CN208778586U - Male-female for intersecting axle transmission engages pure rolling spiral bevel gear mechanism - Google Patents
Male-female for intersecting axle transmission engages pure rolling spiral bevel gear mechanism Download PDFInfo
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- CN208778586U CN208778586U CN201820908326.8U CN201820908326U CN208778586U CN 208778586 U CN208778586 U CN 208778586U CN 201820908326 U CN201820908326 U CN 201820908326U CN 208778586 U CN208778586 U CN 208778586U
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- steamboat
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Abstract
The utility model provides a kind of male-female engagement pure rolling spiral bevel gear mechanism for intersecting axle transmission, it partners transmission including steamboat and bull wheel, steamboat is connected by input shaft and driver, and bull wheel connects output shaft, small wheel axis and bull wheel Axis Cross, steamboat conical exterior surface are equipped with n1The equally distributed spiral circle curved tooth of item, the center line of all spiral circle curved tooths are equal lifts conical spiral, have knuckle between spiral circle curved tooth and steamboat conical exterior surface, bull wheel conical exterior surface is equipped with n2The equally distributed spiral arc groove of item, the center line of all spiral arc grooves is equal lifts conical spiral, there is knuckle between spiral arc groove and bull wheel conical exterior surface, the spiral circle curved tooth of steamboat and the spiral arc groove engagement system of bull wheel are that the pure rolling mesh of point contact is driven.The utility model has the beneficial effects that transmission efficiency is high, registration is big, bearing capacity is strong, the micromechanics for being not easy to lubricate and conventional mechanical field can be widely applied to.
Description
Technical field
The utility model relates to bevel gearing, specifically a kind of male-female engagement for intersecting axle transmission
Pure rolling spiral bevel gear mechanism.
Background technique
Gear is widely used in lathe, automobile, robot, wind-powered electricity generation, coal mine, aviation as mechanical key foundation components
The equipment manufactures such as space flight field and national economy main battle ground, performance superiority and inferiority directly decide that Grand Equipments and high-end industry produce
The quality of product, Performance And Reliability.
The main problem that China's gear industry faces at present is the height of high efficiency, big bearing capacity, lightweight, high reliability
Performance gear product to design and manufacture ability obviously insufficient.In industrial production and manufacturing field widely applied traditional spur gear,
Helical gear and bevel gear pair had not been solved thoroughly always because of fretting wear, gluing, plastic deformation brought by the opposite sliding of the flank of tooth
Etc. transmission failures problem, seriously affected the transmission efficiency, service life of gear product especially high-speed overload gear and reliable
Property, constrain the performance boost of " high point essence " mechanized equipment.The usual way for reducing tooth surface abrasion is using lubricating oil, lubricating grease
Equal lubricants, but in certain extreme environments, such as high temperature, low temperature, high pressure, intense radiation environment, these lubricants can fail.And
And to improve tooth surface abrasion and the gear lubrication system that is equipped with increases complete machine cost and weight, while lubricating oil, lubricating grease
Discharge also pollutes the environment.The development trend of modern equipment manufacturing industry " lightweight, modularization, intelligence " passes gear
Dynamic performance, weight, volume and gear Green design and manufacture propose requirements at the higher level.How to realize resource-effective, environmental-friendly
High-performance gear mechanism Green Design and Manufacturing, the transmission failure for reducing or avoiding the opposite sliding of the flank of tooth to cause further mentions
High transmission efficiency and bearing capacity are that current gear research field is important and one of urgent problems.
The design of pure rolling mesh flank of tooth meaning especially for high speed, heavy duty, precision gear transmission to gear drive
Great, the opposite sliding between even being eliminated the flank of tooth can be effectively reduced in it, the gear tooth friction abrasion that thus causes, glued, plasticity
The transmission failures such as deformation will also be effectively controlled, and can not only reduce the frictional dissipation between the high gear flank of tooth, reduce fever and
Vibration, moreover it is possible to improve the gear drive service life, promote transmission efficiency, it is ensured that there is the better flank of tooth to nibble for transmission accuracy and stationarity
Performance is closed, there is great positive effect to the comprehensive performance for promoting gear pair and train.
The transmitting of movement in plane between two intersecting axles and power at present, industrial application are most widely involute cone teeth
Take turns mechanism.But the theory of engagement of involute bevel gear mechanism follows curved surface mesh theory, and tooth is just certainly existed from design theory
Opposite sliding between face, therefore it is gear-driven universal not to be avoided that tooth surface abrasion, tooth face agglutination and tooth surface plastic deformation etc.
Failure mode affects the service life and reliability of gear pair.
In recent years, the small driver novel with original characteristic is created in gear mesh theory field both at home and abroad
Structure.As Chinese patent literature discloses the " spiral circle for parallel axes external toothing transmission application No. is 201510054843.4
Gear with curved teeth mechanism " discloses " the spiral arc gear for parallel axes Inside gear drive application No. is 201510051923.4
Mechanism ".Above two transmission mechanism is limited in that their design method is based on space curve mesh theory, engaging tooth
Face calculates dependent on curve mesh equation and solves, and engagement system is male-female mesh form, and meshing point is located at the side of concave tooth flank profil
Edge can generate excessive local stress due to EDGE CONTACT when transmission, be easy to cause the fracture of concave tooth tooth top and cause transmission failure,
It cannot be used for the transmission of industrial powered by conventional energy and high-speed overload.In addition, the design method of above two mechanism can not achieve
The stringent design of registration is unfavorable for being evenly distributed with for load so that the registration numerical value of transmission is uncertain.Moreover, they can only
It realizes the movement and power transmitting in plane between two-parallel axis, can not achieve the movement in plane between two quadrature axis and power
Transmitting.Therefore, their use scopes are greatly limited.Chinese patent literature, application No. is 201310049845.5,
" the bevel gear Meshing Pair based on conjugate curves " is disclosed, including mutual point gearing and tooth curve is the bevel gear I of circular arc
With bevel gear II, which has transmission efficiency high；The flank of tooth is easy to manufacture, and driving error is small, long service life
The characteristics of；But there is also flank of tooth when bevel gear I and bevel gear II are engaged to move along conjugate curves for the bevel gear, therefore between the flank of tooth
There are opposite sliding, the flank of tooth has the failure modes such as glued, abrasion and plastic deformation.
