A parametric modeling method for modified helical gears

Abstract

A parametric modeling method for modified helical gears, wherein the modified gear involute is obtained by rotating the standard gear involute around the center of a base circle by σ radians, and the homogeneous coordinate transformation method and the scanning and cutting operation of the three-dimensional CAD software are adopted. The modeling of the modified helical gear tooth surface utilizes the scanning and cutting operation of the three-dimensional CAD software, the scanning path is the tooth modification curve, and the scanning profile is the tooth profile modification curve, and the method includes the following steps: (1) calculating the tooth profile modification curve and the surface equation; (2) establishing a two-dimensional sketch of the tooth profile of the modified helical gear; (3) calculating the tooth modification curve and the surface equation; (4) performing the scanning and cutting operation along the tooth modification curve and creating a three-dimensional geometric model of the modified helical gear. The invention solves the problem of establishing models of modified helical gears of different modification types, and the modeling process is simple, the modeling difficulty is reduced, and the modeling accuracy is improved.

Description

Technical Field

[0001] The invention relates to a method for modeling a modified helical gear, belonging to the technical field of gear design. Background Art

[0002] The modified helical gears have the advantages of avoiding gear root cutting, matching center distance, improving gear tooth strength and increasing wear resistance and adhesion resistance. The tooth surface modification has the advantages of improving transmission accuracy, reducing vibration and noise and increasing gear strength. Modified modified helical gears are widely used in actual production.

[0003] Commonly used 3D CAD software for parametric modeling include Unigraphies (UG), Pro / Engineer, CATIA, SolidWorks, etc. Among the above existing 3D modeling software, there is a lack of basic standard gear generation modules or only standard gears can be generated, and the parametric design module of modified helical gears lacks the introduction of relevant modeling methods. Therefore, most of the existing 3D software has very limited capabilities in processing modified helical gear modeling, which seriously affects the subsequent gear analysis and gear processing and manufacturing work.

[0004] Chinese patent document CN103942397A proposed a digital modeling method for modified gears based on power functions, CN110889194A proposed an NX involute modified helical cylindrical gear modeling method, CN114645930A proposed a non-vertical staggered axis gear and its modeling method, and CN114818378A proposed a gear modeling method based on plane regular curves to generate involute tooth profiles. However, none of the above methods solves the problem of modeling modified helical gears. Summary of the invention

[0005] Based on the deficiencies in the prior art in modeling modified helical gears, the present invention provides a parametric modeling method for modified helical gears with a simple modeling process and high modeling accuracy, and establishes a three-dimensional model of the modified helical gear according to the gear design parameters and the shaping parameters.

[0006] The parametric modeling method of modified helical gears of the present invention is:

[0007] The involute of the modified gear is obtained by rotating the involute of the standard gear around the center of the base circle by σ radians. The homogeneous coordinate transformation method and the scanning and cutting operation of the 3D CAD software are used. The modeling of the modified modified helical gear tooth surface uses the scanning and cutting operation of the 3D CAD software. The scanning path is the tooth modification curve, and the scanning profile is the tooth profile modification curve, which includes the following steps:

[0008] (1) Calculate the tooth profile modification curve and surface equation of the modified helical gear;

[0009] (2) Establish a two-dimensional sketch of the gear tooth profile;

[0010] (3) Calculate the tooth modification curve and surface equations;

[0011] (4) Perform scanning and cutting operations along the tooth modification curve and create a three-dimensional geometric model of the modified helical gear.

[0012] The specific process of calculating the tooth profile modification curve and surface equation of the modified helical gear in step (1) is as follows:

[0013] ① The derivation process of the standard gear tooth profile modification curve equation is as follows:

[0014] The parametric equation of the involute with the center of the base circle at the origin and the starting point at the x-axis is:

[0015]

[0016] Where r b is the radius of the base circle, and parameter t represents the rolling arc of the involute generating line on the base circle. The value of parameter t determines the length of the involute. The coordinates of the starting point are (r b , 0), the involute equation on the upper side of the x-axis is “+”, and the involute equation on the lower side of the x-axis is “-”;

[0017] Rotate the original involute counterclockwise about the origin (center of the base circle) by σ radians to obtain the parametric equation of the involute after displacement:

[0018]

[0019] Parametric equation of involute after displacement:

[0020]

[0021] ② The derivation process of the tooth profile modification curve equation of the modified helical gear is as follows:

[0022] The tooth profile modification curve equation of the unmodified helical gear is:

[0023]

[0024] Rotate the original involute counterclockwise about the origin (center of the base circle) by σ radians to obtain the parametric equation of the tooth profile modification curve after displacement:

[0025]

[0026] Parameter equation of tooth profile modification curve after displacement:

[0027]

[0028] The parameter equation of the tooth profile modification curve H(r) is as follows:

[0029]

[0030] Where l1 is the tooth root modification length, h1 is the tooth root modification amount, l2 is the tooth profile drum length, h2 is the tooth profile drum amount, l3 is the tooth top modification length, h3 is the tooth top modification amount, r is the gear radius, r min is the minimum gear radius with modification, r b is the base circle radius.

