CN111396507B - Design method of worm and helical gear transmission pair - Google Patents
Design method of worm and helical gear transmission pair Download PDFInfo
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- CN111396507B CN111396507B CN202010330898.4A CN202010330898A CN111396507B CN 111396507 B CN111396507 B CN 111396507B CN 202010330898 A CN202010330898 A CN 202010330898A CN 111396507 B CN111396507 B CN 111396507B
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H1/00—Toothed gearings for conveying rotary motion
- F16H1/02—Toothed gearings for conveying rotary motion without gears having orbital motion
- F16H1/04—Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members
- F16H1/12—Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members with non-parallel axes
- F16H1/16—Toothed gearings for conveying rotary motion without gears having orbital motion involving only two intermeshing members with non-parallel axes comprising worm and worm-wheel
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/06—Use of materials; Use of treatments of toothed members or worms to affect their intrinsic material properties
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/08—Profiling
- F16H55/0806—Involute profile
- F16H55/0813—Intersecting-shaft arrangement of the toothed members
Abstract
The invention discloses a design method of a worm and helical gear transmission pair, which comprises the steps of enabling the meshing of the worm and the helical gear on a middle plane to be equal to the meshing between two straight cylindrical gears, determining the modulus and the tooth number of the straight cylindrical gears according to the meshing principle, and drawing a meshing plane diagram of the straight cylindrical gears; and drawing the worm according to the lead angle, the axial circumferential pitch and the diameter of the worm, scanning the section tooth profile of the helical gear to obtain a single tooth profile of the helical gear, and arraying to obtain the helical gear. The meshing of the worm and the helical gear on the middle plane is equal to the meshing of the straight cylindrical gear and the helical gear to design a transmission pair of the worm and the helical gear, so that design parameters are not limited to standard parameters any more, any nonstandard modulus and worm characteristic coefficient can be flexibly selected according to the structural space and transmission requirements of a product to design different shapes and sizes, and the freedom degree is wide. The helical gear is used for replacing a worm gear, so that the manufacturing is easier.
Description
Technical Field
The invention relates to the technical field of gear design, in particular to a design method of a worm and helical gear transmission pair.
Background
The materials of gears (the general names of common gears, worm wheels, worms and the like) are generally made of metal materials and non-metal materials, the common design is designed by referring to standard parameters, the design limitation is more, and in the field of personal care electric appliances, because the internal space of products is limited, the structure is complex, and the standard gear transmission auxiliary parts cannot meet the structural requirements easily.
Plastic gears have many advantages over metal gears in terms of cost, design, processing and performance, and the inherent design freedom of plastic molding ensures more efficient manufacturing. The plastic gear runs quieter, the manufactured gear has better flexibility, and the impact load can be well absorbed. And the requirement of mute operation is met. Plastic gears generally do not require secondary machining, so a reduction of the order of 60% -100% is warranted in cost relative to die cast and machined metal gears. Therefore, plastic gears are often used to replace metal gears in the personal care appliance field with high precision, low noise, more complex geometry and are in wide use. However, for the gear with a special structure and shape, such as a worm gear, a mold mechanism for manufacturing the worm gear is complex, and the gear is moved out through a plurality of sliding mechanisms after being molded, so that the requirements on the mold processing and injection molding precision are extremely high, and due to the limitation of the mold mechanism, a mold clamping line is inevitably arranged at the gear tooth part, so that the precision is influenced, and the requirements on stable transmission and low noise can not be well realized.
Disclosure of Invention
The invention provides a design method of a worm and helical gear transmission pair, aiming at replacing the meshing of a worm wheel and a worm by the meshing of a worm and a helical gear and replacing the worm wheel by the helical gear, so that the worm and helical gear transmission pair is easier to manufacture, higher in precision, lower in cost and more convenient to install.