Utility model content
The purpose of this utility model is to be directed to current mechanical transmission fields problem of the existing technology, and propose a kind of use
In male-female engagement pure rolling spiral bevel gear mechanism and its design method of the plane any angle for intersecting axle transmission, have
Design is simple, easy to process, and without opposite sliding between the flank of tooth when transmission, transmission efficiency is high, registration can realize predefined design, holds
The advantages that loading capability is strong, the small, micromechanics that can be widely applied to be not easy to lubricate and conventional mechanical field.
To achieve the goals above, the technical measures that the utility model is taken are: providing a kind of for intersecting axle transmission
Male-female engages pure rolling spiral bevel gear mechanism, including steamboat and bull wheel partner transmission, and steamboat is by input shaft and drives
Dynamic device is connected, and bull wheel connects output shaft, the Axis Cross of steamboat and bull wheel, and the steamboat conical exterior surface is evenly equipped with spiral
Circle-arc tooth, bull wheel conical exterior surface are evenly equipped with spiral arc groove, and the center line of spiral circle curved tooth and spiral arc groove is
Lift conical spiral, the spiral arc groove cooperation of the spiral circle curved tooth and bull wheel of steamboat；The spiral circle curved tooth of the steamboat with
There is knuckle between steamboat conical exterior surface to reduce root stress concentration, the spiral arc groove and bull wheel cone of bull wheel
There is knuckle between outer surface to eliminate seamed edge cusp；The spiral circle curved tooth and spiral arc groove engagement system is that point connects
The pure rolling mesh of touching is driven, and steamboat rotates under the drive of driver, by between spiral circle curved tooth and spiral arc groove
Continuous engagement realizes that the steady engaged transmission between intersecting axle, all meshing points are located at steamboat and bull wheel theory reference circle
The tangent line of cone, the speed of related movement of all meshing points be zero, and meshing point is respectively formed on steamboat and bull wheel
Contact line is equal lifts conical spiral；
The spiral circle curved tooth and the structure of spiral arc groove and its shape of center line determine by the following method: in o--
x,y,z、ok--xk,yk,zkAnd op--xp,yp,zpIn three space coordinates, z-axis is overlapped with the axis of rotation of steamboat, zpAxis with
The axis of rotation of bull wheel is overlapped, zkAxis is overlapped with the path of contact of steamboat and bull wheel, z-axis and zp、zkAxis intersects at a point；Coordinate system
o1--x1,y1,z1It is connected firmly with steamboat, coordinate system o2--x2,y2,z2Connected firmly with bull wheel, steamboat, bull wheel initial position respectively with seat
Mark system o--x, y, z and op--xp,yp,zpIt is overlapped, ookDistance is R1, opokDistance is R2, zkAcute angle folded by axis and z-axis is δ1, zk
Axis and zpAcute angle folded by axis is δ2, steamboat is with uniform angular velocity ω1It is rotated around z-axis, bull wheel is with uniform angular velocity ω2Around zpAxis rotation, it is small
The angular velocity vector angle of wheel and bull wheel axis of rotation is θ, from initial position after a period of time, coordinate system o1--x1,y1,z1
And o2--x2,y2,z2It moves respectively, meshing point is M at this time, and steamboat is turned over around z-axisAngle, bull wheel is around zpAxis turns overAngle；
When steamboat and bull wheel engaged transmission, meshing point M is from coordinate origin okStart to transport along path of contact k-k uniform rectilinear
It is dynamic, define the parametric equation of M point movement are as follows:
T is the kinematic parameter variable of meshing point M, 0≤t≤Δ t in formula (1)；c1Undetermined coefficient, unit are moved for meshing point
For millimeter (mm)；In order to ensure the pure rolling mesh of steamboat and bull wheel, the movement of the corner and meshing point of steamboat and bull wheel is necessary
It is linear relationship, their relational expression is as follows:
K is the linear scale factor of meshing point movement in formula (2), and unit is radian (rad)；i12Between steamboat and bull wheel
Transmission ratio；
When meshing point M is moved along path of contact k-k, point M is respectively formed contact line C in steamboat and the bull wheel flank of tooth simultaneously1With
C2；According to coordinate transform, ask to obtain coordinate system o--x, y, z, ok--xk,yk,zk、op--xp,yp,zp、o1--x1,y1,z1And o2--
x2,y2,z2Between homogeneous coordinate transformation matrix are as follows:
Wherein:
It acquires:
By formula (6) according to homogeneous coordinate transformation, acquire:
Seek to obtain contact line C on the steamboat flank of tooth by formula (8)1For equal lifts conical spiral, its parametric equation are as follows:
Wushu (2) is brought formula (9) into and is acquired:
T is the angle parameter variable of equal lifts conical spiral, T=kt, and 0≤T≤Δ T in formula (10)；
By formula (7) according to homogeneous coordinate transformation, acquire:
Seek to obtain contact line C on the bull wheel flank of tooth by formula (11)2For equal lifts conical spiral, its parametric equation are as follows:
Wushu (2) is brought formula (12) into and is acquired:
And the transmission ratio of steamboat and bull wheel are as follows:
Wushu (14) substitutes into formula (13) and acquires:
The reference cone angle of steamboat and bull wheel is respectively δ1With δ2, their relational expression are as follows:
The convex side of steamboat spiral circle curved tooth is by the arc toothed section shape L of the axial direction comprising meshing point M1It is transported by right hand helix
It is dynamic to generate, arc toothed section shape L1For the production shape bus of steamboat convex side, the axial pitch parameter and contact line C of screw1
Axial pitch parameter it is consistent, it is ensured that the right hand helix motion profile of meshing point M and contact line C1It is overlapped；Coordinate system o--x, y, z
In, the production shape bus parameter equation of steamboat convex side are as follows:
The convex side for acquiring steamboat spiral circle curved tooth is derived in coordinate system o by right hand helix movement1–x1,y1,z1Middle parameter
Equation are as follows:
At this point, the center line equation of steamboat spiral circle curved tooth convex side are as follows:
