Accurate modeling method for small module involute cylindrical gear

Abstract

The application discloses a kind of small modulus involute cylindrical gear accurate modeling method, which comprises the following steps: constructing tool-tooth shape mapping equation, solving involute tooth profile point coordinates, solving tooth root circular arc point coordinates, solving tooth top circular arc point coordinates and programming calculation and software generation of geometric model.The beneficial effects of the present application: effectively improve the precision of small modulus involute cylindrical gear geometric model, the three-dimensional coordinates of target tooth surface control point are calculated and generated by programming software according to basic design parameters, the point cloud density is controllable, suitable for various CAD, CAE software, the modeling efficiency can be further improved after being written into matching plug-in, and the industrial utility is directly exerted;Using the small modulus gear geometric model provided by the present application, it can be used for dynamics analysis, contact analysis, thermodynamic analysis and other small modulus gear, and can also be used for three-dimensional modeling and numerical simulation of small modulus transmission system, the relevant calculation precision will be effectively improved, and the development of micro precision transmission field technology will be promoted.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of gear modeling, and particularly relates to a precise modeling method of a small-modulus involute cylindrical gear. BACKGROUND

[0002] Small-modulus (normal modulus less than 1 mm) gears are widely used in the fields of aerospace, instruments and intelligent devices as the core components of micro-precision transmission systems. During the product development process, engineering and technical personnel often use three-dimensional models of mechanical parts to assist further shape design or for numerical simulation. Therefore, establishing an accurate three-dimensional model of a small-modulus gear is crucial for the performance analysis and optimization design of small-modulus transmission equipment.

[0003] At present, there are few three-dimensional modeling methods for small-modulus involute cylindrical gears in China. Most technical personnel directly input the modulus less than 1 mm into the common modulus gear program to generate the required gear model. In fact, the tooth profile of the common modulus gear follows the standard basic rack profile of GB / T 1356-2001 Cylindrical Gears for General and Heavy-Duty Machinery, while the tooth profile of the small-modulus gear follows the basic profile of GB / T 2362-1990 Small-Modulus Involute Cylindrical Gears. The dedendum corner coefficients and the addendum clearance coefficients of the two basic profiles are different. Therefore, the existing modeling method ignores the principle differences between small-modulus gears and common modulus gears in the aspect of tooth profile design.

[0004] In addition, the existing modeling methods for involute cylindrical gears can be divided into modeling methods based on ideal tooth profile and modeling methods based on the principle of generating machining. The modeling principle of the former is relatively simple and is mostly used for shape representation in basic modeling software. The latter is more consistent with the actual tooth profile of most metal gears and is mostly used for precise performance evaluation or finite element simulation analysis. In the three-dimensional modeling of cylindrical helical gears, both methods consider the mapping change from the normal tooth profile to the face tooth profile, but often ignore the situation that the dedendum arc is stretched into an elliptical arc in the mapping. In addition, in the hobbing machining of small-modulus gears, a full-cut hob is sometimes used, that is, the hob bottom edge will participate in cutting and form the addendum profile, and the dedendum corner of the hob will also correspondingly process the addendum corner of the gear. In summary, the existing modeling methods for involute cylindrical gears cannot be completely applied to small-modulus involute cylindrical gears, and there is an inevitable error between the obtained results and the real tooth profile. SUMMARY

[0005] The application discloses a small-module involute cylindrical gear precise modeling method, which is based on the mapping relationship between a hobbing cutter and a tooth profile equation constructed by means of the generation machining principle and the coordinate transformation method, fully considers the top gap, tooth root, tooth tip round corner features of the small-module gear, and the end face tooth root circle arc flatness variation of the helical gear, and establishes the precise geometric model of the small-module involute cylindrical gear, thereby providing a good analysis basis for the subsequent performance research and optimal design of the small-module gear and a micro transmission system, and the technical problems involved in the background art can be effectively solved.

