CN104196981A - Design method for tooth profile of double-base cone spiral bevel gear - Google Patents

Abstract

The invention provides a design method for a tooth profile of a double-base cone spiral bevel gear and relates to gears. According to the double-base cone spiral bevel gear, five conical surfaces, four cone angles and two base cones are arranged; the normal tooth profile of each gear tooth comprises an addendum circle, a root circle, a driving side tooth curve, a non-driving side tooth curve and a tooth directional line; the five cone surfaces are a surface cone, a root cone, a pitch cone, a back cone and a front cone respectively; the four cone angles are a face angle, a root angle, a pitch angle and a back angle respectively; for vehicles with gear transmission mechanisms mainly depending on one-way transmission, the property of the spiral bevel gear is improved; the design method for the tooth profile of the double-based cone spiral bevel gear provided by the invention has the advantages that as large tooth profile angles are adopted in the driving surface and small tooth profile angles are adopted in the non-driving surface, the bearing capacity of the gear in the driving direction is increased and the top of tooth is prevented from being tapered, the bearing capacity, fatigue life and output torque of the spiral bevel gear are improved effectively and the vibration and noise in the transmission are reduced.

Description

A kind of design method of double-basis cone spiral bevel gear form of gear tooth

Technical field

The present invention relates to gear, particularly relate to a kind of design method of double-basis cone spiral bevel gear form of gear tooth.

Background technique

Spiral bevel gear is compared with straight-tooth and helical bevel gear, have that contact ratio is large, the Relative radius of curvature of the point of contact place flank of tooth is large, curved surface contact area is easy to control, to advantages such as error are not too responsive, in the transmission of intersection axis and staggered axis, be widely used.Along with the development trend of gear transmission middle/high speed heavy-load, conventional helical umbrella gear has been difficult to meet the requirement of equipment.Especially in system of vehicle transmission parts, more and more higher to the requirement of spiral bevel gear output torque.

In the time that tooth-shape angle increases, the bending bearing capacity of gear with contact bearing capacity all significantly strengthen, but along with the increase of tooth-shape angle, gear teeth tips comes to a point gradually, in the time that addendum thickness is less than 1.5m (m is module), tooth top easily fractures in the time of stand under load, cause failure of gear transmission (Li Huamin, the Quality Index Analysis of large profile of tooth angle involute gear transmission, Harbin Institute of Technology's journal, 1987, Z1:86-98).

Summary of the invention

The object of the invention is for vehicle etc. taking single-direction transmission as main gear drive, in order to improve the performance of spiral bevel gear, provide in drive surface and adopt large tooth-shape angle, adopt little tooth-shape angle in non-drive surface, both increased driving direction gear capacity, avoid again topping, can effectively improve spiral bevel gear bearing capacity, fatigue life and output torque, and reduced the design method of a kind of double-basis cone spiral bevel gear form of gear tooth of vibrations and noise.

The present invention includes following steps:

1) double-basis cone spiral bevel gear is provided with 5 conical surfaces, 4 cone angles, 2 base cones; Single gear teeth normal tooth profile is made up of top circle, root circle, driving side tooth curve, non-drive side tooth curve, teeth directional line; Described 5 conical surfaces are respectively face cone, root cone, pitch cone, back cone and inner cone, and described 4 cone angles are respectively face angle, root angle, joint angle, dorsal horn;

2) double-basis cone spiral bevel gear driving side flank of tooth Ω ₁with basic circle cone angle be δ _bdbase cone be tangential on OP ₁, work as Ω ₁while doing pure rolling along base cone, the circular arc line taking O as gyration center in plane is as M ₁n ₁with M ₂n ₂to form in space spiral bevel gear driving side and the non-drive side flank of tooth, due to spiral bevel gear both sides tooth-shape angle difference, the therefore base cone difference of two lateral tooth flank beginnings;