The concave tooth face of bull wheel spiral arc groove is by the arc toothed section shape L of the axial direction comprising meshing point M2It is transported by left hand helix
It is dynamic to generate, arc toothed section shape L2For the production shape bus in bull wheel concave tooth face, the axial pitch parameter and contact line C of screw2
Axial pitch parameter it is consistent, it is ensured that the left hand helix motion profile of meshing point M and contact line C2It is overlapped, in coordinate system op--xp,
yp,zpThe production shape bus parameter equation in middle bull wheel concave tooth face are as follows:
The concave tooth face for acquiring bull wheel spiral arc groove is derived in coordinate system o by left hand helix movement2–x2,y2,z2Middle parameter
Equation are as follows:
At this point, the center line equation in bull wheel spiral arc groove concave tooth face are as follows:
The length of line of action of steamboat and bull wheel is equal are as follows:
The axial height of steamboat are as follows:
Δz1=Δ zkcosδ1 (24)
The axial height of bull wheel are as follows:
Δz2=Δ zkcosδ2 (25)
The circular cone body space of bull wheel and steamboat are as follows:
E=r1=r2 (26)
In above-mentioned all formulas:
T-meshing point M kinematic parameter variable, and t ∈ [0, Δ t]；
T-waits the parametric variable of lifts conical spiral, and T ∈ [0, Δ T], Δ T=k Δ t； (27)
K-meshing point movement linear scale factor, k > 0；
R1- it is that the theoretical of steamboat indexes cone big end radius；
R1a- be steamboat cone big end radius；R1a=R1-[(ρ2sinγ+e)/cosδ1]； (28)
R2- it is that the theoretical of bull wheel indexes cylindrical body big end radius；
R2a- be bull wheel cone big end radius, R2a=R2+(ρ2sinγ/cosδ2)； (29)
δ1- be steamboat theoretical reference cone angle；
δ2- be bull wheel theoretical reference cone angle；
i12- be steamboat and bull wheel transmission ratio；
r1The radius of spiral circle curved tooth on-steamboat；
r2The radius of spiral arc groove on-bull wheel；
ρ1The arc radius of-steamboat spiral circle curved tooth；
ρ2The arc radius of-bull wheel spiral arc groove；
The axial angle of engagement of γ-steamboat and bull wheel；
ΔzkThe length of line of action of-steamboat and bull wheel；
Δz1The axial height of-steamboat；
Δz2The axial height of-bull wheel；
Δ T-conical spiral angle parameter variable-value range；
Δ t-meshing point M kinematic parameter variable-value range,
Δ T-conical spiral angle parameter variable-value range；
n1- small tooth number, i.e. the spiral arc number of teeth amount of steamboat；
n2- big tooth number, i.e. the spiral arc slot number of bull wheel；
c1- meshing point moves undetermined coefficient；
Wherein: each coordinate system axis, e, r1, r2, ρ1, ρ2, R1, R2And c1Equal length or parasang are millimeter (mm)；δ1, δ2, ξ1, ξ2, T, angularly unit is radian (rad) by Δ T, k, γ and θ；
As angular velocity vector angle theta, the transmission ratio i for determining two intersecting axles12, steamboat theoretical indexing cone big end radius
R1, small tooth number n1, steamboat spiral circle curved tooth arc radius ρ1, bull wheel spiral arc groove arc radius ρ2, registration ε, axis
Undetermined coefficient c is moved to angle of engagement γ, meshing point1, meshing point movement linear scale parameter k, between steamboat and bull wheel cone
When gap e, the cone structure of steamboat and bull wheel, spiral circle curved tooth center line, cutting structure and the shape of steamboat also determine therewith, greatly
Spiral arc groove center line, cutting structure and the shape of wheel also determine that the installation site of steamboat and bull wheel also accordingly determines therewith,
To which the male-female for obtaining being driven for intersecting axle engages pure rolling spiral bevel gear mechanism.
The steamboat and bull wheel form transmission, registration design calculation formula are as follows:
Wushu (27) substitutes into formula (30) and acquires,
The numerical value ε, linear scale factor k and small tooth number n according to registration are needed when design1, comprehensive to determine meshing point M
Kinematic parameter variable t value range Δ t.
The uniformly distributed spiral circle curved tooth of the steamboat conical exterior surface is with axial arc toothed section shape L1, and make its ginseng
Examination point Θ1It moves along the circle-arc tooth center line of steamboat into spiral circle curved tooth；The bull wheel conical exterior surface is uniformly distributed
Spiral arc groove is with axial arc toothed section shape L2, and make its center of circle Θ2Made of being moved along the circular arc groove center line of bull wheel
Spiral arc groove.
Input shaft that the steamboat is connect with bull wheel, output shaft have interchangeability, i.e., connect input shaft, bull wheel using steamboat
Connect output shaft, or using bull wheel connect input shaft, steamboat connect output shaft, correspond respectively to for intersecting axle be driven it is convex-
The deceleration transmission or step-up drive mode of recessed engagement pure rolling spiral bevel gear mechanism；Only when steamboat and big tooth number are equal
When, it is constant speed drive's application that male-female engagement pure rolling spiral bevel gear transmission ratio is 1.
The input shaft direction of rotation of driver connection is clockwise or counterclockwise, to realize steamboat or bull wheel
Forward and backward transmission.
The male-female engagement pure rolling spiral bevel gear mechanism for intersecting axle transmission of the utility model is in conventional gears
Transmission mechanism theoretically carries out the gear mechanism of radical innovation, its design method also different from existing gear mechanism based on
The design method of curved surface mesh equation.Male-female of the utility model for intersecting axle transmission engages pure rolling spiral bevel gear machine
The engagement system of structure is the node engagement system of the Equation of engaged line based on pure rolling, and the speed of related movement of all meshing points is equal
It is zero, continuous-stable can be provided and nibbled for the small of arbitrary angle in plane degree intersecting axle transmission, micromechanics and conventional mechanicals
The method for closing transmission, the utility model male-female engagement pure rolling spiral bevel gear mechanism feature most outstanding are that flank profil intensity is high,
Freely, the flank of tooth is without opposite sliding, the failure modes such as no tooth face agglutination, abrasion and plastic deformation for registration design.
