A method for designing a tooth surface of a non-circular helical gear

Abstract

The embodiment of the application discloses a non-circular helical gear tooth surface design method, and relates to the field of gear design. The method comprises the following steps: establishing a three-dimensional motion relationship of a non-circular helical gear and a circular helical gear generating wheel; obtaining a tooth surface envelope equation of the non-circular helical gear according to the three-dimensional motion relationship; establishing a tooth surface equation of the circular helical gear generating wheel and obtaining a tooth surface meshing equation of the non-circular helical gear and the circular helical gear generating wheel; and obtaining a tooth surface equation of the non-circular helical gear according to the tooth surface envelope equation, the tooth surface equation of the circular helical gear generating wheel and the tooth surface meshing equation. Through the above method, the precision of the tooth surface of the non-circular helical gear can be improved, and the obtaining process is simpler.

Description

[0001] This application is a divisional application of an earlier application filed by the applicant, the earlier application number being CN202210446679.1, entitled "A Design Method for Non-Circular Helical Gears". Technical Field

[0002] This application relates to the field of gear design, and more specifically, to a method for designing non-circular helical gears. Background Technology

[0003] Gear transmission is one of the most important forms of mechanical transmission. Non-circular helical gears can transmit power with variable transmission ratios, and they offer smooth meshing and high load-bearing capacity. The actual model of a non-circular helical gear is obtained through machining. The most effective way to establish an accurate solid model of a non-circular helical gear is to obtain the tooth surface of the gear based on the machining principles.

[0004] Existing methods for obtaining the tooth surface of non-circular helical gears suffer from low accuracy and complex acquisition processes. Currently, the design of non-circular helical gears typically requires simulation using 3D design software. This method only obtains the geometric model of the tooth surface, not the mathematical model, resulting in low accuracy. Patent CN105889456B discloses another method for designing non-circular curved gears, which derives the envelope equation and meshing equation based on the tooth envelope method. Theoretically, this method can yield a more accurate mathematical model of the tooth surface. However, the envelope equation is very complex, and it is difficult to obtain the specific form of the meshing equation, thus making it difficult to obtain the specific form of the tooth surface equation for non-circular helical gears.

[0005] Therefore, traditional methods for obtaining the tooth surface of non-circular helical gears have problems such as low accuracy and complex acquisition process. Summary of the Invention

[0006] This application proposes a design method for non-circular helical gears. By rotating a circular helical gear generating wheel around a fixed center of rotation, the non-circular helical gear undergoes rotation and translation. The node between the circular and non-circular helical gear generating wheels is fixed, establishing a three-dimensional kinematic relationship between them. This yields a relatively simple tooth envelope equation, the tooth surface equation of the circular helical gear generating wheel, and the specific form of the tooth surface meshing equation between the non-circular helical gear and the circular helical gear generating wheel. Finally, a high-precision mathematical model of the non-circular helical gear tooth surface is obtained. This method improves the accuracy of obtaining the tooth surface of the non-circular helical gear and simplifies the acquisition process.

[0007] This application provides a design method for non-circular helical gears, the method comprising: establishing a three-dimensional kinematic relationship between a non-circular helical gear and a circular helical gear generating wheel; obtaining the tooth envelope equation of the non-circular helical gear based on the three-dimensional kinematic relationship; establishing the tooth surface equation of the circular helical gear generating wheel, and obtaining the tooth surface meshing equation of the non-circular helical gear and the circular helical gear generating wheel; and obtaining the tooth surface equation of the non-circular helical gear based on the tooth envelope equation, the tooth surface equation of the circular helical gear generating wheel, and the tooth surface meshing equation.

[0008] In summary, this application has at least the following technical effects:

[0009] 1. This application establishes a three-dimensional motion relationship between the non-circular helical gear and the circular helical gear by rotating the circular helical gear around a fixed rotation center, thereby causing the non-circular helical gear to rotate and translate, and fixing the nodes on the end faces of the circular helical gear and the non-circular helical gear. This results in a relatively simple tooth envelope equation, which in turn simplifies the process of obtaining the tooth surface equation of the non-circular helical gear.

[0010] 2. This application simplifies the process of obtaining the tooth surface equation of a non-circular helical gear by obtaining a specific form of the tooth surface meshing equation between the non-circular helical gear and the circular helical gear.

[0011] 3. This application obtains a specific mathematical model of the tooth surface of a non-circular helical gear through the tooth envelope equation, the tooth surface equation of a circular helical gear, and the tooth surface meshing equation, thereby improving the accuracy of the obtained non-circular helical gear tooth surface.