[0006] To achieve the above object, the technical scheme of the application is as follows:

[0007] A small-module involute cylindrical gear precise modeling method, which comprises the following steps:

[0008] Step one, analyzing the relative position and motion law of the cutter and the workpiece to be cut in the hobbing cutting, and constructing the mapping equation of the cutter surface point to the tooth profile surface point;

[0009] Step two, solving the mapping equation of the hobbing cutter side blade to the involute tooth profile, and calculating the involute tooth profile point coordinates;

[0010] Step three, solving the mapping equation of the hobbing cutter top blade to the tooth root circle arc, and calculating the tooth root circle arc point coordinates;

[0011] Step four, solving the mapping equation of the hobbing cutter bottom blade to the tooth tip circle arc, and calculating the tooth tip circle arc point coordinates;

[0012] Step five, based on the mathematical software MATLAB, the complete end face tooth profile curve equation including the involute tooth profile, the tooth root circle arc and the tooth tip circle arc is established, the end face tooth profile tooth trace is swept along the spiral angle, and the small-module involute cylindrical gear three-dimensional surface equation is obtained;

[0013] Step six, based on the obtained small-module involute cylindrical gear three-dimensional surface equation, the gear design parameters are inputted, the three-dimensional coordinates of the gear surface points are calculated, the gear surface point cloud is generated by importing the three-dimensional software CATIA, the spline curve sweeping and splicing operations are performed, and the three-dimensional geometric model of the small-module involute cylindrical gear is obtained.

[0014] As a preferred improvement of the application, step one specifically comprises the following steps:

[0015] According to the generation machining principle, in the end face view of the workpiece to be cut, the hobbing cutter and the workpiece to be cut are forced to mesh with the rack-gear motion, namely, the cutter pitch line is purely rolled relative to the gear blank division circle, and the workpiece coordinate system is constructed XOY and the cutter coordinate system X 1 PY 1, the longitudinal axis OY is parallel to PY 1 when the initial position is reached.

[0016] When the tool rotates around the workpiece being cut φ When the radius is radian, the tool pitch line PY 1. Contact point with the pitch circle of the gear blank N In the tool coordinate system X 1 PY 1. From the origin P Move from (0, 0) to point (0, rφ The meshing point between the tool and the target tooth profile is located in the workpiece coordinate system. XOY Chinese record M ( x , y In the tool coordinate system X 1 PY 1 is recorded as M’ ( x 1, y 1), then point M ( M’ In the tool coordinate system X 1 PY 1. Workpiece coordinate system XOY The mapping equation between them:

[0017] (1)

[0018] in, r The radius of the pitch circle, x The point of contact between the tool and the target tooth profile in the workpiece coordinate system XOY middle X Position on the axis y The point of contact between the tool and the target tooth profile in the workpiece coordinate system XOY middle Y Position on the axis x 1 represents the meshing point between the tool and the target tooth profile in the tool coordinate system. X 1 PY 1 X Position on axis 1 y 1 represents the meshing point between the tool and the target tooth profile in the tool coordinate system. X 1 PY 1 Y Position on axis 1 φ It is the radius of the cutting tool around the workpiece being cut.

[0019] As a preferred improvement of the present invention, step two specifically includes:

[0020] The effect of the single-sided cutting edge of the hob on the shaping of the single-sided tooth profile of the gear is analyzed. The cutting edge is divided into three parts: top edge, side edge, and bottom edge. The top edge produces the tooth root arc, the side edge produces the involute tooth profile, and the bottom edge produces the tooth tip arc.

[0021] When the hob's side edge cuts and generates an involute tooth profile, the shaft PY 1. The side cutting edge coincides with the pitch line of the cutting tooth, and the coordinates of the intersection point of the side cutting edge and the pitch line are (0, ...). y 0), engagement point M’ ( x 1, y 1) In the tool coordinate system X 1 PY The position in 1 varies with the rotation angle φ The changing coordinate function is:

[0022] (2)

[0023] in, α For pressure angle, y 0 is the intersection of the side cutting edge and the pitch line in the tool coordinate system. X 1 PY 1 Y Position on axis 1;

[0024] meshing point M’ coordinate parameters x 1. y Substituting 1 into equation (1), we obtain the involute tooth profile point. M In static coordinate system XOY The coordinates in the diagram.

