CN107630986A - The planetary gear train planting mechanism and its design method of Some Second Order Elliptic bevel gear driving - Google Patents
The planetary gear train planting mechanism and its design method of Some Second Order Elliptic bevel gear driving Download PDFInfo
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- CN107630986A CN107630986A CN201710877852.2A CN201710877852A CN107630986A CN 107630986 A CN107630986 A CN 107630986A CN 201710877852 A CN201710877852 A CN 201710877852A CN 107630986 A CN107630986 A CN 107630986A
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Abstract
The invention discloses the planetary gear train planting mechanism and its design method of Some Second Order Elliptic bevel gear driving.Traditional rotation duck-beak type planting mechanism falls short of in seedlings picking and approximate dwell time when planting seedlings.The present invention includes Some Second Order Elliptic bevel gear pair, central shaft and planetary gear train planting mechanism；During initial makeup location, planet carrier is horizontally disposed with, and two intersection points of horizontal plane where the central axis of the sphere pitch curve of driven Some Second Order Elliptic bevel gear and central shaft are two minimum points of curvature on the sphere pitch curve of driven Some Second Order Elliptic bevel gear；Point of maximum curvature is meshed with curvature smallest point on driven gear pitch curve on the sphere pitch curve of active Some Second Order Elliptic bevel gear.The present invention extends the approximate dwell time of seedlings picking and stage of planting seedlings on the basis of a time period of motion length is not changed, and improves seedlings picking and the success rate planted seedlings.
Description
Technical field
The present invention relates to the planting mechanism of transplanter in agricultural machinery, and in particular to the planet of Some Second Order Elliptic bevel gear driving
Train planting mechanism and its design method.
Background technology
Transplanting is one of important step in vegetables production process, and transplanting is with the compensating action to weather and proposes fertility
Preceding comprehensive benefit, sunlight-heat reaources can be made full use of, its economic benefit brought and social benefit are considerable.Due to people
The cost of work transplanting is larger, realizes that transplanting mechanization of operation turns into the problem that China's agricultural production is badly in need of solving.
The reciprocal duck-beak type planting mechanism appearance and size driven at present by multi-bar linkage is big, and structure is not compact enough, during operation
Inertia force is larger.Easily occur leakage when clamp type, chain-clip type transplanter planting mechanism operation and plant phenomenon, easily hinder alms bowl when seedling accompanies
Seedling.The rotation duck-beak type planting mechanism of planetary gear train driving can solve the above problems, but traditional rotation duck-beak type planting mechanism
Input speed is constant, long not enough with approximate dwell time when planting seedlings in seedlings picking, causes seedlings picking and plant seedlings easily to lose
Lose, be not suitable for planting seedlings at a high speed.
The content of the invention
The purpose of the present invention is in view of the shortcomings of the prior art, to propose a kind of planetary gear train of Some Second Order Elliptic bevel gear driving
Planting mechanism and design method, the power input of planetary gear train planting mechanism use Some Second Order Elliptic bevel gear pair, are not changing one
Extend seedlings picking and the approximate dwell time in stage of planting seedlings on the basis of individual time period of motion length, improve seedlings picking and plant seedlings into
Power.
To achieve the above object, the technical scheme is that：
The planetary gear train planting mechanism of Some Second Order Elliptic bevel gear driving of the present invention, including Some Second Order Elliptic bevel gear pair, center
Axle and planetary gear train planting mechanism.The active Some Second Order Elliptic bevel gear of described Some Second Order Elliptic bevel gear pair including engaged transmission and
Driven Some Second Order Elliptic bevel gear；Active Some Second Order Elliptic bevel gear drives uniform rotation by external impetus, and driven Some Second Order Elliptic bores tooth
Wheel is fixed on center shaft；The both ends of central shaft are mounted on planetary gear train planting mechanism；Described planetary gear train planting mechanism
Including planet carrier, gear drive and plant mouth；Central shaft is through cultivation of the gear drive passing power to planet carrier both ends
Plant mouth.During initial makeup location, planet carrier is horizontally disposed with, and the sphere pitch curve of driven Some Second Order Elliptic bevel gear and central shaft
Two intersection points of horizontal plane where central axis are two minimum points of curvature on the sphere pitch curve of driven Some Second Order Elliptic bevel gear；
Point of maximum curvature is meshed with curvature smallest point on driven gear pitch curve on the sphere pitch curve of active Some Second Order Elliptic bevel gear.
