CN115859526A - Parametric modeling method for shape-modifying and profile-modifying helical gear - Google Patents
Parametric modeling method for shape-modifying and profile-modifying helical gear Download PDFInfo
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Abstract
A modified profile shifted helical gear parametric modeling method is disclosed, wherein a profile shifted gear involute is obtained by rotating a standard gear involute by sigma radian around the center of a base circle, a homogeneous coordinate transformation method and a scanning and cutting operation of three-dimensional CAD software are adopted, the modeling of the tooth surface of the modified profile shifted helical gear utilizes the scanning and cutting operation of the three-dimensional CAD software, a scanning path is a tooth direction modification curve, and a scanning contour is a tooth profile modification curve, and the method comprises the following steps: calculating a tooth profile modification curve and a curved surface equation; (2) establishing a two-dimensional sketch of the tooth profile of the modified tooth profile gear; (3) calculating a tooth direction modification curve and a curved surface equation; (4) And performing scanning and cutting operation along the tooth direction modification curve and creating a three-dimensional geometric model of the modified profile shifted helical gear. The method solves the problem of establishing the profile-modified helical gear models with different modification types, has simple and convenient modeling process, reduces the modeling difficulty and improves the modeling accuracy.
Description
Technical Field
The invention relates to a method for modeling a shape-modifying and profile-modifying helical gear, and belongs to the technical field of gear design.
Background
The modified gear has the advantages of avoiding gear undercut, matching center distance, improving gear tooth strength and improving wear resistance and gluing resistance, the tooth surface modification has the advantages of improving transmission precision, reducing vibration noise and increasing gear strength, and the modified helical gear is widely applied in actual production.
Common three-dimensional CAD software for parametric modeling are Unigraphics (UG), pro/Engineer, CATIA, solidWorks, etc. In the existing three-dimensional modeling software, a basic standard gear generation module is lacked or only a standard gear can be generated, and a shape modification deflection helical gear parameterization design module is lacked in the introduction of a related modeling method. Therefore, most of the existing three-dimensional software has very limited capability in processing modeling of the modified helical gear, and subsequent gear analysis and gear machining and manufacturing work are seriously influenced.
Chinese patent document CN103942397A proposes a power function-based digital modeling method for a modified gear, CN110889194A proposes a modeling method for an NX involute modified helical cylindrical gear, CN114645930A proposes a non-vertical crossed-axis gear and a modeling method thereof, and CN114818378A proposes a modeling method for a gear generating an involute tooth profile based on a plane regular curve. However, the method does not solve the problem of modeling the shape-modified and profile-shifted helical gear.
Disclosure of Invention
Based on the defects of the prior art in modeling of the shape-modifying and profile-shifting helical gear, the invention provides the parameterized modeling method of the shape-modifying and profile-shifting helical gear, which has simple modeling process and high modeling accuracy, and establishes the three-dimensional model of the shape-modifying and profile-shifting helical gear according to the gear design parameters and the shape-modifying parameters.
The invention discloses a shape modification and displacement bevel gear parametric modeling method, which comprises the following steps:
the involute of the modified gear is obtained by rotating a standard gear involute by sigma radian around the center of a base circle by a homogeneous coordinate transformation method and scanning excision operation of three-dimensional CAD software, the modeling of the tooth surface of the modified helical gear utilizes the scanning excision operation of the three-dimensional CAD software, a scanning path is a tooth direction modification curve, and a scanning contour is a tooth profile modification curve, and the method comprises the following steps:
(1) Calculating a modification curve and a curved surface equation of the tooth profile of the modified helical gear;
(2) Establishing a two-dimensional sketch of the tooth profile modification modified gear;
(3) Calculating a tooth direction modification curve and a curved surface equation;
(4) And performing scanning and cutting operation along the tooth direction modification curve and creating a three-dimensional geometric model of the modified profile shifted helical gear.
