CN113127993A - Worm wheel razor and its design method and shape-modifying method - Google Patents

Worm wheel razor and its design method and shape-modifying method Download PDF

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CN113127993A
CN113127993A CN202110461608.4A CN202110461608A CN113127993A CN 113127993 A CN113127993 A CN 113127993A CN 202110461608 A CN202110461608 A CN 202110461608A CN 113127993 A CN113127993 A CN 113127993A
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王时龙
马驰
王四宝
衡德超
曾令万
杨勇
杨灿辉
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Chongqing University
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Abstract

The invention discloses a design method of a worm gear shaver, which comprises the following steps: 1) solving the tooth surface of the long-pair involute worm according to the equations of the spiral surface end section and the axial section of the normal straight tooth profile worm to obtain the tooth surface equation r of the normal straight tooth profile worm1Sum tooth surface normal vector equation
Figure DDA0003042494750000014
2) According to the meshing relation between the normal straight tooth profile worm and the normal straight tooth profile worm wheel, the tooth surface equation r of the normal straight tooth profile worm is used1And the normal vector equation
Figure DDA0003042494750000013
Solving the tooth surface equation r of normal straight tooth profile type worm wheel2Sum tooth surface normal vector equation
Figure DDA0003042494750000011
3) According to the conjugate relation between the tooth surface of the worm gear shaver and the tooth surface of the normal straight tooth profile type worm gear, the tooth surface equation r of the normal straight tooth profile type worm gear is adopted2Sum tooth surface normal vector equation
Figure DDA0003042494750000012
Solving the tooth surface equation r of a worm gear razor3. The invention also discloses a worm gear shaver shape modification method, a worm gear shaver designed by the worm gear shaver design method and a worm gear shaver modified by the worm gear shaver shape modification method, which can meet the design and shape modification requirements of the worm gear shaver.

Description

Worm wheel razor and its design method and shape-modifying method
Technical Field
The invention relates to a worm gear shaver, in particular to a worm gear shaver and a design method and a modification method thereof.
Background
The normal straight-tooth profile worm gear pair transmission has higher bearing capacity, for example, ship turrets, large astronomical telescopes, precision machine tools, missile interception equipment, radar devices and the like all adopt normal straight-tooth profile worm gear pair transmission, and compared with the common cylindrical worm gear pair transmission, the bearing capacity can be improved by 2-4 times under the condition of the same size and material. Therefore, it is widely applied to mining machinery, metallurgical machinery, coal mine machinery and military equipment at home and abroad.
The improvement of the manufacturing precision of the worm gear pair is one of the key problems of improving the bearing capacity of the worm gear pair, and particularly, the processing of a tooth surface depression generating area of the worm gear is more prominent. At present, flying cutter gear cutting or hob gear cutting are mostly adopted in China to manufacture a normal straight tooth profile worm wheel, and even though hob gear cutting is adopted, a complete ideal hollow pit generation area cannot be formed due to the fact that the number of circumferential teeth of a hob is small. Therefore, the machined worm gear pair is generally assembled and then loaded for running in, and an ideal pit surface is formed so as to meet the design requirement. Although the worm gear shaving processing can not improve the single pitch precision and the pitch accumulated precision of the worm gear, the tooth surface smoothness, the worm gear tooth surface contact area and the tooth surface contact precision can be obviously improved, and thus the bearing capacity and the service performance of the worm gear pair can be improved.
The worm-gear shaver is a single-side acting forced shaving worm, and a plurality of chip-containing grooves are formed in the tooth surface to form a cutting edge, a front face and a chip-containing space of the shaver. When the gear hobbing machine works, the worm gear shaver is arranged on a tool rest of the gear hobbing machine, the workpiece is arranged on a workbench and performs opposite rolling movement, and the relative installation position of the shaver and the workpiece is completely consistent with the position when the worm is meshed with the worm gear. During shaving, the center distance is preset to an accurate position, the position is always unchanged in the machining process, and forced single-side meshing is realized. In order to gradually form the hollow, circumferential feeding is adopted so that the hollow width of the workpiece meets the design requirement.
Disclosure of Invention
In view of the above, the present invention provides a worm gear shaver, and a design method and a modification method thereof, which can meet the design and modification requirements of the worm gear shaver.
