CN108763626B - Involute worm gear precise modeling and assembling method - Google Patents
Involute worm gear precise modeling and assembling method Download PDFInfo
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Abstract
The invention discloses an involute worm gear precise modeling and assembling method, which comprises the following specific steps: s1: modeling of worm gear, S2: modeling of a worm, and S3: according to the assembly of the worm and the worm gear, the three-dimensional solid modeling of the involute worm is realized on the basis of constructing a worm spiral line by utilizing an involute parameter equation, the three-dimensional solid modeling of the involute worm wheel which is matched with the involute worm to drive is finished by utilizing the established involute worm, and finally the three-dimensional solid meshing assembly of the involute worm wheel and the involute worm is finished.
Description
Technical Field
The invention relates to the technical field of mechanical transmission parts, in particular to an involute worm and gear precise modeling and assembling method.
Background
The worm gear transmission belongs to one of important mechanical transmission types, can realize transmission between two staggered shafts in space, has the advantages of large transmission ratio, stable transmission, compact structure, low noise and the like, and is widely applied to various mechanical transmission systems. However, the traditional method for manufacturing has the problems of complex process, low efficiency, easy error and the like. In order to improve the design efficiency of the product, shorten the research and development period and improve the meshing quality of the worm gear, the parameterized assembly design position and function of the worm gear are particularly important.
At present, the design difficulty of the parameterized assembly of the worm and the worm gear is that the meshing problem between the worm and the worm gear is that the interference of the assembly of the worm and the worm gear is minimized on the premise of ensuring the correct meshing condition. The parameterized design of the parts is the basis of parameterized design of an assembly body, design parameters are reasonably planned and accurately modeled in three dimensions according to the assembly relation of the worm and gear, and the integrity, the accuracy and the high efficiency of size association and transmission in the parameterization process are ensured. Therefore, a parameterized design method is needed to model and assemble the involute worm gear in three dimensions.
Disclosure of Invention
The invention aims to provide an involute worm gear precise modeling and assembling method, which comprises the following specific steps:
s1: modeling of the worm wheel,
1) Creating a three-dimensional basic entity of a worm wheel blank in a part design environment;
2) Under the environment of a wire frame and a curved surface design, generating a plurality of model value points on an involute through a rule curve, and constructing a corresponding worm wheel involute curve by utilizing a fourth-order cubic interpolation B spline curve, wherein the rule curve expression of each point on the involute relative to an abscissa x and an ordinate y is as follows:
wherein r is b For the base circle radius, 50 represents that the involute is selected from 0-50 degrees;
3) Under the design environment of parts, sequentially drawing a draft of a reference circle, a addendum circle and a root circle and a draft of a mirror image of a fitted worm wheel involute through three-dimensional projection, and then drawing a two-dimensional diagram of a tooth slot to obtain a draft of a section of the tooth slot;
4) Under the part design environment, firstly setting the center distance between a central axis of a sweep line and a worm gear, and completing the establishment of a spiral line as a sweep track of an involute tooth profile;
5) Under the design environment of parts, a tooth groove is formed after grooving and defining a worm wheel blank, the tooth groove is selected on a model tree, all tooth shapes of the worm wheel are completed after the definition of a circumferential array is used, and a complete worm wheel is created;
s2: modeling of the worm screw,
1) Creating a three-dimensional basic entity of a worm blank in a part design environment;
2) Setting a spiral line starting point coordinate value in a space coordinate system under a wire frame and curved surface design environment, and obtaining a worm scanning spiral line after defining by using the spiral line;
3) In the environment of a wire frame and a curved surface design, the involute generating method of the worm gear is similar to the involute generating method of the worm gear in 1.1, and the rule curve expression of each point on the involute about the abscissa x and the ordinate y is as follows:
x＝r b (cos(50t)+t sin(50t))
y＝r b (sint-t cost)
wherein r is b For the base circle radius, 50 represents that the involute is selected from 0-50 degrees;
4) Generating a worm tooth groove after the definition of the groove under the design environment of the part, and creating a complete worm wheel;
s3: the worm wheel and worm is assembled,
the moving point on the worm screw line and the assembling point on the worm wheel are set to be zero-meshed together, and the movement of the worm wheel and the worm is achieved by controlling the length between the two points (the starting point and the moving point) on the worm screw line.
