CN108533685B - Convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission - Google Patents

Convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission Download PDF

Info

Publication number
CN108533685B
CN108533685B CN201810603774.1A CN201810603774A CN108533685B CN 108533685 B CN108533685 B CN 108533685B CN 201810603774 A CN201810603774 A CN 201810603774A CN 108533685 B CN108533685 B CN 108533685B
Authority
CN
China
Prior art keywords
wheel
spiral
meshing
small wheel
small
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Fee Related
Application number
CN201810603774.1A
Other languages
Chinese (zh)
Other versions
CN108533685A (en
Inventor
陈祯
丁华锋
曾鸣
杨静
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
China University of Geosciences
Original Assignee
China University of Geosciences
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by China University of Geosciences filed Critical China University of Geosciences
Priority to CN201810603774.1A priority Critical patent/CN108533685B/en
Publication of CN108533685A publication Critical patent/CN108533685A/en
Application granted granted Critical
Publication of CN108533685B publication Critical patent/CN108533685B/en
Expired - Fee Related legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H1/00Toothed gearings for conveying rotary motion
    • F16H1/02Toothed gearings for conveying rotary motion without gears having orbital motion
    • F16H1/04Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members
    • F16H1/12Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members with non-parallel axes
    • F16H1/14Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members with non-parallel axes comprising conical gears only
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H55/00Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02Toothed members; Worms
    • F16H55/08Profiling
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H55/00Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02Toothed members; Worms
    • F16H55/17Toothed wheels
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/10Geometric CAD
    • G06F30/17Mechanical parametric or variational design
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/30Circuit design
    • G06F30/36Circuit design at the analogue level
    • G06F30/367Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H55/00Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02Toothed members; Worms
    • F16H55/08Profiling
    • F16H2055/0866Profiles for improving radial engagement of gears, e.g. chamfers on the tips of the teeth

Abstract

The invention provides a convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission, which comprises a pair of transmission pairs consisting of a small wheel and a large wheel, wherein the small wheel is fixedly connected with a driver through an input shaft, the large wheel is connected with an output shaft, the axis of the small wheel is crossed with the axis of the large wheel, and n is arranged on the outer surface of a cone of the small wheel1The spiral circular arc teeth are uniformly distributed, the central lines of all the spiral circular arc teeth are equal-lift-distance conical spiral lines, a transition fillet is arranged between each spiral circular arc tooth and the outer surface of the small wheel cone, and n is arranged on the outer surface of the large wheel cone2The spiral arc grooves are uniformly distributed, the central lines of all the spiral arc grooves are equal-lift-distance conical spiral lines, a transition fillet is arranged between each spiral arc groove and the outer surface of the cone of the large wheel, and the meshing mode of the spiral arc teeth of the small wheel and the spiral arc grooves of the large wheel is point-contact pure rolling meshing transmission. The invention has the beneficial effects that: the transmission efficiency is high, the contact ratio is large, the bearing capacity is strong, and the lubricating oil can be widely applied to the fields of micro machines and conventional machines which are difficult to lubricate.