In order to achieve the purpose, the invention provides the following technical scheme:
a worm gear razor design method comprising the steps of:
1) solving the tooth surface of the normal straight tooth profile worm according to the equations of the spiral surface end section and the axial section of the normal straight tooth profile worm to obtain the tooth surface equation r of the normal straight tooth profile worm1Sum tooth surface normal vector equation
Figure BDA0003042494740000011
2) According to the meshing relation between the normal straight tooth profile worm and the normal straight tooth profile worm wheel, the tooth surface equation r of the normal straight tooth profile worm is used1And the normal vector equation
Figure BDA0003042494740000012
Solving the tooth surface equation r of normal straight tooth profile type worm wheel2Sum tooth surface normal vector equation
Figure BDA0003042494740000013
3) According to the conjugate relation between the tooth surface of the worm gear shaver and the tooth surface of the normal straight tooth profile type worm gear, the tooth surface equation r of the normal straight tooth profile type worm gear is adopted2Sum tooth surface normal vector equation
Figure BDA0003042494740000021
Solving the tooth surface equation r of a worm gear razor3。
Further, in the step 1), a section equation of the spiral surface end of the normal straight tooth profile worm is as follows:
Figure BDA0003042494740000022
the axial section equation of the spiral surface of the normal straight tooth profile worm is as follows:
Figure BDA0003042494740000023
wherein p is the thread pitch of the normal straight tooth profile worm; alpha is the tooth pressure angle of the normal straight tooth profile worm; r isb1The diameter of a base circle of a normal straight tooth profile worm; theta is the angle value of the end section line rotating from the initial position by taking the z axis as the center; r is the worm diameter.
Further, the normal straight tooth profile equation is:
Figure BDA0003042494740000024
from this, the tooth surface (right-hand) equation r of the normal straight tooth profile worm can be obtained1Comprises the following steps:
Figure BDA0003042494740000025
tooth surface (right-handed) normal vector equation of normal straight tooth profile worm
Figure BDA0003042494740000026
Comprises the following steps:
Figure BDA0003042494740000027
wherein u is an independent variable, and
Figure BDA0003042494740000028
wherein the normal length Pa, r at any point P on the normal straight tooth profilebIs the base circle radius.
Further, in the step 2), a tooth surface equation r of the normal straight tooth profile type worm wheel2Comprises the following steps:
Figure BDA0003042494740000029
normal tooth flank normal vector equation of normal straight tooth profile worm gear
Figure BDA00030424947400000210
Comprises the following steps:
Figure BDA0003042494740000031
wherein the content of the first and second substances,
Figure BDA0003042494740000032
the angle rotated by the normal straight tooth profile worm;
Figure BDA0003042494740000033
the angle of the normal straight tooth profile type worm wheel is rotated; and is
Figure BDA0003042494740000034
i12The transmission ratio between the normal straight tooth profile worm and the normal straight tooth profile worm wheel.
Further, in the step 3), a relative motion velocity vector v between the normal straight-tooth profile type worm wheel and the worm gear shaver is obtained by a conjugate relationship between the tooth surface of the worm gear shaver and the tooth surface of the normal straight-tooth profile type worm wheel:
Figure BDA0003042494740000035
from the orthogonal relationship between the tooth surfaces of the worm shaver and the normal straight tooth profile worm wheel and the relative motion velocity vector v, it can be found that:
Figure BDA0003042494740000036
so as to solve the tooth surface equation r of the worm gear shaver3Comprises the following steps:
Figure BDA0003042494740000037
the invention also provides a worm gear shaver, and the tooth surface equation of the worm gear shaver is designed by adopting the design method of the worm gear shaver.