[0031] The expression of r is as follows:

[0032]

[0033] The parameter equation of the tooth profile modification curve H(t) is as follows:

[0034]

[0035] The equation for the original involute rotating counterclockwise about the origin (center of the base circle) by σ radians is as follows:

[0036]

[0037] Where x1 is the normal displacement coefficient, β is the helix angle, α t is the end face pressure angle, Z1 is the number of teeth, and θ is the pitch circle angle of the unmodified gear.

[0038] ③The derivation process of the tooth profile modification surface equation is as follows:

[0039] Set the fixed coordinate system S g and the spatial spiral motion coordinate system S o ; Fixed coordinate system S g Fixed on the center of the gear end face, including X g Axis, Y g Axis, Z g Axis; space spiral motion coordinate system S o Relative to the fixed coordinate system S g Make a spiral upward motion, the initial moment S g and S o coincide;

[0040] According to the principle of homogeneous coordinate transformation, the fixed coordinate system S is obtained g and the spatial spiral motion coordinate system S o The transformation matrix between is:

[0041]

[0042]

[0043] Coordinate system S g With So The conversion relationship between them is as follows:

[0044] Space spiral motion coordinate system S o To the fixed coordinate system S g The transformation is as follows:

[0045]

[0046] Fixed coordinate system S g To the spatial spiral motion coordinate system S o The transformation is as follows:

[0047]

[0048] Spiral motion coordinate system S o The equation of the lower modified tooth profile modification curve is as follows:

[0049]

[0050] Fixed coordinate system S g The tooth surface equation of the modified helical gear is as follows:

[0051]

[0052] in: is the spatial rotation in radians, is the additional rotation radian, β b is the base circle helix angle.

[0053] When there is no tooth modification, the fixed coordinate system S g The tooth surface equation of the lower modified tooth profile is as follows:

[0054]

[0055] The specific process of establishing the two-dimensional sketch of the tooth profile of the gear with modified tooth profile in step (2) is as follows:

[0056] Establish basic coordinate system: The default Cartesian coordinate system is the first basic coordinate system, and the left view is used as the drawing plane to establish the root circle, base circle, pitch circle, and addendum circle;

[0057] Create the tooth groove upper modification curve: create the tooth groove upper modification curve according to the tooth profile modification curve equation on the x-axis;

[0058] Create the tooth groove lower modification curve: create the tooth groove lower modification curve according to the tooth profile modification curve equation on the lower side of the x-axis;

[0059] Create the tooth groove contour: connect the upper tooth groove modification curve and its extension line with the lower tooth groove modification curve and its extension line, draw the root circle and the addendum circle, and obtain the final tooth groove two-dimensional contour.

[0060] The specific process of deriving the tooth modification curve and surface equation of the modified helical gear in step (3) is:

[0061] Fixed coordinate system S g The equation of the tooth modification surface of the lower modified helical gear is as follows:

[0062]

[0063] The relationship function G(z) between the amount of shaping and the motion position is:

[0064]

[0065] The expression for z is as follows:

[0066]

[0067] Additional rotation radians The relationship between the amount of shaping is as follows:

[0068]

[0069]

[0070] Among them: l4 is the tooth end thinning length, g1 is the tooth end thinning amount, l5 is the tooth direction drum length, g2 is the tooth direction drum amount, l6 is the tooth end thinning length, g3 is the tooth end thinning amount, l7 is half of the tooth direction drum length, G2 is the right tooth surface drum amount, z is the tooth width variable, b is the tooth width, r b is the base circle radius, β b is the base circle helix angle.

[0071] The process of performing a scanning and cutting operation along the tooth modification curve and creating a three-dimensional geometric model of the topological modified helical gear is as follows:

[0072] Based on the tooth groove profile, scan along the tooth modification curve to obtain the tooth groove three-dimensional body;

[0073] Create tooth root fillet: Create left and right tooth profile fillets, with a fillet radius of 0.38*m n ;

[0074] Through the circumferential array tooth grooves and tooth root fillets, the three-dimensional model of the entire modified helical gear is obtained.