Description

Convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission
Technical Field
The invention relates to a bevel gear transmission device, in particular to a convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission.
Background
The gear is used as a basic component of a mechanical core, is widely applied to the field of equipment manufacturing industries such as machine tools, automobiles, robots, wind power, coal mines, aerospace and the like and national economy main battlefield, and the quality of the performance directly determines the quality, performance and reliability of major equipment and high-end industrial products.
The main problem faced by the gear industry in China at present is that the design and manufacturing capability of high-performance gear products with high efficiency, large bearing capacity, light weight and high reliability is obviously insufficient. The traditional straight gear, helical gear and bevel gear pair widely applied in the field of industrial production and manufacturing never thoroughly solve the problems of transmission failures such as friction wear, gluing, plastic deformation and the like caused by relative sliding of tooth surfaces, seriously affect the transmission efficiency, service life and reliability of gear products, particularly high-speed heavy-duty gears, and restrict the performance improvement of high-precision mechanical equipment. A common way to reduce tooth surface wear is to use lubricants such as lubricating oils, greases, etc., but these lubricants can fail in certain extreme environments, such as high temperature, low temperature, high pressure, high radiation, etc. Moreover, the gear lubrication system provided for improving the wear of the tooth surfaces increases the overall cost and weight of the machine, and the emission of lubricating oil and grease also causes environmental pollution. The development trend of modern equipment manufacturing industry 'lightweight, modularization and intellectualization' puts higher requirements on gear transmission performance, weight, volume and green gear design and manufacture. How to realize the green design and manufacture of a high-performance gear mechanism with resource saving and environmental friendliness, reduce or avoid transmission failure caused by relative sliding of tooth surfaces, and further improve the transmission efficiency and the bearing capacity is one of the important and urgent problems in the field of gear research at present.
The design of the pure rolling meshing tooth surface has great significance for gear transmission, particularly high-speed, heavy-load and precise gear transmission, and can effectively reduce or even eliminate relative sliding between the tooth surfaces, so that the transmission failures such as tooth surface friction abrasion, gluing, plastic deformation and the like caused by the relative sliding can be effectively controlled, the friction loss between the tooth surfaces of the high-speed gear can be reduced, heat and vibration are reduced, the gear transmission service life can be prolonged, the transmission efficiency is improved, the transmission precision and stability are ensured, the tooth surface meshing performance is better, and the gear system has a great positive effect on improving the comprehensive performance of a gear pair and a gear train.
At present, the transmission of motion and power between two crossed shafts in a plane is the involute bevel gear mechanism which is most widely applied in industry. However, the meshing principle of the involute bevel gear mechanism follows the curved surface meshing theory, and relative sliding between tooth surfaces inevitably exists in the design theory, so that common failure modes of gear transmission such as tooth surface abrasion, tooth surface gluing and tooth surface plastic deformation cannot be avoided, and the service life and reliability of a gear pair are influenced.
In recent years, a novel micro transmission mechanism with original characteristics is innovated in the field of gear meshing theory at home and abroad. As in chinese patent document, application No. 201510054843.4 discloses "a helical circular-arc gear mechanism for parallel-axis external meshing transmission", and application No. 201510051923.4 discloses "a helical circular-arc gear mechanism for parallel-axis internal meshing transmission". The two transmission mechanisms are limited in that the design methods of the two transmission mechanisms are based on a space curve meshing theory, the meshing tooth surface is calculated and solved by a curve meshing equation, the meshing mode is a convex-concave meshing mode, the meshing point is located at the edge of the tooth profile of the concave tooth, excessive local stress can be generated due to edge contact during transmission, the tooth crest of the concave tooth is easy to break to cause transmission failure, and the two transmission mechanisms cannot be used for conventional power and high-speed heavy-load transmission in industrial production. In addition, the design methods of the two mechanisms cannot realize strict design of the contact ratio, so that the contact ratio value of the transmission pair is uncertain, and the uniform distribution of the load is not facilitated. Moreover, they can only realize the motion and power transmission between two parallel axes in a plane, but cannot realize the motion and power transmission between two orthogonal axes in the plane. Therefore, their range of use is greatly limited. Chinese patent document, application number 201310049845.5, discloses a bevel gear meshing pair based on conjugate curves, comprising a bevel gear I and a bevel gear II which are meshed with each other at points and have circular-arc tooth profile curves, and the bevel gear mechanism has high transmission efficiency; the tooth surface is easy to process and manufacture, the transmission error is small, and the service life is long; however, in the bevel gear, the tooth surfaces move along a conjugate curve when the bevel gear I and the bevel gear II are meshed, so that relative sliding exists between the tooth surfaces, and the tooth surfaces have failure modes such as gluing, abrasion, plastic deformation and the like.
Disclosure of Invention
The invention aims to solve the problems in the prior art in the field of mechanical transmission at present, provides a convex-concave meshing pure rolling spiral bevel gear mechanism for cross shaft transmission at any angle of a plane and a design method thereof, and has the advantages of simple design, easiness in processing, no relative sliding between tooth surfaces during transmission, high transmission efficiency, predefined design of contact ratio, strong bearing capacity and the like, and can be widely applied to the fields of micro machinery and conventional machinery which are difficult to lubricate.
In order to achieve the purpose, the technical measures adopted by the invention are as follows: the convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission comprises a pair of transmission pairs consisting of small wheels and large wheels, wherein the small wheels are fixedly connected with a driver through an input shaft, the large wheels are connected with an output shaft, the axes of the small wheels and the large wheels are crossed, spiral arc teeth are uniformly distributed on the outer surface of a cone of the small wheels, spiral arc grooves are uniformly distributed on the outer surface of the cone of the large wheels, the central lines of the spiral arc teeth and the spiral arc grooves are equal-lift-distance conical spiral lines, and the spiral arc teeth of the small wheels are matched with the spiral arc grooves of the large wheels; a transition fillet is arranged between the spiral arc tooth of the small wheel and the outer surface of the cone of the small wheel to reduce the stress concentration of the tooth root, and a transition fillet is arranged between the spiral arc groove of the large wheel and the outer surface of the cone of the large wheel to eliminate sharp points of the edge; the meshing mode of the spiral arc teeth and the spiral arc grooves is point-contact pure rolling meshing transmission, the small wheel rotates under the driving of a driver, stable meshing transmission between crossed shafts is realized through the continuous meshing action between the spiral arc teeth and the spiral arc grooves, all meshing points are positioned on the tangent line of a theoretical indexing cone of the small wheel and the large wheel, the relative movement speed of all the meshing points is zero, and the contact lines of the meshing points respectively formed on the small wheel and the large wheel are equal-lift-distance conical spiral lines;
the structure of the spiral arc teeth and the spiral arc grooves and the shape of the center line of the spiral arc teeth and the spiral arc grooves are determined by the following method: at o- -x, y, z, ok--xk,yk,zkAnd op--xp,yp,zpIn three space coordinate systems, the z axis is coincident with the rotation axis of the small wheel, and z ispThe axis of rotation of the shaft and the bull wheel coinciding, zkThe axis coincides with the line of engagement of the small and large wheels, and the z-axis coincides with the z-axisp、zkThe axes intersect at a point; coordinate system o1--x1,y1,z1Fixedly connected to the small wheel, coordinate system o2--x2,y2,z2Fixedly connected with the big wheel, and the small wheel and the big wheel are respectively arranged at the initial positionsTo coordinate systems o-x, y, z and op--xp,yp,zpCoincidence, ookA distance R1,opokA distance R2,zkThe acute angle between the axis and the z-axis is delta1,zkAxis and zpThe acute angle included by the shaft is delta2With small wheels at uniform angular velocity omega1Rotating about the z-axis, the bull wheel at a uniform angular velocity ω2Around zpThe axes are rotated, the angular velocity vector included angle of the rotation axes of the small wheel and the large wheel is theta, and after a period of time from the initial position, the coordinate system o1--x1,y1,z1And o2--x2,y2,z2Move respectively, at the meshing point M, the small wheel rotates around the axis z
