A method for evaluating the root fillet of internal gears

Abstract

A method for evaluating the root fillet of an internal gear uses a progressive calculation starting from the tooth profile termination circle to determine the maximum radius of the root fillet. The method then calculates the position of a point on the diameter of the root fillet corresponding to the termination point of the tooth profile termination circle based on the radius of the tooth profile termination circle and the maximum radius of the root fillet, thereby determining the position of the root circle. By progressively calculating the maximum radius of the root fillet starting from the tooth profile termination circle, the present invention accurately derives a solution for the root fillet of an internal gear ring, thereby improving the load-bearing capacity of the internal gear ring teeth.

Description

Technical Field

[0001] The present invention relates to a method for evaluating a tooth root fillet, and in particular to a method for evaluating a tooth root fillet of an internal gear. Background Art

[0002] Internal gear rings are widely used in planetary reduction mechanisms in automobiles and engineering machinery. For example, invention patent applications with application number CN202210724400.1, titled "A nitrided internal gear ring for high-speed and heavy-loaded automobiles and its production process" and invention patent applications with application number CN202210231383.8, titled "A high-precision internal gear processing method for planetary gear systems," are both about the application of internal gears.

[0003] Since the speed ratio of the internal gear ring is large and the torque it transmits is also large, damage to the internal gear often occurs due to stress concentration at the root of the tooth when the root is subjected to force. Therefore, we have put forward new requirements for the root shape of the internal gear ring: according to the meshing requirements, the maximum root fillet is designed from the root tooth profile termination circle, so as to ensure the maximum load-bearing capacity of the gear teeth and extend the service life of the internal gear.

[0004] For example, the invention patent application with application number CN201911022159.2, entitled “Bevel gear with variable root radius transition fillet” uses gradient fillets of different radii to smoothly connect the tooth grooves. However, in this method, since the radius of the connecting fillet changes, the structure is complex and difficult to implement. Another example is the invention patent application with application number CN202111576129.3, entitled “Modeling method and system for the tooth root transition fillet of spiral bevel gears based on the full-process method”, which discloses a method for modeling the tooth root transition fillet of spiral bevel gears. However, this method is the operation of the tool during machining, not the calculation of the tooth root fillet of the internal gear itself. Moreover, these two schemes are designed for external gears and cannot be applied to internal gears. Summary of the Invention

[0005] In response to the problem that there is currently no suitable calculation method for the root fillet of internal gears, the present invention proposes a method for evaluating the root fillet of internal gears. The method accurately designs the maximum root fillet according to the root tooth profile termination circle diameter required by the meshing, thereby improving the load-bearing capacity of the gear teeth.

[0006] The technical means adopted by the present invention to solve the above problems are: a method for evaluating the root fillet of an internal gear, which starts from the tooth profile termination circle and progressively calculates the maximum radius of the root fillet, and then calculates the position of the point on the diameter corresponding to the termination point of the tooth profile termination circle on the root fillet based on the tooth profile termination circle radius and the maximum radius of the root fillet, thereby determining the position of the root circle.

[0007] Furthermore, the calculation process of the maximum radius of the root fillet is as follows: a coordinate system is established with the gear center as the coordinate origin (0, 0) and the line connecting the coordinate origin and the midpoint of a certain root as the X-axis, and the position of the end point of the tooth profile end circle in the coordinate system is calculated according to the radius Rz of the tooth profile end circle at the root (x1, y1), and then the maximum radius R of the root fillet is obtained by progressive calculation, and then the point (x2, y2) corresponding to the point (x1, y1) on the root fillet diameter where the point (x1, y1) is located is calculated, so as to obtain the root fillet with the largest radius.

[0008] Furthermore, the maximum radius R of the root fillet obtained by progressive calculation means: setting an initial value R0 and a cyclic increment value r for the radius R, calculating the position (x0, y0) of the center of the root fillet in the coordinate system based on the point (x1, y1) and R, and judging the relationship between the distance Rr between the center (x0, y0) and the coordinate origin (0, 0), the root fillet radius R, and the root circle radius Rcg of the internal gear to determine whether the root fillet radius R has reached the maximum value.