The invention provides a design method of a worm and helical gear transmission pair, which comprises the following steps:
the meshing of the worm and the helical gear on the middle plane is equal to the meshing between two straight cylindrical gears, and the modulus and the tooth number of the straight cylindrical gears are determined according to the meshing principle;
drawing an involute of a base circle of the cylindrical spur gear according to an involute equation, and drawing a meshing plan of the cylindrical spur gear so as to draw the section tooth profiles of the worm and the helical gear;
the requirement of the center distance is met through positive and negative displacement adjustment of the two straight cylindrical gears;
calculating the lead angle and the axial circumferential pitch of the worm by a calculation formula of a preset lead angle and a calculation formula of a preset axial circumferential pitch;
drawing a worm according to the lead angle, the axial circumferential pitch and the diameter of the worm, drawing a spiral line of the helical gear according to the projection of the spiral line of the worm on the addendum circle of the helical gear, acquiring a single tooth profile of the helical gear after scanning the cross-sectional tooth profile of the helical gear, and obtaining all the tooth profiles of the helical gear in an array mode to draw the helical gear.
Further, the engagement principle needs to satisfy the following conditions:
m＝m1＝m2，mZ2＝d2，V＝U，mZ1 cosθ＝d1，
wherein Z is1Number of teeth of said spur gear being equal to said worm, Z2The number of teeth of the cylindrical straight gear is equal to that of the helical gear, m is the modulus of the cylindrical straight gear, m1Is the normal modulus of the worm, d1M is the diameter of the worm2Is the normal modulus of the bevel gear, d2The diameter of the reference circle of the bevel gear is theta, the pressure angle of the involute is theta, D is the center distance between the bevel gear and the worm, V is the lead angle of the worm, U is the helical angle of the bevel gear, and Z is Z1、Z2Taking an integer, taking m as an arbitrary number, and taking K as a constant;
further, the involute equation is: x rb cos (θ) + rb rad (θ) sin (θ), y rb sin (θ) -rb rad (θ) cos (θ);
wherein rb is the base circle radius;
further, the calculation formula of the lead angle is: sinV ═ Z × m/d1；
Wherein Z is the number of the worm heads;
therefore, the calculation formula of the axial section is as follows: px pi m/cosV.
Furthermore, after the meshing plane diagram of the spur gear is drawn, the step of adjusting the center distance or gear displacement within a preset range to modify the tooth shape meshed in the meshing plane diagram of the spur gear is further included.
Specifically, according to the injection molding principle, the plastic gear and the gear fixing frame have different sizes due to different molding conditions and environmental temperatures, so that proper modification is necessary for designing a gear transmission pair with high precision and low noise transmission requirements so as to ensure proper side clearance and top clearance.
Further, the helical gear further comprises a cam integrally formed with the helical gear.
Specifically, the fixed-axis rotation driven by the bevel gear can be converted into off-axis rotation through the cam, and the flexibility of the structure is improved.
Furthermore, the worm and the helical gear are made of engineering plastics.
Specifically, the worm and helical gear is made of engineering plastic materials, and due to the fact that the parts made of the plastic materials and the parts made of the metal materials are different in machining process, design parameters are not limited to standard parameters, any non-standard modulus and worm characteristic coefficient can be flexibly selected according to the structural space and transmission requirements of a product to design different shapes and sizes, and the design freedom degree is wide.
According to the embodiment of the invention, the meshing of the worm and the helical gear is adopted to replace the meshing of the worm and the worm, and the meshing of the worm and the helical gear on the middle plane is equal to the meshing of the straight cylindrical gear and the helical gear to design the transmission pair of the worm and the helical gear, so that the design parameters are not limited to standard parameters any more, any non-standard modulus and worm characteristic coefficient can be flexibly selected according to the structural space and the transmission requirement of a product to design different shapes and sizes, and the design freedom degree is wide. The helical gear is used for replacing a worm gear, so that the manufacturing is easier, the precision is higher, the cost is lower, and the installation is more convenient.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a schematic flow chart of a design method of a worm and bevel gear transmission pair according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a worm and helical gear transmission pair provided in an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of a worm and helical gear transmission pair according to an embodiment of the present invention;
FIG. 4 is a schematic structural diagram of a bevel gear of a worm and bevel gear transmission pair according to an embodiment of the present invention;
fig. 5 is a schematic diagram of an equivalent structure of the middle plane meshing of a worm and helical gear transmission pair provided by the embodiment of the invention.