3) by transformation of coordinates, double-basis is bored to the wide spherical involute of the large end tooth of spiral bevel gear and be transformed into spheric coordinate system, through deriving, under spherical coordinate system, the double-basis cone spiral bevel gear large end tooth exterior feature of driving side flank of tooth equation under spherical coordinate system is

4) drive flank standard pitch circle drift angle with driving side basic circle cone angle δ _bdtried to achieve by following formula

δ _bd＝δ′-arctan[(1-α _d)tanδ′] (3)

5) the double-basis cone spiral bevel gear large end tooth exterior feature of non-drive side flank of tooth equation under spherical coordinate system is

6) non-driving flank standard pitch circle drift angle with non-driving gear side group cone angle δ _bctried to achieve by following formula

δ _bc＝δ′-arctan{[1-arccos(kcosα _d)]tanδ′} (6)

The teeth directional line of double-basis cone spiral bevel gear is formed by the relative position of wheel blank and cutterhead;

7) according to the helixangleβ of designing requirement and add selected cutter radius r in man-hour ₀, determine and the position relationship in facing cutter central position and crown axle center then by transformation of coordinates, teeth directional line equation is transformed into spheric coordinate system, under spherical coordinate system, its teeth directional line equation is

In formula (7), for teeth directional line drift angle, two angle S and j are tried to achieve by following formula

$S=\mathrm{\π}-\arccos \frac{L_1^2+r_0^2-R^2}{2L_1{r}_0}+[\arccos \frac{L_1^2+r_0^2-R^2}{2L_1{r}_0}-\arccos \frac{L_1^2+r_0^2-{(R-B)}^2}{2L_1{r}_0}]\×t---\left(8\right)$

$j=\arctan \frac{r_0\sin S}{L_1+r_0\cos S}---\left(9\right)$

8) in the time that cutterhead is gone to small end by large end, the corresponding angle Q in j angle, Q=j/sin δ ', therefore, the corresponding angle of outermost point and innermost point is respectively Q ₀=j ₀/ sin δ ' and Q ₁=j ₁/ sin δ ', the difference Q of two jiaos ₁-Q ₀be the angle turning over spherical coordinate system to the corresponding double-basis cone gear form of small end curve from large end, according to Q ₁-Q ₀and the value of rho in formula (1), (4) is become to R-B, can try to achieve double-basis cone spiral bevel gear Toe driving side and the equation of non-drive side flank profil under spherical coordinate system;

Double-basis cone spiral bevel gear tip diameter is:

d _a＝m _tz+2h _adcosδ _d (10)

Double-basis cone spiral bevel gear driving side and non-drive side tip angle are:

δ _ad＝δ _d+θ _fd (11)

δ _ac＝δ _c+θ _fc (12)

Double-basis cone spiral bevel gear root diameter is:

d _f＝m _tz-h _fdcosδ _d (13)

Double-basis cone spiral bevel gear driving side and non-drive side Root angle are:

δ _fd＝δ _d-θ _fd (14)

δ _fc＝δ _c-θ _fc (15)

Set up the flank profil curved surface of double-basis cone spiral bevel gear by above-mentioned steps, and set up spiral bevel gear monodentate entity, according to the number of teeth, z waits subarray, can set up double-basis cone spiral bevel gear solid pattern, completes the design of double-basis cone spiral bevel gear form of gear tooth.

Being labeled as in each step:

Z---the number of teeth

B---the facewidth

β---helix angle

Σ---crossed axis angle

Rho---spherical coordinate system utmost point footpath, in Fig. 2

Theta---directed line segment angle with z axle forward

Phi---forward by counter clockwise direction the angle that OS turns over from x axle to from positive z axle, S is the projection of a P on xOy face here

