Method for modeling a cold extruded gear tooth root

Abstract

The application provides a cold extrusion gear tooth root modeling method, and relates to the technical field of gear modeling and processing. It comprises the following steps: drawing a first involute, a second involute and a third involute; obtaining a first correction circle parameter according to a first correction parameter and gear basic parameters, and obtaining a second correction circle parameter according to a second correction parameter and the gear basic parameters; drawing a tooth slot preliminary contour line according to the gear basic parameters, the first correction circle parameter and the second correction circle parameter; drawing a tooth root circular arc according to the third involute and the gear basic parameters; and drawing a tooth root transition curve according to a first transition radius, a second transition radius, the tooth root circular arc, the first involute and the third involute. The application solves the problem that the prior art is not suitable for modeling a cold extrusion gear, and tooth root curves can be drawn only according to some simple addition and subtraction operation formulas and involute equations.

Description

Technical Field

[0001] This invention relates to the field of gear modeling and machining technology, and in particular to a method for modeling the tooth root of cold-extruded gears. Background Technology

[0002] Gears are a crucial component of modern transmission systems, responsible for transmitting power and changing speed and direction of motion. Gears are characterized by a wide power range, high transmission efficiency, accurate transmission ratios, and long service life. Statistics show that gear failure accounts for over 60% of all mechanical failures. Common gear failure modes include gear breakage, pitting, scuffing, and wear, with gear breakage being one of the primary modes of gear failure.

[0003] Since fatigue fracture (caused by bending stress and stress concentration) is a major cause of gear breakage, and the more perfect the transition curve at the gear tooth root is, the less likely the gear is to experience fatigue fracture, in engineering, gears are often designed by using three-dimensional modeling to make the transition curve at the gear tooth root more perfect, thereby extending the time before gear failure and improving the service life of the gear.

[0004] Currently, existing technologies are basically based on gear hobbing processes to model gears. When modeling, designers also need to fully consider the structural design characteristics of the hobbing cutter. For example, when constructing the gear tooth root transition curve, designers need to refer to the hobbing cutter parameters and the hobbing envelope curve.

[0005] Since gear manufacturing via cold extrusion and gear manufacturing via gear hobbing are two completely different gear manufacturing methods, the existing technical solutions described above are not suitable for modeling cold extruded gears. Therefore, improvements are necessary. Summary of the Invention

[0006] The main objective of this invention is to provide a method for modeling the tooth root of cold-extruded gears, aiming to solve the technical problem that existing technical solutions are not suitable for modeling cold-extruded gears.

[0007] To address the aforementioned technical problems, this invention provides a method for modeling the tooth root of a cold-extruded gear, comprising: drawing a first involute curve based on the pitch circle chord tooth thickness, single-sided grinding amount of the tooth surface, and basic gear parameters; drawing a second involute curve based on the pitch circle chord tooth thickness and basic gear parameters; drawing a third involute curve based on the pitch circle chord tooth thickness, transition backcutting amount, and basic gear parameters; obtaining a first correction circle parameter corresponding to the first involute curve based on a first correction parameter and the basic gear parameters; obtaining a second correction circle parameter corresponding to the third involute curve based on a second correction parameter and the basic gear parameters; drawing a preliminary tooth groove contour line based on the basic gear parameters, the first correction circle parameter, and the second correction circle parameter; drawing a tooth root arc based on the third involute curve and the basic gear parameters; and drawing a tooth root transition curve based on a first transition parameter, a second transition parameter, the tooth root arc, the first involute curve, and the third involute curve.

[0008] Preferably, the step of drawing the first involute curve based on the pitch circle chord tooth thickness, single-sided tooth surface grinding amount, and basic gear parameters; drawing the second involute curve based on the pitch circle chord tooth thickness and basic gear parameters; and drawing the third involute curve based on the pitch circle chord tooth thickness, transition countercutting amount, and basic gear parameters includes: calculating the first optimized tooth thickness based on the single-sided tooth surface grinding amount and the pitch circle chord tooth thickness, wherein the calculation formula for the first optimized tooth thickness is: Scn_R=Scn+2δm, where Scn_R is the first optimized tooth thickness, Scn is the pitch circle chord tooth thickness, and δm is... The single-sided grinding amount of the tooth surface; the second optimized tooth thickness is calculated based on the transition undercut amount and the pitch circle chord tooth thickness, wherein the calculation formula for the second optimized tooth thickness is: Scn_g=Scn-2δg, Scn_g is the second optimized tooth thickness, and δg is the transition undercut amount; the first involute is drawn based on the number of gear teeth, module, pressure angle and the first optimized tooth thickness; the second involute is drawn based on the number of gear teeth, module, pressure angle and the pitch circle chord tooth thickness; the third involute is drawn based on the number of gear teeth, module, pressure angle and the second optimized tooth thickness.

[0009] Preferably, the step of obtaining the first correction circle parameter corresponding to the first involute based on the first correction parameter and the gear basic parameters, and obtaining the second correction circle parameter corresponding to the third involute based on the second correction parameter and the gear basic parameters, includes: calculating the first correction circle parameter based on the finished involute evaluation starting circle and the diameter of the first correction parameter, wherein the calculation formula for the first correction circle parameter is: D1 = D_scp + K1, where D1 is the first correction circle parameter, K1 is the first correction parameter, and D_scp is the diameter of the finished involute evaluation starting circle; and calculating the second correction circle parameter based on the finished involute evaluation starting circle and the diameter of the second correction parameter, wherein the calculation formula for the second correction circle parameter is: D2 = D_scp - K2, where D2 is the second correction circle parameter, and K2 is the second correction parameter.

[0010] Preferably, the step of drawing the preliminary contour line of the tooth groove according to the basic parameters of the gear, the first correction circle parameter and the second correction circle parameter includes: drawing the tooth root circle according to the tooth root circle diameter, drawing the tooth tip circle according to the tooth tip circle diameter, drawing the first correction circle according to the first correction circle parameter, and drawing the second correction circle according to the second correction circle parameter.

[0011] The preliminary contour line of the tooth groove is determined based on the first involute, the root circle, the tip circle, the first correction circle, and the second correction circle.