Figure BDA0001693729230000031
Corner, large wheel winding zpThe shaft rotates through
Figure BDA0001693729230000032
An angle;
when the small wheel and the large wheel are in mesh transmission, the mesh point M is from the coordinate origin okStarting to move linearly at a constant speed along the meshing line k-k, and defining a parameter equation of M point motion as follows:
t in the formula (1) is a motion parameter variable of the meshing point M, and t is more than or equal to 0 and less than or equal to delta t; c. C1The undetermined coefficient of the meshing point movement is expressed in millimeters (mm); in order to ensure pure rolling engagement of the small and large wheels, the rotation angle of the small and large wheels and the movement of the engagement point must be in a linear relationship, which is as follows:
Figure BDA0001693729230000034
in the formula (2), k is a linear proportionality coefficient of the movement of the meshing point, and the unit is radian (rad); i.e. i12The transmission ratio between the small wheel and the large wheel is set;
when the engagement point M is engaged alongWhen the line k-k moves, the point M forms contact lines C on the surfaces of the small wheel and the large wheel simultaneously1And C2(ii) a According to the coordinate transformation, the coordinate system o-x, y, z, o is obtainedk--xk,yk,zk、op--xp,yp,zp、o1--x1,y1,z1And o2--x2,y2,z2The homogeneous coordinate transformation matrix in between is:
Figure BDA0001693729230000035
wherein:
Figure BDA0001693729230000036
Figure BDA0001693729230000041
obtaining:
Figure BDA0001693729230000042
from the homogeneous coordinate transformation, equation (6) yields:
Figure BDA0001693729230000044
calculating the contact line C on the tooth surface of the small wheel from the formula (8)1The pitch-equaling conical spiral line has the parameter equation:
the following equation (2) is taken into equation (9):
Figure BDA0001693729230000046
in the formula (10), T is an angle parameter variable of the conical spiral line with equal lift distance, wherein the T is kt, and is more than or equal to 0 and less than or equal to delta T;
from the homogeneous coordinate transformation, equation (7) yields:
Figure BDA0001693729230000047
obtaining a contact line C on the tooth surface of the bull gear from the formula (11)2The pitch-equaling conical spiral line has the parameter equation:
Figure BDA0001693729230000051
the following equation (2) is taken into equation (12):
Figure BDA0001693729230000052
and the transmission ratio of the small wheel to the large wheel is as follows:
Figure BDA0001693729230000053
obtained by substituting formula (14) for formula (13):
Figure BDA0001693729230000054
the index taper angles of the small wheel and the large wheel are respectively delta1And delta2Their relationship is:
Figure BDA0001693729230000055
the convex tooth surface of the helical arc tooth of the small wheel is in a shape of a section L consisting of an axial arc tooth profile containing a meshing point M1Generated by right-handed helical motion, of circular-arc-tooth-shaped cross-section L1Generating generatrix of small wheel convex tooth surface, axial pitch parameter and contact of its screw motionLine C1The parameters of the axial screw pitches are consistent, and the right-handed screw motion track of the meshing point M and the contact line C are ensured1Overlapping; in a coordinate system o-x, y and z, a generatrix parameter equation of the convex tooth surface of the small wheel is as follows:
Figure BDA0001693729230000056
deducing and obtaining convex tooth surface of helical circular arc tooth of small wheel in coordinate system o by right-handed helical motion1–x1,y1,z1The parameter equation is:
at the moment, the equation of the central line of the convex tooth surface of the spiral circular arc tooth of the small wheel is as follows:
Figure BDA0001693729230000062
the concave tooth surface of the helical arc groove of the bull wheel is in a shape of L in a section of an axial arc tooth shape containing a meshing point M2Generated by left-handed spiral motion and shaped like a circular-arc tooth section L2Is a generating bus of a big wheel concave tooth surface, and the axial pitch parameter and the contact line C of the spiral motion of the generating bus2The parameters of the axial thread pitches are consistent, and the left-handed spiral motion track of the meshing point M and the contact line C are ensured2Are superimposed on a coordinate system op--xp,yp,zpThe parameter equation of the shape generating generatrix of the concave tooth surface of the middle and large wheel is as follows:
Figure BDA0001693729230000063
deducing and obtaining the concave tooth surface of the helical arc groove of the bull wheel in the coordinate system o by the left-handed helical motion2–x2,y2,z2The parameter equation is:
Figure BDA0001693729230000064
at the moment, the equation of the central line of the concave tooth surface of the spiral circular arc groove of the bull wheel is as follows:
Figure BDA0001693729230000065
the length of the meshing line of the small wheel and the large wheel is as follows:
Figure BDA0001693729230000066
the axial height of the small wheel is as follows:
Δz1=Δzkcosδ1(24)
the axial height of the bull wheel is:
Δz2=Δzkcosδ2(25)
the cone clearance of the big wheel and the small wheel is as follows:
e=r1=r2(26)
in all the above formulae:
t is the motion parameter variable of the meshing point M, and t belongs to [0, delta t ];
t-parameter variables of the equal-lift-distance conical spiral line, wherein T belongs to [0, delta T ], and delta T is k delta T; (27) k-linear proportionality coefficient of meshing point motion, k > 0;
R1-the theoretical indexing cone large end radius for the small wheel;
R1a-the radius of the large end of the cone being a small wheel; r1a=R1-[(ρ2sinγ+e)/cosδ1]; (28)
R2-the radius of the large end of the theoretical indexing cylinder of the bull wheel;
R2athe radius of the large end of the cone, R, of the large wheel2a=R2+(ρ2sinγ/cosδ2); (29)
δ1-is the theoretical reference cone angle of the small wheel;
δ2-is the theoretical indexing cone angle of the bull wheel;
i12-is the transmission ratio of the small wheel to the large wheel;
r1-radius of transition fillet of spiral circular arc tooth on small wheel;
r2-radius of transition fillet of spiral arc groove on bull wheel;
ρ1the circular arc radius of the spiral circular arc tooth of the small wheel;
ρ2-the radius of the circular arc of the helical circular arc groove of the bull wheel;
gamma is the axial meshing angle of the small wheel and the big wheel;
Δzk-length of meshing line of small and large wheels;
Δz1-the axial height of the small wheel;
Δz2-the axial height of the large wheel;
delta T is the angle parameter variable value range of the conical spiral line;
delta t is the range of the motion parameter variable of the meshing point M,
delta T is the angle parameter variable value range of the conical spiral line;
n1the number of the small gear teeth is the number of the spiral circular arc teeth of the small gear;
n2the number of teeth of the big wheel is the number of spiral arc grooves of the big wheel;
c1-meshing point motion undetermined coefficients;
wherein: axes of each coordinate system, e, r1,r2,ρ1,ρ2,R1,R2And c1The units of equal length or distance are millimeters (mm);
Figure BDA0001693729230000082
δ1,δ2,ξ1,ξ2the angular units of T, Delta T, k, gamma, theta and the like are radians (rads);
when the angular speed vector included angle theta and the transmission ratio i of the two crossed axes are determined12Of small wheelsTheoretical indexing cone large end radius R1Small gear tooth number n1Arc radius rho of helical arc tooth of small wheel1Arc radius rho of large wheel spiral arc groove2Coincidence degree epsilon, axial meshing angle gamma and meshing point motion undetermined coefficient c1The linear proportional parameter k of the movement of the meshing point and the clearance e between the small wheel and the large wheel cone are determined, the cone structures of the small wheel and the large wheel, the central line of the spiral arc tooth of the small wheel, the tooth surface structure and the shape are also determined, the central line of the spiral arc groove of the large wheel, the tooth surface structure and the shape are also determined, and the installation positions of the small wheel and the large wheel are also correspondingly determined, so that the convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission is obtained.
The small wheel and the large wheel form a transmission pair, and the contact ratio design calculation formula is as follows:
obtained by substituting formula (27) for formula (30),
Figure BDA0001693729230000084
the design needs to be carried out according to the numerical value epsilon of the contact ratio, the linear proportionality coefficient k and the number n of the small gear teeth1And comprehensively determining the value range delta t of the motion parameter variable t of the meshing point M.