The male-female engagement pure rolling spiral bevel gear mechanism and prior art phase for intersecting axle transmission of the utility model
Than having the advantage, that
1, the utility model is for the male-female engagement pure rolling spiral bevel gear mechanism biggest advantage of intersecting axle transmission
By the active designs method of pure rolling mesh line parametric equation, mesh tooth face of the construction without opposite sliding, all meshing points
Speed of related movement is zero, therefore can avoid the common mistake such as tooth surface abrasion, gluing and tooth surface plastic deformation in gear drive
Effect form, transmission efficiency are high.
2, registration design of the utility model for the male-female engagement pure rolling spiral bevel gear mechanism of intersecting axle transmission
Freely, evenly distributing for load can be realized by the planform of registration being pre-designed to determine wheel body, improves power
Learn characteristic.
3, cutting structure shape of the utility model for the male-female engagement pure rolling spiral bevel gear mechanism of intersecting axle transmission
Shape is simple, and steamboat is spiral prominence circular-arc tooth surface, and bull wheel is the spiral concave arc slot flank of tooth, is easily worked manufacture, and angle of engagement etc. is joined
Number arbitrarily devised can adjust, and optimize the mechanical property of flank profil.
4, the utility model is cut for the male-female engagement pure rolling spiral bevel gear mechanism unrooted of intersecting axle transmission, minimum
The number of teeth is 1, compared to mechanisms such as existing involute bevel gears, the large transmission ratio high contact ratio transmission of single-stage may be implemented, structure is tight
It gathers, greatly saves installation space, simultaneously because the number of teeth is small, bigger transverse tooth thickness can be designed, thus with higher intensity and just
Degree, has bigger bearing capacity, is suitable for pushing away for small/micromachine, conventional mechanical transmission and high-speed overload transmission field
Wide application.
Detailed description of the invention
Fig. 1 is that the male-female for intersecting axle transmission of the utility model engages the structure of pure rolling spiral bevel gear mechanism
Schematic diagram；
Fig. 2 is that the male-female for intersecting axle transmission of the utility model engages the space of pure rolling spiral bevel gear mechanism
Coordinate system schematic diagram；
Fig. 3 is the axial sectional view of the spiral circle curved tooth and spiral arc groove that engage in Fig. 1；
Fig. 4 is the main view of the steamboat and its spiral circle curved tooth in Fig. 1；
Fig. 5 is the top view of the steamboat and its spiral circle curved tooth in Fig. 1；
Fig. 6 is the axial truncatus L of the spiral circle curved tooth of steamboat in Fig. 11Parameter schematic diagram；
Fig. 7 is the main view of bull wheel and its spiral arc groove in Fig. 1；
Fig. 8 is the top view of bull wheel and its spiral arc groove in Fig. 1；
Fig. 9 is the axial truncatus L of the spiral arc groove of bull wheel in Fig. 12Parameter schematic diagram；
Figure 10 is in the utility model when bull wheel connects structural schematic diagram when input shaft drives steamboat step-up drive.
In above-mentioned figure: 1- steamboat, 2- spiral circle curved tooth, 3- input shaft, 4- driver, 5- knuckle, 6- output shaft, 7-
Spiral arc groove, 8- bull wheel, 9- spiral circle curved tooth center line, 10- spiral arc groove center line, 11- steamboat theory index circular cone
Body, 12-bull wheel theories index cone, 13- steamboat contact line, 14- bull wheel contact line, 15- steamboat mounting hole, 16- bull wheel peace
Fill hole.
Specific embodiment
The utility model is described in further detail with specific embodiment with reference to the accompanying drawing, but the implementation of the utility model
It is without being limited thereto.
Embodiment 1: the utility model provides a kind of male-female engagement pure rolling spiral bevel gear machine for intersecting axle transmission
Structure, applied in plane between two intersecting axles transmission ratio be 1 transmission, structure as shown in Figure 1, include steamboat 1 and bull wheel 8,
Steamboat 1 and bull wheel 8 partner transmission, and steamboat 1 connects input shaft 3, and bull wheel 8 connects output shaft 6, i.e. bull wheel 8 passes through output
Axis 6 is connected with by driving load；The axis of the steamboat 1 and bull wheel 8 intersects, and the angular velocity vector of steamboat 1 and bull wheel 8 presss from both sides
Angle is θ, the π/3 of θ=2 radian (rad) in this example.Fig. 2 is that male-female of the utility model for intersecting axle transmission engages pure rolling
The spatial conjugate coordinate system schematic diagram of spiral bevel gear mechanism.
Referring to Fig. 1,2,3,4,5,6, the theoretical indexing cone big end radius of steamboat is R1, the theoretical indexing circular cone of steamboat
Angle is δ1, spiral circle curved tooth 2 is evenly distributed on 1 conical exterior surface of steamboat, steamboat cone big end radius is R1a, axially nibble
Close angle γ.Knuckle 5, radius r are equipped between the spiral circle curved tooth and steamboat cone of steamboat1Millimeter is small
The arc radius of the spiral arc groove of wheel is ρ1Millimeter.
Referring to Fig. 1,2,3,7,8,9, the theoretical indexing cone big end radius of bull wheel is R2, the theoretical indexing circular cone of bull wheel
Angle is δ2, spiral arc groove 7 is evenly distributed on the conical exterior surface of bull wheel 8, bull wheel cone big end radius is R2a, axial
Angle of engagement γ.Knuckle 5, radius r are equipped between the spiral arc groove and bull wheel cone of bull wheel2Millimeter,
The arc radius of spiral circle curved tooth on bull wheel is ρ2Millimeter.
Steamboat 1 connects input shaft 3, rotates under the drive of driver 4, makes the spiral circle curved tooth 2 of steamboat 1 and bull wheel 8
Spiral arc groove 7 continuously engages, and realizes the movement in plane between intersecting axle and the transmission of power, driver 4 in the present embodiment
For motor.
The center line of the spiral arc groove of the spiral circle curved tooth and bull wheel of the steamboat is equal lifts conical spiral；Spiral shell
Rounding curved tooth 2 is continuously engaged with spiral arc groove 7, realizes the continuous and stable engaged transmission in plane between two intersecting axles.