[0025] As a preferred improvement of the present invention, step three specifically includes:

[0026] When the hob's top edge cuts to generate the tooth root arc, and when the helix angle of the target gear is not 0, the projection of the hob teeth on the end face of the gear blank is elongated along the pitch line, and the projection of the cutter tip fillet is an elliptical arc. Therefore, it can be represented by the parametric equation of an ellipse:

[0027] (3)

[0028] In the formula, x top , y top Representing the tool coordinate system X 1 PY 1 click M’ Distance from the center of the ellipse C The horizontal and vertical distances a , b These are the lengths of the horizontal and vertical semi-axes of the ellipse, respectively. γ Let the ellipse angle parameter be , and let the radius of the tool tip fillet be . ρ 0, helix angle is β ,but a = ρ 0, b = ρ 0 / cosβ ;

[0029] Let the center of the ellipse be C In the tool coordinate system X 1 PY 1, the coordinates of the meshing point x c , y c ) are: M’ ( x 1, y 1) in the tool coordinate system X 1 PY 1 are:

[0030] (4)

[0031] Considering the addendum, the tip clearance, and the displacement, the coordinates of the center of the ellipse in the tool coordinate system C 1 X 1 PY 1 are:

[0032] (5)

[0033] In the formula, h a * is the addendum coefficient, c * is the tip clearance coefficient, x is the displacement coefficient, m is the face module, ρ 0 * is the root fillet coefficient, m n is the normal module, α t is the face pressure angle.

[0034] Draw a normal line of the root arc through the meshing point M’ , and the axis PY 1 intersects at point N (0, rφ ), thereby associating the coordinates of the meshing point M’ with the rotation angle φ , and substituting x 1, y 1 into formula (1), the coordinates of the root arc point M in the workpiece coordinate system XOY are obtained.

[0035] As a preferred improvement of the present application, according to the provisions of GB / T 2362-1990, let c * =0.35, ρ 0* =0.2, and the rest of the coefficient values are the same as the normal modulus gear standard.

[0036] As a preferred improvement of the present application, step four specifically comprises:

[0037] When the hob bottom blade cuts to generate the addendum circle arc, and when the helix angle of the target gear is not 0, the projection of the hob tooth on the end surface of the blank is elongated along the pitch line, and the projection of the tooth root fillet is an elliptical arc, so it is also expressed by an elliptical parameter equation:

[0038] (6)

[0039] wherein, x root 、 y root respectively represent the engagement point in the tool coordinate system X 1 PY 1 The horizontal and vertical distances of M’ 1 from the center of the ellipse C 1 , a 、 b are the horizontal and vertical semi-axis lengths of the ellipse, γ is the elliptical angle parameter variable, and it is assumed that the tooth root fillet radius is also ρ 0 , then a = ρ 0 , b = ρ 0 / cos β ;

[0040] Assuming that the coordinates of the center of the ellipse C 1 in the tool coordinate system X 1 PY 1 are x c1 , y c1 , then the coordinates of the engagement point M’ ( x 1 , y 1 ) in the tool coordinate system X 1 PY 1 are:

[0041] (7)

[0042] Considering the addendum height and the modification, the coordinates of the center of the ellipse C 1 in the tool coordinate system X 1 PY 1 are:

[0043] (8)

[0044] Passing through the engagement point M’The normal of the addendum arc intersects the axis of the gear at a point PY 1 N , rφ (0, M’ ), thereby associating the coordinates of the meshing point φ with the angle of rotation x 1、 y 1 is substituted into equation (1), the coordinates of the addendum arc point M in the workpiece coordinate system XOY are obtained.

[0045] As a preferred improvement of the present application, in step six, the gear design parameters include the number of teeth, the module, the pressure angle, the tooth width, the helix angle, the modification coefficient, the dedendum corner coefficient, the addendum height coefficient, and the tip clearance coefficient.