Preferably, in S1, the origin of the global coordinates is selected as the center of the worm wheel, and the spatial relative position of the worm wheel and worm is determined by the assembled center distance, wherein the center distance is a=m (q+z) 2 ) Wherein m is a modulus, q is a worm diameter coefficient, z 2 Is worm gear number.
Preferably, in the step S1, a plurality of model value points forming the involute are generated on a two-dimensional plane of a basic entity of the worm wheel by utilizing a rule curve according to the generation rule and the function relation of the involute, and spline fitting is carried out on the model value points by a system, so that the involute is generated, and the accuracy of the involute is higher as the model value points are more.
Preferably, in S1, in order to improve the meshing effect of the worm gear and the worm gear during assembly, the involute symmetry axis projected on the two-dimensional plane is coincident with the horizontal axis, so that the axisymmetry of the tooth socket profile about the horizontal axis can be ensured, and the positioning during assembly of the worm gear and the worm gear is facilitated.
Preferably, in S1, the central axis of the sweep spiral line is a center distance from the worm wheel axis.
Preferably, the origin of the global coordinates is selected as the center of the axis of the worm in S2.
Preferably, the starting point (x, y, z) of the spiral is swept in S2, wherein the length of |x| is slightly greater than the length of one axial end of the worm blank, y=0, and |z| is the radius of the tip circle of the worm.
Preferably, in the step S2, a plurality of model value points forming the involute are generated on a two-dimensional plane of a basic entity of the worm by utilizing a rule curve according to the generation rule and the function relation of the involute, and then the model value sample application strips are fitted, so that the involute is generated, and the more the model value points are, the higher the accuracy of the involute is.
Preferably, a line is made in S2 perpendicular to the axis of the worm and passing through the start of the worm spiral, about which the worm tooth slot is symmetrical and gives the tooth slot other constraints including defining the tooth slot axial pitch, the worm root radius, the worm tip radius, the pressure angle, and the worm pitch radius.
Preferably, in the step S3, a moving point on a worm spiral line (a worm top circle) and a point on a worm tooth groove (a worm tooth root circle) are set to be in zero engagement, the movement of the worm and the worm is achieved by controlling the length between the two points (a starting point and a moving point) on the worm spiral line, specifically, a plane determined by the starting point and the moving point of the worm coincides with a center plane of the worm through operations such as translation and rotation, so that the worm and the worm have a better assembly position, the point distance between the worm and the worm is set to be zero, and then the distance between the axis of the worm and the vertical axis of the worm is set to be the center distance, thereby completing the three-dimensional assembly of the worm and the worm.
Compared with the prior art, the invention has the beneficial effects that: according to the invention, three-dimensional solid modeling of the involute worm is realized on the basis of constructing a worm spiral line by utilizing an involute parameter equation, and then three-dimensional solid modeling of the involute worm wheel which is matched with the involute worm is completed by utilizing the established involute worm, and finally three-dimensional solid meshing assembly of the involute worm wheel and the involute worm is completed. The method solves the problems of the meshing interference and the like during the meshing of the three-dimensional entities, performs accurate modeling, can be superior to a theoretical precision value, and the constructed worm and gear three-dimensional assembly has a real motion profile, can provide accurate coordinate parameters for numerical control machining, has strong universality and wide application range, can assist parameterization in mass machining and manufacturing, and can lay a good foundation for subsequent researches on the mechanical properties, manufacturing precision and the like of various complex involute worm and gear.