The specific process of calculating the modified curve and the curved surface equation of the tooth profile of the modified helical gear in the step (1) is as follows:
(1) the standard gear tooth profile modification curve equation derivation process is as follows:
the center of the base circle is at the origin, and the starting point is in the involute parameter equation of the x axis:
in the formula r b The radius of a base circle is adopted, a parameter t represents the rolling radian of an involute generating line on the base circle, and the length of the involute is determined by the value of the parameter t; the coordinates of the starting point are (r) b 0), taking a plus value as an upper formula of an involute equation at the upper side of an x axis, and taking a minus value as an upper formula of an involute equation at the lower side of the x axis;
and (3) anticlockwise rotating the original involute around an original point (the center of a base circle) by the sigma radian to obtain a modified involute parameter equation:
involute parameter equation after deflection:
(2) the derivation process of the modified tooth profile curve equation of the modified helical gear is as follows:
the modification curve equation of the tooth profile of the undelivered bevel gear is as follows:
and (3) anticlockwise rotating the original involute around an original point (the center of a base circle) by the sigma radian to obtain a modified tooth profile modification curve parameter equation after deflection:
modifying curve parameter equation of modified tooth profile:
the parameter equation of the tooth profile modification curve H (r) is as follows:
wherein l 1 For root shaping length, h 1 Amount of root trimming, /) 2 Is the drum length of the tooth profile, h 2 Is the drum-shaped amount of the tooth profile, /) 3 For addendum modification length, h 3 The addendum modification amount, r is the gear radius, r min Is the minimum gear radius in the case of modification, r b Is the base circle radius.
The expression for r is as follows:
the parameter equation of the tooth profile modification curve H (t) is as follows:
the equation expression of counterclockwise rotation sigma radian of the original involute around the origin (the center of a base circle) is as follows:
wherein x 1 Is the normal deflection coefficient, beta is the helix angle, alpha t Is the end face pressure angle, Z 1 And theta is the reference circle spread angle of the undetailed gear.
(3) The tooth profile modification curved surface equation derivation process is as follows:
setting a fixed coordinate system S g And space spiral motion coordinate system S o (ii) a Fixed coordinate system S g Fixed on the center of the end face of the gear and comprises an X g Axis, Y g Axis, Z g A shaft; space spiral motion coordinate system S o Relative to a fixed coordinate system S g Make spiral upward movement, at initial time S g And S o Overlapping;
obtaining a fixed coordinate system S according to the homogeneous coordinate transformation principle g And space spiral motion coordinate system S o The transformation matrix between is:
coordinate system S g And S o The conversion relationship between them is as follows:
space spiral motion coordinate system S o To a fixed coordinate system S g The transformation of (a) is as follows:
fixed coordinate system S g Space-oriented spiral motion coordinate system S o The transformation of (a) is as follows:
spiral motion coordinate system S o The lower modified tooth profile modification curve equation is as follows:
fixed coordinate system S g The equation of the tooth surface of the lower modified profile shifted helical gear is as follows:
wherein:
is spatially rotated and curved>
To add an arc of rotation, beta b Is a base circle helix angle.
When there is no axial modification, the coordinate system S is fixed g The modified tooth surface equation of the lower modified tooth profile is as follows:
the specific process of establishing the tooth profile two-dimensional sketch of the tooth profile modified gear in the step (2) is as follows:
establishing a basic coordinate system: the default Cartesian coordinate system is a first basic coordinate system, a left view is taken as a drawing plane, and a root circle, a base circle, a reference circle and an addendum circle are established;
creating a modification curve on the tooth socket: establishing a modification curve on the tooth socket according to an x-axis upper side tooth profile modification curve equation;
creating a tooth socket lower trimming curve: establishing a tooth space lower modification curve according to an x-axis lower tooth profile modification curve equation;
creating a gullet profile: and connecting the tooth space upper modification curve and the extension line thereof with the tooth space lower modification curve and the extension line thereof, and drawing a tooth root circle and an tooth top circle to obtain a final tooth space two-dimensional profile.
The concrete process of deducing the tooth direction modification curve and the curved surface equation of the modified bevel gear in the step (3) is as follows;
fixed coordinate system S g The tooth direction modification curved surface equation of the lower profile shifted helical gear is as follows:
the relation function G (z) of the modification quantity and the motion position is as follows:
the expression for z is as follows:
additional arc of rotation
The relationship with the modification amount is as follows:
wherein: l 4 Thinning the tooth tips by length, g 1 For thinning of the tooth tips, /) 5 Is the length of the tooth drum, g 2 Is the crown quantity in the tooth direction, /) 6 Thinning the tooth tip by length, g 3 For thinning of the tooth tips, /) 7 Half the length of the tooth drum, G 2 Is the right flank crown magnitude, z is the tooth width variation, b is the tooth width, r b Is the base radius, beta b Is a base circle helix angle.