[0012] 4. This application utilizes a circular helical gear forming wheel to process non-circular helical gears, enabling the design of non-circular helical gears with concave pitch curves, as well as internal meshing non-circular helical gears. It exhibits high adaptability and flexibility in the design of non-circular helical gears of various shapes.

[0013] 5. By fixing the node to the rotation axis of the circular helical gear forming wheel, this application allows the circular helical gear forming wheel to retract from the same direction, thereby avoiding retraction interference and making the operation more convenient when applied to gear machining.

[0014] Therefore, the solution provided in this application can alleviate the problems of low accuracy and complex acquisition process in the methods for obtaining the tooth surface of non-circular helical gears. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 A flowchart illustrating the non-circular helical gear design method provided in Embodiment 1 of this application is shown.

[0017] Figure 2 This paper shows a spatial schematic diagram of a circular helical gear and a non-circular helical gear provided in Embodiment 1 of this application;

[0018] Figure 3 A top view of the pitch curves of a non-circular helical gear and a circular helical gear provided in Embodiment 1 of this application is shown;

[0019] Figure 4 This paper shows a tooth profile diagram of the end face of the circular helical toothed gear provided in Embodiment 1 of this application;

[0020] Figure 5 A schematic diagram of one tooth of the non-circular helical gear provided in Embodiment 1 of this application is shown;

[0021] Figure 6 A schematic diagram of the tooth surface of a non-circular helical gear provided in Embodiment 1 of this application is shown;

[0022] Figure 7 The tooth profile diagram of the end face of the internal meshing non-circular helical gear provided in Embodiment 1 of this application is shown. Detailed Implementation

[0023] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0024] Currently, existing methods for obtaining the tooth surface of non-circular helical gears typically only yield a geometric model of the tooth surface, not a mathematical model, resulting in low accuracy. Methods for obtaining the tooth surface equation of non-circular helical gears through envelope and meshing equations also suffer from complexity, as the envelope equation is intricate and the specific form of the meshing equation is difficult to derive, leading to a complicated process for obtaining the tooth surface.

[0025] Therefore, in order to solve the above-mentioned defects, this application provides a non-circular helical gear design method. The method includes: establishing the three-dimensional motion relationship between the non-circular helical gear and the circular helical gear generating wheel, obtaining the tooth envelope equation of the non-circular helical gear based on the three-dimensional motion relationship, establishing the tooth surface equation of the circular helical gear generating wheel, obtaining the tooth surface meshing equation of the non-circular helical gear and the circular helical gear generating wheel, and obtaining the tooth surface equation of the non-circular helical gear based on the tooth envelope equation, the tooth surface equation of the circular helical gear generating wheel, and the tooth surface meshing equation.

[0026] By rotating a circular helical gear forming wheel with its axis of rotation fixed, and by causing a non-circular helical gear to rotate and translate, the nodes on the end faces of the circular and non-circular helical gears are fixed. Based on this, a three-dimensional kinematic relationship between the non-circular helical gear and the circular helical gear forming wheel is established, resulting in a relatively simple tooth envelope equation. The tooth surface equation of the circular helical gear forming wheel is also established, along with the specific form of the tooth surface meshing equation between the non-circular helical gear and the circular helical gear forming wheel. This yields a high-precision mathematical model of the non-circular helical gear tooth surface, improving the accuracy of obtaining the tooth surface and simplifying the acquisition process. The non-circular helical gear design method involved in this application is described below.

[0027] Example 1

[0028] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating a non-circular helical gear design method provided in Embodiment 1 of this application. In this embodiment, the non-circular helical gear design method may include the following steps:

[0029] Step S110: Establish the three-dimensional kinematic relationship between the non-circular helical gear and the circular helical gear forming wheel.

[0030] Non-circular helical gears are helical gears whose pitch curve is not circular. Compared with non-circular spur gears, non-circular helical gears have a larger contact ratio and smoother meshing.

[0031] In the embodiments of this application, the non-circular helical gear can be a gear with an elliptical pitch curve, a gear with an inwardly concave pitch curve, or a gear with internal meshing and an arbitrary shape of pitch curve.

[0032] In this embodiment, the circular helical tooth forming wheel can be generated by the tooth profile motion trajectory of a gear shaping cutter, which is relatively easy to operate.