Detailed Description
The present invention will be described in further detail with reference to specific embodiments in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Example 1
The invention provides a technical scheme that: the method for accurately modeling and assembling the involute worm gear comprises the following specific steps:
s1: modeling of the worm wheel,
1) Creating a three-dimensional basic entity of a worm wheel blank in a part design environment;
2) Under the environment of a wire frame and a curved surface design, generating a plurality of model value points on an involute through a rule curve, and constructing a corresponding worm wheel involute curve by utilizing a fourth-order cubic interpolation B spline curve, wherein the rule curve expression of each point on the involute relative to an abscissa x and an ordinate y is as follows:
wherein r is b For the base circle radius, 50 represents that the involute is selected from 0-50 degrees;
3) Under the design environment of parts, sequentially drawing a draft of a reference circle, a addendum circle and a root circle and a draft of a mirror image of a fitted worm wheel involute through three-dimensional projection, and then drawing a two-dimensional diagram of a tooth slot to obtain a draft of a section of the tooth slot;
4) Under the part design environment, firstly setting the center distance between a central axis of a sweep line and a worm gear, and completing the establishment of a spiral line as a sweep track of an involute tooth profile;
5) Under the design environment of parts, a tooth groove is formed after grooving and defining a worm wheel blank, the tooth groove is selected on a model tree, all tooth shapes of the worm wheel are completed after the definition of a circumferential array is used, and a complete worm wheel is created;
s2: modeling of the worm screw,
1) Creating a three-dimensional basic entity of a worm blank in a part design environment;
2) Setting a spiral line starting point coordinate value in a space coordinate system under a wire frame and curved surface design environment, and obtaining a worm scanning spiral line after defining by using the spiral line;
3) In the environment of a wire frame and a curved surface design, the involute generating method of the worm gear is similar to the involute generating method of the worm gear in 1.1, and the rule curve expression of each point on the involute about the abscissa x and the ordinate y is as follows:
x＝r b (cos(50t)+t sin(50t))
y＝r b (sint-t cost)
wherein r is b For the base circle radius, 50 represents that the involute is selected from 0-50 degrees;
4) Generating a worm tooth groove after the definition of the groove under the design environment of the part, and creating a complete worm wheel;
s3: the worm wheel and worm is assembled,
the moving point on the worm screw line and the assembling point on the worm wheel are set to be zero-meshed together, and the movement of the worm wheel and the worm is achieved by controlling the length between the two points (the starting point and the moving point) on the worm screw line.
Specifically, in S1, the origin of the overall coordinates is selected as the center of the worm gear, the spatial relative position of the worm gear is determined by the assembled center distance, and the center distance is a=m (q+z) 2 ) Wherein m is a modulus, q is a worm diameter coefficient, z 2 Is worm gear number.
Specifically, in the step S1, according to the generation rule and the function relation of the involute, a plurality of model value points forming the involute are generated on a two-dimensional plane of a basic entity of the worm wheel by utilizing a rule curve, and spline fitting is carried out on the model value points by a system, so that the involute is generated, and the accuracy of the involute is higher as the model value points are more.
The main dimension parameters of the worm wheel are calculated according to the prior theory and are shown in the following table.
Specifically, in order to improve the meshing effect of the worm gear and the worm gear during assembly, the involute symmetry axis projected on the two-dimensional plane is coincident with the horizontal axis in S1, so that the axisymmetry of the tooth socket profile about the horizontal axis can be ensured, and the positioning during assembly of the worm gear and the worm gear is facilitated.
Specifically, in S1, the center axis of the sweep spiral line is the center distance from the worm wheel axis.
Specifically, in S2, the origin of the global coordinates is selected as the center of the axis of the worm.
Specifically, the starting point (x, y, z) of the spiral line is swept in S2, wherein the length of |x| is slightly greater than the length of one axial end of the worm blank, y=0, and |z| is the radius of the tip circle of the worm.
Specifically, in the step S2, a plurality of model value points forming the involute are generated on a two-dimensional plane of a basic entity of the worm by utilizing a rule curve according to the generation rule and the function relation of the involute, and then the model value sample application strips are fitted, so that the involute is generated, and the more the model value points are, the higher the accuracy of the involute is.
Specifically, a straight line perpendicular to the axis of the worm and passing through the start point of the worm spiral line is made in S2, the worm tooth slot is symmetrical about the straight line, and other constraints are given to the tooth slot, including defining the tooth slot axial pitch, the worm tooth root radius, the worm tooth top radius, the pressure angle and the worm pitch radius.
Specifically, in the step S3, a moving point on a worm spiral line (a worm tooth top circle) and a point on a worm tooth groove (a worm tooth root circle) are set to be in zero engagement, the movement of the worm and the worm is achieved by controlling the length between the two points (a starting point and a moving point) on the worm spiral line, specifically, a plane determined by the starting point and the moving point of the worm is enabled to coincide with a center plane of the worm through operations such as translation and rotation, the worm and the worm are enabled to have a good assembly position, the point distance between the worm and the worm is set to be zero, and then the distance between the axis of the worm and the vertical axis of the worm is set to be the center distance, so that the three-dimensional assembly of the worm and the worm is completed.