The spiral arc teeth uniformly distributed on the outer surface of the cone of the small wheel are in a shape of a section L in the form of an axial arc tooth1And let it reference the point theta1Moving along the central line of the circular arc teeth of the small wheel to form spiral circular arc teeth; the spiral arc grooves uniformly distributed on the outer surface of the cone of the bull wheel are in a shape of a section L in the form of an axial arc tooth2And make the center theta2A spiral arc groove formed by moving along the central line of the arc groove of the bull wheel.
The small wheel and the input shaft and the output shaft connected with the large wheel have interchangeability, namely the small wheel is connected with the input shaft and the large wheel is connected with the output shaft, or the large wheel is connected with the input shaft and the small wheel is connected with the output shaft, and the small wheel and the large wheel correspond to a speed reduction transmission mode or a speed increase transmission mode of a convex-concave meshing pure rolling spiral bevel gear mechanism for cross shaft transmission respectively; the constant-speed transmission application with the transmission ratio of 1 of the convex-concave meshing pure rolling spiral bevel gear mechanism is realized only when the number of teeth of the small gear and the large gear is equal.
The rotation direction of an input shaft connected with the driver is clockwise or anticlockwise, so that forward and reverse rotation transmission of a small wheel or a large wheel is realized.
The convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission is a gear mechanism which is fundamentally innovated on the basis of the theory of the traditional gear transmission mechanism, and the design method of the convex-concave meshing pure rolling spiral bevel gear mechanism is also different from the design method of the traditional gear mechanism based on the curved surface meshing equation. The convex-concave meshing pure-rolling spiral bevel gear mechanism for the crossed shaft transmission is a node meshing mode based on a pure-rolling meshing line equation, the relative motion speed of all meshing points is zero, and a continuous stable meshing transmission method can be provided for micro, micro-mechanical and conventional mechanical devices of the crossed shaft transmission at any angle in a plane.
Compared with the prior art, the convex-concave meshing pure rolling spiral bevel gear mechanism for the crossed shaft transmission has the advantages that:
1. the convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission has the greatest advantages that a meshing tooth surface without relative sliding is constructed by an active design method of a pure rolling meshing line parameter equation, the relative motion speed of all meshing points is zero, common failure modes such as tooth surface abrasion, gluing and tooth surface plastic deformation in gear transmission can be avoided, and the transmission efficiency is high.
2. The convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission has free contact ratio design, the structural shape of the gear body can be determined through the pre-design of the contact ratio, the uniform distribution of load is realized, and the dynamic characteristic is improved.
3. The convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission has the advantages that the tooth surface structure shape is simple, the small gear is a spiral convex arc tooth surface, the large gear is a spiral concave arc tooth surface, the processing and the manufacturing are easy, parameters such as a meshing angle and the like can be designed and adjusted at will, and the mechanical property of the tooth profile is optimized.
4. The convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission has no undercut, the minimum tooth number is 1, compared with the existing involute bevel gear and other mechanisms, the single-stage large transmission ratio high contact ratio transmission can be realized, the structure is compact, the installation space is greatly saved, and meanwhile, as the tooth number is small, larger tooth thickness can be designed, so that the convex-concave meshing pure rolling spiral bevel gear mechanism has higher strength and rigidity and larger bearing capacity, and is suitable for popularization and application in the fields of micro/micro machinery, conventional mechanical transmission and high-speed heavy-load transmission.
Drawings
FIG. 1 is a schematic structural diagram of a male-female meshing pure rolling helical bevel gear mechanism for a crossed shaft transmission according to the present invention;
FIG. 2 is a schematic diagram of the spatial coordinate system of the male-female meshing pure rolling helical bevel gear mechanism for cross-shaft transmission of the present invention;
FIG. 3 is an axial cross-sectional view of the engaged spiral-arc tooth and spiral-arc groove of FIG. 1;
FIG. 4 is a front view of the small wheel of FIG. 1 and its helical circular arc teeth;
FIG. 5 is a top view of the small wheel of FIG. 1 and its spiral-arc teeth;
FIG. 6 is an axial section L of the helical circular arc teeth of the small wheel of FIG. 11A parameter schematic diagram;
FIG. 7 is a front view of the bull wheel of FIG. 1 and its spiral arcuate groove;
FIG. 8 is a top view of the bull wheel of FIG. 1 and its spiral arcuate groove;
FIG. 9 is an axial section L of the spiral arc groove of the bull wheel of FIG. 12A parameter schematic diagram;
FIG. 10 is a schematic structural view of the present invention when a large wheel is connected to an input shaft to drive a small wheel to increase speed.
In the above figures: 1-small wheel, 2-spiral arc tooth, 3-input shaft, 4-driver, 5-transition fillet, 6-output shaft, 7-spiral arc groove, 8-large wheel, 9-spiral arc tooth central line, 10-spiral arc groove central line, 11-small wheel theory indexing cone, 12-large wheel theory indexing cone, 13-small wheel contact line, 14-large wheel contact line, 15-small wheel mounting hole and 16-large wheel mounting hole.
Detailed Description
The invention is further described with reference to the following drawings and specific examples, but the practice of the invention is not limited thereto.
Example 1: the invention provides a convex-concave meshing pure rolling spiral bevel gear mechanism for transmission of crossed shafts, which is applied to transmission with the transmission ratio of 1 between two crossed shafts in a plane, and the structure of the mechanism is shown in figure 1, and the mechanism comprises a small wheel 1 and a large wheel 8, wherein the small wheel 1 and the large wheel 8 form a pair of transmission pairs, the small wheel 1 is connected with an input shaft 3, the large wheel 8 is connected with an output shaft 6, namely the large wheel 8 is connected with a driven load through the output shaft 6; the axes of the small wheel 1 and the large wheel 8 are intersected, and the angular velocity vector included angle of the small wheel 1 and the large wheel 8 is theta, which is 2 pi/3 radian (rad) in the example. Fig. 2 is a schematic diagram of a space meshing coordinate system of the convex-concave meshing pure rolling spiral bevel gear mechanism for the crossed shaft transmission.
Referring to fig. 1, 2, 3, 4, 5 and 6, the radius of the large end of the theoretical indexing cone of the small wheel is R1Theoretical reference cone angle of the small wheel is delta1The outer surface of the cone of the small wheel 1 is evenly distributed with spiral arc teeth 2, and the radius of the large end of the cone of the small wheel is R1aAxial engagement angle γ. A transition fillet 5 is arranged between the spiral circular arc tooth of the small wheel and the cone of the small wheel, and the radius of the transition fillet is r1Millimeter, the arc radius of the spiral arc groove of the small wheel is rho1And (4) millimeter.
Referring to fig. 1, 2, 3, 7, 8 and 9, the radius of the large end of the theoretical indexing cone of the bull wheel is R2The theoretical reference cone angle of the bull wheel is delta2The outer surface of the cone of the bull wheel 8 is evenly distributed with spiral arc grooves 7, and the radius of the big end of the cone of the bull wheel is R2aAxial engagement angle γ. A transition fillet 5 is arranged between the spiral arc groove of the bull wheel and the bull wheel cone, and the radius of the transition fillet is r2Of helical circular teeth on the large wheelRadius of arc is rho2And (4) millimeter.
The small wheel 1 is connected with an input shaft 3 and is driven by a driver 4 to rotate, so that the spiral arc teeth 2 of the small wheel 1 are continuously meshed with the spiral arc grooves 7 of the large wheel 8, and the motion and power transmission between crossed shafts in a plane is realized, wherein the driver 4 is a motor in the embodiment.
The central lines of the spiral arc teeth of the small wheel and the spiral arc grooves of the large wheel are equal-lift-distance conical spiral lines; the spiral arc teeth 2 are continuously meshed with the spiral arc grooves 7, so that continuous and stable meshing transmission between two crossed shafts in a plane is realized.