Wherein, the spiral arc groove and the structure of spiral circle curved tooth and its shape of center line curve are true by the following method
It is fixed: referring to fig. 2, in o--x, y, z, ok--xk,yk,zkAnd op--xp,yp,zpIn three space coordinates, the revolution of z-axis and steamboat
Axis is overlapped, zpAxis is overlapped with the axis of rotation of bull wheel, zkAxis is overlapped with the path of contact of steamboat and bull wheel, z-axis and zp、zkAxis phase
It meets at a bit；Coordinate system o1--x1,y1,z1It is connected firmly with steamboat, coordinate system o2--x2,y2,z2It is connected firmly with bull wheel, steamboat, bull wheel are rising
Beginning position respectively with coordinate system o--x, y, z and op--xp,yp,zpIt is overlapped, ookDistance is R1, opokDistance is R2, zkAxis and z-axis
Folded acute angle is δ1, zkAxis and zpAcute angle folded by axis is δ2, steamboat is with uniform angular velocity ω1It is rotated around z-axis, bull wheel is with uniform angular velocity
ω2Around zpThe angular velocity vector angle of axis rotation, steamboat and bull wheel axis of rotation is θ, from initial position after a period of time, is sat
Mark system o1--x1,y1,z1And o2--x2,y2,z2It moves respectively, meshing point is M at this time, and steamboat is turned over around z-axisAngle, bull wheel is around zp
Axis turns overAngle；
When steamboat and bull wheel engaged transmission, meshing point M is from coordinate origin okStart to transport along path of contact k-k uniform rectilinear
It is dynamic, define the parametric equation of M point movement are as follows:
T is the kinematic parameter variable of meshing point M, 0≤t≤Δ t in formula (1)；c1Undetermined coefficient, unit are moved for meshing point
For millimeter (mm)；In order to ensure the pure rolling mesh of steamboat and bull wheel, the movement of the corner and meshing point of steamboat and bull wheel is necessary
It is linear relationship, their relational expression is as follows:
K is the linear scale factor of meshing point movement in formula (2), and unit is radian (rad)；i12Between steamboat and bull wheel
Transmission ratio；
When meshing point M is moved along path of contact k-k, point M is respectively formed contact line C in steamboat and the bull wheel flank of tooth simultaneously1With
C2；According to coordinate transform, ask to obtain coordinate system o--x, y, z, ok--xk,yk,zk、op--xp,yp,zp、o1--x1,y1,z1And o2--
x2,y2,z2Between homogeneous coordinate transformation matrix are as follows:
Wherein:
It acquires:
By formula (6) according to homogeneous coordinate transformation, acquire:
Seek to obtain contact line C on the steamboat flank of tooth by formula (8)1For equal lifts conical spiral, its parametric equation are as follows:
Wushu (2) is brought formula (9) into and is acquired:
T is the angle parameter variable of equal lifts conical spiral, T=kt, and 0≤T≤Δ T in formula (10)；
By formula (7) according to homogeneous coordinate transformation, acquire:
Seek to obtain contact line C on the bull wheel flank of tooth by formula (11)2For equal lifts conical spiral, its parametric equation are as follows:
Wushu (2) is brought formula (12) into and is acquired:
And the transmission ratio of steamboat and bull wheel are as follows:
Wushu (14) substitutes into formula (13) and acquires:
The reference cone angle of steamboat and bull wheel is respectively δ1With δ2, their relational expression are as follows:
The convex side of steamboat spiral circle curved tooth is by the arc toothed section shape L of the axial direction comprising meshing point M1It is transported by right hand helix
It is dynamic to generate, arc toothed section shape L1For the production shape bus of steamboat convex side, the axial pitch parameter and contact line C of screw1
Axial pitch parameter it is consistent, it is ensured that the right hand helix motion profile of meshing point M and contact line C1It is overlapped, in coordinate system o--x,
In y, z, the production shape bus parameter equation of steamboat convex side are as follows:
The convex side for acquiring steamboat spiral circle curved tooth is derived in coordinate system o by right hand helix movement1–x1,y1,z1Middle parameter
Equation are as follows:
At this point, the center line equation of steamboat spiral circle curved tooth convex side are as follows:
The concave tooth face of bull wheel spiral arc groove is by the arc toothed section shape L of the axial direction comprising meshing point M2It is transported by left hand helix
It is dynamic to generate, arc toothed section shape L2For the production shape bus in bull wheel concave tooth face, the axial pitch parameter and contact line C of screw2
Axial pitch parameter it is consistent, it is ensured that the left hand helix motion profile of meshing point M and contact line C2It is overlapped；Coordinate system op--xp,
yp,zpIn, the production shape bus parameter equation in bull wheel concave tooth face are as follows:
The concave tooth face for acquiring bull wheel spiral arc groove is derived in coordinate system o by left hand helix movement2–x2,y2,z2Middle parameter
Equation are as follows:
At this point, the center line equation in bull wheel spiral arc groove concave tooth face are as follows:
The length of line of action of steamboat and bull wheel is equal are as follows:
The axial height of steamboat are as follows:
Δz2=Δ zkcosδ2 (24)
The axial height of bull wheel are as follows:
Δz2=Δ zkcosδ2 (25)
The circular cone body space of bull wheel and steamboat are as follows:
E=r1=r2 (26)
In above-mentioned all formulas:
T-meshing point M kinematic parameter variable, and t ∈ [0, Δ t]；
T-waits the parametric variable of lifts conical spiral, and T ∈ [0, Δ T], Δ T=k Δ t； (27)
K-meshing point movement linear scale factor, k > 0；
R1- it is that the theoretical of steamboat indexes cone big end radius；
R1a- be steamboat cone big end radius；R1a=R1-[(ρ2sinγ+e)/cosδ1]； (28)
R2- it is that the theoretical of bull wheel indexes cylindrical body big end radius；
R2a- be bull wheel cone big end radius, R2a=R2+(ρ2sinγ/cosδ2)； (29)
δ1- be steamboat theoretical reference cone angle；
δ2- be bull wheel theoretical reference cone angle；
i12- be steamboat and bull wheel transmission ratio；
r1The radius of spiral circle curved tooth on-steamboat；
r2The radius of spiral arc groove on-bull wheel；
ρ1The arc radius of-steamboat spiral circle curved tooth；
ρ2The arc radius of-bull wheel spiral arc groove；
The axial angle of engagement of γ-steamboat and bull wheel；
ΔzkThe length of line of action of-steamboat and bull wheel；
Δz1The axial height of-steamboat；
Δz2The axial height of-bull wheel；
Δ T-conical spiral angle parameter variable-value range；
Δ t-meshing point M kinematic parameter variable-value range,
Δ T-conical spiral angle parameter variable-value range；
n1- small tooth number, i.e. the spiral arc number of teeth amount of steamboat；
n2- big tooth number, i.e. the spiral arc slot number of bull wheel；
c1- meshing point moves undetermined coefficient；
Wherein: each coordinate system axis, e, r1, r2, ρ1, ρ2, R1, R2And c1Equal length or parasang are (mm) millimeter；δ1, δ2, ξ1, ξ2, T, angularly unit is (rad) radian by Δ T, k, γ and θ；
Steamboat and bull wheel form transmission, registration design calculation formula are as follows:
Wushu (27) substitutes into formula (30) and acquires,
The numerical value ε, linear scale factor k and small tooth number n according to registration are needed when design1, comprehensive to determine meshing point M
Kinematic parameter variable t value range Δ t.