The step (4) of performing scanning and cutting operation along the tooth direction modification curve and creating the topological modification profile shifted helical gear three-dimensional geometric model comprises the following steps:
on the basis of the tooth socket profile, scanning along a tooth direction modification curve to obtain a tooth socket three-dimensional body;
creating root fillet: creating a left profile fillet and a right profile fillet with a fillet radius of 0.38 m n ；
And obtaining a three-dimensional model of the whole shape-modifying and profile-shifting helical gear through the circumferential array tooth grooves and the tooth root fillets.
According to the invention, the three-dimensional model of the modified profile shifted helical gear is established according to the gear design parameters and the modification parameters, and the profile modification curve equation and the tooth direction modification curve equation of the modified profile helical gear are derived by adopting a homogeneous coordinate transformation method and the scanning excision operation of three-dimensional CAD software, so that the problem of establishing modified helical gear models of different modification types is solved, the modeling process is simple and convenient, the modeling difficulty is reduced, and the modeling accuracy is improved.
Drawings
FIG. 1 is a flow chart of the modeling method of the shape-modifying and profile-modifying helical gear of the invention.
FIG. 2 is a schematic diagram of the derivation of the involute equation for a tooth profile.
FIG. 3 is a schematic view of a profile modification curve.
Fig. 4 is a schematic view of a tooth relief curve.
Figure 5 is a schematic view of the end profile screw motion.
FIG. 6 is a schematic view of a shaping profile shifted helical gear modeling process; wherein: the method comprises the following steps of (a) forming a two-dimensional sketch on the upper side of an x axis of a gear end face tooth profile, (b) forming an integral two-dimensional sketch of the gear end face tooth profile, (c) forming an established three-dimensional tooth space model, and (d) forming modified helical gear models of different modification types.
FIG. 7 is a schematic diagram of a three-dimensional model of a single tooth of a modified profile shifted helical gear of different modification types; wherein: (a) is an unmodified profile, (b) is a modified profile, (c) is a modified axial profile, and (d) is a modified topological profile.
Detailed Description
The invention relates to a modeling method of a modified profile shifted helical gear, which obtains a profile shifted gear involute after a standard gear involute rotates around the center of a base circle by a certain radian, adopts a homogeneous coordinate transformation method and the scanning and cutting operation of three-dimensional CAD software, and utilizes the scanning and cutting operation of the three-dimensional CAD software to model the tooth surface of the modified profile shifted helical gear, wherein the scanning path is a tooth direction modification curve, and the scanning contour is a tooth profile modification curve.
As shown in fig. 1, the method of the present invention specifically includes the following steps: the method comprises the steps of (1) calculating a tooth profile modification curve and a curved surface equation, (2) establishing a tooth profile two-dimensional sketch of the tooth profile modification modified profile shifted gear, (3) calculating a tooth direction modification curve and a curved surface equation, and (4) performing scanning excision operation along the tooth direction modification curve and establishing a three-dimensional geometric model of the modified profile shifted helical gear.
The method comprises the following steps: calculating tooth profile modification curve and curved surface equation
(1) The standard gear tooth profile modification curve equation derivation process is as follows:
as shown in fig. 2, the base circle center is at the origin, and the starting point is in the involute parameter equation of the x axis:
in the formula r b The parameter t represents the rolling radian of an involute on a base circle, and the value of the parameter t determines the length of the involute. The coordinates of the starting point are (r) b 0), the formula above the involute equation on the upper side of the x axis is represented by "+", and the formula above the involute equation on the lower side of the x axis is represented by "-".
And (3) anticlockwise rotating the original involute around the original point by the sigma radian to obtain a modified involute parameter equation:
involute parameter equation after deflection:
(2) The derivation process of the modified tooth profile curve equation of the modified helical gear is as follows:
the modification curve equation of the tooth profile of the undelivered bevel gear is as follows:
and (3) anticlockwise rotating the original involute around the original point by the sigma radian to obtain a modified tooth profile curve parameter equation after modification:
the modified curve parameter equation of the tooth profile after modification:
the tooth profile modification curve is shown in fig. 3, and the parameter equation of the tooth profile modification curve H (r) is as follows:
wherein l 1 For root shaping length, h 1 Amount of root trimming, /) 2 Is the drum length of the tooth profile, h 2 Is the drum-shaped amount of the tooth profile, /) 3 For addendum modification length, h 3 The addendum modification amount, r is the gear radius, r min Is the minimum gear radius in the case of modification, r b Is the base circle radius.