[0046] The beneficial effects of the present application are as follows:

[0047] 1. The precision of the involute cylindrical gear geometric model of small module is effectively improved. The three-dimensional coordinates of the target tooth surface control points are calculated and generated by the programming software according to the basic design parameters. The point cloud density is controllable, suitable for various CAD and CAE software, and the modeling efficiency can be further improved after being written into a matching plug-in, which can directly exert industrial utility.

[0048] 2. The small module gear geometric model provided by the present application can be used for dynamics analysis, contact analysis, thermodynamic analysis, etc. of small module gears, and can also be used for three-dimensional modeling and numerical simulation of small module transmission systems. The related calculation precision will be effectively improved, promoting the development of micro-precision transmission technology. BRIEF DESCRIPTION OF DRAWINGS

[0049] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0050] Figure 1 is the initial pose diagram of the tool relative to the workpiece to be cut when the present application is developed and processed;

[0051] Figure 2 is the pose diagram of the tool relative to the workpiece to be cut after the tool rotates through an arc of φ when the present application is developed and processed;

[0052] Figure 3 is the diagram for distinguishing each segment of the hob tooth of the present application;

[0053] Figure 4 is the coordinate diagram of the side edge point of the hob of the present application;

[0054] Figure 5 The top blade point coordinate graph of the hob of the present application;

[0055] Figure 6 The bottom blade point coordinate graph of the hob of the present application;

[0056] Figure 7 The single-side two-dimensional end face tooth profile graph of the present application;

[0057] Figure 8 The hob envelope graph of the present application;

[0058] Figure 9 The tooth profile modeling comparison graph between the modeling method provided by the present application and the existing method;

[0059] Figure 10 The tooth profile graph when the displacement coefficient of the present application is-0.5 respectively;

[0060] Figure 11 The tooth profile graph when the displacement coefficient of the present application is 0 respectively;

[0061] Figure 12 The tooth profile graph when the displacement coefficient of the present application is 0.5 respectively;

[0062] Figure 13 The three-dimensional tooth surface graph in the mathematical software MATLAB of the present application;

[0063] Figure 14 The point cloud graph in the three-dimensional software CATIA of the present application;

[0064] Figure 15 The small modulus involute cylindrical gear model graph in the three-dimensional software CATIA of the present application. DETAILED DESCRIPTION

[0065] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present application.

[0066] It should be noted that all the directionality indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present application are only used to explain the relative position relationship, movement condition, etc. between the components in a certain specific posture (as shown in the drawings), and if the specific posture changes, the directionality indications will also change accordingly.

[0067] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0068] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection or an electrical connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0069] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0070] This invention provides a method for accurate modeling of small-module involute cylindrical gears, the method comprising the following steps:

[0071] Step 1: Analyze the relative position and motion law between the tool and the workpiece in gear hobbing, and construct the mapping equation between points on the tool surface and points on the tooth profile surface. Specifically, this includes:

[0072] According to the generating machining principle, in the end face view of the workpiece being cut, the hobbing tool and the workpiece undergo a rack-gear forced meshing motion, that is, the tool pitch line rolls purely relative to the pitch circle of the gear blank, thus establishing the workpiece coordinate system. XOY With the tool coordinate system X 1 PY 1. Set the vertical axis OY and PY 1. The initial position is when parallel; see details below. Figure 1 As shown, where, z Number of teeth m For end face module, r R is the radius of the pitch circle.

[0073] When the tool rotates around the workpiece being cut φ When the radius is radian, the tool pitch line PY 1. Contact point with the pitch circle of the gear blank N In the tool coordinate system X 1PY 1. From the origin P (0, 0) Move to point (0, rφ ), specifically as Figure 2 As shown. The engagement point between the tool and the target tooth profile is located in the workpiece coordinate system. XOY Chinese record M ( x , y In the tool coordinate system X 1 PY 1 is recorded as M’ ( x 1, y 1), then point M ( M’ In the tool coordinate system X 1 PY 1. Workpiece coordinate system XOY The mapping equation between them:

[0074] (1)

[0075] in, r The radius of the pitch circle, x The point of contact between the tool and the target tooth profile in the workpiece coordinate system XOY middle X Position on the axis y The point of contact between the tool and the target tooth profile in the workpiece coordinate system XOY middle Y Position on the axis x 1 represents the meshing point between the tool and the target tooth profile in the tool coordinate system. X 1 PY 1 X Position on axis 1 y 1 represents the meshing point between the tool and the target tooth profile in the tool coordinate system. X 1 PY 1 Y Position on axis 1 φ It represents the radius of the cutting tool as it rotates around the workpiece being cut.

[0076] Step 2: Solve the mapping equation of the hob side edge to the involute tooth profile, and calculate the coordinates of the involute tooth profile points, specifically including:

[0077] The effect of the hob's single-sided cutting edge on the shaping of the gear's single-sided tooth profile is analyzed. The cutting edge is divided into three parts: the top edge, the side edge, and the bottom edge. Figure 3 As shown, the top cutting edge produces the root arc, the side cutting edge produces the involute tooth profile, and the bottom cutting edge produces the tip arc. The involute tooth profile is the main part of the entire tooth shape, so it is calculated first.

[0078] When the hob's side edge cuts and generates an involute tooth profile, the meshing point...M’ ( x 1, y 1) In the moving coordinate system X 1 PY The position in 1 is as follows Figure 4 As shown, the shaft PY 1. The side cutting edge coincides with the pitch line of the cutting tooth, and the coordinates of the intersection point of the side cutting edge and the pitch line are (0, ...). y 0), engagement point M’ ( x 1, y 1) In the tool coordinate system X 1 PY The position in 1 varies with the rotation angle φ The changing coordinate function is:

[0079] (2)

[0080] in, α For pressure angle, y 0 is the intersection of the side cutting edge and the pitch line in the tool coordinate system. X 1 PY 1 Y Position on axis 1;

[0081] meshing point M’ coordinate parameters x 1. y Substituting 1 into equation (1), we obtain the involute tooth profile point. M In static coordinate system XOY The coordinates in the diagram.

[0082] Step 3: Solve the mapping equation of the hob tip to the tooth root arc, and calculate the coordinates of the tooth root arc point. This includes:

[0083] When the hob's top edge cuts to generate the tooth root arc, the meshing point M’ ( x 1, y 1) In the moving coordinate system X 1 PY The position in 1 is as follows Figure 5 As shown, when the helix angle of the target gear is not 0, the projection of the hob teeth on the end face of the gear blank is elongated along the pitch line, and the projection of the cutter tip fillet is an elliptical arc. Therefore, it can be represented by the parametric equation of an ellipse:

[0084] (3)

[0085] In the formula, x top , y top Representing the tool coordinate system X 1 PY 1 click M’ Distance from the center of the ellipseC The horizontal and vertical distances a , b These are the lengths of the horizontal and vertical semi-axes of the ellipse, respectively. γ Let the ellipse angle parameter be , and let the radius of the tool tip fillet be . ρ 0, helix angle is β ,but a = ρ 0, b = ρ 0 / cos β ;

[0086] Let the center of the ellipse be C In the tool coordinate system X 1 PY The coordinates in 1 are ( x c , y c ), then the meshing point M’ ( x 1, y 1) In the tool coordinate system X 1 PY The coordinates in 1 are:

[0087] (4)

[0088] Considering tooth tip height, clearance, and displacement, the center of the ellipse is obtained. C In the tool coordinate system X 1 PY Coordinates in 1:

[0089] (5)

[0090] In the formula, h a * This is the tooth tip height coefficient. c * The top void coefficient, x For displacement coefficients, m For end face module, ρ 0 * This is the root fillet factor. m n Normal modulus, α t This is the end face pressure angle. According to GB / T 2362-1990, let... c * =0.35, ρ 0 * =0.2, and the other coefficient values ​​are the same as those of the standard for constant module gears.