[0033] In an exemplary embodiment, the three-dimensional motion relationship may include: the non-circular helical gear revolving around the axis of rotation L. g The rotating shaft L performs a rotational motion. gThe intersection point with the end face of the non-circular helical gear is the rotation center O of the end face of the non-circular helical gear. g Meanwhile, the non-circular helical gear also performs translational motion on a plane parallel to its end face;

[0034] The circular helical tooth forming wheel rotates around axis L c The rotating shaft L performs a rotational motion. c The intersection point with the end face of the circular helical tooth generating wheel is the center O of the end face of the circular helical tooth generating wheel. c The end face of the non-circular helical gear and the end face of the circular helical gear are located on the same plane.

[0035] Among them, the non-circular helical gear and the circular helical gear forming wheel are in motion, but the rotation axis L of the circular helical gear forming wheel is in motion. c Fixed and perpendicular to the end face of the circular helical tooth forming wheel, intersecting the end face at the center O. c The circular helical gear producing gear rotates only around the axis L. c It rotates on its own axis, but does not translate or revolve around a non-circular helical gear.

[0036] The end face of the non-circular helical gear can be either the upper or lower surface of the non-circular helical gear. The end face of the circular helical gear forming wheel can be either the upper or lower surface of the circular helical gear forming wheel. As an optional embodiment, the end face of the non-circular helical gear is the upper surface of the non-circular helical gear, the end face of the circular helical gear forming wheel is the upper surface of the circular helical gear forming wheel, and the end face of the non-circular helical gear and the end face of the circular helical gear forming wheel are located on the same plane.

[0037] In an exemplary embodiment, step S110 may further include sub-steps S111 to S114.

[0038] Sub-step S111: The point of tangency between the pitch curve on the end face of the non-circular helical gear and the pitch curve on the end face of the circular helical gear is node P. At the initial moment, node P and the rotation center O are... g and the center O c They are on the same straight line at the initial moment, with the center O of the circle. c With the origin O0, The direction is the positive x0 axis. The positive y0 axis is the direction of rotating 90° clockwise from the positive x0 axis on the end face of the circular helical tooth forming wheel. The positive z0 axis is the direction perpendicular to the end face of the circular helical tooth forming wheel and pointing downwards. A fixed coordinate system S0 (O0-x0-y0-z0) is established, and the coordinates of the node P in the coordinate system S0 remain fixed.

[0039] like Figure 2 As shown, Figure 2 This is a schematic diagram of the pitch curves of a non-circular helical gear and a circular helical gear at the initial moment, with node P fixed at coordinate (-r) in coordinate system S0. g At position 0, r g It is equal to the pitch circle radius of the circular helical gear.

[0040] Sub-step S112: At the initial moment, with the center O c With the origin O1, The direction is defined as the positive x1 axis. The positive y1 axis is defined as the direction of the positive x1 axis rotated 90° clockwise from the end face of the circular helical tooth forming wheel. The positive z1 axis is defined as the direction perpendicular to the end face of the circular helical tooth forming wheel and pointing downwards. A moving coordinate system S1 (O1-x1-y1-z1) is established. The origin O1 and the z1 axis of the coordinate system S1 are fixed. The x1 axis and the y1 axis rotate with the circular helical tooth forming wheel.

[0041] In the embodiments of this application, such as Figure 2 As shown, at the initial moment and during the motion, the center O c It coincides with the origin O0 and the origin O1, and is fixed in the plane.

[0042] At the initial moment and during the motion, the rotation axis L c It coincides with the z0 and z1 axes and is fixed in space.

[0043] At the initial moment, the x0 axis coincides with the x1 axis, and the y0 axis coincides with the y1 axis.

[0044] During the motion, the x0 and y0 axes are fixed; the x1 and y1 axes move around the center O along with the circular helical gear. c It rotates on its own axis, and the rotation angle of the circular helical gear is equal to the rotation angle of the x1 axis and the y1 axis.

[0045] Sub-step S113: At the initial moment, with the rotation center O g O is the origin p ,by The direction is x p In the positive direction of the axis, with the x p The positive direction of the shaft is the direction of a 90° counterclockwise rotation from the end face of the non-circular helical gear. p The positive direction of the axis, with z as the direction perpendicular to the end face of the non-circular helical gear and upward. P Establish a moving coordinate system S along the positive axis. p (O p -x p -y p -z P The coordinate system S p Origin p xp axis, y p axis and z P The shaft moves in translational motion along with the non-circular helical gear.

[0046] Sub-step S114: At the initial moment, with the rotation center O g With the origin O2, The direction is defined as the positive x2 axis. The positive y2 axis is defined as the direction of the non-circular helical gear end face rotated 90° counterclockwise from the positive x2 axis. The positive z2 axis is defined as the direction perpendicular to the non-circular helical gear end face and pointing upwards. A moving coordinate system S2 (O2-x2-y2-z2) is established. The origin O2 and z2 axis of the coordinate system S2 translate with the non-circular helical gear. The x2 axis and y2 axis of the coordinate system S2 rotate and translate with the non-circular helical gear.