The invention also provides a worm gear shaver shaping method, which comprises the following steps:
1) the tooth surface equation r of the worm gear shaver is obtained by adopting the design method of the worm gear shaver as described above3；
2) Modifying the shape of the worm gear shaver;
due to the tooth surface equation r of worm gear razors3With theoretical error, the profile curve Δ of the worm shaver is thus modifiedfoSetting as a piecewise function:
Figure BDA0003042494740000038
wherein m istRepresenting the end face modulus of a worm gear razor;
tip diameter d of throat part of modified worm gear shavera10Comprises the following steps:
Figure BDA0003042494740000039
wherein d isa1Representing the diameter of the tip circle of the throat of the worm gear shaver before modification; c is the tooth top clearance;
addendum arc radius Ra of modified worm gear shaver10Comprises the following steps:
Figure BDA0003042494740000041
wherein, a0Representing the variable parameter modification center distance;
root diameter d of throat part of modified worm gear shaverf10Comprises the following steps:
Figure BDA0003042494740000042
wherein d isf1Representing the throat root circle diameter of the worm gear razor before modification;
root arc radius R of modified worm gear shaverf10Comprises the following steps:
Figure BDA0003042494740000043
length L of screw thread of worm gear shaver after modificationWOComprises the following steps:
Figure BDA0003042494740000044
wherein L isWShowing the thread length of the worm gear shaver before modification;
maximum excircle diameter d of modified worm gear shavera10maxComprises the following steps:
Figure BDA0003042494740000045
left side back inclination angle beta of modified worm gear shaver1Comprises the following steps:
Figure BDA0003042494740000046
wherein, γminRepresents the minimum value of the helix angle; i.e. i0Modifying the transmission ratio for variable parameters; arctan represents the arctangent function;
right side back inclination angle beta of modified worm gear shaver2Comprises the following steps:
Figure BDA0003042494740000051
in the formula, gammamaxRepresents the maximum value of the helix angle;
axial chordal tooth height ha of modified worm gear shaver10Comprises the following steps:
ha10＝ha1+0.5(da10-da1)
wherein, ha1The axial chordal tooth height of the worm gear shaver before modification is shown;
axial chord tooth thickness Sx of modified worm gear shaver10Comprises the following steps:
Figure BDA0003042494740000052
wherein, Sx1Showing the axial chordal tooth thickness of the worm gear shaver before modification; gamma raymIndicating the helix angle.
The invention also provides a worm gear shaver which is obtained by adopting the worm gear shaver shape modification method.
The invention has the beneficial effects that:
the invention relates to a design method of a worm gear shaver, which comprises the steps of firstly solving and obtaining a tooth surface equation r of a normal straight tooth profile type worm1Sum tooth surface normal vector equation
Figure BDA0003042494740000053
Then, the tooth surface equation r of the normal straight tooth profile worm wheel is obtained by solving according to the meshing relation between the normal straight tooth profile worm and the normal straight tooth profile worm wheel2Sum tooth surface normal vector equation
Figure BDA0003042494740000054
Finally, solving and obtaining a tooth surface equation r of the worm gear shaver according to the conjugate relation between the tooth surface of the worm gear shaver and the tooth surface of the normal straight tooth profile type worm gear3(ii) a Namely, the design method of the worm gear shaver can meet the design requirement of the worm gear shaver with high precision.
The invention relates to a modification method of a worm gear shaver, which creatively modifies the modification curve delta of the modified worm gear shaverfoDiameter of throat tip da10Radius of addendum arc Ra10Diameter d of root circle of throatf10Root arc radius Rf10Length L of threadWOMaximum outer diameter da10maxLeft side back tilt angle beta1Right side back tilt angle beta2And axial chordal tooth thickness Sx10Are all set as the end face module m of a worm gear shavertThe piecewise function can avoid the worm gear razor tooth surface equation r in the design stage of the worm gear razor3The theoretical error of (2) has an influence on the precision of the modified worm gear shaver, thereby improving the precision of the worm gear machined by the modified worm gear shaver.
Detailed Description
The present invention is further described with reference to specific examples to enable those skilled in the art to better understand the present invention and to practice the same, but the examples are not intended to limit the present invention.
Example 1
The design method of the worm gear shaver comprises the following steps:
1) solving the tooth surface of the long-pair involute worm according to the equations of the spiral surface end section and the axial section of the normal straight tooth profile worm to obtain the tooth surface equation r of the normal straight tooth profile worm1Sum tooth surface normal vector equation
Figure BDA0003042494740000061
Specifically, the section equation of the spiral surface end of the normal straight tooth profile worm is as follows:
Figure BDA0003042494740000062
the axial section equation of the spiral surface of the normal straight tooth profile worm is as follows:
Figure BDA0003042494740000063
wherein p is the thread pitch of the normal straight tooth profile worm; alpha is the tooth pressure angle of the normal straight tooth profile worm; r isb1The diameter of a base circle of a normal straight tooth profile worm; theta is the angle value of the end section line rotating from the initial position by taking the z axis as the center; r is the worm diameter.