[0075] The present invention establishes a three-dimensional model of a modified helical gear according to gear design parameters and shaping parameters, and adopts a homogeneous coordinate transformation method and a scanning and cutting operation of three-dimensional CAD software to derive the tooth profile modification curve equation and the tooth direction modification curve equation of the modified helical gear, thereby solving the problem of establishing models of modified helical gears of different shaping types. The modeling process is simple, the modeling difficulty is reduced, and the accuracy of modeling is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a flow chart of the method for modeling modified helical gears of the present invention.

[0077] Figure 2 It is a schematic diagram for deriving the involute equation of the tooth profile.

[0078] Figure 3 It is a schematic diagram of the tooth profile modification curve.

[0079] Figure 4 It is a schematic diagram of the tooth modification curve.

[0080] Figure 5 It is a schematic diagram of the spiral motion of the end face tooth profile.

[0081] Figure 6 It is a schematic diagram of the modeling process of modified helical gears; among them: (a) is the two-dimensional sketch of the upper side of the gear end face tooth profile on the x-axis, (b) is the overall two-dimensional sketch of the gear end face tooth profile, (c) is the established three-dimensional tooth groove model, and (d) is the modified helical gear model with different modification types.

[0082] Figure 7 is a schematic diagram of the three-dimensional model of a single tooth of a modified helical gear with different modification types; among them: (a) is unmodified, (b) is tooth profile modified, (c) is tooth direction modified, and (d) is topological modified. DETAILED DESCRIPTION

[0083] A method for modeling a modified helical gear of the present invention is to obtain a modified gear involute by rotating a standard gear involute around the center of a base circle by a certain arc, adopt a homogeneous coordinate transformation method and a scanning and cutting operation of a three-dimensional CAD software, and model the tooth surface of the modified helical gear using a scanning and cutting operation of the three-dimensional CAD software. The scanning path is a tooth direction modification curve, and the scanning contour is a tooth profile modification curve.

[0084] like Figure 1 As shown, the method of the present invention specifically includes the following steps: (1) calculating the tooth profile modification curve and surface equation, (2) establishing a two-dimensional sketch of the tooth profile of the tooth profile modified and shifted gear, (3) calculating the tooth direction modification curve and surface equation, (4) performing a scanning and cutting operation along the tooth direction modification curve and creating a three-dimensional geometric model of the modified and shifted helical gear.

[0085] Step 1: Calculate the tooth profile modification curve and surface equation

[0086] (1) The derivation process of the standard gear tooth profile modification curve equation is as follows:

[0087] like Figure 2 As shown, the parametric equation of the involute with the base circle centered at the origin and the starting point at the x-axis is:

[0088]

[0089] Where r b is the radius of the base circle, and parameter t represents the rolling arc of the involute generating line on the base circle. The value of parameter t determines the length of the involute. The coordinates of the starting point are (r b , 0), the involute equation on the upper side of the x-axis is taken as “+”, and the involute equation on the lower side of the x-axis is taken as “-”.

[0090] Rotate the original involute counterclockwise around the origin by σ radians to obtain the parametric equation of the involute after displacement:

[0091]

[0092] Parametric equation of involute after displacement:

[0093]

[0094] (2) The derivation process of the tooth profile modification curve equation of the modified helical gear is as follows:

[0095] The tooth profile modification curve equation of the unmodified helical gear is:

[0096]

[0097] Rotate the original involute counterclockwise around the origin by σ radians to obtain the parametric equation of the tooth profile modification curve after displacement:

[0098]

[0099] Parameter equation of tooth profile modification curve after displacement:

[0100]

[0101] Tooth profile modification curve Figure 3 As shown, the parameter equation of the tooth profile modification curve H(r) is as follows:

[0102]

[0103] Where l1 is the tooth root modification length, h1 is the tooth root modification amount, l2 is the tooth profile drum length, h2 is the tooth profile drum amount, l3 is the tooth top modification length, h3 is the tooth top modification amount, r is the gear radius, r min is the minimum gear radius with modification, rb is the base circle radius.

[0104] The expression of r is as follows:

[0105]

[0106] The parameter equation of the tooth profile modification curve H(t) is as follows:

[0107]

[0108] The equation for the original involute rotating counterclockwise around the origin by σ radians is as follows:

[0109]

[0110] Where x1 is the normal displacement coefficient, β is the helix angle, α t is the end face pressure angle, Z1 is the number of teeth, and θ is the pitch circle angle of the unmodified gear.