[0047] In the embodiments of this application, such as Figure 2 As shown, at the initial moment and during the motion, the center of rotation O g With the origin O p The origin O2 coincides with the origin and moves with the non-circular helical gear, and its translation trajectory is the same as that of the non-circular helical gear.

[0048] At the initial moment and during the motion, the rotation axis L g With z P The axis and the z2 axis coincide, and the axis moves in translational motion with the non-circular helical gear. Its translational trajectory is the same as that of the non-circular helical gear.

[0049] At the initial moment, the x0 axis and the x1 axis, x p The x-axis and x2-axis coincide, the y0-axis coincides with the y1-axis, and the y... p The axis coincides with the y2 axis.

[0050] During the motion, x p axis and y p The x2 axis only moves in translational motion with the non-circular helical gear, and its translational trajectory is the same as that of the non-circular helical gear; the x2 axis and y2 axis not only move in translational motion with the non-circular helical gear, but also move around the rotation center O with the non-circular helical gear. g It rotates on its own axis, and the rotation angle of the non-circular helical gear is equal to the rotation angle of the x2 axis and the y2 axis.

[0051] Step S120: Obtain the tooth envelope equation of the non-circular helical gear based on the three-dimensional motion relationship.

[0052] In the embodiments of this application, the tooth envelope equation is the envelope equation formed by the tooth surface of the non-circular helical gear and the tooth surface of the circular helical gear. This tooth envelope equation is used to calculate the tooth surface equation of the non-circular helical gear.

[0053] In an exemplary embodiment, step S120 may further include sub-steps S121 to S126.

[0054] Sub-step S121: Establish the pitch curve equation of the non-circular helical gear. in, The transmission ratio of the non-circular helical gear is given. The radius vector of node P in coordinate system S2 The angle between the x2 axis and the x2 axis, where α is the center distance of the non-circular helical gear pair.

[0055] In the embodiments of this application, the non-circular helical gear and the circular helical gear forming wheel are in motion, such as Figure 3 As shown, Figure 3 This is a top view of the pitch curve of a non-circular helical gear and a circular helical gear at a certain moment during their motion.

[0056] Sub-step S122: Establish the transformation relation M for transforming coordinate system S1 to coordinate system S0. 01 Where, S0 = M 01 S1,

[0057] φ1 is the rotation angle of the circular helical toothed forming wheel, and in, equal to the initial time value, r g Let be the pitch circle radius of the circular helical toothed gear.

[0058] like Figure 3 As shown, φ1 is the rotation angle of the circular helical toothed gear, that is, the angle between the y0 axis and the y1 axis. For radial The angle with the x2 axis, equal to the initial time Value, optionally, in the embodiments of this application, It equals 0°.

[0059] In this embodiment, the pitch curve of the non-circular helical gear and the pitch curve of the circular helical gear generating wheel have a pure rolling relationship; that is, in a unit time, the rolling arc length of the pitch curve of the non-circular helical gear is equal to the rolling arc length of the pitch curve of the circular helical gear generating wheel. The rolling arc length of the non-circular helical gear is... The rolling arc length of the circular helical toothed feed wheel is φ1r g Therefore, there is

[0060] Sub-step S123: Establish a transformation from coordinate system S0 to coordinate system S p Transformation relation M p0 , among which, Sp =M p0 S0,

[0061] μ is the tangent line between the pitch curve on the end face of the non-circular helical gear and the pitch curve on the end face of the circular helical gear at node P, and the radial direction of the non-circular helical gear. The included angle, and

[0062] like Figure 3 As shown, t is the tangent line at node P between the pitch curve on the end face of the non-circular helical gear and the pitch curve on the end face of the circular helical gear, and μ is the distance between the tangent line t and the radial vector. The included angle.

[0063] In this embodiment, the expression for the movement trajectory of the non-circular helical gear in the plane in the fixed coordinate system S0 can be directly derived from... Figure 3 The geometric relationships shown yield the following:

[0064] Therefore, we can obtain the transformation from coordinate system S0 to coordinate system S. p Transformation relationship

[0065] Sub-step S124: Establish coordinate system S p Transformation relation M to coordinate system S2 2p Where, S2 = M 2p S p ,

[0066] φ2 is the rotation angle of the non-circular helical gear, and Where μ0 is equal to the value of μ at the initial time.