[0091] Through the point of engagement M’Draw the normal to the root arc, intersecting with the axis. PY 1. Intersect at point N (0, rφ ), thereby making the meshing point M’ Coordinates and rotation angles φ Related, will x 1. y Substituting into equation (1), we obtain the root arc point. M In the workpiece coordinate system XOY The coordinates in the diagram.

[0092] Step 4: Solve the mapping equation of the hob bottom edge to the tooth tip arc, and calculate the coordinates of the tooth tip arc point. This includes:

[0093] When the bottom edge of the hob cuts to generate the tooth tip arc, the meshing point M’ ( x 1, y 1) In the moving coordinate system X 1 PY The position in 1 is as follows Figure 6 As shown, when the helix angle of the target gear is not 0, the projection of the hob teeth on the end face of the gear blank is elongated along the pitch line, and the projection of the cutter root fillet is an elliptical arc, so it is also represented by the elliptical parametric equation:

[0094] (6)

[0095] in, x root , y root Representing the tool coordinate system X 1 PY The engagement point under 1 M’ Distance from the center of the ellipse C The horizontal and vertical distances of 1 a , b These are the lengths of the horizontal and vertical semi-axes of the ellipse, respectively. γ Let the ellipse angle parameter be , and let the radius of the fillet at the knife root also be . ρ 0, then a = ρ 0, b = ρ 0 / cos β ;

[0096] Let the center of the ellipse be C 1. In the tool coordinate system X 1 PY The coordinates in 1 are ( x c1 , y c1 ), then the meshing point M’ ( x 1, y1) In the tool coordinate system X 1 PY 1, the coordinates are:

[0097] (7)

[0098] Considering the addendum and the displacement, the center of the ellipse is C 1 In the tool coordinate system X 1 PY 1, the coordinates are:

[0099] (8)

[0100] Passing through the meshing point M’ The normal line of the addendum circle arc intersects the axis PY 1 at point N (0, rφ ), thereby associating the coordinates of the meshing point M’ with the rotation angle φ , substituting x 1, y 1 into equation (1), the coordinates of the addendum circle arc point M in the workpiece coordinate system XOY are obtained.

[0101] Step five, based on the mathematical software MATLAB, the complete face tooth profile curve equation including the involute tooth profile, the tooth root circle arc and the addendum circle arc is established, the face tooth profile tooth line is swept along the spiral angle to obtain the three-dimensional surface equation of the small modulus involute cylindrical gear;

[0102] Step six, based on the obtained three-dimensional surface equation of the small modulus involute cylindrical gear, the gear design parameters are input, the three-dimensional coordinates of the gear surface points are calculated, the three-dimensional software CATIA is imported, the gear surface point cloud is generated, and the three-dimensional geometric model of the small modulus involute cylindrical gear is obtained through spline curve sweeping and splicing operations.

[0103] Specifically, the gear design parameters include the number of teeth, the modulus, the pressure angle, the tooth width, the spiral angle, the displacement coefficient, the tooth root corner coefficient, the addendum height coefficient and the tip clearance coefficient.

[0104] The small modulus involute cylindrical gear precise modeling method provided by the application is verified by Example 1.

[0105] Example 1

[0106] According to the design parameters in Table 1, the method provided by the application is used to establish the small modulus involute cylindrical gear geometric model.

[0107] Table 1 Small modulus involute cylindrical gear design parameters

[0108]

[0109] Calculate and generate a single-sided two-dimensional end face tooth profile in MATLAB, such as... Figure 7 As shown.

[0110] Calculate and generate the hob toolpath, encapsulate and verify the correctness of the obtained tooth profile, as follows: Figure 8 As shown.

[0111] Compared with the tooth profile obtained by existing constant module gear modeling methods, for example Figure 9 As shown, there is a clear difference between the tooth root and the tooth tip.

[0112] The tooth profiles of the driving gear with displacement coefficients of -0.5, 0, and 0.5 are as follows: Figures 10-12 As shown, when the displacement is large enough, the bottom edge of the hob does not participate in cutting, and the tooth tip arc disappears.