The main dimension parameters of the worm are calculated according to the prior theory and are shown in the following table.
According to the invention, three-dimensional solid modeling of the involute worm is realized on the basis of constructing a worm spiral line by utilizing an involute parameter equation, and then three-dimensional solid modeling of the involute worm wheel which is matched with the involute worm is completed by utilizing the established involute worm, and finally three-dimensional solid meshing assembly of the involute worm wheel and the involute worm is completed. The method solves the problems of the meshing interference and the like during the meshing of the three-dimensional entities, performs accurate modeling, can be superior to a theoretical precision value, and the constructed worm and gear three-dimensional assembly has a real motion profile, can provide accurate coordinate parameters for numerical control machining, has strong universality and wide application range, can assist parameterization in mass machining and manufacturing, and can lay a good foundation for subsequent researches on the mechanical properties, manufacturing precision and the like of various complex involute worm and gear.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (10)
1. An involute worm gear precise modeling and assembling method is characterized in that: the method for accurately modeling and assembling the involute worm gear comprises the following specific steps:
s1: modeling of the worm wheel,
1) Creating a three-dimensional basic entity of a worm wheel blank in a part design environment;
2) Under the environment of a wire frame and a curved surface design, generating a plurality of model value points on an involute through a rule curve, and constructing a corresponding worm wheel involute curve by utilizing a fourth-order cubic interpolation B spline curve, wherein the rule curve expression of each point on the involute relative to an abscissa x and an ordinate y is as follows:
wherein r is b For the base circle radius, 50 represents that the involute is selected from 0-50 degrees;
3) Under the design environment of parts, sequentially drawing a draft of a reference circle, a addendum circle and a root circle and a draft of a mirror image of a fitted worm wheel involute through three-dimensional projection, and then drawing a two-dimensional diagram of a tooth slot to obtain a draft of a section of the tooth slot;
4) Under the part design environment, firstly setting the center distance between a central axis of a sweep line and a worm gear, and completing the establishment of a spiral line as a sweep track of an involute tooth profile;
5) Under the design environment of parts, a tooth groove is formed after grooving and defining a worm wheel blank, the tooth groove is selected on a model tree, all tooth shapes of the worm wheel are completed after the definition of a circumferential array is used, and a complete worm wheel is created;
s2: modeling of the worm screw,
1) Creating a three-dimensional basic entity of a worm blank in a part design environment;
2) Setting a spiral line starting point coordinate value in a space coordinate system under a wire frame and curved surface design environment, and obtaining a worm scanning spiral line after defining by using the spiral line;
3) In the environment of a wire frame and a curved surface design, the involute generating method of the worm gear is similar to the generating method of the involute curve of the worm gear in S1, and the rule curve expression of each point on the involute with respect to the abscissa x and the ordinate y is as follows:
x＝r b (cos(50t)+tsin(50t))
y＝r b (sint-tcost)
wherein r is b For the base circle radius, 50 represents that the involute is selected from 0-50 degrees;
4) Generating a worm tooth groove after the definition of the groove under the design environment of the part, and creating a complete worm wheel;
s3: the worm wheel and worm is assembled,
the moving point on the worm screw line and the assembling point on the worm wheel are set to be zero-meshed together, and the length between the starting point and the moving point is controlled to achieve the movement of the worm wheel and the worm by controlling the two points on the worm screw line.
2. The method for accurately modeling and assembling the involute worm gear according to claim 1, characterized by comprising the following steps: s1, selecting an overall origin of coordinates as a worm wheel center, and determining the spatial relative position of a worm wheel and a worm by an assembled center distance, wherein the center distance is a=m (q+z) 2 ) Wherein m is a modulus, q is a worm diameter coefficient, z 2 Is worm gear number.
3. The method for accurately modeling and assembling the involute worm gear according to claim 1, characterized by comprising the following steps: and S1, generating a plurality of model value points forming the involute on a two-dimensional plane of a basic entity of the worm wheel by utilizing a rule curve according to the generating rule and the functional relation of the involute, and performing spline fitting on the model value points by a system so as to generate the involute, wherein the more the model value points are, the higher the accuracy of the involute is.