[0009] Furthermore, when the maximum radius R of the tooth root fillet is obtained by progressive calculation, first set R=R0 and judge whether R+Rr is less than Rcg; if not, judge whether the tooth root fillet radius R has reached the maximum value; if so, assign R+r as the new value of R, and judge again whether R+Rr is less than Rcg, and repeat this cycle until R+Rr is less than Rcg.

[0010] Furthermore, calculating the position (x1, y1) of the end point of the tooth profile termination circle in the coordinate system based on the radius Rz of the tooth profile termination circle at the tooth root means: calculating based on the radius Rz of the tooth profile termination circle and the angle Az between the radius Rz of the tooth profile termination circle and the X-axis, x1=Rz*cos Az, y1=Rz*sin Az.

[0011] Furthermore, Az is calculated as follows: based on half of the arc tooth thickness center angle As, the pitch circle involute function angle inv(A1) and the termination circle involute function angle inv(A2), Az=As+inv(A1)-inv(A2), where A1 is the pitch circle end face pressure angle, and A2 is the tooth profile termination circle end face pressure angle.

[0012] Furthermore, half of the arc tooth thickness center angle As is calculated as: As=SS / (2*Rd), where SS is the arc tooth thickness and Rd is the pitch circle radius.

[0013] Furthermore, the calculation of A1 in inv(A1) is: A1=arcos(Rb / Rd), where Rb is the base circle radius; the calculation of A2 in inv(A2) is: A2=arcos(Rb / Rz).

[0014] Furthermore, the position of the center of the root fillet in the coordinate system (x0, y0) is calculated based on the point (x1, y1) and R as follows: x0=x1-R*sin Ax, y0=y1-R*cos Ax, where Ax is the angle between the normal on the involute at the point (x1, y1) and the Y axis.

[0015] Furthermore, the angle Ax is calculated as: Ax=A2-arctan(y1 / x1).

[0016] Furthermore, the calculation of the point (x2, y2) corresponding to the point (x1, y1) on the root fillet diameter where the point (x1, y1) is located is: x2 = x1-2R*sin Ax, y2 = y1-2R*cos Ax.

[0017] The beneficial effects of the present invention are:

[0018] 1. The present invention progressively calculates the maximum radius of the tooth root fillet starting from the tooth profile termination circle, accurately derives a solution method for the tooth root fillet of the inner ring gear, and improves the load-bearing capacity of the inner ring gear teeth. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a schematic diagram of the internal gear structure of embodiment 1;

[0020] Figure 2 for Figure 1 A partial enlarged schematic diagram;

[0021] Figure 3 for Figure 2 A partially enlarged schematic diagram. DETAILED DESCRIPTION

[0022] The present invention is further described below with reference to the accompanying drawings. The accompanying drawings are for illustrative purposes only and are schematic, not actual, representations. They should not be construed as limiting this patent. To better illustrate the embodiments of the present invention, some components in the accompanying drawings may be omitted, enlarged, or reduced in size, and do not represent the actual dimensions of the products. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted from the accompanying drawings.

[0023] Example 1

[0024] like Figure 1-Figure 3As shown in the figure, a method for evaluating the root fillet of an internal gear is established, in which a plane coordinate system is established with the gear center as the coordinate origin (0, 0) and the line connecting the coordinate origin and the midpoint of a certain root as the X-axis. The normal line L is tangent to the base circle BC at the tooth profile termination circle of this root (the root tooth profile termination circle is the termination point of the meshing between the internal gear and the external gear, and its radius Rz can be calculated based on the meshing conditions). The intersection point (x1, y1) of the normal line L and the tooth profile termination circle is the starting point of the desired root fillet, and since the normal line on the involute will definitely pass through the center of the tangent circle, the center of the desired root fillet must be on the normal line L. The radius R of the root fillet is calculated using the position of point (x1, y1) in the coordinate system, and then the center position of the root fillet is calculated. Then, based on symmetry, the position of another point (x2, y2) symmetrical to point (x1, y1) on the circle where the root fillet is located is calculated. At this time, the line connecting point (x1, y1) and point (x2, y2) is the direct line of the root fillet, and the position of the root fillet in the coordinate system is also calculated.