The curvature of two minimum points of curvature is equal on the sphere pitch curve of described driven Some Second Order Elliptic bevel gear.
The design method of the planetary gear train planting mechanism of the Some Second Order Elliptic bevel gear driving, is comprised the following steps that：
Step 1: establish the mathematical modeling of active Some Second Order Elliptic bevel gear.
The sphere pitch curve of active Some Second Order Elliptic bevel gear (onlys demand the sphere pitch curve of big end (or small end), three-dimensional here
(filling into) cone angle is cut off during model modeling directly inside the model of gear, you can obtain the sphere pitch curve at small end (or big end))
By Some Second Order Elliptic, orthographic projection obtains on sphere；In coordinate system XYZ, the sphere pitch curve equation of active Some Second Order Elliptic bevel gear expires
The following relation of foot：
In formula, a is the semi-major axis of Some Second Order Elliptic, and b is the semi-minor axis of Some Second Order Elliptic, and R is spherical radius, and τ is active second order
Polar angle of the point in X/Y plane on oval bevel-gear spherical pitch curve, span are [0,2 π], x1、y1、z1Respectively actively
Coordinate of the point on X-axis, Y-axis, Z axis on the sphere pitch curve of Some Second Order Elliptic bevel gear.
Step 2: solve geodetic centre-to-centre spacing and the sphere pitch curve equation of driven Some Second Order Elliptic bevel gear.
Two rotary shafts of Some Second Order Elliptic bevel gear pair are concurrent aces, and the angle between two rotary shafts is set to θ, and θ uses radian
System, span areIf the rotary shaft of active Some Second Order Elliptic bevel gear and intersection point (the i.e. active Some Second Order Elliptic of sphere
Centre of radius of the pitch curve of bevel gear on sphere) coordinate is (0,0, R), the rotary shaft of driven Some Second Order Elliptic bevel gear
Intersecting point coordinate with sphere is (R sin θs, 0, R cos θ).
By plane noncircular gear pair centre-to-centre spacing analogy, the centre-to-centre spacing of Some Second Order Elliptic bevel gear pair is one section of circular arc on sphere
Arc length and be a length of definite value of shortest arc between definite value, i.e. two rotary shafts of Some Second Order Elliptic bevel gear pair and the intersection point of sphere.Adopt
Pitch curve radius of curvature of the driving and driven Some Second Order Elliptic bevel gear on sphere, i.e. geodesic curvature radius are calculated with polar form.
The pitch curve geodesic curvature radius of active Some Second Order Elliptic bevel gear is obtained by the sphere pitch curve equation of active Some Second Order Elliptic bevel gear
ρ1For：
By conditional：L=R θ, obtain geodetic centre-to-centre spacing l (centers of the driving and driven Some Second Order Elliptic bevel gear on sphere
Away from).
The pitch curve geodesic curvature radius ρ of driven Some Second Order Elliptic bevel gear2For：
ρ2=l- ρ1
Try to achieve gearratio：
In formula, w1、w2The angular speed of respectively driving and driven Some Second Order Elliptic bevel gear, w1For the definite value of setting.
Corner based on the not rounded driven gear pitch curve of plane seeks method, is generalized to sphere driven gear pitch curve corner and asks
Method, try to achieve the sphere pitch curve corner of driven Some Second Order Elliptic bevel gear
In formula,For the corner of active Some Second Order Elliptic bevel gear.
By the radius of curvature of driven Some Second Order Elliptic bevel gear, corresponding corner and sphere centre away from establishing driven Some Second Order Elliptic
The sphere pitch curve equation of bevel gear.
In formula, x2、y2、z2Point is on X-axis, Y-axis, Z axis on the sphere pitch curve of respectively driven Some Second Order Elliptic bevel gear
Coordinate.
Step 3: solve the angular speed and angular acceleration of driven Some Second Order Elliptic bevel gear.
By gearratio formulaObtain angular speed：
To w2On the derivation of time t, angular acceleration is obtained：
Step 4: setting w1, θ values, select a, b, R initial value；
Step 5: by w1, θ, a, b, R value substitute intoWithCalculate corner WithCorresponding angular speed and angular acceleration in two sections.