4. The method for accurately modeling and assembling the involute worm gear according to claim 1, characterized by comprising the following steps: in S1, in order to improve the meshing effect of the worm and the gear during assembly, the involute symmetry axis projected on the two-dimensional plane is coincident with the horizontal axis, so that the axisymmetry of the tooth socket profile about the horizontal axis can be ensured, and the positioning during assembly of the worm and the gear is facilitated.
5. The method for accurately modeling and assembling the involute worm gear according to claim 1, characterized by comprising the following steps: and S1, the center distance between the center shaft of the sweeping spiral line and the axis of the worm wheel is the center distance.
6. The method for accurately modeling and assembling the involute worm gear according to claim 1, characterized by comprising the following steps: and S2, selecting the global origin of coordinates as the center of the axis of the worm.
7. The method for accurately modeling and assembling the involute worm gear according to claim 1, characterized by comprising the following steps: the starting point (x, y, z) of the swept spiral in S2, wherein the length of |x| is slightly greater than the length of one axial end of the worm blank, y=0, and |z| is the radius of the tip circle of the worm.
8. The method for accurately modeling and assembling the involute worm gear according to claim 1, characterized by comprising the following steps: and S2, generating a plurality of model value points forming the involute on a two-dimensional plane of the basic entity of the worm by utilizing a rule curve according to the generating rule and the functional relation of the involute, and fitting the model value sample strips, so that the involute is generated, and the accuracy of the involute is higher as the model value points are more.
9. The method for accurately modeling and assembling the involute worm gear according to claim 1, characterized by comprising the following steps: and S2, making a straight line perpendicular to the axis of the worm and passing through the starting point of the spiral line of the worm, wherein the tooth slot of the worm is symmetrical about the straight line, and other constraints are given to the tooth slot, including defining the axial tooth pitch of the tooth slot, the radius of the root circle of the tooth of the worm, the radius of the top circle of the tooth tip of the worm, the pressure angle and the radius of the indexing circle of the worm.
10. The method for accurately modeling and assembling the involute worm gear according to claim 1, characterized by comprising the following steps: in S3, a worm spiral line, a moving point and a worm gear tooth groove are arranged on a worm tooth top circle, a distance between one point on the worm gear tooth top circle is zero, the length between a starting point and the moving point reaches the movement of a worm gear through controlling two points on the worm spiral line, specifically, a plane determined by the starting point and the moving point of the worm and a worm gear center plane coincide through translation and rotation operation, the worm gear has a good assembly position, the distance between the points on the worm and the worm gear is zero, and then the distance between the axis of the worm and the vertical axis of the worm gear is the center distance, so that the three-dimensional assembly of the worm gear is completed.
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| CN109635478B (en) * | 2018-12-20 | 2023-03-31 | 广州华立科技职业学院 | Modeling method of worm gear |
| CN109740269B (en) * | 2019-01-08 | 2022-12-13 | 厦门理工学院 | Involute worm turning tooth surface three-dimensional modeling method |
| CN109858113B (en) * | 2019-01-16 | 2022-06-14 | 厦门理工学院 | Modeling method, device and equipment for extended involute worm machining tooth surface |
| CN110021066A (en) * | 2019-03-13 | 2019-07-16 | 厦门理工学院 | A kind of prolate involute worm gear hobbing three-dimensional modeling method, device and equipment |
| CN110110420B (en) * | 2019-04-28 | 2022-06-10 | 厦门理工学院 | Modeling method, device and equipment for machining tooth surface of cambered surface worm |
| CN110766801B (en) * | 2019-10-23 | 2023-04-07 | 吉林大学 | Three-dimensional modeling method for involute line contact conical worm transmission pair |
| CN110765621B (en) * | 2019-10-28 | 2023-06-06 | 南京高精齿轮集团有限公司 | NX involute spline modeling method |
| CN113221290B (en) * | 2021-06-01 | 2024-05-14 | 杭州兴龙泵业有限公司 | Modeling system for main rod and auxiliary rod disc milling cutter of three-screw pump |
| CN117786900B (en) * | 2024-02-28 | 2024-05-17 | 烟台环球机床装备股份有限公司 | Mathematical physical method for modeling worm |
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| CN104565285A (en) * | 2013-10-14 | 2015-04-29 | 空中客车营运有限公司 | Gear construction method and digital equipment |
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