The structure of the spiral arc groove and the spiral arc tooth and the shape of the central line curve of the spiral arc groove and the spiral arc tooth are determined by the following method: see FIG. 2, at o- -x, y, z, ok--xk,yk,zkAnd op--xp,yp,zpIn three space coordinate systems, the z axis is coincident with the rotation axis of the small wheel, and z ispThe axis of rotation of the shaft and the bull wheel coinciding, zkThe axis coincides with the line of engagement of the small and large wheels, and the z-axis coincides with the z-axisp、zkThe axes intersect at a point; coordinate system o1--x1,y1,z1Fixedly connected to the small wheel, coordinate system o2--x2,y2,z2Fixedly connected with the big wheel, the small wheel and the big wheel are respectively connected with the coordinate system o-x, y, z and o at the initial positionsp--xp,yp,zpCoincidence, ookA distance R1,opokA distance R2,zkThe acute angle between the axis and the z-axis is delta1,zkAxis and zpThe acute angle included by the shaft is delta2With small wheels at uniform angular velocity omega1Rotating about the z-axis, the bull wheel at a uniform angular velocity ω2Around zpThe axes are rotated, the angular velocity vector included angle of the rotation axes of the small wheel and the large wheel is theta, and after a period of time from the initial position, the coordinate system o1--x1,y1,z1And o2--x2,y2,z2Move respectively, at the meshing point M, the small wheel rotates around the axis z
Figure BDA0001693729230000111
Corner, large wheel winding zpThe shaft rotates through
Figure BDA0001693729230000112
An angle;
when the small wheel and the large wheel are in mesh transmission, the mesh point M is from the coordinate origin okStarting to move linearly at a constant speed along the meshing line k-k, and defining a parameter equation of M point motion as follows:
Figure BDA0001693729230000113
t in the formula (1) is a motion parameter variable of the meshing point M, and t is more than or equal to 0 and less than or equal to delta t; c. C1The undetermined coefficient of the meshing point movement is expressed in millimeters (mm); in order to ensure pure rolling engagement of the small and large wheels, the rotation angle of the small and large wheels and the movement of the engagement point must be in a linear relationship, which is as follows:
Figure BDA0001693729230000114
in the formula (2), k is a linear proportionality coefficient of the movement of the meshing point, and the unit is radian (rad); i.e. i12The transmission ratio between the small wheel and the large wheel is set;
when the meshing point M moves along the meshing line k-k, the point M simultaneously forms contact lines C on the surfaces of the small wheel and the large wheel respectively1And C2(ii) a According to the coordinate transformation, the coordinate system o-x, y, z, o is obtainedk--xk,yk,zk、op--xp,yp,zp、o1--x1,y1,z1And o2--x2,y2,z2The homogeneous coordinate transformation matrix in between is:
Figure BDA0001693729230000115
wherein:
Figure BDA0001693729230000121
obtaining:
Figure BDA0001693729230000123
Figure BDA0001693729230000124
from the homogeneous coordinate transformation, equation (6) yields:
Figure BDA0001693729230000125
calculating the contact line C on the tooth surface of the small wheel from the formula (8)1The pitch-equaling conical spiral line has the parameter equation:
the following equation (2) is taken into equation (9):
Figure BDA0001693729230000127
in the formula (10), T is an angle parameter variable of the conical spiral line with equal lift distance, wherein the T is kt, and is more than or equal to 0 and less than or equal to delta T;
from the homogeneous coordinate transformation, equation (7) yields:
obtaining a contact line C on the tooth surface of the bull gear from the formula (11)2The pitch-equaling conical spiral line has the parameter equation:
Figure BDA0001693729230000132
the following equation (2) is taken into equation (12):
Figure BDA0001693729230000133
and the transmission ratio of the small wheel to the large wheel is as follows:
obtained by substituting formula (14) for formula (13):
Figure BDA0001693729230000135
the index taper angles of the small wheel and the large wheel are respectively delta1And delta2Their relationship is:
Figure BDA0001693729230000136
the convex tooth surface of the helical arc tooth of the small wheel is in a shape of a section L consisting of an axial arc tooth profile containing a meshing point M1Generated by right-handed helical motion, of circular-arc-tooth-shaped cross-section L1Is a generating bus of a small wheel convex tooth surface, and the axial pitch parameter and the contact line C of the spiral motion of the generating bus1The parameters of the axial screw pitches are consistent, and the right-handed screw motion track of the meshing point M and the contact line C are ensured1And (3) coincidence, wherein in a coordinate system o-x, y and z, a parameter equation of a generating generatrix of a convex tooth surface of the small wheel is as follows:
Figure BDA0001693729230000141
deducing and obtaining convex tooth surface of helical circular arc tooth of small wheel in coordinate system o by right-handed helical motion1–x1,y1,z1The parameter equation is:
Figure BDA0001693729230000142
at the moment, the equation of the central line of the convex tooth surface of the spiral circular arc tooth of the small wheel is as follows:
Figure BDA0001693729230000143
the concave tooth surface of the helical arc groove of the bull wheel is in a shape of L in a section of an axial arc tooth shape containing a meshing point M2Generated by left-handed spiral motion and shaped like a circular-arc tooth section L2Is a generating bus of a big wheel concave tooth surface, and the axial pitch parameter and the contact line C of the spiral motion of the generating bus2The parameters of the axial thread pitches are consistent, and the left-handed spiral motion track of the meshing point M and the contact line C are ensured2Overlapping; coordinate system op--xp,yp,zpIn the middle, the parameter equation of the shape generating generatrix of the concave tooth surface of the bull wheel is as follows:
Figure BDA0001693729230000144
deducing and obtaining the concave tooth surface of the helical arc groove of the bull wheel in the coordinate system o by the left-handed helical motion2–x2,y2,z2The parameter equation is:
at the moment, the equation of the central line of the concave tooth surface of the spiral circular arc groove of the bull wheel is as follows:
the length of the meshing line of the small wheel and the large wheel is as follows:
the axial height of the small wheel is as follows:
Δz2=Δzkcosδ2(24)
the axial height of the bull wheel is:
Δz2=Δzkcosδ2(25)
the cone clearance of the big wheel and the small wheel is as follows:
e=r1=r2(26)
in all the above formulae:
t is the motion parameter variable of the meshing point M, and t belongs to [0, delta t ];
t-parameter variables of the equal-lift-distance conical spiral line, wherein T belongs to [0, delta T ], and delta T is k delta T; (27) k-linear proportionality coefficient of meshing point motion, k > 0;
R1-the theoretical indexing cone large end radius for the small wheel;
R1a-the radius of the large end of the cone being a small wheel; r1a=R1-[(ρ2sinγ+e)/cosδ1]; (28)
R2-the radius of the large end of the theoretical indexing cylinder of the bull wheel;
R2athe radius of the large end of the cone, R, of the large wheel2a=R2+(ρ2sinγ/cosδ2); (29)
δ1-is the theoretical reference cone angle of the small wheel;
δ2-is the theoretical indexing cone angle of the bull wheel;
i12-is the transmission ratio of the small wheel to the large wheel;
r1-radius of transition fillet of spiral circular arc tooth on small wheel;
r2-radius of transition fillet of spiral arc groove on bull wheel;
ρ1the circular arc radius of the spiral circular arc tooth of the small wheel;
ρ2-the radius of the circular arc of the helical circular arc groove of the bull wheel;
gamma is the axial meshing angle of the small wheel and the big wheel;
Δzk-length of meshing line of small and large wheels;
Δz1-the axial height of the small wheel;
Δz2-the axial height of the large wheel;
delta T is the angle parameter variable value range of the conical spiral line;
delta t is the range of the motion parameter variable of the meshing point M,
Figure BDA0001693729230000161
delta T is the angle parameter variable value range of the conical spiral line;
n1the number of the small gear teeth is the number of the spiral circular arc teeth of the small gear;
n2the number of teeth of the big wheel is the number of spiral arc grooves of the big wheel;
c1-meshing point motion undetermined coefficients;
wherein: axes of each coordinate system, e, r1,r2,ρ1,ρ2,R1,R2And c1The units of equal length or distance are (mm) millimeters;
Figure BDA0001693729230000162
δ1,δ2,ξ1,ξ2the angular units of T, Delta T, k, gamma, theta and the like are (rad) radians;
the small wheel and the large wheel form a transmission pair, and the design and calculation formula of the contact ratio is as follows:
obtained by substituting formula (27) for formula (30),
Figure BDA0001693729230000164
the design needs to be carried out according to the numerical value epsilon of the contact ratio, the linear proportionality coefficient k and the number n of the small gear teeth1And comprehensively determining the value range delta t of the motion parameter variable t of the meshing point M.