[0067] Optional, such as Figure 2 As shown in the embodiments of this application, μ0 equals 90°. (By...) Figure 3 The geometric relationships in can be obtained

[0068] Sub-step S125: Based on the pitch curve equation of the non-circular helical gear Transformation relation M 01 The transformation relationship M p0 and the transformation relationship M 2p Determine the transformation relationship M for converting the coordinate system S1 of the circular helical gear tooth surface to the coordinate system S2 of the non-circular helical gear tooth surface. 21 Where, S2 = M 21 S1, M 21 =M 2p M p0 M01 .

[0069] Sub-step S126: According to the transformation relationship M 21 The tooth envelope equation of the non-circular helical gear is obtained as follows:

[0070] Wherein, (x1, y1, z1) are the coordinates of the tooth surface of the circular helical gear in the coordinate system S1, and (x2, y2, z2) are the coordinates of the tooth surface of the non-circular helical gear in the coordinate system S2.

[0071] The non-circular helical gear design method provided in this application involves causing a circular helical gear to rotate around a fixed center, thereby causing the non-circular helical gear to rotate and translate. The node between the circular helical gear and the non-circular helical gear is fixed in the S0 coordinate system. Based on this, a three-dimensional motion relationship between the non-circular helical gear and the circular helical gear is established, resulting in a relatively simple tooth envelope equation, which further simplifies the process of obtaining the tooth surface equation of the non-circular helical gear.

[0072] Step S130 establishes the tooth surface equation of the circular helical gear and obtains the tooth surface meshing equation between the non-circular helical gear and the circular helical gear.

[0073] In the embodiments of this application, the tooth surface meshing equation is the meshing equation between the tooth surface of the non-circular helical gear and the tooth surface of the circular helical gear. This tooth surface meshing equation is used to calculate the tooth surface equation of the non-circular helical gear.

[0074] In an exemplary embodiment, step S130 may further include sub-steps S131 and S132.

[0075] Sub-step S131: Establish the tooth surface equation of the circular helical tooth generating wheel: Where, r b Let u be the base circle radius of the circular helical toothed forming wheel. s Here, δ0 is the involute variation parameter on the end face of the circular helical tooth forming wheel, and v is the involute starting point angle of the circular helical tooth forming wheel. s denoted as the tooth width parameter of the circular helical tooth forming wheel, and p as the helical parameter of the circular helical tooth forming wheel.

[0076] The tooth surface of a circular helical tooth generating wheel can be an involute spiral surface; therefore, the form of the tooth surface equation of a circular helical tooth generating wheel can be the form of an involute spiral surface equation.

[0077] As an alternative implementation method, such as Figure 4As shown, the first complete tooth on the upper side of axis x1 is the first gear tooth, the second complete tooth is the second gear tooth, and the Nth complete tooth is the Nth gear tooth. Point E is the starting point of the involute of the first gear tooth, δ 01 Let θ be the involute starting point angle of the first tooth, and the involute starting point angle of each tooth constitutes the variable δ0.

[0078] Point F is a point on the first gear tooth, line PQ is the normal at point F, and line PQ is tangent to the base circle at point G. The angle between lines O1G and O1E is a variable u. s .

[0079] The tooth surface of a circular helical gear forming wheel can be formed by the helical motion of the tooth profile on the end face of a circular gear shaper. The tooth profile of each tooth on the end face of the circular gear shaper moves simultaneously along the z1 axis and rotates around the z1 axis, causing the tooth profile of each tooth on the end face of the circular gear shaper to undergo helical motion in space. The motion trajectory of the tooth profile of each tooth on the end face of the gear shaper forms an involute helical surface, which is the tooth surface of the circular helical gear forming wheel.

[0080] The helical parameter *p* represents the distance the involute profile on the end face of the circular gear shaper moves along the z1 axis when it undergoes helical motion and rotates through a unit angle. The tooth width parameter *v*... s This represents the angle by which the involute profile of the tooth on the end face of the circular gear shaper rotates around the z1 axis during its helical motion.