[0111] (3) The derivation process of the tooth profile modification surface equation is as follows:

[0112] Set the fixed coordinate system S g and the spatial spiral motion coordinate system S o , fixed coordinate system S g Fixed on the center of the gear end face, including X g Axis, Y g Axis, Z g Axis, space spiral motion coordinate system S o Relative to the fixed coordinate system S g Make a spiral upward motion, the initial moment S g and S o coincide;

[0113] According to the principle of homogeneous coordinate transformation, the fixed coordinate system S is obtained g and the spatial spiral motion coordinate system S o The transformation matrix between is:

[0114]

[0115]

[0116] Coordinate system S g With S o The conversion relationship between them becomes as follows:

[0117] Space spiral motion coordinate system S o To the fixed coordinate system S g The transformation is as follows:

[0118]

[0119] Fixed coordinate system S g To the spatial spiral motion coordinate system S o The transformation is as follows:

[0120]

[0121] Spiral motion coordinate system S o The lower tooth profile equation is as follows:

[0122]

[0123] Fixed coordinate system S g The tooth profile modification surface equation of the lower topological modified helical gear is as follows:

[0124]

[0125] is the spatial rotation in radians, is the additional rotation radian, β b is the base circle helix angle.

[0126] When there is no tooth modification, the fixed coordinate system S g The equation of the lower modified tooth profile modification surface is as follows:

[0127]

[0128] ① Only the tooth top trimming curve and surface equations:

[0129] The parameter equation of the tooth profile modification curve H(t) is as follows:

[0130]

[0131] The equation of the tooth tip trimming surface is as follows:

[0132]

[0133] The equation of the tooth tip trimming curve is as follows:

[0134]

[0135] ②Only the tooth profile crowning curve and surface equations:

[0136] The parameter equation of the tooth profile modification curve H(t) is as follows:

[0137]

[0138] The equation of the tooth profile crowning surface is as follows:

[0139]

[0140] The equation of the tooth profile crowning modification curve is as follows:

[0141]

[0142] ③ Only slope modification curve and surface equations:

[0143] The parameter equation of the tooth profile modification curve H(t) is as follows:

[0144]

[0145] The slope-only contoured surface equation is as follows:

[0146]

[0147] The equation of the slope-modified curve only is as follows:

[0148]

[0149] Where r is the gear radius, r min is the minimum gear radius with modification amount.

[0150] Step 2: Create a two-dimensional sketch of the gear tooth profile with modified tooth profile.

[0151] Establish basic coordinate system: The default Cartesian coordinate system is the first basic coordinate system, and the left view is used as the drawing plane to establish the root circle, base circle, pitch circle, and addendum circle;

[0152] Create the tooth groove upper modification curve: create the tooth groove upper modification curve according to the tooth profile modification curve equation on the x-axis;

[0153] Create the tooth groove lower modification curve: create the tooth groove lower modification curve according to the tooth profile modification curve equation on the lower side of the x-axis;

[0154] Create tooth groove profile: connect the upper tooth groove modification curve and its extension line with the lower tooth groove modification curve and its extension line, draw the root circle and the addendum circle, and obtain the final tooth groove two-dimensional profile;

[0155] Step 3: Derive the tooth modification curve and surface equations of the modified helical gear.

[0156] Fixed coordinate system S g The equation of the tooth modification surface of the lower modified helical gear is as follows:

[0157]

[0158] The relationship function G(z) between the amount of shaping and the motion position is:

[0159]

[0160] The spiral motion of the tooth tip is as follows Figure 4As shown in Figure 2, the tooth modification curve is as follows: Figure 5 As shown, the expression of z is as follows:

[0161]

[0162] Additional rotation radians The relationship between the amount of shaping is as follows:

[0163]

[0164]

[0165] Where l4 is the tooth end thinning length, g1 is the tooth end thinning amount, l5 is the tooth direction drum length, g2 is the tooth direction drum amount, l6 is the tooth end thinning length, g3 is the tooth end thinning amount, l7 is half of the tooth direction drum length, G2 is the right tooth surface drum amount, z is the tooth width variable, b is the tooth width, r b is the base circle radius, β b is the base circle helix angle.