When the angular speed vector included angle theta and the transmission ratio i of the two crossed axes are determined12Radius R of big end of theoretical indexing cone of small wheel1Small gear tooth number n1Circle with helical circular arc teeth of small wheelRadius of arc ρ1Arc radius rho of large wheel spiral arc groove2Coincidence degree epsilon, axial meshing angle gamma and meshing point motion undetermined coefficient c1The linear proportional parameter k of the movement of the meshing point and the clearance e between the small wheel and the large wheel cone are determined, the cone structures of the small wheel and the large wheel, the central line of the spiral arc tooth of the small wheel, the tooth surface structure and the shape are also determined, the central line of the spiral arc groove of the large wheel, the tooth surface structure and the shape are also determined, and the installation positions of the small wheel and the large wheel are also correspondingly determined, so that the convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission is obtained.
When in the above formula: the relevant parameters take the values as follows:
Figure BDA0001693729230000171
ε=2,i12=1,c130 mm (mm), k pi, R125 millimeters (mm), ρ12.5 millimeters (mm), ρ23 mm (mm) and e 1 mm (mm), and the value obtained by the formula (16)
Figure BDA0001693729230000172
Δ T is determined to be 1 in substitution for expression (31), and Δ T is determined to be pi in expression (27).
The tooth surface parameter equation of the helical circular arc tooth of the small wheel in the embodiment is obtained by taking the numerical values into the formula (18):
0≤T≤π,ξ1∈[0,π]
the numerical values are taken into the formula (19) to obtain the equation of the central line of the helical circular arc tooth of the small wheel in the embodiment as follows:
Figure BDA0001693729230000174
the tooth surface parameter equation of the spiral arc groove in the embodiment is obtained by taking the above numerical values into formula (21) as follows:
Figure BDA0001693729230000175
0≤T≤π,ξ2∈[0,π]
the equation for obtaining the central line of the spiral arc groove of the large wheel in the embodiment is obtained by substituting the formula (22):
calculating the length of the meshing line between the small wheel and the large wheel as delta z by substituting formula (23)kThe axial height of the small wheel is obtained by substituting the formula (24) of 30 millimeters (mm)
Figure BDA0001693729230000181
Mm, with the axial height of the bull wheel determined by the formula (25)
Figure BDA0001693729230000182
Millimeters (mm); the radius of the large end of the cone of the small wheel is R by the formula (28)1aThe radius of the large end of the cone of the large wheel is R as obtained by the formula (29) when the radius is 22.691 millimeters (mm)2a26.732 millimeters (mm); the transition fillet radius r of the small wheel and the large wheel is obtained from the formula (26)1r 21 millimeter (mm).
Setting the number of spiral arc teeth as n1When the number of spiral arc grooves is n, the number of spiral arc grooves is obtained from the formula (14) as 42And (4) determining the shapes of the pair of spiral arc bevel gear transmission pairs of the small wheel 1 and the large wheel 8 according to the central line equations of the spiral arc teeth 2 and the spiral arc grooves 7 and the data of the cone structure parameters of the small wheel and the large wheel respectively, so as to obtain the shape of the pure rolling convex-concave meshing bevel gear mechanism and carry out correct assembly.
When the driver 4 drives the input shaft 3 and the small wheel 1 to rotate, because a pair of spiral arc teeth 2 and spiral arc grooves 7 are in a meshed state when the small wheel 1 and the large wheel 8 are installed, and the contact ratio of the spiral arc bevel gear is defined to be epsilon, 2, which is larger than 1 when the small wheel 1 and the large wheel 8 are installed, when the pair of spiral arc teeth 2 and the spiral arc grooves 7 rotate, namely, are disengaged but are not completely disengaged, another pair of adjacent spiral arc teeth 2 and spiral arc grooves 7 are engaged again, so that continuous and stable meshing transmission of the spiral arc bevel gear mechanism in the rotating motion is realized. The rotation direction of an input shaft connected with the driver of the embodiment is clockwise, and the constant-speed transmission of the spiral circular arc bevel gear mechanism is corresponding to the constant-speed transmission of the spiral circular arc bevel gear mechanism, so that the constant-speed transmission of the anticlockwise rotation of the large wheel is realized.
Example 2: the convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission is applied to speed-up transmission between two vertical crossed shafts, and theta is pi/2 radian (rad). As shown in fig. 10, a large wheel 8 is connected with an input shaft 3, and a small wheel 1 is connected with an output shaft 6, namely, the small wheel 1 is connected with a driven load through the output shaft 6; the axes of the small wheel 1 and the large wheel 8 are perpendicular to each other, and the angular speed included angle theta is pi/2 (rad) radian. In this embodiment, eight spiral arc grooves 7 are formed in the large wheel 8, four spiral arc teeth 2 are formed in the small wheel 1, and when the input shaft 3 drives the large wheel 8 to rotate, the design contact ratio epsilon is 4/3. When the big wheel 8 and the small wheel 1 are installed, the spiral arc groove 7 on the big wheel 8 and the spiral arc tooth 2 on the small wheel are in a meshing state, and when the big wheel 8 rotates, the big wheel and the small wheel rotate to keep the meshing contact ratio of the spiral arc tooth and the spiral arc groove larger than 1, so that continuous and stable meshing transmission of a spiral arc bevel gear mechanism is realized. At this time, the transmission ratio of the small wheel to the large wheel is 2, namely, the speed increasing ratio of the large wheel to the small wheel is 2.
The relevant parameters take the values as follows:
Figure BDA0001693729230000183
ε=4/3,i12=2,c130 mm (mm), k pi, R125 millimeters (mm), ρ12.5 millimeters (mm), ρ23 millimeters (mm), e 1 mm. Calculating δ by substituting formula (16)10.4636 radians (rad), δ21.1071 radians (rad). When Δ T is 2/3 obtained by substituting expression (31), Δ T is 2 pi/3 obtained by expression (27).
The tooth surface parameter equation of the helical circular arc tooth of the small wheel in the embodiment is obtained by taking the numerical values into the formula (18):
Figure BDA0001693729230000191
0≤T≤2π/3,ξ1∈[0,π]
the numerical values are taken into the formula (19) to obtain the equation of the central line of the helical circular arc tooth of the small wheel in the embodiment as follows:
Figure BDA0001693729230000192
the tooth surface parameter equation of the helical arc groove of the bull wheel in the embodiment is obtained by taking the numerical values into formula (21) as follows:
0≤T≤2π/3,ξ2∈[0,π]
the equation for obtaining the central line of the spiral arc groove of the large wheel in the embodiment is obtained by substituting the formula (22):
Figure BDA0001693729230000194
calculating the length of the meshing line between the small wheel and the large wheel as delta z by substituting formula (23)kThe axial height of the small wheel is calculated as Δ z by substituting 20 millimeters (mm) into the formula (24)1The axial height of the large wheel is determined by the belt-in-type (25) as Δ z (17.8886 mm)28.9443 millimeters (mm); the radius of the large end of the cone of the small wheel is R by the formula (28)1aThe radius of the large end of the cone of the large wheel is obtained by the formula (29) of 22.7639 millimeters (mm)2a53.3535 millimeters (mm); the transition fillet radius r of the small wheel and the large wheel is obtained from the formula (26)1r 21 millimeter (mm).
Because the number of the spiral arc grooves is 8, the number of the spiral arc teeth is 4, and then the shapes of the pair of spiral arc bevel gear transmission pairs of the small wheel 1 and the large wheel 8 can be determined according to the central line equation of the spiral arc teeth 2 and the spiral arc grooves 7 and the data of the cone structure parameters of the small wheel and the large wheel respectively, so that the shape of the pure rolling convex-concave meshing bevel gear mechanism is obtained and the assembly is carried out correctly.
The rotation direction of an input shaft connected with the driver of the embodiment is clockwise, and the driving device corresponds to a speed-increasing driving mode of the spiral arc bevel gear mechanism and is used for realizing the transmission of anticlockwise rotation of the small wheel.
The invention is used for the protruding-concave meshing pure rolling spiral bevel gear mechanism of the crossed shaft transmission, because there is no undercut, there is no restriction of the minimum number of teeth, can carry on the design of the large tooth thickness, have higher bending strength, contact strength and greater rigidity, the invention has also provided the design method of the bevel gear mechanism of the continuous stable meshing transmission between two crossed shafts of arbitrary angle in the level, can design the protruding-concave meshing pure rolling bevel gear mechanism parameter according to the numerical value of the degree of contact ratio, it is high to have tooth profile intensity, tooth surface have relative slip, have no undercut, the single-stage drive ratio is large, high transmission efficiency, greatly reduce the tooth surface and glue, wear and plastic deformation, etc. and invalid probability, can simplify the structure of the conventional gear mechanism and micromechanical drive unit, suitable for the application in the fields of the small, miniature machinery and conventional machinery.