[0081] Sub-step S132: Obtain the tooth surface normal vector of the circular helical tooth generating wheel according to the tooth surface equation of the circular helical tooth generating wheel:

[0082]

[0083] Sub-step S133: When the coordinates of the meshing point between the circular helical gear tooth surface and the non-circular helical gear tooth surface in the coordinate system S1 are (x1, y1, z1), the meshing equation of the tooth surfaces of the non-circular helical gear and the circular helical gear tooth surface is obtained:

[0084]

[0085] Combining the tooth surface normal vector with the meshing equation, we can obtain:

[0086]

[0087] In an exemplary embodiment, the tooth surface meshing equation can also be expressed as:

[0088]

[0089] The non-circular helical gear design method provided in this application establishes the tooth surface meshing equation between the non-circular helical gear and the circular helical gear generating wheel, and fixes the node P of the non-circular helical gear and the circular helical gear generating wheel to obtain the specific form of the tooth surface meshing equation. Then, it combines the tooth envelope equation to carry out subsequent steps, avoiding a large number of envelope curve family boundary solution processes, and thus making the process of obtaining the tooth surface equation of the non-circular helical gear simpler.

[0090] Step S140: Obtain the tooth surface equation of the non-circular helical gear based on the tooth envelope equation, the tooth surface equation of the circular helical gear, and the tooth meshing equation.

[0091] In an exemplary embodiment, the trajectory equation of the meshing point between the tooth surface of the circular helical gear and the tooth surface of the non-circular helical gear in the coordinate system S1 is the tooth surface equation of the circular helical gear, and the trajectory equation of the meshing point between the tooth surface of the circular helical gear and the tooth surface of the non-circular helical gear in the coordinate system S2 is the tooth surface equation of the non-circular helical gear.

[0092] In an exemplary embodiment, step S140 may further include sub-step S141.

[0093] Sub-step S141: Obtain the tooth surface equation of the non-circular helical gear based on the tooth envelope equation, the tooth surface equation of the circular helical gear, and the tooth meshing equation.

[0094]

[0095] From the tooth surface meshing equation, we know that φ1 can be derived from u s δ0 and v s The expression is obtained.

[0096] Depend on It can be known that: It can be obtained from the expression for φ1, therefore It can be made by u s δ0 and v s The expression is obtained.

[0097] Depend on It can be seen that μ can be derived from... The expression is obtained from, by It can be seen that φ2 can be derived from... The expression is obtained from u, therefore φ2 can be obtained from u. s δ0 and v s The expression is obtained.

[0098] Therefore, the trajectory equation of the tooth surface coordinates (x2, y2, z2) of a non-circular helical gear can be derived from u s ,δ0,vs The expression for p is obtained.

[0099] like Figure 5 As shown, Figure 5 It is one of the teeth of a non-circular helical gear, and the tooth surface of the tooth can be an involute helical surface.

[0100] In a non-circular helical gear, each tooth corresponds to a left and a right tooth face, and the left and right tooth faces of each tooth form a complete tooth. Figure 5 Taking the gear teeth shown in the figure as an example, the tooth surface to the left of the dashed line L1 is the left tooth surface of the gear tooth, and the tooth surface to the right of the dashed line L1 is the right tooth surface of the gear tooth.

[0101] In the tooth surface equation, when

[0102]

[0103] When the equation of the tooth surface is obtained, it represents the left tooth surface of each tooth of the non-circular helical gear.

[0104] In the tooth surface equation, when

[0105]

[0106] When the equation of the tooth surface is obtained, it represents the right tooth surface of each tooth of the non-circular helical gear.

[0107] This application provides a design method for non-circular helical gears. Taking a non-circular helical gear with a known curve equation as an example, the tooth surface of the non-circular helical gear is designed according to the above method. The design parameters of the non-circular helical gear are shown in Table 1.

[0108] Table 1 Parameters of Non-Circular Helical Gears

[0109]

[0110] Circular helical gear pitch circle radius r g =17, base circle radius r b =15.97. Combining the above data and the tooth surface equation of the circular helical tooth production wheel, the involute parameter u of the circular helical tooth production wheel is used. s Involute starting angle δ0, helix parameter p, and tooth width parameter v s Using the independent variable, the tooth surface equation of the non-circular helical gear can be obtained. Specifically, the results are as follows: Figure 6 As shown.

[0111] The non-circular helical gear design method provided in this application obtains a specific mathematical model of the tooth surface of the non-circular helical gear through the tooth envelope equation, the tooth surface equation of the circular helical gear, and the tooth surface meshing equation, thereby improving the accuracy of the obtained non-circular helical gear tooth surface.

[0112] The non-circular helical gear design method provided in this application generates the tooth surface of non-circular helical gears by utilizing a circular helical gear generating wheel. It can design non-circular helical gears with concave pitch curves and can also design internally meshing non-circular helical gears, such as... Figure 7 As shown, the solution provided in this application has high adaptability and flexibility in the design of non-circular helical gears of various shapes.