Description of reference numerals:
1 helical gear and 2 worm.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It will be understood that the terms "comprises" and/or "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the specification of the present invention and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be further understood that the term "and/or" as used in this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.
Referring to fig. 1, which is a schematic flow chart of a design method of a worm and helical gear transmission pair according to an embodiment of the present invention, the design method of the worm and helical gear transmission pair includes the following steps S101 to S105:
step S101: meshing of a worm and a helical gear on a middle plane is equal to that of a straight cylindrical gear and a helical gear, and the modulus and the tooth number of the straight cylindrical gear are determined according to a meshing principle;
step S102: and drawing an involute of a base circle of the cylindrical spur gear according to an involute equation, and drawing a meshing plan of the cylindrical spur gear so as to draw the section tooth profiles of the worm and the helical gear.
The involute equation is: x rb cos (θ) + rb rad (θ) sin (θ), y rb sin (θ) -rb rad (θ) cos (θ);
wherein rb is the base radius.
Step S103: the requirement of center distance is met through positive and negative displacement adjustment of the two straight cylindrical gears, and the center distance of the two straight cylindrical gear transmission pairs is equal to the center distance between the worm and the helical gear.
Step S104: calculating the lead angle and the axial circumferential pitch of the worm by a calculation formula of a preset lead angle and a calculation formula of a preset axial circumferential pitch, wherein the calculation formula of the lead angle is as follows: sinV ═ Z × m/d1V is the number of the heads of the worm, and the calculation formula of the axial circumferential section is as follows: px pi m/cosV.
Step S105: drawing a worm according to the lead angle, the axial circumferential pitch and the diameter of the worm, drawing a spiral line of the helical gear according to the projection of the spiral line of the worm on the addendum circle of the helical gear, acquiring a single tooth profile of the helical gear after scanning the cross-sectional tooth profile of the helical gear, and obtaining all the tooth profiles of the helical gear in an array mode to draw the helical gear.
The meshing of the worm and the helical gear is adopted to replace the meshing of the worm and the worm, and the meshing of the worm and the helical gear on the middle plane is equal to the meshing of the straight spur gear and the helical gear to design a transmission pair of the worm and the helical gear, so that design parameters are not limited to standard parameters any more, any non-standard modulus and worm characteristic coefficient can be flexibly selected according to the structural space and the transmission requirement of a product to design different shapes and sizes, and the design freedom degree is wide. The helical gear is used for replacing a worm gear, so that the manufacturing is easier, the precision is higher, the cost is lower, and the installation is more convenient.
In one embodiment, the engagement principle needs to satisfy the following conditions:
m＝m1＝m2，mZ2＝d2，V＝U，mZ1 cosθ＝d1，
wherein Z is1The number of teeth of the spur gear with the same worm, Z2The number of teeth of the cylindrical straight gear after the helical gears are identical to the number of teeth Z2The number of teeth is the same as that of the helical gear, m is the modulus of the straight cylindrical gear, and m is1Is the normal modulus of the worm, d1M is the diameter of the worm2Is the normal modulus of the bevel gear, d2The diameter of the reference circle of the bevel gear is theta, the pressure angle of the involute is theta, D is the center distance between the bevel gear and the worm, V is the lead angle of the worm, U is the helical angle of the bevel gear, and Z is Z1、Z2Taking an integer, taking m as an arbitrary number, and taking K as a constant.
In an embodiment, after the drawing of the meshing plan view of the spur gear, the step of modifying the meshing tooth shapes in the meshing plan view of the spur gear by adjusting the center distance or the gear shift within a predetermined range is further included.
Specifically, according to the injection molding principle, the plastic gear and the gear fixing frame have different sizes due to different molding conditions and environmental temperatures, so that proper modification is necessary for designing a gear transmission pair with high precision and low noise transmission requirements so as to ensure proper side clearance and top clearance.
In one embodiment, the helical gear further comprises a cam integrally formed with the helical gear.