[0012] Preferably, drawing the tooth root arc according to the third involute and the basic parameters of the gear includes: obtaining the intersection point of the third involute and the second correction circle, denoted as the fifth point; drawing a fifth arc tangent to the third involute and the tooth root circle through the fifth point, wherein the fifth arc is the tooth root arc.

[0013] Preferably, the step of drawing the tooth root arc based on the third involute and the basic parameters of the gear further includes: after obtaining the fifth arc, cutting off the arc line on the tooth root circle that connects to the fifth arc as the tooth root connecting arc; and taking the fifth arc and the tooth root connecting arc together as the tooth root arc.

[0014] Preferably, the step of drawing the tooth root transition curve based on the first transition parameter, the second transition parameter, the tooth root arc, the first involute, and the third involute includes: taking a portion of the length of the third involute as a fourth curve based on the intersection of the third involute and the second correction circle; drawing a first transition arc based on the first involute, the first transition parameter, and the first correction circle; drawing a second transition arc based on the fourth curve, the second transition parameter, and the second correction circle; drawing a tangent arc between the first transition arc and the second transition arc based on the first transition arc and the second transition arc; and determining the tooth root transition curve based on the fourth curve, the tangent arc, the first transition arc, and the second transition arc.

[0015] Preferably, the step of drawing the first transition arc based on the first involute, the first transition parameter, and the first correction circle includes: obtaining the intersection point of the first involute and the first correction circle, denoted as the first point; and drawing a first transition arc tangent to the first involute through the first point according to the first transition parameter.

[0016] Preferably, the step of drawing the second transition arc according to the fourth curve, the second transition parameter, and the second correction circle includes: marking the endpoint of the fourth curve near the second involute as the fourth point; and drawing a second transition arc tangent to the third involute through the fourth point according to the second transition parameter.

[0017] Preferably, the tooth tip chamfer is drawn according to the preset chamfer parameters and the second involute, and the extension line of the tooth tip chamfer intersects the first involute and the tooth tip circle respectively.

[0018] This invention discloses a method for modeling the tooth root of cold-extruded gears, including sequentially drawing a first involute, a second involute, a third involute, a preliminary tooth groove contour, a tooth root transition curve limiting circle, a tooth root arc, and a tooth root transition curve. Since this invention does not involve hobbing tool parameters or hobbing envelope curves when constructing the tooth root curve, it does not require reference to the structural design characteristics of the hobbing tool during modeling. Thus, this invention effectively solves the technical problem that existing solutions are unsuitable for modeling cold-extruded gears. Furthermore, since this invention mainly uses preset gear basic parameters and preset cold-extruded parameters to model the cold-extruded gear, and does not use complex modeling equations to draw the gear tooth root during the gear modeling process, the modeling method of this invention is simpler and more convenient. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the cold-extruded gear at the tooth root according to the present invention;

[0020] Figure 2 for Figure 1 A magnified view of a portion of the image;

[0021] Figure 3 This is a schematic diagram of a single tooth model of the cold-extruded gear described in this invention;

[0022] Figure 4 This is a schematic diagram of the structure of the finished gear at the tooth root after grinding the cold extruded gear described in this invention;

[0023] Figure 5 for Figure 4 A magnified view of a portion of the image;

[0024] Figure 6 This is a schematic diagram of a single tooth of the finished gear after grinding of the cold extruded gear described in this invention;

[0025] Figure 7 This is a partial schematic diagram of the tooth root curve constructed according to the technical requirements described in Example 1 of the present invention and in conjunction with the cold extrusion gear tooth root modeling method described in the present invention;

[0026] Figure 8This is a partial schematic diagram of the tooth root curve constructed according to the technical requirements described in Embodiment 2 of the present invention and in conjunction with the cold extrusion gear tooth root modeling method described in the present invention;

[0027] Figure 9 This is a partial schematic diagram of the tooth root curve constructed according to the technical requirements described in Example 3 of the present invention, and in conjunction with the cold extrusion gear tooth root modeling method described in the present invention;

[0028] Figure 10 This is a physical image of the straight-tooth cold-extruded gear of the present invention;

[0029] Figure 11 This is a physical image of the helical cold-extruded gear of the present invention;

[0030] Figure 12 This is a schematic diagram of the straight-tooth cold-extruded gear of the present invention and its accuracy test results;

[0031] Figure 13 A partial schematic diagram of a ground-cooled extruded gear manufactured according to the technical requirements of a comparative experiment;

[0032] Figure 14 This is a flowchart illustrating the cold extrusion gear tooth root modeling method described in this invention.

[0033] In the diagram: 1. First involute; 2. Second involute; 3. Third involute; 4. First transition arc; 5. Tangent arc; 6. Second transition arc; 7. Fourth curve; 8. Fifth arc; 9. Tooth tip chamfer surface; 10. Tooth tip arc surface; 11. First correction circle; 12. Starting circle for evaluating the finished involute; 13. Second correction circle; 14. Tooth root circle; 15. Tooth tip circle. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. At the same time, it should be understood that the specific embodiments described herein are merely used to explain the present invention and are not intended to limit the present invention.

[0035] Currently, the failure modes of gears typically include: gear breakage, pitting, scuffing, and wear. A major cause of gear breakage is fatigue fracture due to repeated bending stress and stress concentration.

[0036] The root fillet has a significant impact on the bending stress and stress concentration at the tooth root. CAE results show that a larger root fillet results in lower bending stress and a lower risk of root fatigue cracking.

[0037] In the national standard, the root fillet radius of involute gears is specified as 0.38*m (m: gear module). To improve the bending fatigue strength of gearbox gears, the root fillet radius is usually increased, or a full circular arc root is used directly. On the other hand, the transition curve between the root fillet and the involute tooth surface is an important factor affecting whether stress concentration occurs after tooth surface grinding. A perfect transition curve is tangent to the involute tooth surface, but since it is difficult to achieve this in terms of grinding error, in engineering, a subsurface cutting design method is generally used to reserve subsurface cutting allowance to avoid the appearance of grinding steps.

[0038] In conventional hobbing of gears with full circular arc tooth roots, a hob with a full circular arc tooth tip is used for pre-grinding. The transition curve between the tooth root fillet and the involute of the tooth surface is formed by the envelope of the hob tooth tip radius during hobbing.