Solving the tooth surface of the long pair involute worm by using a worm long pair involute equation to obtain a tooth surface (right-handed) equation r of the normal straight tooth profile worm1And calculating the normal of the tooth surface of the normal straight tooth profile type worm
Figure BDA0003042494740000064
Specifically, the normal straight tooth profile equation is:
Figure BDA0003042494740000065
from this, the tooth surface (right-hand) equation r of the normal straight tooth profile worm can be obtained1Comprises the following steps:
Figure BDA0003042494740000066
tooth surface (right-handed) normal vector equation of normal straight tooth profile worm
Figure BDA0003042494740000067
Comprises the following steps:
Figure BDA0003042494740000068
Figure BDA0003042494740000069
Figure BDA00030424947400000610
Figure BDA00030424947400000611
wherein u is an independent variable, and
Figure BDA00030424947400000612
wherein the normal length Pa, r at any point P on the normal straight tooth profilebIs the base circle radius;
Figure BDA00030424947400000613
and
Figure BDA00030424947400000614
are respectively normal vector
Figure BDA00030424947400000615
The components in the x, y and z directions.
2) According to the meshing relation between the normal straight tooth profile worm and the normal straight tooth profile worm wheel, the tooth surface equation r of the normal straight tooth profile worm is used1And the normal vector equation
Figure BDA0003042494740000071
Solving the tooth surface equation r of normal straight tooth profile type worm wheel2Sum tooth surface normal vector equation
Figure BDA0003042494740000072
Firstly, the tooth surface (right-handed) equation r of a normal straight tooth profile type worm is utilized1Combining a transfer matrix M between the worm wheel and the worm, solving a tooth surface equation r of the normal straight tooth profile type worm wheel2In particular, the tooth surface equation r for a normal straight-tooth profile worm gear2Comprises the following steps:
Figure BDA0003042494740000073
secondly, the normal of the tooth surface of the straight-tooth profile worm is utilized
Figure BDA0003042494740000074
Combining the transmission matrix M between the worm wheel and the worm, and processing the equation through a coordinate transformation equation to obtain a normal tooth surface normal vector equation of the normal straight tooth profile type worm wheel
Figure BDA0003042494740000075
In particular, the normal tooth flank normal vector equation of a normal straight tooth profile worm gear
Figure BDA0003042494740000076
Comprises the following steps:
Figure BDA0003042494740000077
wherein the content of the first and second substances,
Figure BDA0003042494740000078
the angle rotated by the normal straight tooth profile worm;
Figure BDA0003042494740000079
the angle of the normal straight tooth profile type worm wheel is rotated; and is
Figure BDA00030424947400000710
i12The transmission ratio between the normal straight tooth profile worm and the normal straight tooth profile worm wheel.
3) According to the conjugate relation between the tooth surface of the worm gear shaver and the tooth surface of the normal straight tooth profile type worm gear, the tooth surface equation r of the normal straight tooth profile type worm gear is adopted2Sum tooth surface normal vector equation
Figure BDA00030424947400000711
Solving worm wheel razorEquation of tooth surface r3。
The worm gear razor tooth flanks may be considered as conjugate tooth flanks that mesh with the worm gear tooth flanks. Since the worm shaver flanks are conjugate to the worm flanks. Therefore, the tooth surface equation r of the normal straight tooth profile type worm wheel can be utilized2Solving the worm-gear razor tooth surface equation r3。
Specifically, the relative motion velocity vector v between the normal straight tooth profile worm gear and the worm gear razor is:
Figure BDA0003042494740000081
according to the space gear meshing theory, two tooth surfaces are In line contact at any time In worm gear transmission, and a common normal plane and a common normal In of the two tooth surfaces are divided by a tangent point on the contact line. If the two tooth surfaces are always kept in continuous meshing state in the transmission and the disengagement and interference situations do not occur, the orthogonal relation between the relative motion velocity vector v between the two tooth surfaces at the point and the normal vector thereof is proved, and the meshing equation can be derived according to the conclusion:
Figure BDA0003042494740000082
so as to solve the tooth surface equation r of the worm gear shaver3Comprises the following steps:
Figure BDA0003042494740000083
through the above calculation process, the worm-gear razor tooth surface equation without taking the modification into account can be calculated. The equation expresses the relationship between the parameters of the worm gear razor and has a very important role.