Specifically, the fixed-axis rotation driven by the bevel gear can be converted into off-axis rotation through the cam, and the flexibility of the structure is improved.
In one embodiment, the worm and the helical gear are made of engineering plastics.
Specifically, the worm and helical gear is made of engineering plastic materials, and due to the fact that the parts made of the plastic materials and the parts made of the metal materials are different in machining process, design parameters are not limited to standard parameters, any non-standard modulus and worm characteristic coefficient can be flexibly selected according to the structural space and transmission requirements of a product to design different shapes and sizes, and the design freedom degree is wide.
Referring to fig. 2-5, a single-sided engagement design is illustrated below (the same asymmetric-sided engagement design):
in this design case, the following design parameters are clear: diameter d of worm1Center distance D between helical gears and worm, number of worm heads Z, number of helical gear teeth Z2An included angle Σ between the worm and the helical gear shaft is 90 °, and the pressure angle θ is 20 °. And the normal surface modulus of the worm and the helical gear is m respectively1、m2Worm lead angle V, wheel helix angle U, helical gear pitch diameter d2And the design is unknown, and needs to be balanced in various aspects such as a gear transmission principle, mechanical strength, a forming process and the like.
According to the transmission principle, the correct transmission at least meets the following conditions: m is1＝m2，V＝U。
The meshing of the worm and the helical gear on the middle plane is equal to the meshing of two common straight cylindrical gears, and the design utilizing the characteristic sets the modulus of the two straight cylindrical gears to be m and the tooth number to be Z1And Z2According to the principle of engagement, m ═ m1＝m2,m*Z1*cosθ＝d1,D＝(d1/cosθ+d2)/2,mZ2＝d2,Z1、Z2It must be an integer and m can be any number.
Determining m, Z1And Z2Value of wherein Z2An integral value is automatically selected according to design requirements, the helical gear in the embodiment adopts negative displacement, and the positive and negative positions of the straight spur teeth of the cylinder are set so as to meet the requirement of the center distance.
And drawing the involute of the set spur gear and bevel gear base circle by using an involute equation x (rb) cos (theta) + rb rad (theta) sin (theta), and y (rb) sin (theta) -rb rad (theta) cos (theta).
The gear mesh plane diagram of the middle plane is drawn by a geometric drawing method, and the optimal design can be achieved by properly adjusting the center distance or modifying the gear profile.
According to the injection molding principle, the sizes of the plastic gear and the gear fixing frame are different due to different molding conditions and environmental temperatures, so that proper modification is necessary in the design of a gear transmission pair with high precision and low noise transmission requirements so as to ensure proper side clearance and top clearance.
By the formula sinV ═ Z m/d1Calculating Px pi m/cosV to obtain the lead angle V and axial circumferential pitch of worm
Drawing a worm according to the lead angle, the axial circumferential pitch and the diameter of the worm, drawing a spiral line of the helical gear according to the projection of the spiral line of the worm on the addendum circle of the helical gear, acquiring a single tooth profile of the helical gear after scanning the cross-sectional tooth profile of the helical gear, and obtaining all the tooth profiles of the helical gear in an array mode to draw the helical gear.
The diameter, the tooth profile shape, the center distance, the tooth height coefficient and the top clearance coefficient of the worm designed by the embodiment of the invention are not limited by standards, and the worm can be flexibly designed according to the requirements of transmission speed ratio, structural space and processing technology.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications and substitutions can be easily made by those skilled in the art within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (7)
1. A design method of a worm and helical gear transmission pair is characterized by comprising the following steps:
step S101: the meshing of the worm and the helical gear on the middle plane is equal to the meshing between two straight cylindrical gears, and the modulus and the tooth number of the straight cylindrical gears are determined according to the meshing principle;
step S102: drawing an involute of a base circle of the cylindrical spur gear according to an involute equation, and drawing a meshing plan of the cylindrical spur gear so as to draw the section tooth profiles of the worm and the helical gear;
step S103: the requirement of the center distance is met through positive and negative displacement adjustment of the two straight cylindrical gears;
step S104: calculating the lead angle and the axial circumferential pitch of the worm by a calculation formula of a preset lead angle and a calculation formula of a preset axial circumferential pitch;
step S105: drawing a worm according to the lead angle, the axial circumferential pitch and the diameter of the worm, drawing a spiral line of the helical gear according to the projection of the spiral line of the worm on the addendum circle of the helical gear, acquiring a single tooth profile of the helical gear after scanning the cross-sectional tooth profile of the helical gear, and obtaining all the tooth profiles of the helical gear in an array mode to draw the helical gear.