[0039] The article "A Discussion on the Equation of the Tooth Root Transition Curve of Cylindrical Gears" derives the parametric equation for the tooth root transition curve formed by hobbing in a combined hobbing and shaving process. This includes establishing the parametric equations for extending the involute curve, extending the involute envelope equation, and extending the equation of the equidistant line of the involute curve at a distance r from it. The equation of the equidistant line of the involute curve at a distance r is a general formula, which is the parametric equation for the tooth root transition curve formed by hobbing of cylindrical gears. This parametric equation belongs to a system of multivariate transcendental equations, making calculation cumbersome.

[0040] The article "Simplified Calculation of the Starting Circle for Gear Countercutting" uses two circular arcs to replace the countercutting curve and the gear involute. The intersection of the two arcs is taken as the starting point of the countercutting. The equations of the circular arcs for the countercutting curve and the circular arcs for the gear involute are listed separately and solved simultaneously to obtain the radius of the starting point of the countercutting, thus obtaining a simplified calculation formula. However, this simplified method results in a cusp at the intersection of the two circular arcs. Since cusps are not allowed in the design of cold extrusion gear dies, a circular arc transition is required. Furthermore, using a circular arc to replace the involute introduces certain errors.

[0041] The theoretical calculation process of the transition curves in the above references is complex, and they are all based on the design of transition curves for gear hobbing processes. The structural design characteristics of the gear hobbing cutter must also be considered, which is not suitable for the tooth root construction of cold extruded gear semi-finished products.

[0042] This invention directly constructs the ideal tooth root geometry during the design of the cold-extruded gear semi-finished product (the state after heat treatment and before grinding) to obtain the best bending fatigue strength, thereby reducing the probability of gear failure due to fatigue fracture of the cold-extruded gear.

[0043] In actual operation, the gear tooth number Z, module m, pressure angle α, addendum circle diameter Da, dedendum circle diameter Df, finished involute evaluation starting circle diameter D_scp, and pitch circle chord tooth thickness Scn are all known basic gear parameters before constructing the gear root curve. The transition undercut amount, first correction parameter, second correction parameter, first transition parameter, and second transition parameter are known cold extrusion parameters before constructing the gear root curve. Among these, the aforementioned basic gear parameters are essential parameters for constructing gears, such as those required for constructing rolled gears and cold extruded gears. The cold extrusion parameters are special parameters designed specifically for cold extruded gears in this invention, and are more suitable for use in cold extruded gears.

[0044] This invention only requires some simple addition and subtraction operations based on the aforementioned basic gear parameters and cold extrusion parameters to obtain the corresponding gear construction parameters. These parameters are then imported into the involute equation preset in drawing software (such as CAD) to obtain three separately drawn involute segments (first involute 1, second involute 2, and third involute 3), as shown below. Figure 1 and Figure 2 As shown, the designer can then draw the tooth root curve of the cold-extruded gear based on the involute curve, basic gear parameters, cold extrusion parameters, and gear construction parameters drawn separately above. In this way, the designer can complete the modeling of the cold-extruded gear based on the tooth root curve.

[0045] In practical applications, when modeling cold-extruded gears, the tooth root curve can be drawn using drawing software based on some simple addition and subtraction formulas and involute equations. Furthermore, since there is only one involute equation in this invention, the modeling method for cold-extruded gears described in this invention is simpler and more convenient to use.

[0046] In practice, designers can calculate the pitch circle arc tooth thickness S of the gear based on the known common normal length Wk (number of teeth k) using the tooth thickness formula, and then calculate the corresponding pitch circle chord tooth thickness Scn. The formula for calculating the pitch circle chord tooth thickness is as follows:

[0047] d = m * Z;

[0048] S=Wk / cos(α)-d*inv(α)-(k-1)*pi*m;

[0049] Scn = d*sin(S / d*180 / pi);

[0050] Inv(α)=tan(α)-α*pi / 180;

[0051] Where d is the pitch circle diameter, m is the gear module, Wk is the known common normal length of the gear, k is the tooth span coefficient of the common normal length Wk, pi is pi, and S is the pitch circle arc tooth thickness.

[0052] In this invention, the involute curve of the gear is drawn using equations in a Cartesian coordinate system in CAD software. The equation of the involute curve is:

[0053] δ=60*t

[0054] Rb = d*cos(α)

[0055] X=Rb*cos(δ)+pi*Rb*δ / 180*sin(δ)

[0056] Y=Rb*sin(δ)-pi*Rb*δ / 180*cos(δ)

[0057] Z = 0

[0058] Rb is the base circle radius of the gear, δ is the pressure angle variation, t is the formal parameter of the CAD software, d is the pitch circle diameter, and pi is pi.

[0059] This invention can calculate the rotation angle ψ of the involute based on the pitch circle chord tooth thickness Scn, using the following formula:

[0060] Ψ=inv(α)*180 / pi+arcsin(Scn / d)

[0061] Rotating the involute drawn according to the involute equation by the aforementioned angle Ψ yields the involute on one side of the tooth profile with the pitch circle chord tooth thickness Scn. Mirroring the involute on the other side of the tooth profile with the line connecting the midpoint of the pitch circle chord tooth thickness Scn to the center of the circle yields the involute on the other side of the tooth profile.

[0062] In practical operation, the parameter requirements and corresponding calculation formulas for the cold-extruded gear of this invention are as follows:

[0063] (1) The tooth root of the gear adopts a full circle arc or a near full circle arc structure. When a near full circle arc structure is adopted, the length of the tooth root circle 14 connecting segment (tooth root connecting arc) is ≤0.2mm when it is not a full circle arc.

[0064] (2) Single-sided grinding amount δm: The single-sided grinding amount δm is obtained based on the first involute 1 and the second involute 2, and the distance between the first involute 1 and the second involute 2 is 0.1 to 0.15 mm.

[0065] The formula for calculating the first optimized tooth thickness is: Scn_R=Scn+2δm, where Scn_R is the first optimized tooth thickness, Scn is the pitch circle chord tooth thickness, and δm is the single-sided grinding amount of the tooth surface.