Step 6: if corresponding angular acceleration is respectively less than 0.002m/s in two sections2, and corresponding angle in two sections
Speed is respectively less than 0.005m/s, then into the value reduction 0.01 of step 11, otherwise a 0.01, b of value increase；
Step 7: calculate e=a/b value；If e ＜ 0.9 (e values are excessive can not to generate preferable flank profil), return to step 5,
Otherwise step 8 is entered.
Step 8: a reduces 0.01, b on the basis of initial value increases by 0.01 on the basis of initial value；Calculate e=a/b value；If e
＜ 0.6, then into step 10, otherwise into step 9.
Step 9: by w1, θ, a, b, R value substitute intoWithCalculate cornerTwo sections
Angular speed and angular acceleration corresponding to interior, if corresponding angular acceleration is respectively less than 0.002m/s in two sections2, and two sections
Angular speed corresponding to interior is respectively less than 0.005m/s, then into step 11, otherwise returns to step 8.
Step 10: R value reduces 0.002, a, b, R are entered as initial value, repeat step five, six, seven, eight, nine again.
Step 11: according to a, b, R final preferred value, with reference to w1, θ values, try to achieve driving and driven Some Second Order Elliptic bevel gear section
Curvilinear equation.
The device have the advantages that：
1st, for the present invention when driving shaft at the uniform velocity rotates, driven shaft (central shaft) realizes speed-changing rotation so that seedlings picking is with planting seedlings
Stage, plant mouth have longer approximate dwell time, and seedlings picking and the success rate planted seedlings greatly improve.
2nd, exponent number, the driving wheel pitch curve planar obit simulation equation of driven wheel known to the present invention, is led by projecting method
Driving wheel sphere pitch curve equation, further derive the geodesic curvature radius and corresponding angle, gearratio of driven pulley.Wherein, two
Sphere arc centre-to-centre spacing between root concurrent aces is space curve section, and pitch curve is in the sphere curvature radius corresponding to meshing point
It is space curve.This method effectively solves position and the meshing problem of space curve, bent suitable for the gear section on three dimensions
Line.
Brief description of the drawings
Fig. 1 is the structure diagram of the planetary gear train planting mechanism of Some Second Order Elliptic bevel gear driving of the present invention；
Fig. 2 is that active Some Second Order Elliptic bevel gear engages signal with the pitch curve of driven Some Second Order Elliptic bevel gear in the present invention
Figure；
Fig. 3 is the angular displacement graph of a relation of main shaft and central shaft when using standard cones gear drive；
The angular displacement graph of a relation of main shaft and central shaft when Fig. 4 is the not rounded bevel gear pair transmission of the present invention；
Fig. 5 is the wide figure of big end tooth of active Some Second Order Elliptic bevel gear in the present invention；
Fig. 6 is the wide figure of big end tooth of driven Some Second Order Elliptic bevel gear in the present invention；
Fig. 7 is the flank profil mesh schematic representation of active Some Second Order Elliptic bevel gear and driven Some Second Order Elliptic bevel gear in the present invention.
In figure：1- Some Second Order Elliptics bevel gear pair, 2- central shafts, 3- planet carriers, 4- plants mouth, 5- actives Some Second Order Elliptic cone tooth
Angle of eccentricity when the sphere pitch curve of the driven Some Second Order Elliptic bevel gear of sphere pitch curve, 6- of wheel, 7- standard cones gear drives
Passed with stage angle of eccentricity section of being planted seedlings when central shaft angle relation curve, 8- standard cones gear drives, the not rounded bevel gears of 9-
Plant seedlings stage angle of eccentricity section, 11- during the not rounded Bevel Gear Transmission of angle of eccentricity and central shaft angle relation curve when dynamic, 10-
Flank profil line, the 13- actives Some Second Order Elliptic cone tooth of the driven Some Second Order Elliptic bevel gear of flank profil line, 12- of active Some Second Order Elliptic bevel gear
Wheel, the driven Some Second Order Elliptic bevel gears of 14-.
Embodiment
Below in conjunction with the accompanying drawings and embodiment the invention will be further described.