[0166] ① Only the tooth end is thinned and the tooth profile is modified

[0167] Additional rotation radians The relationship between the amount of shaping is as follows:

[0168]

[0169] The tooth surface equation for only the tooth end thinning and tooth profile modification is as follows:

[0170]

[0171] The equation of the tooth modification curve for only tooth end thinning is as follows:

[0172]

[0173] where t f is the rolling arc on the pitch circle.

[0174] ② Only the helix angle is modified, and the tooth direction is modified. Curve and surface equations

[0175] Additional rotation radians The relationship between the amount of shaping is as follows:

[0176]

[0177] The equation of the tooth modification surface with only helix angle modification is as follows:

[0178]

[0179] The equation of the tooth modification curve for helix angle modification only is as follows:

[0180]

[0181] ③Only tooth crowning tooth modification curve and surface equation

[0182] Additional rotation radians The relationship between the amount of shaping is as follows:

[0183]

[0184] The tooth crowning surface equation is as follows:

[0185]

[0186] The tooth modification curve equation for tooth crowning only is as follows:

[0187]

[0188] ④ Tooth surface modification equation with both tooth profile drumming and tooth end thinning

[0189] The parameter equation of the tooth profile modification curve H(y0) is as follows:

[0190]

[0191] Additional rotation radians The relationship between the amount of shaping is as follows:

[0192]

[0193] The equation of the tooth surface modification surface with both tooth profile drumming and tooth end thinning is as follows:

[0194]

[0195] The equation of the tooth surface modification curve with both tooth profile drumming and tooth end thinning is as follows:

[0196]

[0197] Step 4: Perform a scan cut operation along the tooth modification curve and create a 3D geometric model of the topological modified helical gear

[0198] Based on the tooth groove contour, scan along the tooth modification curve to obtain the tooth groove 3D body, create the left tooth profile fillet and the right tooth profile fillet, and the fillet radius is 0.38*m n , through the circumferential array tooth groove and tooth root fillet, the three-dimensional model of the entire modified helical gear is obtained. Figure 6As shown, (a) is the two-dimensional sketch of the upper side of the gear end face tooth profile on the x-axis, (b) is the overall two-dimensional sketch of the gear end face tooth profile, (c) is the established three-dimensional tooth groove model, and (d) is the modified helical gear model with different modification types.

[0199] The following is a specific embodiment of the method for modeling a modified helical gear according to the present invention:

[0200] Taking the left-handed helical gear with a module of 4.25mm, a number of teeth of 21, a normal pressure angle of 19°, a helix angle of 17.81°, a tooth width of 46mm, a normal modification coefficient of 0.15, a tooth top height of 6.138mm, and a tooth root height of 6.375mm as an example, helical gears with different modification types are established. The tooth profile tooth top modification amount is 25μm, the tooth profile drum amount is 6μm, and the tooth drum amount is 10μm.

[0201] According to the above parameters, the tooth profile modification curve and the tooth guide modification curve equations are calculated and imported into Solidworks 3D CAD software to create a workpiece swept body model; and a gear model is created according to the gear parameters.

[0202] The single tooth models of the modified helical gears with different modification types are shown in Figure 7, where (a) is unmodified, (b) is tooth profile modified, (c) is tooth tip modified, and (d) is topological modified.

Claims

1. A parametric modeling method for modified helical gears, characterized by: The involute of the modified gear is obtained by rotating the involute of the standard gear around the center of the base circle by σ radians. The homogeneous coordinate transformation method and the scanning and cutting operation of the 3D CAD software are used. The modeling of the modified modified helical gear tooth surface uses the scanning and cutting operation of the 3D CAD software. The scanning path is the tooth modification curve, and the scanning profile is the tooth profile modification curve, which includes the following steps: (1) Calculate the tooth profile modification curve and surface equation of the modified helical gear; (2) Establish a two-dimensional sketch of the gear tooth profile; (3) Calculate the tooth modification curve and surface equations; (4) Perform scanning and cutting operations along the tooth modification curve and create a three-dimensional geometric model of the modified helical gear; The specific process of deriving the tooth modification curve and surface equation of the modified helical gear in step (3) is: Fixed coordinate system S g The equation of the tooth modification surface of the lower modified helical gear is as follows: The relationship function G(z) between the amount of shaping and the motion position is: The expression for z is as follows: Additional rotation radians The relationship between the amount of modification is as follows: Among them: l4 is the tooth end thinning length, g1 is the tooth end thinning amount, l5 is the tooth direction drum length, g2 is the tooth direction drum amount, l6 is the tooth end thinning length, g3 is the tooth end thinning amount, l7 is half of the tooth direction drum length, G2 is the right tooth surface drum amount, z is the tooth width variable, b is the tooth width, r b is the base circle radius, β b is the base circle helix angle, is the spatial rotation in radians, is the additional rotation in radians.