[0066] (3) Transition sinking amount δg: The distance between the extension of the second involute 2 and the tooth root transition curve DE is 0.02~0.05mm, and the length of the tooth root transition curve DE is 0.1~0.2mm;

[0067] The formula for calculating the second optimized tooth thickness is: Scn_g=Scn-2δg, where Scn_g is the second optimized tooth thickness and δg is the transition depth cut amount;

[0068] (4) The calculation formula for the first correction circle parameter is: D1 = D_scp + K1, where D1 is the first correction circle parameter, K1 is the first correction parameter, and D_scp is the diameter of the starting circle for evaluating the finished involute.

[0069] The formula for calculating the second correction circle parameter is: D2 = D_scp - K2, where D2 is the second correction circle parameter and K2 is the second correction parameter;

[0070] The first correction parameter K1 has a value range of 0.5 to 1 mm, and the second correction parameter K2 has a value range of 1 to 2 mm.

[0071] (5) Tooth root transition curve: The radius (i.e. the first transition parameter) of the first transition arc AB is R1≥1mm, the radius (i.e. the second transition parameter) of the second transition arc CD is R2≥2mm, and the tangent arc (third curve) BC is the tangent line connecting the first transition arc AB and the second transition arc CD.

[0072] In practical work, to more clearly illustrate the technical solutions of this application, the terms used in this invention are explained as follows:

[0073] The first involute 1 can be called a semi-finished involute, while the second involute 2 and the third involute 3 can both be called finished involutes;

[0074] Semi-finished products (gears) refer to the gear state obtained after processing according to steps S1 to S6 described in this invention, such as... Figure 2 As shown, the coarse spline curve composed of the first involute 1, the tooth root transition curve (curve ABCDE) located between the first involute and the third involute, and the tooth root arc 8 is the tooth root curve of the cold extruded gear when it is in the semi-finished product state.

[0075] Finished product (gear) refers to the gear state obtained after the above-mentioned semi-finished gears have undergone grinding treatment, such as... Figure 2 , Figure 4 and Figure 5 As shown, Figure 2The first involute 1, the portion of the tangent arc 5 (curve BC) near the first involute 1, and the first transition curve 4 (curve AB) together form the grinding curve. This grinding curve will be ground off after the aforementioned semi-finished gear has undergone grinding treatment (e.g., Figure 4 and Figure 5 As shown in the figure, at this time, the tooth root curve of the cold extruded gear in the finished product state does not include the above grinding curve;

[0076] The first correction circle 11 and the second correction circle 13 can be collectively referred to as the tooth root transition curve limiting circle. The initial profile line of the tooth groove refers to the tooth root curve of the cold-extruded gear (e.g., Figure 2 (As shown) does not include the tooth root transition curve (curve ABCDE) located between the first and third involutes, nor the spline curve determined by the state when the tooth tip is chamfered.

[0077] like Figure 14 As shown, this invention provides a flowchart of a method for modeling the tooth root of cold-extruded gears. It should be noted that if substantially the same result is obtained, the method of this invention is not necessarily identical. Figure 14 The illustrated process sequence is limited. In actual work, the method for modeling the tooth root of (semi-finished) cold-extruded gears includes:

[0078] S1. Draw the first involute 1 based on the pitch circle chord tooth thickness, single-sided grinding amount of the tooth surface and the basic parameters of the gear; draw the second involute 2 based on the pitch circle chord tooth thickness and the basic parameters of the gear; draw the third involute 3 based on the pitch circle chord tooth thickness, transition undercut amount and the basic parameters of the gear.

[0079] In this step, the first involute 1, the second involute 2, and the third involute 3 were all drawn by the designer using drawing software based on the known involute equations. Specifically, the steps for drawing the involute include:

[0080] S11. Calculate the first optimized tooth thickness based on the single-sided grinding amount of the tooth surface and the pitch circle chord tooth thickness. The calculation formula for the first optimized tooth thickness is: Scn_R=Scn+2δm, where Scn_R is the first optimized tooth thickness, Scn is the pitch circle chord tooth thickness, and δm is the single-sided grinding amount of the tooth surface.

[0081] S12. Calculate the second optimized tooth thickness based on the transition undercut amount and the pitch circle chord tooth thickness, wherein the calculation formula for the second optimized tooth thickness is: Scn_g=Scn-2δg, where Scn_g is the second optimized tooth thickness and δg is the transition undercut amount;

[0082] S13. Draw the first involute 1 according to the number of gear teeth, module, pressure angle and the first optimized tooth thickness; draw the second involute 2 according to the number of gear teeth, module, pressure angle and the pitch circle chord tooth thickness; draw the third involute 3 according to the number of gear teeth, module, pressure angle and the second optimized tooth thickness.

[0083] This invention employs parametric CAD design and pre-sets the above involute equations and parameters for parametric modeling. Then, the designer inputs the gear tooth number Z, module m, pressure angle α, and pitch circle chord tooth thickness Scn parameters into the CAD system to draw the corresponding tooth profile involute (second involute 2).

[0084] When drawing the first involute 1, the designer only needs to replace the pitch circle chord tooth thickness Scn with the first optimized tooth thickness. When drawing the third involute 3, the designer only needs to replace the pitch circle chord tooth thickness Scn with the second optimized tooth thickness. Therefore, when drawing the above three separately arranged involutes, this invention only needs to use the same involute equation, which is simple to operate and convenient to use.

[0085] S2. Obtain the first correction circle parameter corresponding to the first involute 1 according to the first correction parameter and the gear basic parameter, and obtain the second correction circle parameter corresponding to the first involute 1 according to the second correction parameter and the gear basic parameter;

[0086] In this step, the first and second correction circle parameters mentioned above are two correction circle parameters specifically set by the present invention for modeling the tooth root of cold gears. These correction circle parameters mainly provide a limiting range for the tooth root transition curve, and the correction circle parameters can be either the correction circle diameter or the correction circle radius (preferably the correction circle diameter). Specifically, the steps for obtaining the above two correction circle parameters include:

[0087] S21. Calculate the first correction circle parameter based on the evaluation starting circle 12 of the finished involute and the diameter of the first correction parameter. The calculation formula for the first correction circle parameter is: D1 = D_scp + K1, where D1 is the first correction circle parameter, K1 is the first correction parameter, and D_scp is the diameter of the evaluation starting circle 12 of the finished involute.