[0113] Further generating three-dimensional tooth surfaces in MATLAB, such as... Figure 13 As shown.

[0114] Import the coordinates of the tooth surface points into CATIA to generate a point cloud, as shown below. Figure 14 As shown, the final 3D model is as follows. Figure 15 As shown.

[0115] The beneficial effects of this invention are as follows:

[0116] 1. Effectively improves the accuracy of the geometric model of small module involute cylindrical gears. The programming software calculates and generates the three-dimensional coordinates of the target tooth surface control points based on the basic design parameters. The point cloud density is controllable and it is applicable to various CAD and CAE software. After being written into a supporting plug-in, it can further improve the modeling efficiency and directly exert industrial benefits.

[0117] 2. The small module gear geometric model provided by this invention can be used for dynamic analysis, contact analysis, thermodynamic analysis, etc. of small module gears, as well as for three-dimensional modeling and numerical simulation of small module transmission systems. The relevant calculation accuracy will be effectively improved, promoting the development of technology in the field of micro-miniature precision transmission.

[0118] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. Other modifications can be easily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A method for accurate modeling of a fine module involute spur gear, characterized in that, The method comprises the following steps: Step one, analyzing the relative position and movement law of the cutter and the workpiece to be cut in the hobbing cutting, and constructing a mapping equation of the cutter surface point to the tooth profile surface point; Step two, solving the mapping equation of the hobbing side edge to the involute tooth profile, and calculating the involute tooth profile point coordinates; Step three, solving the mapping equation of the hobbing top edge to the dedendum arc, and calculating the dedendum arc point coordinates, specifically including: When the hobbing top edge cutting generates the dedendum arc, and when the helix angle of the target gear is not 0, the projection of the hobbing tooth on the blank end face is elongated along the pitch line, and the projection of the tooth tip fillet is an elliptical arc, so an elliptical parameter equation is used to represent: (3) wherein x top , y top respectively represent the tool coordinate system X 1 PY 1lower point M’ horizontal and vertical distance from the center of the ellipse, C , a , b respectively represent the horizontal and vertical semi-axis length of the ellipse, γ is the angle variable of the ellipse, and the tool tip radius is set as ρ 0, the helix angle is β , a = ρ 0, b = ρ 0 / cos β ; Let the center of the ellipse be C In the tool coordinate system X 1 PY 1, the coordinates of the engagement point x c , y c ) in the tool coordinate system M’ ( x 1, y 1) are X 1 PY 1 (4) Consider the addendum, top clearance, displacement, get the center of the ellipse C In the tool coordinate system X 1 PY Coordinates in 1: (5) wherein h a * is the addendum coefficient, c * is the tip clearance coefficient, x is the displacement coefficient, m is the face module, PY 0 * is the root radius coefficient, m n is the normal module, α t is the face pressure angle; Point of over engagement M’ The normal to the root fillet intersects the axis rφ 1 at the point N (0, φ ) so that the coordinates of the point of engagement M’ are related to the angle of rotation XOY and x 1, y 1 are substituted, the coordinates of the point of the root fillet M in the workpiece coordinate system Step four, solving the mapping equation of the hobbing bottom edge to the addendum arc, and calculating the addendum arc point coordinates; are obtained; Step five, based on the mathematical software MATLAB, a complete end face tooth profile curve equation including the involute tooth profile, the dedendum arc and the addendum arc is established, the end face tooth profile tooth trace is swept along the helix angle, and a three-dimensional surface equation of the small-module involute cylindrical gear is obtained; Step one specifically includes the following steps: XOY 2. The method according to claim 1, wherein: PY According to the principle of generating machining, in the end view of the workpiece to be cut, the gear hobbing cutter and the workpiece to be cut are forced to mesh like a rack and pinion, i.e. the cutter pitch line makes pure rolling relative to the tooth blank distribution circle, and the workpiece coordinate system is constructed OY with the cutter coordinate system X 1 PY 1, the longitudinal axis φ is parallel to PY 1 when it is the initial position; When the tool is rotated around the workpiece to be cut PY through an arc, the contact point of the tool pitch circle rφ 1with the blank pitch circle N In the tool coordinate system X 1 XOY 1 P from the origin (0, 0) to the point (0, PY ), the meshing point of the tool and the target tooth profile in the workpiece coordinate system PY is recorded as M ( x , y ), recorded as X ( XOY 1, M’ 1) in the tool coordinate system x 1 y 1, then the point M ( M’ ) mapping equation between the tool coordinate system X 1 XOY 1and the workpiece coordinate system XOY ​ （1） wherein r is the radius of the index circle, x is the position of the meshing point of the tool and the target tooth profile on the workpiece coordinate system PY in X the axial direction, y is the position of the meshing point of the tool and the target tooth profile on the workpiece coordinate system PY in Y the axial direction, x 1is the position of the meshing point of the tool and the target tooth profile on the tool coordinate system X 1 Step two specifically includes: 1in X 1the axial direction, y 1is the position of the meshing point of the tool and the target tooth profile on the tool coordinate system X 1 The forming action of the single-side cutting edge of the hobbing tooth on the single-side tooth profile of the gear is analyzed, and the cutting edge is divided into three parts of the top edge, the side edge and the bottom edge, wherein the top edge cutting generates the dedendum arc, the side edge cutting generates the involute tooth profile, and the bottom edge cutting generates the addendum arc; 1in Y 1the axial direction, is the radian turned by the tool around the workpiece being cut.