As shown in figure 1, the planetary gear train planting mechanism of Some Second Order Elliptic bevel gear driving, including Some Second Order Elliptic bevel gear pair 1,
Central shaft 2 and planetary gear train planting mechanism.Some Second Order Elliptic bevel gear pair 1 includes the active Some Second Order Elliptic bevel gear 13 of engaged transmission
With driven Some Second Order Elliptic bevel gear 14；Active Some Second Order Elliptic bevel gear drives uniform rotation by main shaft, and driven Some Second Order Elliptic bores tooth
Wheel is fixed on central shaft 2；The both ends of central shaft 2 are mounted on planetary gear train planting mechanism；Planetary gear train planting mechanism includes
Planet carrier 3, gear drive and plant mouth 4；Central shaft 2 is through cultivation of the gear drive passing power to the both ends of planet carrier 3
Plant mouth 4.Planetary gear train planting mechanism uses planetary gear train type transplantation device disclosed in Patent No. 201010210215.8.Initially
During installation site, planet carrier is horizontally disposed with, and the central axis of the sphere pitch curve 6 of driven Some Second Order Elliptic bevel gear and central shaft
Two intersection points of place horizontal plane are two minimum points of curvature on the sphere pitch curve of driven Some Second Order Elliptic bevel gear；Driven second order
The curvature of two minimum points of curvature is equal on the sphere pitch curve of oval bevel gear；The sphere section of active Some Second Order Elliptic bevel gear
Point of maximum curvature is meshed with curvature smallest point on driven gear pitch curve on curve 5.
In Some Second Order Elliptic bevel gear pair 1, active Some Second Order Elliptic bevel gear at the uniform velocity rotates, and driven Some Second Order Elliptic bevel gear is in
The speed-changing rotation of mandrel 2, realize that the speed change of planting mechanism on central shaft 2 rotates.Planetary gear train planting mechanism is in the seedlings picking stage with planting
Seedling stage rotating speed is relatively low, and other stage rotating speeds are higher.
As illustrated in fig. 1 and 2, the design method of the planetary gear train planting mechanism of the Some Second Order Elliptic bevel gear driving, specifically such as
Under：
Step 1: establish the mathematical modeling of active Some Second Order Elliptic bevel gear.
The sphere pitch curve of active Some Second Order Elliptic bevel gear (onlys demand the sphere pitch curve of big end (or small end), three-dimensional here
(filling into) cone angle is cut off during model modeling directly inside the model of gear, you can obtain the sphere pitch curve at small end (or big end))
By Some Second Order Elliptic, orthographic projection obtains on sphere；In coordinate system XYZ, the sphere pitch curve equation of active Some Second Order Elliptic bevel gear expires
The following relation of foot：
In formula, a is the semi-major axis of Some Second Order Elliptic, and b is the semi-minor axis of Some Second Order Elliptic, and R is spherical radius, and τ is active second order
Polar angle of the point in X/Y plane on oval bevel-gear spherical pitch curve, span are [0,2 π].
Step 2: solve geodetic centre-to-centre spacing and the sphere pitch curve equation of driven Some Second Order Elliptic bevel gear.
Two rotary shafts of Some Second Order Elliptic bevel gear pair are concurrent aces, and the angle between two rotary shafts is set to θ, and θ uses radian
System, span areIf the rotary shaft of active Some Second Order Elliptic bevel gear and intersection point (the i.e. active Some Second Order Elliptic of sphere
Centre of radius of the pitch curve of bevel gear on sphere) coordinate is (0,0, R), the rotary shaft of driven Some Second Order Elliptic bevel gear
Intersecting point coordinate with sphere is (R sin θs, 0, R cos θ).
By plane noncircular gear pair centre-to-centre spacing analogy, the centre-to-centre spacing of Some Second Order Elliptic bevel gear pair is one section of circular arc on sphere
Arc length and be a length of definite value of shortest arc between definite value, i.e. two rotary shafts of Some Second Order Elliptic bevel gear pair and the intersection point of sphere.Adopt
Pitch curve radius of curvature of the driving and driven Some Second Order Elliptic bevel gear on sphere, i.e. geodesic curvature radius are calculated with polar form.
The pitch curve geodesic curvature radius of active Some Second Order Elliptic bevel gear is obtained by the sphere pitch curve equation of active Some Second Order Elliptic bevel gear
ρ1For：
By conditional：L=R θ, obtain geodetic centre-to-centre spacing l (centers of the driving and driven Some Second Order Elliptic bevel gear on sphere
Away from).
The pitch curve geodesic curvature radius ρ of driven Some Second Order Elliptic bevel gear2For：
ρ2=l- ρ1
Try to achieve gearratio：
In formula, w1、w2The angular speed of respectively driving and driven Some Second Order Elliptic bevel gear, w1For the definite value of setting.