The expression for r is as follows:
the parameter equation of the tooth profile modification curve H (t) is as follows:
the equation expression for counterclockwise rotation of the original involute about the origin by sigma radians is as follows:
wherein x 1 Is the normal deflection coefficient, beta is the helix angle, alpha t Is the end face pressure angle, Z 1 Theta is the tooth number, theta is the non-modified gear pitch angle.
(3) The tooth profile modification curved surface equation derivation process is as follows:
setting a fixed coordinate system S g And space spiral motion coordinate system S o Fixed coordinate system S g Fixed on the center of the end face of the gear and comprises an X g Axis, Y g Axis, Z g Axial, space spiral motion coordinate system S o Relative to a fixed coordinate system S g Make spiral upward movement, at initial time S g And S o Overlapping;
obtaining a fixed coordinate system S according to the homogeneous coordinate transformation principle g And space spiral motion coordinate system S o The transformation matrix between is:
coordinate system S g And S o The conversion relationship between becomes as follows:
space spiral motion coordinate system S o To a fixed coordinate system S g The transformation of (a) is as follows:
fixed coordinate system S g Space-oriented spiral motion coordinate system S o The transformation of (a) is as follows:
spiral motion coordinate system S o The lower tooth profile equation is as follows:
fixed coordinate system S g The equation of the tooth profile modification curved surface of the lower topological modification modified helical gear is as follows:
When there is no axial modification, the coordinate system S is fixed g The equation of the lower modified tooth profile modification curved surface is as follows:
(1) addendum only modification profile curve and surface equation:
the parameter equation of the tooth profile modification curve H (t) is as follows:
the tooth tip relief edge only surface equation is as follows:
the addendum-only trim curve equation is as follows:
(2) tooth profile only drum profile modification curves and surface equations:
the parameter equation of the tooth profile modification curve H (t) is as follows:
the tooth profile-only drum-shaped modification surface equation is as follows:
the tooth profile-only drum-shape modification curve equation is as follows:
(3) slope-only modification curves and surface equations:
the parameter equation of the tooth profile modification curve H (t) is as follows:
the slope-only modified surface equation is as follows:
the slope-only modification curve equation is as follows:
wherein r is the gear radius, r min The smallest gear radius with a modification.
Step two: and (3) establishing a two-dimensional sketch of the tooth profile of the modified profile shifted gear.
Establishing a basic coordinate system: the default Cartesian coordinate system is a first basic coordinate system, a left view is taken as a drawing plane, and a root circle, a base circle, a reference circle and an addendum circle are established;
creating a modification curve on the tooth socket: establishing a modification curve on the tooth socket according to an x-axis upper side tooth profile modification curve equation;
creating a tooth space lower modification curve: establishing a tooth space lower modification curve according to an x-axis lower tooth profile modification curve equation;
creating a gullet profile: connecting the tooth space upper modification curve and an extension line thereof with the tooth space lower modification curve and an extension line thereof, and drawing a tooth root circle and an tooth top circle to obtain a final tooth space two-dimensional profile;
step three: and deducing a tooth direction modification curve and a curved surface equation of the modified helical gear.
Fixed coordinate system S g The tooth direction modification curved surface equation of the lower profile shifted helical gear is as follows:
the relation function G (z) of the modification quantity and the motion position is as follows:
the tip spiral motion is shown in fig. 4, the tooth-wise modification curve is shown in fig. 5, and the expression for z is as follows:
additional arc of rotation
The relationship with the modification amount is as follows:
wherein l 4 Thinning the tooth tips by length, g 1 For thinning of the tooth tips, /) 5 Is the length of the tooth drum, g 2 Is the crown quantity in the tooth direction, /) 6 Thinning the tooth tips by length, g 3 For thinning of the tooth tips, /) 7 Half the length of the tooth drum, G 2 Is the right flank crown magnitude, z is the tooth width variation, b is the tooth width, r b Is the base radius, beta b Is a base circle helix angle.
(1) Axial modification equation for thinning only tooth end
Additional arc of rotation
The relationship with the modification amount is as follows:
the tip-only relieved flank equation is as follows:
the equation of the axial modification curve of only the tooth end thinning is as follows:
wherein t is f Is the rolling arc on the reference circle.