Requiring solution of the tooth surface equation r for worm razors3The pitch p of the worm, the tooth pressure angle α, the angle value θ of the end section line from the initial position about the z-axis, the diameter r of the worm, and the angle of the worm
Figure BDA0003042494740000084
Angle of rotation of worm gear
Figure BDA0003042494740000085
And the like. At the same time, the number z of worm heads needs to be determined1Number of teeth of worm gear z2Modulus m, diameter of pitch circle of worm d1Basic parameters such as helix angle gamma and tooth width b, and calculating other parameters of worm and worm wheel including transmission ratio i21Center distance A0Diameter d of addendum circle of worma1Root diameter d of wormf1And the like, thereby obtaining a specific worm gear razor, that is, a worm gear razor designed by the worm gear razor design method of the present embodiment.
The design method of the worm gear razor of the embodiment comprises the steps of firstly solving and obtaining a tooth surface equation r of a normal straight tooth profile type worm1Sum tooth surface normal vector equation
Figure BDA0003042494740000086
Then, the tooth surface equation r of the normal straight tooth profile worm wheel is obtained by solving according to the meshing relation between the normal straight tooth profile worm and the normal straight tooth profile worm wheel2Sum tooth surface normal vector equation
Figure BDA0003042494740000087
Finally, solving and obtaining a tooth surface equation r of the worm gear shaver according to the conjugate relation between the tooth surface of the worm gear shaver and the tooth surface of the normal straight tooth profile type worm gear3(ii) a Namely, the design method of the worm gear shaver can meet the design requirement of the worm gear shaver.
Example 2
However, when the flank modification is not considered, when the flank of the worm shaver is engaged with the flank of the worm gear, the engagement is not smooth due to the small contact area, and the life of the worm gear is reduced. Therefore, in order to improve the worm-wheel meshing performance, it is necessary to take into consideration modification of the worm-wheel tooth surface. The modification of the tooth surface of the worm gear is completed by modification of a worm gear shaver.
When the worm gear shaver is modified, the original design parameters of the normal straight tooth profile worm need to be considered, such asThe following: a is0Modifying the center distance for variable parameters; i.e. i0Modifying the transmission ratio for variable parameters; z10The number of the head of the variable parameter modification worm is; z20The tooth number of the worm gear is modified according to variable parameters; m istIs the end face modulus; da1The diameter of the root circle of the throat part of the worm gear shaver before the modification; df1The diameter of the root circle of the throat part of the worm gear shaver before the modification; c is the tooth top clearance; h isa1The axial chordal tooth height of the worm gear shaver before modification; sn1The axial chord tooth thickness of the worm gear shaver before the modification.
Specifically, the worm gear razor modification method of the embodiment includes the following steps:
1) the worm gear razor design method described in example 1 was used to obtain the tooth surface equation r for a worm gear razor3；
2) And (5) modifying the shape of the worm gear shaver.
To reduce the sensitivity to manufacturing errors, the razor has no inlet trim, with slight differences in the trim curve at different locations. Due to the tooth surface equation r of worm gear razors3With theoretical error, the embodiment is based on the end modulus m of the worm wheeltCreatively modifies the profile curve delta of the worm gear razorfoSetting as a piecewise function:
Figure BDA0003042494740000091
wherein m istRepresenting the end face modulus of a worm gear razor;
the tooth height direction of the worm gear shaver is also modified. The geometry of the worm gear razor is calculated as follows.
The diameter d of the tip circle of the throat part of the modified worm gear shaver of the embodimenta10Comprises the following steps:
Figure BDA0003042494740000092
wherein d isa1Representing the diameter of the tip circle of the throat of the worm gear shaver before modification; c is the tooth top clearance;
the addendum arc radius Ra of the modified worm gear shaver of the embodiment10Comprises the following steps:
Figure BDA0003042494740000093
wherein, a0Representing the variable parameter modification center distance;
the diameter d of the root circle of the throat part of the worm gear shaver after modification of the embodimentf10Comprises the following steps:
Figure BDA0003042494740000101
wherein d isf1Representing the throat root circle diameter of the worm gear razor before modification;
the root arc radius R of the worm gear shaver after modification of the embodimentf10Comprises the following steps:
Figure BDA0003042494740000102
the length L of the thread of the worm gear shaver after modification of the embodimentWOComprises the following steps:
Figure BDA0003042494740000103
wherein L isWShowing the thread length of the worm gear shaver before modification;
the maximum excircle diameter d of the worm gear shaver after modification of the embodimenta10maxComprises the following steps:
Figure BDA0003042494740000104
the left side back inclination angle beta of the worm gear shaver after modification of the embodiment1Comprises the following steps:
Figure BDA0003042494740000105
wherein, γminRepresents the minimum value of the helix angle; i.e. i0Modifying the transmission ratio for variable parameters; arctan represents the arctangent function;
tip diameter d of throat part of worm gear razora10And the maximum outer diameter d of the worm gear shavera10maxAlso a piecewise function, so that the left side back rake angle beta of the worm gear razor1Is a piecewise function.