Corner based on the not rounded driven gear pitch curve of plane seeks method, is generalized to sphere driven gear pitch curve corner and asks
Method, try to achieve the sphere pitch curve corner of driven Some Second Order Elliptic bevel gear
In formula,For the corner of active Some Second Order Elliptic bevel gear.
By the radius of curvature of driven Some Second Order Elliptic bevel gear, corresponding corner and sphere centre away from establishing driven Some Second Order Elliptic
The sphere pitch curve equation of bevel gear.
Step 3: solve the angular speed and angular acceleration of driven Some Second Order Elliptic bevel gear.
By gearratio formulaObtain angular speed：
To w2On the derivation of time t, angular acceleration is obtained：
Required according to the plant cusp of mouth 4 in approximate pause that seedlings picking and section of planting seedlings need to meet, it is desirable to Some Second Order Elliptic plane section
Curve semi-major axis a and semi-minor axis b ratio is as big as possible in the case where not influenceing mechanism service life and using effect, and this is just
Will be after step 3, the preferred sphere pitch curve design parameter of the active Some Second Order Elliptic bevel gear of Some Second Order Elliptic bevel gear pair 1
a、b、R。
Step 4: setting w1, θ values, select a, b, R initial value；
Step 5: by w1, θ, a, b, R value substitute intoWithCalculate corner WithCorresponding angular speed and angular acceleration in two sections.
Step 6: if corresponding angular acceleration is respectively less than 0.002m/s in two sections2, and corresponding angle in two sections
Speed is respectively less than 0.005m/s, then into the value reduction 0.01 of step 11, otherwise a 0.01, b of value increase；
Step 7: calculate e=a/b value；If e ＜ 0.9 (e values are excessive can not to generate preferable flank profil), return to step 5,
Otherwise step 8 is entered.
Step 8: a reduces 0.01, b on the basis of initial value increases by 0.01 on the basis of initial value；Calculate e=a/b value；If e
＜ 0.6, then into step 10, otherwise into step 9.
Step 9: by w1, θ, a, b, R value substitute intoWithCalculate cornerTwo sections
Angular speed and angular acceleration corresponding to interior, if corresponding angular acceleration is respectively less than 0.002m/s in two sections2, and two sections
Angular speed corresponding to interior is respectively less than 0.005m/s, then into step 11, otherwise returns to step 8.
Step 10: R value reduces 0.002, a, b, R are entered as initial value, repeat step five, six, seven, eight, nine again.
Step 11: according to a, b, R final preferred value, with reference to w1, θ values, try to achieve driving and driven Some Second Order Elliptic bevel gear section
Curvilinear equation.
After trying to achieve driving and driven Some Second Order Elliptic bevel gear pitch curve equation, using sphere gear profile normal method, second order can be obtained
Flank profil (the flank profil line 11 of active Some Second Order Elliptic bevel gear, the flank profil line of driven Some Second Order Elliptic bevel gear of elliptic bevel gear pair
12).Sphere gear profile normal method solution procedure is shown in the paper that Sun Liang etc. is delivered《Not rounded bevel-gear spherical flank profil numerical computation method》,
Agricultural mechanical journal, 2013,29 (8)：29~33.The space flank profil of Some Second Order Elliptic bevel gear pair is as shown in Fig. 5,6 and 7.
According to the angular speed w of driven Some Second Order Elliptic bevel gear2With angular acceleration, with reference to the tool of planetary gear train planting mechanism
Body structure, the angle for calculating the plant cusp of mouth 4 in planetary gear train planting mechanism (add) speed, and the solution procedure can be found in Chen Jianneng etc.
The paper delivered《Pot seedling transplanter deformed elliptic gear planetary system planting mechanism optimizes and experiment》, agricultural mechanical journal, 2013,
44(10)：52~55.