(2) Axial modification curve and surface equation for only helix angle modification
Additional arc of rotation
The relationship with the modification amount is as follows:
the equation for the axial modification camber of the helix angle-only modification is as follows:
the helix angle trimming tooth direction trimming curve equation only is as follows:
(3) axial crowned tooth profile curve and surface equation only
Additional arc of rotation
The relationship with the modification amount is as follows:
the tooth direction only crowned tooth direction modification surface equation is as follows:
the tooth direction only crowned tooth direction modification curve equation is as follows:
(4) tooth surface modification equation with tooth profile drum shape and tooth end thinning
Tooth profile modification curve H (y) 0 ) The parametric equation is as follows:
additional arc of rotation
The relationship with the modification amount is as follows:
the tooth surface modification curved surface equation of the existing tooth profile drum shape and the tooth end modification is as follows:
the tooth surface modification curve equation of both the crowning shape and the thinning tooth end of the tooth profile is as follows:
step four: scanning and cutting operation is carried out along a tooth direction modification curve, and a topological modification profile shifted helical gear three-dimensional geometric model is created
On the basis of the tooth space profile, scanning is carried out along the tooth direction modification curve to obtain a tooth space three-dimensional body, a left tooth profile fillet and a right tooth profile fillet are created, and the fillet radius value is 0.38 m n And passing through the circumferential array tooth socket and the tooth root fillet to obtain a three-dimensional model of the whole profile-modified helical gear. As shown in fig. 6, itThe method comprises the following steps of (a) obtaining a gear end face tooth profile x-axis upper side two-dimensional sketch, (b) obtaining a gear end face tooth profile whole two-dimensional sketch, (c) obtaining an established three-dimensional tooth space model, and (d) obtaining different modification type modified helical gear models.
The following is a concrete embodiment of the modeling method for the shape-modifying deflection helical gear according to the invention:
the modulus is 4.25mm, the number of teeth is 21, the normal pressure angle is 19 degrees, the helix angle is 17.81 degrees, the tooth width is 46mm, the normal deflection coefficient is 0.15, the tooth crest height is 6.138mm, and the tooth root height is 6.375 mm. The tooth profile addendum modification amount is 25 microns, the tooth profile drum amount is 6 microns, and the tooth direction drum amount is 10 microns.
Calculating a tooth profile modification curve and a tooth direction modification curve equation according to the parameters, and importing the tooth profile modification curve and the tooth direction modification curve equation into Solidworks three-dimensional CAD software to create a workpiece swept volume model; a gear model is created from the gear parameters.
The obtained single tooth model of the profile shifted helical gear with different modification types is shown in fig. 7, wherein (a) is unmodified shape, (b) is tooth profile modified shape, (c) is axial modified shape, and (d) is topological modified shape.
Claims (5)
1. A shape modification and deflection helical gear parametric modeling method is characterized by comprising the following steps: the involute of the modified gear is obtained by rotating a mouth radian around the center of a base circle by a standard involute of the gear, a homogeneous coordinate transformation method and a scanning excision operation of three-dimensional cAD software are adopted, the modeling of the tooth surface of the modified helical gear utilizes the scanning excision operation of the three-dimensional CAD software, a scanning path is a tooth direction modification curve, and a scanning contour is a tooth profile modification curve, and the method comprises the following steps:
(1) Calculating a modification curve and a curved surface equation of the tooth profile of the modified helical gear;
(2) Establishing a two-dimensional sketch of the tooth profile modification modified gear;
(3) Calculating a tooth direction modification curve and a curved surface equation;
(4) And performing scanning and cutting operation along the tooth direction modification curve and creating a three-dimensional geometric model of the modified profile shifted helical gear.