[0088] S22. Calculate the second correction circle parameter based on the evaluation starting circle 12 of the finished involute and the diameter of the second correction parameter. The calculation formula for the second correction circle parameter is: D2 = D_scp - K2, where D2 is the second correction circle parameter and K2 is the second correction parameter.

[0089] S3. Draw the preliminary outline of the tooth groove according to the basic gear parameters, the first correction circle parameter and the second correction circle parameter;

[0090] In this step, the center of the first correction circle 11 and the center of the second correction circle 13 are both the center of the gear circle. The step of drawing the preliminary outline of the tooth root includes: S31, drawing the tooth root circle 14 according to the diameter of the tooth root circle, drawing the tooth tip circle 15 according to the diameter of the tooth tip circle, drawing the first correction circle 11 according to the first correction circle parameters, and drawing the second correction circle 13 according to the second correction circle parameters; S32, determining the preliminary outline of the tooth groove according to the first involute 1, the tooth root circle 14, the tooth tip circle 15, the first correction circle 11 and the second correction circle 13.

[0091] The main function of the aforementioned preliminary tooth groove contour line and tooth root transition curve limiting circle is to make the subsequent tooth root transition curve construction method more reasonable. After obtaining the aforementioned preliminary tooth groove contour line and tooth root transition curve limiting circle, the present invention only needs to construct the corresponding tooth root arc 8 and tooth root transition curve.

[0092] S4. Draw the tooth root arc 8 according to the third involute 3 and the basic parameters of the gear;

[0093] In this step, the gear tooth root of the present invention can adopt a full circular arc or a near-full circular arc structure. When a near-full circular arc structure is adopted, the arc length of the non-full circular arc connecting the tooth root is ≤0.2mm.

[0094] The steps for using a full circular arc include: S41, obtaining the intersection point of the third involute 3 and the second modified circle 13, denoted as the fifth point, i.e., point E; S42, drawing a fifth circular arc tangent to both the third involute 3 and the tooth root circle 14 through the fifth point. At this point, the aforementioned fifth circular arc is the tooth root arc.

[0095] In actual operation, an arc R is drawn through point E that is tangent to both the third involute 3 and the root circle 14, with the point of tangency between arc R and the third involute 3 located at point E. At this point, the arc R is the fifth arc. When the point of tangency between arc R and the root circle 14 intersects at a single point, the tooth root of the gear in this invention is a full circular arc tooth root, and the radius of arc R is at its maximum.

[0096] The steps of adopting a near-whole circular arc structure include: S43, after obtaining the fifth circular arc, cutting the arc line on the tooth root circle 14 that connects to the fifth circular arc as the tooth root connecting arc; S44, taking the fifth circular arc and the tooth root connecting arc together as the tooth root arc 8.

[0097] In actual operation, if the length of the connecting arc of the tooth root in the tooth root arc 8 is not zero, then the tooth root of the gear in this invention is a near-full arc tooth root. In this case, the radius of the aforementioned arc R is relatively reduced.

[0098] S5. Draw the tooth root transition curve based on the first transition parameter, the second transition parameter, the tooth root arc 8, the first involute 1, the third involute 3, and the tooth root transition curve limiting circle.

[0099] In this step, the tooth root transition curve is mainly composed of the first transition arc (curve AB), the third curve (curve BC), the second transition arc (curve CD), and the fourth curve (curve DE). The steps for drawing this tooth root transition curve include:

[0100] S51. Based on the intersection of the third involute 3 and the second modified circle 13, a portion of the length of the third involute 3 is taken as the fourth curve 7.

[0101] In this step, the designer only needs to cut a certain length of the third involute 3 along point E towards the first involute 1 as the fourth curve 4. The end of the fourth curve 7 is point D. Therefore, the fourth curve 7 is also called the arc DE or the cut segment DE. The length of the fourth curve is 0.1 to 0.2 mm.

[0102] S52. Draw the first transition arc 4 according to the first involute 1, the first transition parameter and the first correction circle 11;

[0103] In this step, the steps for drawing the first transition arc 4 are as follows: S521, obtain the intersection point of the first involute 1 and the first correction circle 11, and record it as the first point, i.e., point A; S522, draw the first transition arc 4 tangent to the first involute 1 through the first point according to the first transition radius.

[0104] In this step, the curve that coincides with the first transition arc 4 in the tooth root transition curve is the first curve. The other endpoint of the first curve is point B. Therefore, the first transition arc 4 is also called arc AB or curve AB. The radius of the first curve is 1 to 1.5 mm.

[0105] S53. Draw the second transition arc 6 according to the fourth curve 7, the second transition radius and the second correction circle 13;

[0106] In this step, the steps for drawing the second transition arc are as follows: S531, mark the endpoint of the fourth curve 7 near the second involute 2 as the fourth point, i.e., point D; S532, draw the second transition arc 6 tangent to the first involute 1 through the fourth point according to the second transition parameter (radius).

[0107] In this step, the fourth point mentioned above can be called point D. The curve in the tooth root transition curve that coincides with the second transition arc is the second transition arc. The other endpoint of the second transition arc is point C. Therefore, the second transition arc is also called arc CD or curve CD. The radius of the second transition arc is 2 to 3 mm.

[0108] S54. Draw the tangent arc 5 of the first transition arc 4 and the second transition arc 6 based on the first transition arc 4 and the second transition arc 6.

[0109] In this step, the curve that coincides with the tangent arc in the tooth root transition curve is the third curve. One end of the third curve is point B, and the other end is point C. The tangent arc 5 is also called arc BC or curve BC. As long as the first transition arc 4 and the second transition arc are kept within the range determined in steps S52 and S53, the length of the third curve can be accepted.

[0110] In actual operation, the arc determined by the first transition circle s (the first transition arc) is also called the convex arc, and the arc determined by the second transition circle (the second transition arc) is also called the concave arc. The arc spacing between the first point A and the fourth point D is relatively small (0.75~1.5mm), and the variation values ​​of the above-mentioned convex and concave arcs will not be too large.

[0111] S55. Determine the tooth root transition curve based on the fourth curve 7, the tangent circle 5, the first transition circle 4, and the second transition circle 6.

[0112] In this step, if the fourth curve 7, tangent circle 5, first transition circle 4 and second transition circle 6 are already available in the drawing software (such as CAD), the designer only needs to determine the above-mentioned tooth root transition curve according to the technical requirements of the gear tooth root and the shape it should have, which will not be elaborated here.