The present embodiment combination sphere gear profile normal method, from paper《Pot seedling transplanter deformed elliptic gear planetary system plants seedlings
Mechanism Optimization and experiment》In deformed elliptic gear planetary system planting mechanism, be then respectively adopted standard cones gear drive and
Some Second Order Elliptic bevel gear pair is driven, and solves the gear-driven planetary gear train planting mechanism of standard cones and Some Second Order Elliptic bevel gear
The planetary gear train planting mechanism of driving contrast as follows：
As shown in figure 3, Some Second Order Elliptic bevel gear pair (provides driving and driven number of gear teeth according to standard cones gear drive
It is identical, similarly hereinafter), the consistent (standard cones of central shaft crank degree change of the angle of eccentricity of fixed driving wheel and fixed driven pulley
Angle of eccentricity and central shaft angle relation curve 7 during gear drive), plant seedlings and turn with seedlings picking stage angle of eccentricity section and central shaft
Angle range is basically identical.As shown in figure 4, when Some Second Order Elliptic bevel gear pair uses the not rounded Bevel Gear Transmission of the present embodiment, main shaft
Corner is different from the change of center Shaft angle (angle of eccentricity and central shaft angle relation curve 9 during not rounded Bevel Gear Transmission), and plants
Seedling and seedlings picking stage angle of eccentricity section are significantly greater than central shaft corner section.Angle of eccentricity and central shaft angle relation curve
7 and 9 contrasts can be found：Because main shaft is uniform rotation, in seedlings picking section (central shaft relative initial position rotates 85~95 °) and plant
In seedling section (central shaft relative initial position rotates 265~275 °), planetary gear train is extended using Some Second Order Elliptic bevel gear pair and planted
The time that the cusp of mouth 4 is in seedlings picking and section of planting seedlings is transplanted in seedling mechanism, seedlings picking and the success rate planted seedlings are higher, overcome existing row
Star wheel series planting mechanism is difficult to this technological difficulties of increase in seedlings picking and a time of planting seedlings, and substantially increases seedlings picking, plants seedlings
Reliability.Stage angle of eccentricity section 8 is planted seedlings with Fig. 4 by taking seedlings picking section as an example, during standard cones gear drive in Fig. 3
In not rounded Bevel Gear Transmission when stage angle of eccentricity section 10 of planting seedlings contrast, when transplanting mouth and needing to meet 85~95 ° of rotation,
Angle of eccentricity corresponding to section 8 is 85~95 °, and angle of eccentricity corresponding to section 10 is 81~99 °, i.e. the angle range of main shaft becomes
Greatly, and main shaft is uniform rotation, it is seen then that main shaft is in the time lengthening shared by seedlings picking section.
The planetary gear train planting mechanism of the Some Second Order Elliptic bevel gear driving, operation principle are as follows：
Power is defeated by central shaft through Some Second Order Elliptic bevel gear pair, and central shaft both ends are provided with two planetary gears of structure identical
It is planting mechanism, planetary gear train planting mechanism is driven by two-stage gear drive, is driven respectively respectively by the planet axis at both ends
From plant mouth relative to the planet carrier cycle rotate.The rotating speed of central shaft is the change of class cosine line, in seedlings picking and is planted seedlings the stage pair
The rotating speed answered is relatively low.Time cycle constant planetary gear train planting mechanism is in and requires approximate dwell angle scope (seedlings picking and plant
Seedling angular range) when, it is relatively more using the time occupied by the planetary gear train planting mechanism of Some Second Order Elliptic bevel gear pair driving,
Seedlings picking has higher success rate with planting seedlings.
Claims (3)
1. the planetary gear train planting mechanism of Some Second Order Elliptic bevel gear driving, including Some Second Order Elliptic bevel gear pair, central shaft and planet
Train planting mechanism, it is characterised in that：Described Some Second Order Elliptic bevel gear pair includes the active Some Second Order Elliptic cone tooth of engaged transmission
Wheel and driven Some Second Order Elliptic bevel gear；Active Some Second Order Elliptic bevel gear uniform rotation, during driven Some Second Order Elliptic bevel gear is fixed on
In mandrel；The both ends of central shaft are mounted on planetary gear train planting mechanism；Described planetary gear train planting mechanism include planet carrier,
Gear drive and plant mouth；Central shaft is through plant mouth of the gear drive passing power to planet carrier both ends；Initial peace
During holding position, planet carrier is horizontally disposed with, and the central axis institute of the sphere pitch curve of driven Some Second Order Elliptic bevel gear and central shaft
It is two minimum points of curvature on the sphere pitch curve of driven Some Second Order Elliptic bevel gear in two intersection points of horizontal plane；Active second order is ellipse
Point of maximum curvature is meshed with curvature smallest point on driven gear pitch curve on the sphere pitch curve of conical gear.
2. the planetary gear train planting mechanism of Some Second Order Elliptic bevel gear driving according to claim 1, it is characterised in that：It is described
Driven Some Second Order Elliptic bevel gear sphere pitch curve on minimum two points of curvature curvature it is equal.