M _t---transverse module

D---standard pitch diameter

R---Outer cone distance

R _m---Mean cone distance

α _d---driving side tooth-shape angle

α _c---non-drive side tooth-shape angle

K---tooth-shape angle coefficient

δ ₁---reference cone angle

---drive flank standard pitch circle drift angle

---non-driving flank standard pitch circle drift angle

δ _ad---driving side tip angle

δ _ac---non-drive side tip angle

δ _fd---driving side Root angle

δ _fc---non-drive side Root angle

δ _bd---driving side basic circle cone angle

δ _bc---non-drive side basic circle cone angle

δ '---pitch cone angle

---teeth directional line drift angle

D _a---addendum circle diameter of gear

D _f---root diameter of gear

R ₀---cutter radius

L ₁---cutterhead center is to the distance at vertex of a cone center

The drift angle, the center of circle with respect to cutterhead center of S---teeth directional line

The drift angle, the center of circle with respect to vertex of a cone center of j---teeth directional line

β _p---tooth root drift angle

θ _fd---driving side Dendendum angle

θ _fc---non-drive side Dendendum angle

H _ad---driving side addendum

H _ac---non-drive side addendum

H _fd---driving side dedendum of the tooth

H _fc---non-drive side dedendum of the tooth

X---height change coefficient

X _t---coefficient of profile tangential shift dangerous section.

Because driving side and the non-drive side of double-basis cone spiral bevel gear have the gear parameters such as different base cones, addendum cone and root vertebra, completely different from geometrical property and the design method of conventional helical umbrella gear, therefore need to set up a kind of tooth Shape Design method of double-basis cone spiral bevel gear, lay the foundation for carrying out Tool Design, manufacturing, the calculating of tooth root bending fatigue strength and the calculating of flank of tooth contact fatigue strength.

The present invention is directed to vehicle etc. taking single-direction transmission as main gear drive, improve the performance of spiral bevel gear, provide in drive surface and adopt large tooth-shape angle, adopt little tooth-shape angle in non-drive surface, both increased driving direction gear capacity, avoid again topping, can effectively improve spiral bevel gear bearing capacity, fatigue life and output torque, and reduced the design method of a kind of double-basis cone spiral bevel gear form of gear tooth of vibrations and noise.

Brief description of the drawings

Fig. 1 is the double-basis cone spiral bevel gear conical surface and cone angle.

Fig. 2 is that double-basis cone spiral bevel gear driving side, non-drive side spherical involute form.

Fig. 3 is double-basis cone spiral bevel gear flywheel rotor and wheel blank relative position schematic diagram.

Fig. 4 is the modeling process of double-basis cone spiral bevel gear.

Fig. 5 is double-basis cone spiral bevel gear pair engagement model.

In the drawings, respectively be labeled as: 1---double-basis cone spiral bevel gear driving side profile of tooth, 2---double-basis cone spiral bevel gear non-drive side profile of tooth, 3---double-basis cone spiral bevel gear tooth top, 4---double-basis cone spiral bevel gear tooth root, 5---double-basis cone spiral bevel gear teeth directional line.

Embodiment

Referring to Fig. 1～5, double-basis cone spiral bevel gear is provided with 5 conical surfaces, 4 cone angles, 2 base cones; Single gear teeth normal tooth profile is made up of top circle, root circle, driving side tooth curve, non-drive side tooth curve, teeth directional line, described 5 conical surfaces are respectively face cone, root cone, pitch cone, back cone and inner cone, and described 4 cone angles are respectively face angle, root angle, joint angle, dorsal horn; As shown in Figure 1.

Double-basis cone spiral bevel gear driving side flank of tooth Ω ₁with basic circle cone angle be δ _bdthe 1st base cone (being expressed as base cone 11 in Fig. 2) be tangential on OP ₁, work as Ω ₁while doing pure rolling along base cone 1, the circular arc line taking O as gyration center in plane is as M ₁n ₁with M ₂n ₂to form in space spiral bevel gear driving side and the non-drive side flank of tooth.Due to spiral bevel gear both sides tooth-shape angle difference, thus the base cone difference of two lateral tooth flank beginnings, as shown in Figure 2.In Fig. 2, also mark the 2nd base cone (being expressed as base cone 21 in Fig. 2).