[0113] S6. Draw the tooth tip chamfer according to the preset chamfer parameters and the second involute 2, and make the extension line of the tooth tip chamfer intersect the first involute 1 and the tooth tip circle 15 respectively.

[0114] In this step, the chamfering parameters mentioned above are determined by the staff based on the final product requirements of the cold-extruded gear.

[0115] In actual work, such as Figure 3 As shown, the present invention has obvious features including a first involute 1, a first curve 4 (the tooth surface where the convex arc is located), a fifth arc 8 (that is, the tooth root arc (8) surface), a tooth tip arc surface 10, a second transition arc 6 (the tooth surface where the convex arc is located), and a tooth tip chamfer surface 9.

[0116] like Figure 4The finished product of the cold-extruded gear constructed according to the modeling method described in this invention after grinding is shown. Figure 4 There is no protrusion at the intersection point N shown, the first curve 4 disappears, and the distance between the extension of the second involute 2 and the tooth root transition curve DE (the fourth curve) is 0.02 to 0.05 mm.

[0117] In actual work, given the first involute 1, the second involute 2, the third involute 3, the preliminary tooth groove outline, the tooth root arc 8, the tooth root transition curve, the first correction circle 11, and the second correction circle 13, designers only need to determine the tooth root curve of the cold-extruded gear in drawing software (such as CAD) based on existing gear modeling methods and the existing technical requirements and required shape of the gear tooth root. Then, based on the aforementioned tooth root curve of the cold-extruded gear and existing gear modeling requirements, the modeling of the cold-extruded gear can be completed. This will not be elaborated further here.

[0118] The model of a single tooth of a cold-extruded gear after grinding, constructed according to the modeling method described in this invention, is shown below. Figure 5 As shown, at this time, the cold-extruded gear has obvious characteristics: the tooth surface defined by the second involute 2, the fifth arc 8, the tooth tip arc surface 10, the tooth surface defined by the second transition arc 3, and the remaining surface of the tooth tip chamfer 9.

[0119] To more clearly illustrate the technical solution of the present invention, several embodiments are also provided based on the above-mentioned requirements for cold-extruded gears, as follows:

[0120] Example 1:

[0121] like Figure 6 As shown, the rear auxiliary gearbox of a heavy-duty transmission uses planetary spur gear transmission. Its planetary gears have 19 teeth (Z), a module (m) of 3.755, a pressure angle (α) of 22.5°, a tip circle diameter of Φ83.35, a root circle diameter of Φ67.0, a starting circle diameter (D_scp) of Φ70.0, and a pitch circle chordal tooth thickness (Scn) of 8.200. The construction requirements for this cold-extruded gear are as follows:

[0122] (1) The tooth root adopts a full circular arc structure and is tangent to the tooth root circle 14 at a point F;

[0123] (2) Single-sided grinding amount δm: The distance between the first involute 1 and the second involute 2 is 0.10 mm;

[0124] (3) Transition sinking amount δg: The distance between the extension of the second involute 2 and the tooth root transition curve DE (fourth curve) is 0.035mm, and the length of the sinking section arc DE (fourth curve) is 0.15mm;

[0125] (4) First correction circle parameter D1 = Φ70.5~Φ71 (actual size Φ71), second correction circle parameter D2 = Φ68~Φ69 (actual size Φ68.9);

[0126] (5) Tooth root transition curve: The radius of the first transition arc (i.e., the first transition parameter) R1 is 1.2mm, the radius of the second transition arc (i.e., the first transition parameter) R2 is 2.2mm, and the connecting tangent of the two arcs is the third curve (arc BC).

[0127] According to the construction method (2) in the above embodiment 1, the first optimized tooth thickness can be calculated as 8.400, and according to the construction method (3) in embodiment 1, the second optimized tooth thickness (the thickness of the hypothetical tooth for sinking) can be calculated as 8.130.

[0128] Example 2:

[0129] like Figure 7 As shown, the rear auxiliary gearbox of a heavy-duty transmission uses planetary spur gear transmission. Its sun gear has 24 teeth (Z), a module (m) of 3.755, a pressure angle (α) of 22.5°, a tip circle diameter (Φ100.35), a root circle diameter (Φ83.9), a starting circle diameter (D_SCP) of Φ88.0, and a pitch circle chordal tooth thickness (Scn) of 7.123. The method for constructing this gear as a cold-extruded semi-finished product is as follows:

[0130] (1) The tooth root adopts a near-full circular arc structure. The two circular arcs are tangent to the tooth root arc (8) at points F and G respectively. The length of the connecting segment FG of the tooth root circle 14 is 0.1mm.

[0131] (2) Single-sided grinding amount δm: The distance between the first involute 1 and the second involute 2 is 0.12mm;

[0132] (3) Transition sinking amount δg: The distance between the extension of the second involute 2 and the tooth root transition curve DE (fourth curve) is 0.035mm, and the length of the sinking section arc DE (fourth curve) is 0.15mm;

[0133] (4) First correction circle parameter D1 = Φ88.5~Φ89 (actual size Φ88.5), second correction circle parameter D2 = Φ86~Φ87 (actual size Φ86.3);

[0134] (5) Tooth root transition curve: The radius of the first transition arc (i.e., the first transition parameter) R1 is 1mm, the radius of the second transition arc (i.e., the second transition parameter) R2 is 2mm, and the connecting tangent of the two arcs is the third curve (arc BC).

[0135] According to the construction method (2) in the above embodiment 1, the first optimized tooth thickness can be calculated as 7.363. According to the construction method (3) in embodiment 1, the second optimized tooth thickness (the thickness of the hypothetical tooth for sinking) can be calculated as 7.053.