3. the design method of the planetary gear train planting mechanism of Some Second Order Elliptic bevel gear driving according to claim 1, it is special
Sign is：This method is specific as follows：
Step 1: establish the mathematical modeling of active Some Second Order Elliptic bevel gear；
By Some Second Order Elliptic, the orthographic projection on sphere obtains the sphere pitch curve of active Some Second Order Elliptic bevel gear；It is main in coordinate system XYZ
The sphere pitch curve equation of dynamic Some Second Order Elliptic bevel gear meets following relation：
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In formula, a is the semi-major axis of Some Second Order Elliptic, and b is the semi-minor axis of Some Second Order Elliptic, and R is spherical radius, and τ is active Some Second Order Elliptic
Polar angle of the point in X/Y plane on bevel-gear spherical pitch curve, span are [0,2 π]；
Step 2: solve geodetic centre-to-centre spacing and the sphere pitch curve equation of driven Some Second Order Elliptic bevel gear；
Two rotary shafts of Some Second Order Elliptic bevel gear pair are concurrent aces, and the angle between two rotary shafts is set to θ, and θ uses Circular measure, taken
Value scope isIf the rotary shaft of active Some Second Order Elliptic bevel gear and the intersecting point coordinate of sphere are (0,0, R), driven two
The rotary shaft of rank ellipse bevel gear and the intersecting point coordinate of sphere are (R sin θs, 0, R cos θ)；
The pitch curve geodesic curvature of active Some Second Order Elliptic bevel gear is obtained by the sphere pitch curve equation of active Some Second Order Elliptic bevel gear
Radius ρ1For：
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By conditional：L=R θ, obtain geodetic centre-to-centre spacing l；
The pitch curve geodesic curvature radius ρ of driven Some Second Order Elliptic bevel gear2For：
ρ2=l- ρ1
Try to achieve gearratio：
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</mfrac>
</mrow>
In formula, w1、w2The angular speed of respectively driving and driven Some Second Order Elliptic bevel gear, w1For the definite value of setting；
Corner based on the not rounded driven gear pitch curve of plane seeks method, is generalized to sphere driven gear pitch curve corner and seeks method, asks
Obtain the sphere pitch curve corner of driven Some Second Order Elliptic bevel gear
In formula,For the corner of active Some Second Order Elliptic bevel gear；
Driven Some Second Order Elliptic cone tooth is established by the radius of curvature of driven Some Second Order Elliptic bevel gear, corresponding corner and geodetic centre-to-centre spacing
The sphere pitch curve equation of wheel；
Step 3: solve the angular speed and angular acceleration of driven Some Second Order Elliptic bevel gear；
By gearratio formulaObtain angular speed：
To w2On the derivation of time t, angular acceleration is obtained：
<mrow>
<mi>&alpha;</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>dw</mi>
<mn>2</mn>
</msub>
</mrow>
<mrow>
<mi>d</mi>
<mi>t</mi>
</mrow>
</mfrac>
</mrow>
Step 4: setting w1, θ values, select a, b, R initial value；
Step 5: by w1, θ, a, b, R value substitute intoWithCalculate corner WithCorresponding angular speed and angular acceleration in two sections；
Step 6: if corresponding angular acceleration is respectively less than 0.002m/s in two sections2, and corresponding angular speed in two sections
Respectively less than 0.005m/s, then into the value reduction 0.01 of step 11, otherwise a 0.01, b of value increase；
Step 7: calculate e=a/b value；If e ＜ 0.9, returning to step 5, otherwise into step 8；
Step 8: a reduces 0.01, b on the basis of initial value increases by 0.01 on the basis of initial value；Calculate e=a/b value；If e ＜
0.6, then into step 10, otherwise into step 9；
Step 9: by w1, θ, a, b, R value substitute intoWithCalculate cornerIt is right in two sections
The angular speed and angular acceleration answered, if corresponding angular acceleration is respectively less than 0.002m/s in two sections2, and it is right in two sections
The angular speed answered is respectively less than 0.005m/s, then into step 11, otherwise returns to step 8；
Step 10: R value reduces 0.002, a, b, R are entered as initial value, repeat step five, six, seven, eight, nine again；
Step 11: according to a, b, R final preferred value, with reference to w1, θ values, try to achieve driving and driven Some Second Order Elliptic bevel gear pitch curve
Equation.
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