As angular velocity vector angle theta, the transmission ratio i for determining two intersecting axles12, steamboat theoretical indexing cone big end radius
R1, small tooth number n1, steamboat spiral circle curved tooth arc radius ρ1, bull wheel spiral arc groove arc radius ρ2, registration ε, axis
Undetermined coefficient c is moved to angle of engagement γ, meshing point1, meshing point movement linear scale parameter k, between steamboat and bull wheel cone
When gap e, the cone structure of steamboat and bull wheel, spiral circle curved tooth center line, cutting structure and the shape of steamboat also determine therewith, greatly
Spiral arc groove center line, cutting structure and the shape of wheel also determine that the installation site of steamboat and bull wheel also accordingly determines therewith,
To which the male-female for obtaining being driven for intersecting axle engages pure rolling spiral bevel gear mechanism.
When in above-mentioned formula: relevant parameter distinguishes value are as follows:ε=2, i12=1, c1=30 millimeters
(mm), k=π, R1=25 millimeters (mm), ρ1=2.5 millimeters (mm), ρ2It=3 millimeters (mm), e=1 millimeters (mm), substitutes into formula (16)
It acquiresSubstitution formula (31) acquires Δ t=1, acquires Δ T=π by formula (27).
The above numerical value is brought into the tooth surface parameters equation that formula (18) acquires steamboat spiral arc tooth in the present embodiment are as follows:
0≤T≤π, ξ1∈[0,π]
The above numerical value is brought into formula (19) and acquires steamboat spiral arc tooth center line equation in the present embodiment are as follows:
The above numerical value is brought into the tooth surface parameters equation that formula (21) acquires spiral arc groove in the present embodiment are as follows:
0≤T≤π, ξ2∈[0,π]
Substitution formula (22) acquires the spiral arc groove center line equation of bull wheel in the present embodiment are as follows:
It is Δ z that substitution formula (23), which acquires steamboat and the length of line of action of bull wheel,kIt=30 millimeters (mm), substitutes into formula (24) and acquires
The axial height of steamboat isMillimeter (mm), brings formula (25) into and acquires the axial height of bull wheel and beIn the least
Rice (mm)；Bringing formula (28) into and acquiring the cone big end radius of steamboat is R1aIt=22.691 millimeters (mm), brings formula (29) into and acquires
The cone big end radius of bull wheel is R2a=26.732 millimeters (mm)；The radius of steamboat and bull wheel is acquired by formula (26)
r1=r2=1 millimeter (mm).
Spiral arc number of teeth amount is set as n1=4, then acquiring spiral arc slot number by formula (14) is n2=4, then distinguish
According to the data of the conical structure parameter of above-mentioned spiral circle curved tooth 2, the center line equation of spiral arc groove 7 and steamboat, bull wheel,
It just can determine that this shape to spiral arc Bevel Gear Transmission pair of steamboat 1, bull wheel 8, to obtain the cone of pure rolling male-female engagement
The external form of gear mechanism is simultaneously correctly assembled.
When driver 4 is rotated with driven input shaft 3, steamboat 1, due to installing steamboat 1 and when bull wheel 8, one pair of them spiral shell
Rounding curved tooth 2 and spiral arc groove 7 are meshing state, and the registration of defined spiral arc bevel gear is ε when design
=2 are greater than 1, therefore when this pair of of spiral arc tooth 2 and spiral arc groove 7 will be disengaged from rotation but not completely disengaged
When engagement, the adjacent spiral circle curved tooth 2 of another pair and spiral arc groove 7 then take part in engagement again, to realize spiral circle
The engaged transmission of arc bevel gear mechanism continuous-stable in rotary motion.The input shaft direction of rotation of the present embodiment driver connection
To be clockwise, corresponding to the constant speed drive of spiral arc bevel gear mechanism, to realize the constant speed drive of bull wheel turned counterclockwise.
Embodiment 2: the male-female engagement pure rolling spiral bevel gear mechanism for being used for intersecting axle transmission of the utility model is answered
For the step-up drive between two square crossing axis, θ=pi/2 radian (rad) at this time.As shown in Figure 10, it is connected using bull wheel 8 defeated
Enter axis 3, steamboat 1 connects output shaft 6, i.e. steamboat 1 is connected by output shaft 6 with by driving load；The axis of steamboat 1 and bull wheel 8
Orthogonal, their angular speed angle is θ=pi/2 (rad) radian at this time.There are eight spiral circles in the present embodiment on bull wheel 8
Arc slot 7, there are four spiral circle curved tooths 2 on steamboat 1 designs registration ε=4/3 when input shaft 3 drives bull wheel 8 to rotate.Due to
When installing bull wheel 8 and steamboat 1, spiral arc groove 7 and a spiral circle curved tooth 2 on steamboat are meshing state on bull wheel 8, with
When bull wheel 8 rotates, large and small wheel rotation keeps spiral circle curved tooth and the registration of spiral arc groove engagement to be greater than 1, to realize spiral shell
Revolve the engaged transmission of circular-arc bevel gear mechanism continuous-stable.At this point, steamboat is 2 to the transmission ratio of bull wheel, i.e., bull wheel is to steamboat
Speed increasing ratio is 2.