Claims (8)

1. The convex-concave meshing pure rolling spiral bevel gear driven by the crossed shaft comprises a pair of transmission pairs consisting of a small wheel and a large wheel, wherein the small wheel is fixedly connected with a driver through an input shaft, the large wheel is connected with an output shaft, and the axis of the small wheel is crossed with the axis of the large wheel, and the pure rolling spiral bevel gear is characterized in that: the outer surface of the cone of the small wheel is provided with n1The spiral circular arc teeth are evenly distributed, the central lines of all the spiral circular arc teeth are equal-lift-distance conical spiral lines, transition fillets are arranged between the spiral circular arc teeth and the outer surface of the cone of the small wheel, and n is arranged on the outer surface of the cone of the large wheel2The spiral arc groove of strip evenly distributed, the central line of all spiral arc grooves is the circular cone helix of equal lift-off distance, spiral arc groove with there is transition fillet between the bull wheel cone surface, the spiral arc tooth of steamboat with the pure rolling engagement transmission that the spiral arc groove meshing mode of bull wheel was the point contact, through spiral arc tooth on the bull wheel with continuous meshing effect between the spiral arc groove on the steamboat drives the bull wheel rotates, spiral arc tooth structure and institute's straight line circleThe spiral arc groove structure is determined by the following method:
s1, constructing a coordinate system, and defining the position relation between the small wheel and the large wheel and each coordinate system:
construction of o- -x, y, z, ok--xk,yk,zkAnd op--xp,yp,zpThree spatial coordinate systems, with the z-axis coinciding with the axis of rotation of the small wheel, zpThe axis of rotation of the shaft and the bull wheel coinciding, zkThe axis coincides with the line of engagement of the small wheel and the large wheel, and the z-axis coincides with zp、zkThe axes intersect at a point to construct a coordinate system o fixedly connected with the small wheel1--x1,y1,z1A coordinate system o fixedly connected to said large wheel2--x2,y2,z2The small wheel and the large wheel respectively have initial positions in a coordinate system o-x, y, z and op--xp,yp,zpCoincidence, ookA distance R1,opokA distance R2,zkThe acute angle between the axis and the z-axis is delta1,zkAxis and zpThe acute angle included by the shaft is delta2The small wheel has a uniform angular speed omega1Rotating around the z-axis, the large wheel being at a uniform angular velocity ω2Around zpThe shaft rotates, the angular velocity vector included angle of the rotation axes of the small wheel and the large wheel is theta, and after a period of time from the initial position, a coordinate system o1--x1,y1,z1And o2--x2,y2,z2Move respectively, at the point of engagement M, the small wheel rotates around the z-axis
Figure FDA0002241109730000013
Angle, said large wheel winding zpThe shaft rotates through
Figure FDA0002241109730000014
An angle;
s2, determining a motion parameter equation of the meshing point M:
when the small wheel and the large wheel are in meshing transmission, the meshing point M is drivenOrigin of the mark okThe constant-speed linear motion is carried out along the meshing line k-k, and the parameter equation of M point motion is defined as follows:
Figure FDA0002241109730000011
wherein t is a motion parameter variable of the meshing point M, and t is more than or equal to 0 and less than or equal to delta t; c. C1Determining a undetermined coefficient for the movement of the meshing point, wherein the small wheel is in pure rolling meshing with the large wheel, and the rotation angles of the small wheel and the large wheel and the movement of the meshing point are necessarily in a linear relation, wherein the relation is as follows:
Figure FDA0002241109730000012
where k is the linear proportionality coefficient of the movement of the engagement point, k>0,i12The transmission ratio between the small wheel and the large wheel is set;
s3, determining the value range delta t of the motion parameter variable t of the meshing point M:
design calculation formula for degree of contact of transmission pair formed by small wheel and large wheelTo obtain
Figure FDA0002241109730000022
S4 determining contact line C on small wheel tooth surface1And the contact line C on the tooth surface of the bull wheel2The parameter equation of (2):
when the meshing point M moves along the meshing line k-k, the point M simultaneously forms contact lines C on the surfaces of the small wheel and the large wheel respectively1And C2According to the coordinate transformation, the coordinate system o-x, y, z, o can be obtainedk--xk,yk,zk、op--xp,yp,zp、o1--x1,y1,z1And o2--x2,y2,z2The homogeneous coordinate transformation matrix in between is:
Figure FDA0002241109730000023
respectively solving the contact line C on the tooth surface of the small wheel by homogeneous coordinate transformation1And the contact line C on the tooth surface of the bull wheel2Equation of parameters, contact line C1Is a conical spiral line with equal lift distance and the parameter equation is as follows:
contact wire C2Is a conical spiral line with equal lift distance and the parameter equation is as follows:
Figure FDA0002241109730000025
in the formula, T is an angle parameter variable of the conical spiral line with equal lift distance, wherein T is kt, and T is more than or equal to 0 and less than or equal to delta T;
s5, determining a generating generatrix parameter equation and a convex tooth surface parameter equation of the small wheel convex tooth surface:
the convex tooth surface of the helical arc tooth of the small wheel is in a shape of a section L consisting of an axial arc tooth profile containing a meshing point M1Generated by right-handed helical motion, of circular-arc-tooth-shaped cross-section L1Is a generating bus of a small wheel tooth surface, and the axial pitch parameter and the contact line C of the spiral motion of the generating bus1The parameters of the axial screw pitches are consistent, and the right-handed screw motion track of the meshing point M and the contact line C are ensured1And (3) coincidence, wherein the parameter equation of the shape generating generatrix of the convex tooth surface of the small wheel in a coordinate system o-x, y and z is as follows:
Figure FDA0002241109730000026
deducing and obtaining the convex tooth surface of the helical circular arc tooth of the small wheel in a coordinate system o by right-handed helical motion1--x1,y1,z1The parameter equation is:
s6, determining a generating generatrix parameter equation of the concave tooth surface of the bull wheel and a parameter equation of the concave tooth surface:
the concave tooth surface of the helical arc groove of the bull wheel is in a shape of L in a section of an axial arc tooth shape containing a meshing point M2Generated by left-handed spiral motion and shaped like a circular-arc tooth section L2Is a generating bus of the tooth surface of a helical arc groove of a bull wheel, and the axial pitch parameter and the contact line C of the helical motion of the generating bus2The parameters of the axial thread pitches are consistent, and the left-handed spiral motion track of the meshing point M and the contact line C are ensured2Are superimposed on a coordinate system op--xp,yp,zpThe parameter equation of the generating bus of the spiral arc groove concave tooth surface of the medium and large wheel is as follows:
Figure FDA0002241109730000032
deducing and obtaining the concave tooth surface of the helical arc groove of the bull wheel in a coordinate system o by left-handed helical motion2--x2,y2,z2The parameter equation is:
Figure FDA0002241109730000033
in all the above formulae:
epsilon-is the contact ratio of the small wheel and the large wheel;
R1-the theoretical indexing cone large end radius for the small wheel;
R2-the radius of the large end of the theoretical indexing cylinder of the bull wheel;
δ1-is the theoretical reference cone angle of the small wheel;
δ2-is the theoretical indexing cone angle of the bull wheel;
ρ1the circular arc radius of the spiral circular arc tooth of the small wheel;
ρ2-the radius of the circular arc of the helical circular arc groove of the bull wheel;
gamma is the axial meshing angle of the small wheel and the big wheel;
i12-is the transmission ratio of the small wheel to the large wheel;
delta T is the angle parameter variable value range of the conical spiral line;
c1-the meshing point movement undetermined coefficient.
2. The cross-shaft driven male-female meshing pure rolling spiral bevel gear according to claim 1,
the center line of the convex tooth surface of the helical circular-arc tooth of the small wheel is positioned in a coordinate system o1--x1,y1,z1The parameter equation in (1) is:
the central line of the concave tooth surface of the helical arc groove of the bull wheel is in a coordinate system o2--x2,y2,z2The parameter equation in (1) is:
3. the cross-shaft driven male-female meshing pure rolling spiral bevel gear according to claim 1, wherein the length of the meshing line of the small wheel and the large wheel is:
Figure FDA0002241109730000043
4. the cross-shaft driven male-female meshing pure rolling spiral bevel gear according to claim 3,
the axial height of the small wheel is as follows: Δ z1=Δzkcosδ1
The axial height of the bull wheel is as follows: Δ z2=Δzkcosδ2
5. The cross-shaft driven male-female meshing pure rolling spiral bevel gear according to claim 1, wherein: the cone clearance of the large wheel and the small wheel is as follows: e-r1=r2,r1Representing the radius of the transition fillet, r, of the helical circular-arc tooth on the small wheel2And the transition fillet radius of the spiral arc groove on the bull wheel is shown.
6. The cross-shaft driven male-female meshing pure rolling spiral bevel gear according to claim 1, wherein: the input shaft and the output shaft which are connected with the small wheel and the large wheel have interchangeability.
7. The cross-shaft driven male-female meshing pure rolling spiral bevel gear according to claim 1, wherein: the number of teeth n of the small gear1And the number n of teeth of said large gear2Are equal.
8. The cross-shaft driven male-female meshing pure rolling spiral bevel gear according to claim 1, wherein: the rotation direction of the input shaft is clockwise or anticlockwise.
CN201810603774.1A 2018-06-12 2018-06-12 Convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission Expired - Fee Related CN108533685B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810603774.1A CN108533685B (en) 2018-06-12 2018-06-12 Convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810603774.1A CN108533685B (en) 2018-06-12 2018-06-12 Convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission

Publications (2)

Publication Number Publication Date
CN108533685A CN108533685A (en) 2018-09-14
CN108533685B true CN108533685B (en) 2020-01-17

Family

ID=63470765

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810603774.1A Expired - Fee Related CN108533685B (en) 2018-06-12 2018-06-12 Convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission

Country Status (1)

Country Link
CN (1) CN108533685B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110414078B (en) * 2019-07-08 2023-06-02 三峡大学 Construction method of meshing line gear mechanism in parallel shaft convex-concave circular arc section

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101733483A (en) * 2009-12-10 2010-06-16 吉林大学 Spiral bevel gear cutting machine tool and gear cutting method
CN104598665A (en) * 2014-11-25 2015-05-06 武汉理工大学 Design method for shrinkage tooth curved-tooth noncircular bevel gear
CN105114532A (en) * 2015-09-08 2015-12-02 华南理工大学 Convex-concave arc gear mechanism used for transmission of parallel shaft
CN107345567A (en) * 2017-08-31 2017-11-14 华南理工大学 A kind of coplanar axis gear mechanism that active line tooth is constructed with conical spiral

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103075493B (en) * 2012-12-29 2015-07-15 重庆大学 Bevel gear based on conjugate curves and meshing pair thereof
CN104565223B (en) * 2015-02-02 2017-02-22 中国地质大学(武汉) Helical arc gear mechanism meshing transmission in parallel shafts
CN105485254B (en) * 2016-01-19 2018-07-31 中国地质大学(武汉) A kind of spiral arc bevel gear mechanism that nothing is slided relatively
CN106763592B (en) * 2017-01-10 2018-11-02 中国地质大学(武汉) A kind of concave-convex engaging circle-arc tooth wheel rackwork that nothing is slided relatively
CN106523632B (en) * 2017-01-10 2018-11-02 中国地质大学(武汉) A kind of male-female engaging circle-arc tooth wheel rackwork that nothing is slided relatively

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101733483A (en) * 2009-12-10 2010-06-16 吉林大学 Spiral bevel gear cutting machine tool and gear cutting method
CN104598665A (en) * 2014-11-25 2015-05-06 武汉理工大学 Design method for shrinkage tooth curved-tooth noncircular bevel gear
CN105114532A (en) * 2015-09-08 2015-12-02 华南理工大学 Convex-concave arc gear mechanism used for transmission of parallel shaft
CN107345567A (en) * 2017-08-31 2017-11-14 华南理工大学 A kind of coplanar axis gear mechanism that active line tooth is constructed with conical spiral

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
产形轮纵向齿廓为摆线的圆弧齿锥齿轮啮合原理;刘鹄然;《包头钢铁学院学报》;19920730;第11卷(第1期);31-36 *
摆线齿锥齿轮切齿加工仿真系统的研究;汤剑等;《机电工程》;20110930;第28卷(第9期);1036-1059 *

Also Published As

Publication number Publication date
CN108533685A (en) 2018-09-14

Similar Documents

Publication Publication Date Title
CN105626816B (en) One kind is single-row to subtract speed change integration Cylinder Sine oscillating tooth mechanism
CN108533683B (en) Convex-convex meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission
WO2020238075A1 (en) Double-arc gapped meshing small-tooth-difference planetary transmission device
CN108533681B (en) flat-convex meshing pure rolling gear mechanism with internal meshing transmission of parallel shafts
CN108533685B (en) Convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission
CN110008610A (en) Cycloid tooth profile subsection optimization design method
CN110081148B (en) Convex-convex contact contra-structural gear based on conjugate curve
CN108533686B (en) Concave-convex mesh pure rolling bevel gear mechanism for crossed shaft transmission
CN108691954B (en) flat-convex meshing pure rolling bevel gear mechanism for crossed shaft transmission
CN104819267A (en) Harmonic gear device adopting non-interference and wide range meshing tooth profile
CN108533684B (en) Convex-flat meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission
CN111173896B (en) Single-stage undercut cycloid oscillating tooth transmission unit
CN108533680B (en) flat-convex meshing pure rolling gear mechanism with parallel shaft external meshing transmission
CN111237397A (en) Two-tooth differential close-packed combined tooth surface cycloid oscillating tooth transmission unit
CN108533679B (en) Parallel shaft external engagement transmission convex-Ping Niege pure rolling gear mechanism
CN112065950A (en) High-contact-ratio internal gear and RV speed reducer taking same as transmission core
CN201496509U (en) Male and female full rolling gear
CN115013482A (en) Inner-gearing pure rolling gear mechanism with combined tooth profile
CN105626800B (en) Ball reducer
CN113944728B (en) Unequal-pressure-angle end face double-arc gear mechanism driven by parallel shafts
CN111601984B (en) Double-inner-gear-ring variable linear speed planetary-row balanced speed reducer
CN210153157U (en) Double-arc planetary transmission device with small tooth difference and meshed with gaps
CN108533682B (en) Convex-flat engagement pure rolling gear mechanism of parallel axes Inside gear drive
CN111765213A (en) Industrial robot inner gearing RV speed reducer
CN116498728A (en) Arc tooth trace gear mechanism with end face arc and parabolic combined tooth profile

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant
CF01 Termination of patent right due to non-payment of annual fee
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20200117