Γ ₁With inter_curve Γ ₂Be smoothed curve.

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