2. The parameterized modeling method for the modified profile shifted helical gear according to claim 1, wherein the specific process for calculating the modified profile curve and the curved surface equation of the profile of the modified helical gear in the step (1) is as follows:
(1) The standard gear tooth profile modification curve equation derivation process is as follows:
the center of the base circle is at the origin, and the starting point is at the involute parameter equation of the x axis:
in the formula r b The radius of a base circle is adopted, a parameter t represents the rolling radian of an involute generating line on the base circle, and the length of the involute is determined by the value of the parameter t; the coordinates of the starting point are (r) b 0), taking a plus sign as an upper formula of an involute equation at the upper side of an x axis, and taking a minus sign as an upper formula of an involute equation at the lower side of the x axis;
and (3) rotating the original involute counterclockwise around the original point by the sigma radian to obtain a modified involute parameter equation:
involute parameter equation after deflection:
(2) The derivation process of the modified tooth profile curve equation of the modified helical gear is as follows:
the modification curve equation of the tooth profile of the undelivered bevel gear is as follows:
rotating the original involute around the original point by a radian in a counterclockwise way to obtain a modified tooth profile curve parameter equation after modification:
the modified curve parameter equation of the tooth profile after modification:
the equation for σ is expressed as follows:
wherein x 1 Is the normal deflection coefficient, beta is the helix angle, alpha t Is the end face pressure angle, Z 1 The number of teeth is, theta is the reference circle spread angle of the undetailed gear;
the parameter equation of the tooth profile modification curve H (r) is as follows:
wherein: l1 is the length of the root relief, h 1 Amount of root trimming, /) 2 Is the drum length of the tooth profile, h 2 Is the drum-shaped amount of the tooth profile l 3 For addendum modification length, h 3 The addendum modification amount, r is the gear radius, r min Is the minimum gear radius in the case of modification, r b Is the base circle radius;
the expression for r is as follows:
the parameter equation of the tooth profile modification curve H (t) is as follows:
(3) The tooth profile modification curved surface equation derivation process is as follows:
setting a fixed coordinate system S g And space spiral motion coordinate system S o Fixed coordinate system S g Fixed on the center of the end face of the gear and comprises an X g Axis, Y g Axis, Z g Axial, space spiral motion coordinate system S o Relative to a fixed coordinate system S g Make spiral upward movement at initial time S g And S o Overlapping;
obtaining a fixed coordinate system S according to the homogeneous coordinate transformation principle g And space spiral motion coordinate system S o The transformation matrix between is:
wherein:
is spatially rotated and curved>
To add an arc of rotation, beta b Is a base circle helical angle;
coordinate system S g And S o The conversion relationship between them is as follows:
space spiral motion coordinate system S o To a fixed coordinate system S g The transformation of (a) is as follows:
fixed coordinate system S g The transformation to the spatial spiral motion coordinate system So is as follows:
spiral motion coordinate system S o The lower modified tooth profile modification curve equation is as follows:
fixed coordinate system S g The curved surface equation of the lower modification profile shifted helical gear is as follows:
when there is no axial modification, the coordinate system S is fixed g The equation of the modified curved surface of the lower modified tooth profile is as follows:
3. the parameterized modeling method for the modified profile shifted helical gear according to claim 1, wherein the specific process of establishing the two-dimensional draft of the tooth profile of the modified profile shifted gear in the step (2) is as follows:
establishing a basic coordinate system: the default Cartesian coordinate system is a first basic coordinate system, the left view is taken as a drawing plane, and a root circle, a base circle, a reference circle and an addendum circle are established;
creating a correction curve on the tooth socket: establishing a modification curve on the tooth socket according to an x-axis upper side tooth profile modification curve equation;
creating a tooth socket lower trimming curve: establishing a tooth space lower modification curve according to an x-axis lower tooth profile modification curve equation;
creating a tooth slot profile: and connecting the tooth space upper modification curve and the extension line thereof with the tooth space lower modification curve and the extension line thereof, and drawing a tooth root circle and an tooth top circle to obtain a final tooth space two-dimensional profile.
4. The parameterized modeling method for the modified and modified helical gear according to claim 1, wherein the specific process for deriving the tooth direction modification curve and the curved surface equation of the modified and modified helical gear in the step (3) is;
fixed coordinate system S g The tooth direction modification curved surface equation of the lower profile shifted helical gear is as follows:
the relation function G (z) of the modification quantity and the motion position is as follows:
the expression of Z is as follows:
additional arc of rotation
The relationship with the modification amount is as follows: />
Wherein: l 4 Thinning the tooth tips by length, g 1 For thinning of the tooth tips, /) 5 Is the axial crown length, g 2 Is the crown quantity in the tooth direction, /) 6 Thinning the tooth tip by length, g 3 For thinning of the tooth tips, /) 7 Half the length of the tooth drum, G 2 Is the right flank crown magnitude, z is the tooth width variation, b is the tooth width, r b Is a base radius of circle，β b Is a base circle helix angle.
5. The parameterized modeling method for the shape-modified and shifted helical gear according to claim 1, wherein the step (4) of performing the scanning and cutting operation along the tooth-wise shape-modified curve and creating the topological shape-modified and shifted helical gear three-dimensional geometric model comprises the following steps:
on the basis of the two-dimensional profile of the tooth socket, scanning along a tooth direction modification curve to obtain a three-dimensional body of the tooth socket;
creating root fillet: creating a left profile fillet and a right profile fillet with a fillet radius of 0.38 m n ；
And obtaining a three-dimensional model of the whole profile modification helical gear through the circumferential array tooth grooves and the tooth root fillets.
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