3. The method for accurate modeling of small module involute cylindrical gears according to claim 2, characterized in that: PY PY When the hob's side edge cuts and generates an involute tooth profile, the shaft φ 1. The side cutting edge coincides with the pitch line of the cutting tooth, and the coordinates of the intersection point of the side cutting edge and the pitch line are (0, ...). y 0), meshing point M’ ( x 1, y 1) In the tool coordinate system X 1 PY The position in 1 varies with the rotation angle XOY The changing coordinate function is: （2） wherein α is the pressure angle, y 0 is the intersection of the side edge and the pitch line in the tool coordinate system X 1 ρ 1 in the position on the axis Y 1 The coordinates of the point of engagement M’ are inserted into equation (1), i.e. x 1, y 1 into equation (1), i.e. M the coordinates in the stationary coordinate system Step four specifically includes: .

4. The method of claim 3, wherein: According to the provisions of GB / T 2362-1990, let c * = 0.35, When the hobbing bottom edge cutting generates the addendum arc, and when the helix angle of the target gear is not 0, the projection of the hobbing tooth on the blank end face is elongated along the pitch line, and the projection of the tooth root fillet is an elliptical arc, so an elliptical parameter equation is used to represent: 0 * = 0.2, and the rest of the coefficient values are the same as the standard of the normal modulus gear.

5. The method of claim 3, wherein: PY γ (6) wherein, x root , y root respectively denote the engagement point in the tool coordinate system X 1 ρ 1 M’ the horizontal and vertical distance from the center of the ellipse C 1 a , b the horizontal and vertical semi-axis length of the ellipse, ρ the angle argument of the ellipse, and let the corner radius of the tool tip also be ρ 0 a = PY 0 b = PY 0 / cos β ; Let the center of the ellipse be C 1 X 1 PY 1 x c1 , y c1 , M’ x 1 y 1 X 1 PY 1​ (7) Considering addendum and relief, the center of the ellipse is obtained C 1In the tool coordinate system X 1 rφ 1coordinates: (8) Point of over engagement M’ The normal to the addendum circle intersects the axis φ 1 at the point N (0, XOY ) and thus the point of engagement M’ is associated with the angle of rotation In step six, the gear design parameters include the number of teeth, the module, the pressure angle, the tooth width, the helix angle, the modification coefficient, the dedendum fillet coefficient, the addendum height coefficient and the tip clearance coefficient. and the x 1, y 1 is substituted into equation (1) to give the coordinates of the point of the addendum circle in the workpiece coordinate system M . ​ ​ 6. The method of claim 1, wherein: ​

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