[0136] Example 3:

[0137] like Figure 8 As shown, the rear auxiliary gearbox of a heavy-duty automatic transmission uses planetary helical gear transmission. The planetary gears have 26 teeth (Z), a module (m) of 3, a pressure angle (α) of 22.5°, a helix angle of 11°, a tip circle diameter of 86.3, a root circle diameter of 71.5, a finished involute evaluation starting circle (D_scp) diameter of Φ75.172, and a common normal length (W4) of 32.383. Based on these parameters, the end face tooth parameters of the helical gear can be calculated: end face module of 3.056 and end face tooth thickness of 5.102. The cold extrusion semi-finished product construction method for this gear is as follows:

[0138] (1) The tooth root adopts a full circular arc structure and is tangent to the tooth root circle 14 at a point F;

[0139] (2) Single-sided grinding amount δm: The distance between the first involute 1 and the second involute 2 is 0.15mm;

[0140] (3) Transition sinking amount δg: The distance between the extension of the second involute 2 and the tooth root transition curve DE (fourth curve) is 0.035mm, and the length of the sinking section arc DE (fourth curve) is 0.15mm;

[0141] (4) First correction circle parameter D1 = Φ75.672~Φ76.172 (actual size Φ76), second correction circle parameter D2 = Φ73.172~Φ74.172 (actual size Φ73.730);

[0142] (5) Tooth root transition curve: The radius of the first transition arc (i.e., the first transition parameter) R1 is 1mm, the radius of the first transition arc (i.e., the first transition parameter) R2 is 2mm, and the connecting tangent of the two arcs is the third curve (arc BC).

[0143] According to the construction method (2) in the above embodiment 3, the first optimized tooth thickness can be calculated as 5.402, and according to the construction method (3) in embodiment 3, the second optimized tooth thickness (the thickness of the hypothetical tooth for sinking) can be calculated as 5.032.

[0144] In actual operation, the main production process of cold-extruded gears includes: billet annealing – cleaning and lubrication – cold extrusion of the gear shape – high-temperature tempering – rough turning and finish turning – tooth end chamfering – marking – carburizing and quenching, low-temperature tempering – grinding the inner bore – grinding the gears. Those skilled in the art can complete the above-mentioned main production process of cold-extruded gears based on existing production processes, which will not be elaborated upon here.

[0145] like Figure 10 As shown, Figure 10 The image shows a physical photograph of a spur-tooth cold-extruded gear manufactured according to the method described in this invention after cold extrusion grinding; as shown. Figure 11 As shown, Figure 11 The image shows a finished product of a helical cold-extruded gear manufactured according to the method described in this invention, after cold extrusion grinding. Gear measuring instruments show that both the spur and helical cold-extruded gears exhibit significant undercutting characteristics at the tooth root. For example, Figure 12 The report on the tooth profile inspection of the spur-tooth cold-extruded gear is presented, showing that the helical-tooth cold-extruded gear meets the design requirements.

[0146] To further illustrate that the transition undercutting amount δg in this invention is a solution not easily conceived by those skilled in the art, a comparative experiment was also conducted for Example 2, as follows: The distance between the extension of the first involute 1 and the tooth root transition curve DE (fourth curve) is 0.07–0.085 mm, the undercutting section DE is 0.15 mm long, and after grinding with a 0.12 mm allowance on one side, the distance between the extension of the second involute 2 and the tooth root transition curve DE (fourth curve) is -0.035–-0.05 mm. For this comparative experiment, the technical requirements are the same as in Example 2, except that the transition undercutting amount δg differs from that in Example 2.

[0147] In actual operation, the physical image of the cold-extruded gear product manufactured according to the technical requirements of the above comparative test is as follows: Figure 13 As shown, by Figure 13 It can be seen that the finished cold-extruded gear has grinding steps at the tooth root.

[0148] Furthermore, to further demonstrate that the tooth root undercut δg of the present invention can improve the single-tooth bending fatigue strength of cold-extruded gears, the present invention also conducted single-tooth bending fatigue performance tests on cold-extruded gears manufactured according to the technical requirements of the above comparative experiment and cold-extruded gears manufactured according to the technical requirements of Example 2. The results are as follows:

[0149] Table 1. Example 2: Single-tooth bending fatigue performance test

[0150]

[0151] As shown in Table 1, for the ground-cooled extruded gear manufactured according to the technical requirements of the above comparative experiment, its single-tooth bending fatigue strength is 88.8KN, which is less than the 100KN of the hobbing gear. Compared with the hobbing gear, the single-tooth bending fatigue strength is reduced by 11.2%. It can be seen that the tooth root undercutting amount δg in the comparative experiment exceeds the range of the above semi-finished tooth root construction parameters, and its tooth root bending fatigue strength is significantly lower than that of the hobbing gear.

[0152] For the cold-extruded gear manufactured according to the technical requirements of Example 2, its single-tooth bending fatigue strength is 119.5KN, exceeding the 100KN of the hobbing gear. Compared with the hobbing gear, the single-tooth bending fatigue strength is improved by 19.5%. Therefore, the cold-extruded semi-finished gear root construction method described in this invention is feasible. In particular, a reasonable tooth root undercut can improve the single-tooth bending fatigue strength of the cold-extruded gear, fully leveraging the advantages of cold-extruded gears in reducing processing costs, improving production efficiency, and enhancing product performance.

[0153] In actual work, after the designer draws the tooth root curve of the cold extruded gear according to the method described in steps S1 to S6 of the present invention, the cold extruded gear can be modeled by simply following the existing gear modeling method, which will not be elaborated here.

[0154] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0155] (1) This invention is not affected by hobbing cutters and hobbing programs, and the design process is simple and suitable for cold extrusion forming. As can be seen from the parameters and drawing steps of tooth root construction, the tooth root transition curve does not involve hobbing cutter parameters and hobbing envelope curves during construction, nor does it design multiple complex modeling equations such as extended involute parameter equations and extended involute envelope equations. This invention only uses the first transition arc, tangent arc, second transition arc and fourth curve to complete the drawing of the tooth root transition curve, which is simple and convenient to operate.

[0156] (2) After grinding, the cold extruded gear made according to the method of the present invention has a complete involute evaluation section on its tooth surface, no tooth root protrusion and no stress concentration; at the same time, the intersection of its transition curve and the second involute 2 is located below the second involute evaluation starting circle (that is, the finished product involute evaluation starting circle) D_scp, that is, after the finished product is ground, the tooth surface above D_scp can be used for inspection and evaluation, and due to the existence of the sink cut determined by the fourth curve (arc DE), the cold extruded gear will not produce grinding steps formed by stress concentration.