By transformation of coordinates, double-basis is bored to the wide spherical involute of the large end tooth of spiral bevel gear and be transformed into spheric coordinate system, through deriving, under spherical coordinate system, the double-basis cone spiral bevel gear large end tooth exterior feature of driving side flank of tooth equation under spherical coordinate system is

Drive flank standard pitch circle drift angle with driving side basic circle cone angle δ _bdcan be tried to achieve by following formula

δ _bd＝δ′-arctan[(1-α _d)tanδ′] (3)

The double-basis cone spiral bevel gear large end tooth exterior feature of non-drive side flank of tooth equation under spherical coordinate system is

Non-driving flank standard pitch circle drift angle with non-driving gear side group cone angle δ _bccan be tried to achieve by following formula

δ _bc＝δ′-arctan{[1-arccos(kcosα _d)]tanδ′} (6)

The teeth directional line of double-basis cone spiral bevel gear is to be formed by the relative position of wheel blank and cutterhead, as shown in Figure 3.

According to the helixangleβ of designing requirement and add selected cutter radius r in man-hour ₀, determine and the position relationship in facing cutter central position and crown axle center then by transformation of coordinates, teeth directional line equation be transformed into spheric coordinate system.Under spherical coordinate system, its teeth directional line equation is:

In formula, for teeth directional line drift angle, two angle S and j can be tried to achieve by following formula

$S=\mathrm{\π}-\arccos \frac{L_1^2+r_0^2-R^2}{2L_1{r}_0}+[\arccos \frac{L_1^2+r_0^2-R^2}{2L_1{r}_0}-\arccos \frac{L_1^2+r_0^2-{(R-B)}^2}{2L_1{r}_0}]\×t---\left(8\right)$

$j=\arctan \frac{r_0\sin S}{L_1+r_0\cos S}---\left(9\right)$

From the cutterhead position shown in Fig. 3, in the time that cutterhead is gone to small end by large end, the corresponding angle Q in j angle, Q=j/sin δ ', therefore, the corresponding angle of outermost point and innermost point is respectively Q ₀=j ₀/ sin δ ' and Q ₁=j ₁/ sin δ '.The difference Q of two jiaos ₁-Q ₀be the angle turning over spherical coordinate system to the corresponding double-basis cone gear form of small end curve from large end, according to Q ₁-Q ₀and the value of rho in formula (1), (4) is become to R-B, can try to achieve double-basis cone spiral bevel gear Toe driving side and the equation of non-drive side flank profil under spherical coordinate system.

Double-basis cone spiral bevel gear tip diameter is:

d _a＝m _tz+2h _adcosδ _d (10)

Double-basis cone spiral bevel gear driving side and non-drive side tip angle are:

δ _ad＝δ _d+θ _fd (11)

δ _ac＝δ _c+θ _fc (12)

Double-basis cone spiral bevel gear root diameter is:

d _f＝m _tz-h _fdcosδ _d (13)

Double-basis cone spiral bevel gear driving side and non-drive side Root angle are:

δ _fd＝δ _d-θ _fd (14)

δ _fc＝δ _c-θ _fc (15)

By the above-mentioned flank profil curved surface that step can be set up to double-basis cone spiral bevel gear, and set up spiral bevel gear monodentate entity, according to the number of teeth, z waits subarray, can set up double-basis cone spiral bevel gear solid pattern.

According to the designing requirement of double-basis cone spiral bevel gear, select the basic design parameters such as suitable modulus, normal plane driving side, non-drive side tooth-shape angle, addendum coefficient, modification coefficient, radial clearance coefficient, the number of teeth, helix angle, rotation direction, then according to conversion relation, calculate each parameter.