Relevant parameter distinguishes value are as follows:ε=4/3, i12=2, c1=30 millimeters (mm), k=π, R1=
25 millimeters (mm), ρ1=2.5 millimeters (mm), ρ2=3 millimeters (mm), e=1 millimeters (mm).Substitution formula (16) acquires δ1=0.4636
Radian (rad), δ2=1.1071 radians (rad).Substitution formula (31) acquires Δ t=2/3, acquires π/3 Δ T=2 by formula (27).
The above numerical value is brought into the tooth surface parameters equation that formula (18) acquires steamboat spiral arc tooth in the present embodiment are as follows:
0≤T≤2 π/3, ξ1∈[0,π]
The above numerical value is brought into formula (19) and acquires steamboat spiral arc tooth center line equation in the present embodiment are as follows:
The above numerical value is brought into the tooth surface parameters equation that formula (21) acquires bull wheel spiral arc groove in the present embodiment are as follows:
0≤T≤2 π/3, ξ2∈[0,π]
Substitution formula (22) acquires the spiral arc groove center line equation of bull wheel in the present embodiment are as follows:
It is Δ z that substitution formula (23), which acquires steamboat and the length of line of action of bull wheel,kIt=20 millimeters (mm), substitutes into formula (24) and acquires
The axial height of steamboat is Δ z1=17.8886 millimeters (mm), bringing formula (25) into and acquiring the axial height of bull wheel is Δ z2=
8.9443 millimeter (mm)；Bringing formula (28) into and acquiring the cone big end radius of steamboat is R1a=22.7639 millimeters (mm), bring formula into
(29) the cone big end radius for acquiring bull wheel is R2a=53.3535 millimeters (mm)；The mistake of steamboat and bull wheel is acquired by formula (26)
Cross radius of corner r1=r2=1 millimeter (mm).
Due to spiral arc slot number be 8, spiral arc number of teeth amount be 4, then respectively according to above-mentioned spiral circle curved tooth 2,
The data of the center line equation and steamboat of spiral arc groove 7, the conical structure parameter of bull wheel, just can determine that steamboat 1, bull wheel 8
This shape to spiral arc Bevel Gear Transmission pair, so that the external form for obtaining the bevel gear mechanism of pure rolling male-female engagement is gone forward side by side
The correct assembly of row.
The present embodiment driver connection input shaft direction of rotation be it is clockwise, corresponding to spiral arc bevel gear mechanism
Step-up drive mode, to realize the transmission of steamboat turned counterclockwise.
The utility model for intersecting axle transmission male-female engagement pure rolling spiral bevel gear mechanism because cut without root,
Limitation without minimum number of teeth can carry out big transverse tooth thickness design, bending strength, contact strength and biggish rigidity with higher, sheet
Utility model also provides the design of the bevel gear mechanism of continuous-stable engaged transmission between two any angle intersecting axles in plane
Method can engage the bevel gear mechanism parameter of pure rolling according to registration numerical Design male-female, have flank profil intensity height, the flank of tooth
Without opposite sliding, unrooted is cut, single staged transmission ratio is big, transmission efficiency is high, greatly reduces the mistake such as tooth face agglutination, abrasion and plastic deformation
The advantages that imitating probability, can simplify the structure of conventional gear mechanism and micromechanics transmission device, be suitable in small, micromachine and
The application in conventional mechanical field.
Claims (8)
1. the male-female for intersecting axle transmission engages pure rolling spiral bevel gear mechanism, including steamboat and bull wheel partner biography
Dynamic pair, the steamboat are connected by input shaft and driver, and the bull wheel connects output shaft, the axis of the steamboat and described big
The Axis Cross of wheel, it is characterised in that: the steamboat conical exterior surface is equipped with n1The equally distributed spiral circle curved tooth of item owns
The center line of spiral circle curved tooth is equal lifts conical spiral, the spiral circle curved tooth and the steamboat conical exterior surface it
Between have a knuckle, the bull wheel conical exterior surface is equipped with n2The equally distributed spiral arc groove of item, all spiral arc grooves
Center line be equal lifts conical spiral, have transition circle between the spiral arc groove and the bull wheel conical exterior surface
Angle, the spiral circle curved tooth of the steamboat and the spiral arc groove engagement system of the bull wheel are that the pure rolling mesh of point contact passes
It is dynamic, by the continuous engagement between the spiral arc groove on the spiral circle curved tooth and the steamboat on the bull wheel, drive
The bull wheel rotation, the spiral arc toothing and the spiral arc slot structure determine by the following method:
S1 constructs coordinate system, defines the positional relationship of the steamboat and the bull wheel and each coordinate system:
Construct o--x, y, z, ok--xk,yk,zkAnd op--xp,yp,zpThree space coordinates, make the revolution of z-axis Yu the steamboat
Axis is overlapped, zpAxis is overlapped with the axis of rotation of the bull wheel, zkAxis is overlapped with the path of contact of the steamboat and the bull wheel, z-axis
With zp、zkAxis intersects at a point, the coordinate system o that building is connected firmly with the steamboat1--x1,y1,z1, the coordinate that is connected firmly with the bull wheel
It is o2--x2,y2,z2, the steamboat and the bull wheel initial position respectively with coordinate system o--x, y, z and op--xp,yp,zpWeight
It closes, ookDistance is R1, opokDistance is R2, zkAcute angle folded by axis and z-axis is δ1, zkAxis and zpAcute angle folded by axis is δ2, described small
Wheel is with uniform angular velocity ω1It is rotated around z-axis, the bull wheel is with uniform angular velocity ω2Around zpAxis rotation, the steamboat and the The Grand Circle
The angular velocity vector angle of shaft axis is θ, from initial position after a period of time, coordinate system o1--x1,y1,z1And o2--x2,y2,
z2It moves respectively, meshing point is M at this time, and the steamboat is turned over around z-axisAngle, the bull wheel is around zpAxis turns overAngle；
S2 determines the kinematic parameter equation of meshing point M:
When the steamboat and bull wheel engaged transmission, meshing point M is from coordinate origin okAlong path of contact k-k linear uniform motion,
Define the parametric equation of M point movement are as follows:
T is the kinematic parameter variable of meshing point M, 0≤t≤Δ t in formula；c1Undetermined coefficient, the steamboat and institute are moved for meshing point