[0113] The non-circular helical gear design method provided in this application also fixes the node with the center of the circular helical gear forming wheel, so that the circular helical gear forming wheel can retract from the same direction to avoid tool retraction interference, making the operation more convenient when applied to gear machining.

[0114] Example 2

[0115] Embodiment 2 of this application also provides a design method for non-circular helical gears. Unlike Embodiment 1, in this embodiment, the method for establishing the three-dimensional kinematic relationship between the non-circular helical gear and the circular helical gear generating wheel can be:

[0116] In the fixed coordinate system S0(O0-x0-y0-z0), the positive direction of the y0 axis is opposite to that in Example 1, that is, the positive direction of the y0 axis is the direction of rotating the positive direction of the x0 axis counterclockwise by 90° on the end face of the circular helical tooth forming wheel; the positive direction of the z0 axis is opposite to that in Example 1, that is, the positive direction of the z0 axis is the direction perpendicular to the end face of the circular helical tooth forming wheel and upward.

[0117] In the moving coordinate system S1 (O1-x1-y1-z1), the positive direction of the y1 axis is opposite to that in Example 1, that is, the positive direction of the y1 axis is the direction of rotating the positive direction of the x1 axis counterclockwise by 90° on the end face of the circular helical tooth forming wheel; the positive direction of the z1 axis is opposite to that in Example 1, that is, the positive direction of the z1 axis is the direction perpendicular to the end face of the circular helical tooth forming wheel and upward.

[0118] Moving coordinate system S p (O p -x p -y p -z P ), y p The positive direction of the axis is opposite to that in Embodiment 1, that is, with the x-axis... p The positive direction of the axis is the direction of rotation 90° clockwise from the end face of the non-circular helical gear. p Positive direction of the axis; z P The positive direction of the axis is opposite to that in Embodiment 1, that is, the direction perpendicular to the end face of the non-circular helical gear is defined as z. P Positive direction of the axis.

[0119] In the moving coordinate system S2(O2-x2-y2-z2), the positive direction of the y2 axis is opposite to that in Example 1, that is, the positive direction of the y2 axis is the direction of rotating the positive direction of the x2 axis 90° clockwise on the end face of the non-circular helical gear; the positive direction of the z2 axis is opposite to that in Example 1, that is, the positive direction of the z2 axis is the direction perpendicular to the end face of the non-circular helical gear and downward.

[0120] Those skilled in the art will know that the specific method for establishing the three-dimensional kinematic relationship between the non-circular helical gear and the circular helical gear generating wheel using this method, and subsequently obtaining the tooth surface equation of the non-circular helical gear, is the same as in Example 1, and will not be repeated here.