[0157] (3) This invention can guide the design of cold extrusion tooth molds. The semi-finished gears formed by cold extrusion process have complete metal flow lines. The tooth root part will not be processed during grinding. The tooth root bending fatigue strength of the gear is improved compared with the hobbing part.

[0158] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0159] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0160] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes several instructions to cause a terminal device to execute the methods described in the various embodiments of the present invention.

[0161] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A method of modeling a cold extruded gear tooth root, characterized by, include: The first involute (1) is drawn based on the pitch circle chord tooth thickness, single-sided grinding amount of the tooth surface and the basic parameters of the gear. The second involute (2) is drawn based on the pitch circle chord tooth thickness and the basic parameters of the gear. The third involute (3) is drawn based on the pitch circle chord tooth thickness, transition undercut amount and the basic parameters of the gear. The first optimized tooth thickness is calculated based on the single-sided grinding amount of the tooth surface and the pitch circle chord tooth thickness. The calculation formula for the first optimized tooth thickness is: Scn_R=Scn+2δm, where Scn_R is the first optimized tooth thickness, Scn is the pitch circle chord tooth thickness, and δm is the single-sided grinding amount of the tooth surface. The second optimized tooth thickness is calculated based on the transition undercut amount and the pitch circle chord tooth thickness. The calculation formula for the second optimized tooth thickness is: Scn_g = Scn - 2δg, where Scn_g is the second optimized tooth thickness and δg is the transition undercut amount. The first involute (1) is drawn based on the number of gear teeth, module, pressure angle and the first optimized tooth thickness. The second involute (2) is drawn based on the number of gear teeth, module, pressure angle and the pitch circle chord tooth thickness. The third involute (3) is drawn based on the number of gear teeth, module, pressure angle and the second optimized tooth thickness. The first correction circle parameter corresponding to the first involute (1) is obtained according to the first correction parameter and the gear basic parameter, and the second correction circle parameter corresponding to the third involute (3) is obtained according to the second correction parameter and the gear basic parameter; The first correction circle parameter is calculated based on the evaluation starting circle (12) of the finished involute and the diameter of the first correction parameter. The calculation formula of the first correction circle parameter is: D1 = D_ scp + K1, where D1 is the first correction circle parameter, K1 is the first correction parameter, and D_ scp is the diameter of the evaluation starting circle (12) of the finished involute. The second correction circle parameter is calculated based on the evaluation starting circle (12) of the finished involute and the diameter of the second correction parameter. The calculation formula of the second correction circle parameter is: D2 = D_scp - K2, where D2 is the second correction circle parameter and K2 is the second correction parameter. Based on the basic gear parameters, the first correction circle parameter, and the second correction circle parameter, a preliminary outline of the tooth groove is drawn; Draw the tooth root arc (8) based on the third involute (3) and the basic parameters of the gear. The tooth root transition curve is drawn based on the first transition parameter, the second transition parameter, the tooth root arc (8), the first involute (1), and the third involute (3); The first correction parameter, the second correction parameter, the first transition parameter, and the second transition parameter are cold extrusion parameters known before constructing the gear tooth root curve.

2. The cold-extruded gear root modeling method of claim 1, wherein, The step of drawing the preliminary contour line of the tooth groove based on the basic parameters of the gear, the first correction circle parameter, and the second correction circle parameter includes: Draw the root circle (14) according to the root circle diameter, draw the tip circle (15) according to the tip circle diameter, draw the first correction circle (11) according to the first correction circle parameter, and draw the second correction circle (13) according to the second correction circle parameter. The preliminary contour line of the tooth groove is determined based on the first involute (1), the root circle (14), the tip circle (15), the first correction circle (11), and the second correction circle (13).

3. The cold-extruded gear root modeling method of claim 2, wherein, The step of drawing the tooth root arc (8) based on the third involute (3) and the basic parameters of the gear includes: Obtain the intersection point of the third involute (3) and the second modified circle (13), and denote it as the fifth point; A fifth arc is drawn through the fifth point, which is tangent to the third involute (3) and the tooth root circle (14). The fifth arc is the tooth root circle (8).

4. The cold-extruded gear root modeling method of claim 3, wherein, The step of drawing the tooth root arc based on the third involute (3) and the basic parameters of the gear also includes: After obtaining the fifth arc, the arc line on the tooth root circle (14) that connects to the fifth arc is cut off as the tooth root connecting arc; The fifth arc and the tooth root connecting arc are combined to form the tooth root arc (8).

5. The cold-extruded gear root modeling method of claim 2, wherein, The step of drawing the tooth root transition curve based on the first transition parameter, the second transition parameter, the tooth root arc (8), the first involute (1), and the third involute (3) includes: The third involute (3) is cut off at the intersection of the third involute (3) and the second correction circle (13) to form a portion of the length of the third involute (3) as the fourth curve (7); Draw the first transition arc (4) based on the first involute (1), the first transition parameter and the first correction circle (11); The second transition arc (6) is drawn based on the fourth curve (7), the second transition parameter and the second correction circle (13); Draw the tangent arc of the first transition arc and the second transition arc based on the first transition arc and the second transition arc (5); The tooth root transition curve is determined based on the fourth curve (7), the tangent arc (5), the first transition arc (4), and the second transition arc (6).

6. The cold extrusion gear tooth root modeling method as described in claim 5, characterized in that, The step of drawing the first transition arc (4) based on the first involute (1), the first transition parameter, and the first correction circle (11) includes: Obtain the intersection point of the first involute (1) and the first modified circle (11), and denote it as the first point; Draw a first transition arc (4) tangent to the first involute (1) through the first point according to the first transition parameters.

7. The cold extrusion gear tooth root modeling method as described in claim 5, characterized in that, The step of drawing the second transition arc (6) based on the fourth curve (7), the second transition parameter, and the second correction circle (13) includes: Mark the endpoint of the fourth curve (7) near the second involute (2) as the fourth point; Draw a second transition arc (6) tangent to the third involute (3) through the fourth point according to the second transition parameters.

8. The cold extrusion gear tooth root modeling method as described in claim 5, characterized in that, Draw the tooth tip chamfer according to the preset chamfer parameters and the second involute (2), and make the extension line of the tooth tip chamfer intersect the first involute (1) and the tooth tip circle (15) respectively.

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