A) according to transverse module m _t, number of teeth z, facewidth B, helixangleβ, crossed axis angle Σ, driving side tooth-shape angle α _d, non-drive side tooth-shape angle α _c, the parameter such as modification coefficient x can be in the hope of driving gear side standard pitch circle drift angle driving gear side group cone angle δ _bd, non-driving flank standard pitch circle drift angle with non-driving gear side group cone angle δ _bcetc. parameter, according to profile of tooth equation (1)～(6), can set up the large end driving side of double-basis cone spiral bevel gear profile of tooth, hold non-drive side profile of tooth, small end driving side profile of tooth and small end non-drive side profile of tooth greatly.

B), according to above-mentioned parameter, according to equation (10)～(15), can set up the large end tooth root of double-basis cone spiral bevel gear circular arc, large end tooth tip circle arc, small end tooth root circular arc and small end tooth top circular arc.

C), according to above-mentioned parameter, according to equation (7)～(9), can set up double-basis cone spiral bevel gear driving side teeth directional line and non-drive side teeth directional line.

D) generate the entity of first double-basis cone spiral bevel gear monodentate.

E) wait subarray according to number of teeth z, can set up double-basis cone spiral bevel gear full-depth tooth model.

According to the parameter of the given double-basis cone spiral bevel gear of table 1, set up model process as shown in Figure 4.

Table 1 double-basis cone spiral bevel gear parameter

By the above-mentioned flank profil curved surface that step can be set up to double-basis cone spiral bevel gear, and set up double-basis cone spiral bevel gear monodentate entity, according to the number of teeth, z waits subarray, can set up double-basis cone spiral bevel gear driving wheel, driven wheel engagement model, as shown in Figure 5.

Claims (1)

1. a design method for double-basis cone spiral bevel gear form of gear tooth, is characterized in that comprising the following steps:

1) double-basis cone spiral bevel gear is provided with 5 conical surfaces, 4 cone angles, 2 base cones; Single gear teeth normal tooth profile is made up of top circle, root circle, driving side tooth curve, non-drive side tooth curve, teeth directional line; Described 5 conical surfaces are respectively face cone, root cone, pitch cone, back cone and inner cone, and described 4 cone angles are respectively face angle, root angle, joint angle, dorsal horn;

2) double-basis cone spiral bevel gear driving side flank of tooth Ω ₁with basic circle cone angle be δ _bdbase cone be tangential on OP ₁, work as Ω ₁while doing pure rolling along base cone, the circular arc line taking O as gyration center in plane is as M ₁n ₁with M ₂n ₂to form in space spiral bevel gear driving side and the non-drive side flank of tooth, due to spiral bevel gear both sides tooth-shape angle difference, the therefore base cone difference of two lateral tooth flank beginnings;

3) by transformation of coordinates, double-basis is bored to the wide spherical involute of the large end tooth of spiral bevel gear and be transformed into spheric coordinate system, through deriving, under spherical coordinate system, the double-basis cone spiral bevel gear large end tooth exterior feature of driving side flank of tooth equation under spherical coordinate system is

4) drive flank standard pitch circle drift angle with driving side basic circle cone angle δ _bdtried to achieve by following formula

${\mathrm{\δ}}_{\mathrm{bd}}={\mathrm{\δ}}^{\′}-\arctan \left[(1-{\mathrm{\α}}_d)\tan {\mathrm{\δ}}^{\′}\right]---\left(3\right)$

5) the double-basis cone spiral bevel gear large end tooth exterior feature of non-drive side flank of tooth equation under spherical coordinate system is

6) non-driving flank standard pitch circle drift angle with non-driving gear side group cone angle δ _bctried to achieve by following formula

${\mathrm{\δ}}_{\mathrm{bc}}={\mathrm{\δ}}^{\′}-\arctan \left\{\right[1-\arccos \left(k\cos {\mathrm{\α}}_d\right)\left]\tan {\mathrm{\δ}}^{\′}\right\}---\left(6\right)$

The teeth directional line of double-basis cone spiral bevel gear is formed by the relative position of wheel blank and cutterhead;

7) according to the helixangleβ of designing requirement and add selected cutter radius r in man-hour ₀, determine and the position relationship in facing cutter central position and crown axle center then by transformation of coordinates, teeth directional line equation is transformed into spheric coordinate system, under spherical coordinate system, its teeth directional line equation is