Right side back inclination angle beta of modified worm gear shaver2Comprises the following steps:
Figure BDA0003042494740000106
in the formula, gammamaxRepresents the maximum value of the helix angle;
diameter d of throat tip circle of worm gear razorf10And the maximum outer diameter d of the worm gear shavera10maxAre piecewise functions, so that the right flank angle beta of the worm gear shaver2Is a piecewise function.
Axial chordal tooth height ha of modified worm gear shaver10Comprises the following steps:
ha10＝ha1+0.5(da10-da1)
wherein h isa1The axial chordal tooth height of the worm gear shaver before modification is shown;
diameter d of throat tip circle of worm gear razora10Is a piecewise function, thus the razor axial chordal tooth height ha10Is a piecewise function.
Axial chord tooth thickness Sx of modified worm gear shaver10Comprises the following steps:
Figure BDA0003042494740000111
wherein, Sx1Axial chordal tooth thickness of the worm gear razor before trimming; gamma raymIndicating the helix angle.
The embodiment also provides a worm gear shaver which is obtained by modification by the worm gear shaver modification method of the embodiment.
The worm gear shaver shape modification method of the embodiment creatively modifies the shape modification curve delta of the modified worm gear shaverfoDiameter of throat tip da10Radius of addendum arc Ra10Diameter d of root circle of throatf10Root arc radius Rf10Length L of threadWOMaximum outer diameter da10maxLeft side back tilt angle beta1Right side back tilt angle beta2And axial chordal tooth thickness Sx10Are all set as piecewise functions segmented by the end face modulus of the worm gear shaver, and can avoid the worm gear shaver tooth surface equation r3The theoretical error of (2) has an influence on the precision of the modified worm gear shaver, thereby improving the precision of the worm gear machined by the modified worm gear shaver.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.

Claims (8)

1. A method of designing a worm gear razor, comprising: the method comprises the following steps:
1) solving the tooth surface of the normal straight tooth profile worm according to the equations of the spiral surface end section and the axial section of the normal straight tooth profile worm to obtain the tooth surface equation r of the normal straight tooth profile worm1Sum tooth surface normal vector equation
Figure FDA0003042494730000011
2) According to the meshing relation between the normal straight tooth profile worm and the normal straight tooth profile worm wheel, the tooth surface equation r of the normal straight tooth profile worm is used1And the normal vector equation
Figure FDA0003042494730000012
Solving the tooth surface equation r of normal straight tooth profile type worm wheel2Sum tooth surface normal vector equation
Figure FDA0003042494730000013
3) According to the conjugate relation between the tooth surface of the worm gear shaver and the tooth surface of the normal straight tooth profile type worm gear, the tooth surface equation r of the normal straight tooth profile type worm gear is adopted2Sum tooth surface normal vector equation
Figure FDA0003042494730000014
Solving the tooth surface equation r of a worm gear razor3。
2. The worm-gear razor design method of claim 1, wherein: in the step 1), the section equation of the spiral surface end of the normal straight tooth profile worm is as follows:
Figure FDA0003042494730000015
the axial section equation of the spiral surface of the normal straight tooth profile worm is as follows:
Figure FDA0003042494730000016
wherein p is the thread pitch of the normal straight tooth profile worm; alpha is the tooth pressure angle of the normal straight tooth profile worm; r isb1The diameter of a base circle of a normal straight tooth profile worm; theta is the angle value of the end section line rotating from the initial position by taking the z axis as the center; r is the worm diameter.