2. The parametric modeling method for modified helical gears according to claim 1 is characterized in that: The specific process of calculating the tooth profile modification curve and surface equation of the modified helical gear in step (1) is: (1) The derivation process of the standard gear tooth profile modification curve equation is as follows: The parametric equation of the involute with the center of the base circle at the origin and the starting point at the x-axis is: Where r b is the radius of the base circle, and parameter t represents the rolling arc of the involute generating line on the base circle. The value of parameter t determines the length of the involute. The coordinates of the starting point are (r b ,0), the equation of the involute on the upper side of the x-axis is "+", and the equation of the involute on the lower side of the x-axis is "-"; Rotate the original involute counterclockwise around the origin by σ radians to obtain the parametric equation of the involute after displacement: Parametric equation of involute after displacement: (2) The derivation process of the tooth profile modification curve equation of the modified helical gear is as follows: The tooth profile modification curve equation of the unmodified helical gear is: Rotate the original involute counterclockwise around the origin by σ radians to obtain the parametric equation of the tooth profile modification curve after displacement: Parameter equation of tooth profile modification curve after displacement: The equation for σ is as follows: Where x1 is the normal displacement coefficient, β is the helix angle, α t is the end face pressure angle, Z1 is the number of teeth, and θ is the pitch circle angle of the unmodified gear; The parameter equation of the tooth profile modification curve H(r) is as follows: Where: l1 is the tooth root modification length, h1 is the tooth root modification amount, l2 is the tooth profile drum length, h2 is the tooth profile drum amount, l3 is the tooth top modification length, h3 is the tooth top modification amount, r is the gear radius, r min is the minimum gear radius with modification, r b is the base circle radius; The expression of r is as follows: The parameter equation of the tooth profile modification curve H(t) is as follows: (3) The derivation process of the tooth profile modification surface equation is as follows: Set the fixed coordinate system S g and the spatial spiral motion coordinate system S o , fixed coordinate system S g Fixed on the center of the gear end face, including X g Axis, Y g Axis, Z g Axis, space spiral motion coordinate system S o Relative to the fixed coordinate system S g Make a spiral upward motion, the initial moment S g and S o coincide; According to the principle of homogeneous coordinate transformation, the fixed coordinate system S is obtained g and the spatial spiral motion coordinate system S o The transformation matrix between is: in: is the spatial rotation in radians, is the additional rotation radian, β b is the base circle helix angle; Coordinate system S g With S o The conversion relationship between them is as follows: Space spiral motion coordinate system S o To the fixed coordinate system S g The transformation is as follows: Fixed coordinate system S g To the space spiral motion coordinate system S o The transformation is as follows: Spiral motion coordinate system S o The equation of the lower modified tooth profile modification curve is as follows: Fixed coordinate system S g The surface equation of the modified helical gear is as follows: When there is no tooth modification, the fixed coordinate system S g The equation of the lower modified tooth profile modification surface is as follows:

3. The parametric modeling method for modified helical gears according to claim 1 is characterized in that: The specific process of establishing the two-dimensional sketch of the tooth profile of the gear with modified tooth profile in step (2) is as follows: Establish basic coordinate system: The default Cartesian coordinate system is the first basic coordinate system, and the left view is used as the drawing plane to establish the root circle, base circle, pitch circle and addendum circle; Create the tooth groove upper modification curve: create the tooth groove upper modification curve according to the tooth profile modification curve equation on the x-axis; Create the tooth groove lower modification curve: create the tooth groove lower modification curve according to the tooth profile modification curve equation on the lower side of the x-axis; Create the tooth groove contour: connect the upper tooth groove modification curve and its extension line with the lower tooth groove modification curve and its extension line, draw the root circle and the addendum circle, and obtain the final tooth groove two-dimensional contour.

4. The parametric modeling method for modified helical gears according to claim 1 is characterized in that: The process of performing a scanning and cutting operation along the tooth modification curve and creating a three-dimensional geometric model of the topological modified helical gear is as follows: Based on the two-dimensional contour of the tooth groove, scan along the tooth modification curve to obtain the three-dimensional body of the tooth groove; Create tooth root fillet: Create left and right tooth profile fillets, with a fillet radius of 0.38*m n ; Through the circumferential array tooth grooves and tooth root fillets, the three-dimensional model of the entire modified helical gear is obtained.

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