The pure rolling mesh for stating bull wheel, the movement of the corner and meshing point that determine the steamboat and the bull wheel must be linear relationships,
Relational expression is as follows:
K is the linear scale factor of meshing point movement, k > 0, i in formula12Transmission ratio between steamboat and bull wheel；
S3 determines the value range Δ t of the kinematic parameter variable t of meshing point M:
The right design calculation formula of transmission is made of the steamboat and bull wheelIt acquires
S4 determines contact line C on the steamboat flank of tooth1With contact line C on the bull wheel flank of tooth2Parametric equation:
When meshing point M is moved along path of contact k-k, point M is respectively formed contact line C in steamboat and the bull wheel flank of tooth simultaneously1And C2,Root
According to coordinate transform, available coordinate system o--x, y, z, ok--xk,yk,zk、op--xp,yp,zp、o1--x1,y1,z1And o2--x2,
y2,z2Between homogeneous coordinate transformation matrix are as follows:
Homogeneous coordinate transformation acquires contact line C on the steamboat flank of tooth respectively1With contact line C on the bull wheel flank of tooth2Parameter side
Journey, contact line C1For equal lifts conical spiral and parametric equation are as follows:
Contact line C2For equal lifts conical spiral and parametric equation are as follows:
T is the angle parameter variable of equal lifts conical spiral, T=kt, and 0≤T≤Δ T in formula；
S5 determines the parametric equation of production the shape bus parameter equation and convex side of the steamboat convex side:
The convex side of steamboat spiral circle curved tooth is by the arc toothed section shape L of the axial direction comprising meshing point M1It is moved and is given birth to by right hand helix
At arc toothed section shape L1For the production shape bus of the steamboat flank of tooth, the axial pitch parameter and contact line C of screw1Axial direction
Screw pitch parameter is consistent, it is ensured that the right hand helix motion profile and contact line C of meshing point M1It is overlapped, it is small in coordinate system o--x, y, z
Take turns the production shape bus parameter equation of convex side are as follows:
The convex side for acquiring the steamboat spiral circle curved tooth is derived in coordinate system o by right hand helix movement1--x1,y1,z1Middle parameter
Equation are as follows:
S6 determines the parametric equation of production the shape bus parameter equation and concave tooth face in bull wheel concave tooth face:
The concave tooth face of bull wheel spiral arc groove is by the arc toothed section shape L of the axial direction comprising meshing point M2It is moved and is given birth to by left hand helix
At arc toothed section shape L2For the production shape bus of the bull wheel spiral arc groove flank of tooth, the axial pitch parameter of screw with connect
Touch line C2Axial pitch parameter it is consistent, it is ensured that the left hand helix motion profile of meshing point M and contact line C2It is overlapped, in coordinate system
op--xp,yp,zpMiddle bull wheel spiral arc groove concave tooth face produces the parametric equation of shape bus are as follows:
The concave tooth face for acquiring the bull wheel spiral arc groove is derived in coordinate system o by left hand helix movement2--x2,y2,z2Middle parameter
Equation are as follows:
In above-mentioned all formulas:
ε-is the registration of steamboat and bull wheel；
R1- it is that the theoretical of steamboat indexes cone big end radius；
R2- it is that the theoretical of bull wheel indexes cylindrical body big end radius；
δ1- be steamboat theoretical reference cone angle；
δ2- be bull wheel theoretical reference cone angle；
ρ1The arc radius of-steamboat spiral circle curved tooth；
ρ2The arc radius of-bull wheel spiral arc groove；
The axial angle of engagement of γ-steamboat and bull wheel；
i12- be steamboat and bull wheel transmission ratio；
Δ T-conical spiral angle parameter variable-value range；
c1- meshing point moves undetermined coefficient.
2. the male-female for intersecting axle transmission engages pure rolling spiral bevel gear mechanism as described in claim 1, feature exists
In,
The center line of the steamboat spiral circle curved tooth convex side is in coordinate system o1--x1,y1,z1In parametric equation are as follows:
The center line in the bull wheel spiral arc groove concave tooth face is in coordinate system o2--x2,y2,z2In parametric equation are as follows:
3. the male-female for intersecting axle transmission engages pure rolling spiral bevel gear mechanism as described in claim 1, feature exists
In the length of line of action of the steamboat and the bull wheel are as follows:
4. the male-female for intersecting axle transmission engages pure rolling spiral bevel gear mechanism as claimed in claim 3, feature exists
In,
The axial height of the steamboat are as follows: Δ z1=Δ zkcosδ1,
The axial height of the bull wheel are as follows: Δ z2=Δ zkcosδ2。
5. the male-female for intersecting axle transmission engages pure rolling spiral bevel gear mechanism as described in claim 1, feature exists
In: the circular cone body space of the bull wheel and the steamboat are as follows: e=r1=r2, r1Indicate the transition of spiral circle curved tooth on the steamboat
Radius of corner, r2Indicate the radius of spiral arc groove on the bull wheel.
6. the male-female for intersecting axle transmission engages pure rolling spiral bevel gear mechanism as described in claim 1, feature exists
In: input shaft that the steamboat is connect with bull wheel, output shaft have interchangeability.
7. the male-female for intersecting axle transmission engages pure rolling spiral bevel gear mechanism as described in claim 1, feature exists
In: the number of teeth n of the steamboat1With the number of teeth n of the bull wheel2It is equal.
8. the male-female for intersecting axle transmission engages pure rolling spiral bevel gear mechanism as described in claim 1, feature exists
In: the input shaft direction of rotation is clockwise or counterclockwise.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201820908326.8U CN208778586U (en) | 2018-06-12 | 2018-06-12 | Male-female for intersecting axle transmission engages pure rolling spiral bevel gear mechanism |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201820908326.8U CN208778586U (en) | 2018-06-12 | 2018-06-12 | Male-female for intersecting axle transmission engages pure rolling spiral bevel gear mechanism |
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| CN201820908326.8U Expired - Fee Related CN208778586U (en) | 2018-06-12 | 2018-06-12 | Male-female for intersecting axle transmission engages pure rolling spiral bevel gear mechanism |
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