3. The worm-gear razor design method of claim 2, wherein: the normal straight tooth profile equation is:
Figure FDA0003042494730000017
from this, the tooth surface (right-hand) equation r of the normal straight tooth profile worm can be obtained1Comprises the following steps:
Figure FDA0003042494730000018
tooth surface (right-handed) normal vector equation of normal straight tooth profile worm
Figure FDA0003042494730000019
Comprises the following steps:
Figure FDA00030424947300000110
wherein u is an independent variable, and
Figure FDA00030424947300000111
wherein the normal length Pa, r at any point P on the normal straight tooth profilebIs the base circle radius.
4. The worm-gear razor design method of claim 3, wherein: in the step 2), a tooth surface equation r of the normal straight tooth profile type worm wheel2Comprises the following steps:
Figure FDA0003042494730000021
normal tooth flank normal vector equation of normal straight tooth profile worm gear
Figure FDA0003042494730000022
Comprises the following steps:
Figure FDA0003042494730000023
wherein the content of the first and second substances,
Figure FDA0003042494730000024
the angle rotated by the normal straight tooth profile worm;
Figure FDA0003042494730000025
the angle of the normal straight tooth profile type worm wheel is rotated; and is
Figure FDA0003042494730000026
i12The transmission ratio between the normal straight tooth profile worm and the normal straight tooth profile worm wheel.
5. The worm-gear razor design method of claim 4, wherein: in the step 3), the relative motion velocity vector v between the normal straight tooth profile type worm wheel and the worm gear shaver is obtained by the conjugate relation between the tooth surface of the worm gear shaver and the tooth surface of the normal straight tooth profile type worm wheel:
Figure FDA0003042494730000027
from the orthogonal relationship between the tooth surfaces of the worm shaver and the normal straight tooth profile worm wheel and the relative motion velocity vector v, it can be found that:
Figure FDA0003042494730000028
so as to solve the tooth surface equation r of the worm gear shaver3Comprises the following steps:
Figure FDA0003042494730000029
6. a worm gear razor characterized by: the tooth surface equation is designed by the worm gear razor design method according to any one of claims 1 to 5.
7. A worm gear shaver reshaping method is characterized in that: the method comprises the following steps:
1) the tooth surface equation r of the worm gear shaver is obtained by the design method of the worm gear shaver according to any one of claims 1 to 53；
2) Modifying the shape of the worm gear shaver;
due to the tooth surface equation r of worm gear razors3With theoretical error, the profile curve Δ of the worm shaver is thus modifiedfoSetting as a piecewise function:
Figure FDA0003042494730000031
wherein m istRepresenting the end face modulus of a worm gear razor;
diameter d of top circle of throat part of modified worm gear shavera10Comprises the following steps:
Figure FDA0003042494730000032
wherein d isa1Representing the diameter of the tip circle of the throat of the worm gear shaver before modification; c is the tooth top clearance;
addendum arc radius Ra of modified worm gear shaver10Comprises the following steps:
Figure FDA0003042494730000033
wherein, a0Representing the variable parameter modification center distance;
root diameter d of throat part of modified worm gear shaverf10Comprises the following steps:
Figure FDA0003042494730000034
wherein d isf1Representing the throat root circle diameter of the worm gear razor before modification;
root arc radius R of modified worm gear shaverf10Comprises the following steps:
Figure FDA0003042494730000035
length L of screw thread of worm gear shaver after modificationWOComprises the following steps:
Figure FDA0003042494730000036
wherein L isWShowing the thread length of the worm gear shaver before modification;
maximum excircle diameter d of modified worm gear shavera10maxComprises the following steps:
Figure FDA0003042494730000041
left side back inclination angle beta of modified worm gear shaver1Comprises the following steps:
Figure FDA0003042494730000042
wherein, γminRepresents the minimum value of the helix angle; i.e. i0Modifying the transmission ratio for variable parameters; arctan represents the arctangent function; right side back inclination angle beta of modified worm gear shaver2Comprises the following steps:
Figure FDA0003042494730000043
in the formula, gammamaxRepresents the maximum value of the helix angle;
axial chordal tooth height ha of modified worm gear shaver10Comprises the following steps:
ha10＝ha1+0.5(da10-da1)
wherein, ha1The axial chordal tooth height of the worm gear shaver before modification is shown;
axial chord tooth thickness Sx of modified worm gear shaver10Comprises the following steps:
Figure FDA0003042494730000044
wherein, Sx1The axial chordal tooth thickness of the worm gear razor before modification is shown; gamma raymIndicating the helix angle.
8. A worm gear razor characterized by: the worm gear shaver is obtained by modification according to the modification method of claim 7.
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