In formula (7), for teeth directional line drift angle, two angle S and j are tried to achieve by following formula

$S=\mathrm{\π}-\arccos \frac{L_1^2+r_0^2-R^2}{2L_1{r}_0}+[\arccos \frac{L_1^2+r_0^2-R^2}{2L_1{r}_0}-\arccos \frac{L_1^2+r_0^2-{(R-B)}^2}{2L_1{r}_0}]\×t---\left(8\right)$

$j=\arctan \frac{r_0\sin S}{L_1+r_0\cos S}---\left(9\right)$

8) in the time that cutterhead is gone to small end by large end, the corresponding angle Q in j angle, Q=j/sin δ ', therefore, the corresponding angle of outermost point and innermost point is respectively Q ₀=j ₀/ sin δ ' and Q ₁=j ₁/ sin δ ', the difference Q of two jiaos ₁-Q ₀be the angle turning over spherical coordinate system to the corresponding double-basis cone gear form of small end curve from large end, according to Q ₁-Q ₀and the value of rho in formula (1), (4) is become to R-B, can try to achieve double-basis cone spiral bevel gear Toe driving side and the equation of non-drive side flank profil under spherical coordinate system;

Double-basis cone spiral bevel gear tip diameter is:

d _a＝m _tz+2h _adcosδ _d (10)

Double-basis cone spiral bevel gear driving side and non-drive side tip angle are:

δ _ad＝δ _d+θ _fd (11)

δ _ac＝δ _c+θ _fc (12)

Double-basis cone spiral bevel gear root diameter is:

d _f＝m _tz-h _fdcosδ _d (13)

Double-basis cone spiral bevel gear driving side and non-drive side Root angle are:

δ _fd＝δ _d-θ _fd (14)

δ _fc＝δ _c-θ _fc (15)

Set up the flank profil curved surface of double-basis cone spiral bevel gear by above-mentioned steps, and set up spiral bevel gear monodentate entity, according to the number of teeth, z waits subarray, can set up double-basis cone spiral bevel gear solid pattern, completes the design of double-basis cone spiral bevel gear form of gear tooth;

Being labeled as in each step:

Z---the number of teeth

B---the facewidth

β---helix angle

Σ---crossed axis angle

Rho---spherical coordinate system utmost point footpath, in Fig. 2

Theta---directed line segment angle with z axle forward

Phi---forward by counter clockwise direction the angle that OS turns over from x axle to from positive z axle, S is the projection of a P on xOy face here

M _t---transverse module

D---standard pitch diameter

R---Outer cone distance

R _m---Mean cone distance

α _d---driving side tooth-shape angle

α _c---non-drive side tooth-shape angle

K---tooth-shape angle coefficient

δ ₁---reference cone angle

---drive flank standard pitch circle drift angle

---non-driving flank standard pitch circle drift angle

δ _ad---driving side tip angle

δ _ac---non-drive side tip angle

δ _fd---driving side Root angle

δ _fc---non-drive side Root angle

δ _bd---driving side basic circle cone angle

δ _bc---non-drive side basic circle cone angle

δ '---pitch cone angle

---teeth directional line drift angle

D _a---addendum circle diameter of gear

D _f---root diameter of gear

R ₀---cutter radius

L ₁---cutterhead center is to the distance at vertex of a cone center

The drift angle, the center of circle with respect to cutterhead center of S---teeth directional line

The drift angle, the center of circle with respect to vertex of a cone center of j---teeth directional line

β _p---tooth root drift angle

θ _fd---driving side Dendendum angle

θ _fc---non-drive side Dendendum angle

H _ad---driving side addendum

H _ac---non-drive side addendum

H _fd---driving side dedendum of the tooth

H _fc---non-drive side dedendum of the tooth

X---height change coefficient

X _t---coefficient of profile tangential shift dangerous section.