2. The design method of the worm and helical gear transmission pair according to claim 1, wherein the meshing principle is satisfied by the following conditions:
m＝m1＝m2，mZ2＝d2，V＝U，mZ1cosθ＝d1，
wherein Z is1Number of teeth of said spur gear being equal to said worm, Z2The number of teeth of the cylindrical straight gear is equal to that of the helical gear, m is the modulus of the cylindrical straight gear, m1Is the normal modulus of the worm, d1M is the diameter of the worm2Is the normal modulus of the bevel gear, d2The diameter of the reference circle of the bevel gear is theta, the pressure angle of the involute is theta, D is the center distance between the bevel gear and the worm, V is the lead angle of the worm, U is the helical angle of the bevel gear, and Z is Z1、Z2Taking an integer, taking m as an arbitrary number, and taking K as a constant.
3. The design method of the worm and helical gear transmission pair according to claim 2, wherein the involute equation is as follows: x rb cos (θ) + rb rad (θ) sin (θ), y rb sin (θ) -rb rad (θ) cos (θ);
wherein rb is the base radius.
4. The design method of the worm and helical gear transmission pair according to claim 3,
the calculation formula of the lead angle is as follows: sinV ═ Z × m/d1；
Wherein Z is the number of the worm heads;
therefore, the calculation formula of the axial section is as follows: px pi m/cosV.
5. The design method of the worm and helical gear transmission pair according to claim 1, wherein the drawing of the meshing plan view of the spur gear further comprises adjusting a center distance or a gear shift within a predetermined range to modify the shape of the tooth profile meshed in the meshing plan view of the spur gear.
6. The method of claim 1, wherein the bevel gear further comprises a cam integrally formed with the bevel gear.
7. The design method of the worm and helical gear transmission pair according to claim 1, wherein the worm and the helical gear are made of engineering plastics.
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| CN112052535B (en) * | 2020-07-24 | 2023-03-24 | 重庆大学 | Backlash-adjustable worm and helical gear transmission device |
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| DE2237421C2 (en) * | 1972-07-29 | 1982-11-25 | Zahnradfabrik Friedrichshafen Ag, 7990 Friedrichshafen | Variable ratio steering gears for automobiles |
| ES2801377T3 (en) * | 2017-05-24 | 2021-01-11 | Ims Gear Se & Co Kgaa | Pair of sprockets for a worm gear or spur gear, worm gear or spur gear with such a pair of sprockets as well as use of such a pair of sprockets in helical gears and spur gears |
| ES2858073T3 (en) * | 2017-05-24 | 2021-09-29 | Ims Gear Se & Co Kgaa | Pair of sprockets for a worm gear, worm gear with such a pair of sprockets, as well as use of such a pair of sprockets in worm gears |
| CN107247856B (en) * | 2017-08-01 | 2019-10-11 | 西安电子科技大学 | A kind of list roller enveloping enveloping worm pair time-variant mesh stiffness analytic method |
| CN109190227A (en) * | 2018-06-12 | 2019-01-11 | 南京聚能传动设备有限公司 | Based on the complicated tooth base Meshing Stiffness of Spur Gears calculation method of parsing-finite element |
| CN209557585U (en) * | 2018-12-18 | 2019-10-29 | 西华大学 | Heavy-load type cosine gear double enveloped hourglass worm drives |
| CN110792754B (en) * | 2019-10-12 | 2021-01-15 | 西华大学 | Method for calculating indexing circular-arc tooth thickness of straight gear according to meshing parameters of worm and straight gear |
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