Claims

1. A method for designing the tooth surface of a non-circular helical gear, characterized in that, The method includes: S110. Establish the three-dimensional kinematic relationship between non-circular helical gears and circular helical gears; S120. Obtain the tooth envelope equation of the non-circular helical gear based on the three-dimensional motion relationship; S130. Establish the tooth surface equation of the circular helical gear generating wheel, and obtain the tooth surface meshing equation of the non-circular helical gear and the circular helical gear generating wheel; S140. The tooth surface equation of the non-circular helical gear is obtained based on the tooth envelope equation, the tooth surface equation of the circular helical gear, and the tooth surface meshing equation. The three-dimensional motion relationship includes: the non-circular helical gear rotating around the axis of rotation. The rotating shaft undergoes rotational motion. The intersection point with the end face of the non-circular helical gear is the center of rotation of the end face of the non-circular helical gear. Meanwhile, the non-circular helical gear also performs translational motion on a plane parallel to its end face; The circular helical tooth forming wheel rotates around the axis The rotating shaft undergoes rotational motion. The intersection point with the end face of the circular helical tooth generating wheel is the center of the end face of the circular helical tooth generating wheel. The end face of the non-circular helical gear and the end face of the circular helical gear are located on the same plane; Step S110 includes: taking the tangent point P between the pitch curve on the end face of the non-circular helical gear and the pitch curve on the end face of the circular helical gear as node P, and at the initial moment, taking the center of the circle as the reference point. Origin ,by The direction is In the positive direction of the axis, with the aforementioned The positive direction of the shaft rotates 90° counterclockwise on the end face of the circular helical gear. The positive direction of the axis is the direction perpendicular to the end face of the circular helical tooth forming wheel and upwards. Establish a fixed coordinate system along the positive axis. ( - - - And the node P is in the coordinate system The coordinates in the image remain constant. At the initial moment, with the center of the circle Origin ,by The direction is In the positive direction of the axis, with the aforementioned The positive direction of the shaft is the direction of rotating 90° counterclockwise from the end face of the circular helical gear. The positive direction of the axis is the direction perpendicular to the end face of the circular helical tooth forming wheel and upwards. Establish a moving coordinate system along the positive axis. ( - - - The coordinate system The origin and Shaft fixed, shaft and The shaft rotates along with the circular helical toothed forming wheel; At the initial moment, with the center of rotation Origin ,by The direction is In the positive direction of the axis, with the aforementioned The positive direction of the shaft is the direction of rotating 90° clockwise from the end face of the non-circular helical gear. The positive direction of the axis is defined as the direction perpendicular to the end face of the non-circular helical gear and pointing downwards. Establish a moving coordinate system along the positive axis. ( - - - The coordinate system The origin , axis, shaft and The shaft moves in translational motion along with the non-circular helical gear. At the initial moment, with the center of rotation Origin ,by The direction is In the positive direction of the axis, with the aforementioned The positive direction of the shaft is the direction of rotating 90° clockwise from the end face of the non-circular helical gear. The positive direction of the axis is defined as the direction perpendicular to the end face of the non-circular helical gear and pointing downwards. Establish a moving coordinate system along the positive axis. ( - - - The coordinate system The origin and The shaft translates along with the non-circular helical gear, and the coordinate system... of shaft and The shaft rotates and translates along with the non-circular helical gear. Step S120 includes: Establish the pitch curve equation of the non-circular helical gear. ,in, The transmission ratio of the non-circular helical gear is given. For the node P in the coordinate system directional vector With the The included angle of the shafts, where α is the center distance of the non-circular helical gear pair; Establish a coordinate system Convert to coordinate system Transformation relationship ,in, , , Let be the rotation angle of the circular helical toothed forming wheel, and ,in, equal to the initial time value, The pitch circle radius of the circular helical toothed gear; Establish a coordinate system Convert to coordinate system Transformation relationship ,in, , , The tangent at node P to the pitch curve on the end face of the non-circular helical gear and the pitch curve on the end face of the circular helical gear is the radial direction of the non-circular helical gear. The included angle, and ; Establish a coordinate system Convert to coordinate system Transformation relationship ,in, , , Let be the rotation angle of the non-circular helical gear, and ,in, equal to the initial time value; According to the pitch curve equation of the non-circular helical gear Transformation Relationship The transformation relationship and the transformation relationship Determine the coordinate system for the tooth surface of the circular helical gear. Transformed into the coordinate system of the non-circular helical gear tooth surface Transformation relationship ,in, , ; According to the transformation relationship The tooth envelope equation of the non-circular helical gear is obtained as follows: ,in,( The tooth surface of the circular helical gear in the coordinate system is... Coordinates in ( , The tooth surface of the non-circular helical gear in the coordinate system is... The coordinates in the diagram.

2. The non-circular helical gear tooth surface design method according to claim 1, characterized in that, Step S130 includes: Establish the tooth surface equation of the circular helical tooth generating wheel: ,in, The base circle radius of the circular helical tooth forming wheel is [missing information]. The involute variable parameters are those on the end face of the circular helical tooth forming wheel. The angle at the starting point of the involute of the circular helical tooth forming wheel is [angle missing]. denoted as the tooth width parameter of the circular helical tooth forming wheel, and p as the helical parameter of the circular helical tooth forming wheel.

3. The non-circular helical gear tooth surface design method according to claim 2, characterized in that, Step S130 further includes: The normal vector of the tooth surface of the circular helical tooth generating wheel is obtained from the tooth surface equation of the circular helical tooth generating wheel: ； When the meshing point of the circular helical gear tooth surface and the non-circular helical gear tooth surface is in the coordinate system The coordinates in are ( When the non-circular helical gear and the circular helical gear are meshed, the tooth surface meshing equation is obtained as follows: 。 4. The non-circular helical gear tooth surface design method according to claim 3, characterized in that, The tooth surface meshing equation is expressed as: .

5. The non-circular helical gear tooth surface design method according to claim 4, characterized in that, The meshing point between the circular helical gear tooth surface and the non-circular helical gear tooth surface in the coordinate system The trajectory equation in the coordinate system is the tooth surface equation of the circular helical gear, and the meshing point between the tooth surface of the circular helical gear and the tooth surface of the non-circular helical gear is in the coordinate system. The trajectory equation in the equation is the tooth surface equation of the non-circular helical gear. Step S140 includes: The tooth surface equation of the non-circular helical gear is obtained based on the tooth envelope equation, the tooth surface equation of the circular helical gear, and the tooth meshing equation: 。

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