[0025] Since the tooth profile end circle radius Rz can be calculated based on the meshing conditions, the angle Az between the tooth profile end circle radius Rz and the X-axis must be calculated to determine the position of the point (x1, y1) in the coordinate system. This angle Az is calculated based on the arc tooth thickness center angle 2*As, the pitch circle involute function angle inv(A1), and the end circle involute function angle inv(A2). As is calculated based on the proportional relationship SS / (2π*Rd) = 2As / 2π: As = SS / (2*Rd), where SS is the arc tooth thickness and Rd is the pitch circle radius. A1 in inv(A1) is the end pressure angle of the pitch circle, calculated as A1 = arcos(Rb / Rd), where Rb is the base circle radius. A2 in inv(A2) is the end pressure angle of the tooth profile end circle, calculated as A2 = arcos(Rb / Rz). Az is calculated as: Az = As + inv(A1) - inv(A2). As, inv(A1), and inv(A2) are all in radians, so the calculated result is also in radians. You can change the value of Az to degrees as needed, but this is not explained in detail here. Then, calculate the position of the point (x1, y1) in the coordinate system: x1 = Rz * cos Az, and y1 = Rz * sin Az.

[0026] After determining the position of the point (x1, y1) in the coordinate system, the position of the center (x0, y0) of the root fillet in the coordinate system is calculated according to the radius R of the root fillet. The calculation of the position of the center (x0, y0) needs to be obtained according to the angle Ax between the normal line L and the Y-axis and the angle An between the radius Rz of the tooth profile termination circle and the Y-axis. Among them: An = arctan(x1 / y1), Ax = An - (π - A2) = arctan(x1 / y1) - π + A2 = A2 - arctan(y1 / x1). And x0 = x1 - R * sin Ax, y0 = y1 - R * cos Ax.

[0027] According to symmetry, the position of another point (x2, y2) symmetric to the point (x1, y1) on the circle where the root fillet is located is: x2 = x1 - 2R * sin Ax, y2 = y1 - 2R * cos Ax. Taking the line segment connecting the point (x1, y1) and the point (x2, y2) as the diameter to make a circle is the circle where the root fillet is located. Thus, the root fillet of the internal gear with the largest radius is obtained.

[0028] In the above process, the evaluation process of the maximum radius R of the root fillet of the internal gear is as follows:

[0029] In the first step, assign an initial value R0 to the radius R, so that R = R0. This initial value can be 0, or a smaller initial value can be selected according to experience combined with the meshing situation;

[0030] In the second step, calculate the position of the center (x0, y0) according to the value of R, and then calculate the distance Rr between the center (x0, y0) and the origin (0, 0), where Rr = (x0 2 + y0 2 ) 1 / 2 ;

[0031] In the third step, judge whether R + Rr < Rcg holds, where Rcg is the radius of the root circle. If not, this R is the maximum radius; if so, enter the fourth step;

[0032] In the fourth step, increase R by a certain length r on its own basis. This r is a cyclic increment set according to the empirical value. For example, set it to 0.001, and then return to the second step.

[0033] The above embodiments are only for illustrating the present invention, rather than limiting the present invention. Those skilled in the relevant technical fields can also make various changes or transformations without departing from the spirit and scope of the present invention. Therefore, all equivalent technical solutions should also belong to the protection scope of the present invention. The protection scope of the present invention should be defined by each claim.

Claims

1. A method for evaluating the root fillet of an internal gear, characterized by: The calculation process of the maximum radius of the tooth root fillet is as follows: a coordinate system is established with the gear center as the coordinate origin (0, 0) and the line connecting the coordinate origin and the midpoint of a tooth root as the X-axis. The position of the end point of the tooth profile end circle in the coordinate system (x1, y1) is calculated based on the radius Rz of the tooth profile end circle at the tooth root. The maximum radius R of the tooth root fillet is then calculated incrementally. The point (x2, y2) corresponding to the point (x1, y1) on the tooth root fillet diameter where the point (x1, y1) is located is then calculated, thereby obtaining the tooth root fillet with the largest radius. The maximum radius R of the tooth root fillet obtained by progressive calculation means: setting an initial value R0 and a cyclic increment value r for the radius R, calculating the position of the center of the tooth root fillet in the coordinate system (x0, y0) based on the point (x1, y1) and R, and judging the relationship between the distance Rr between the center (x0, y0) and the coordinate origin (0, 0), the tooth root fillet radius R, and the tooth root circle radius Rcg of the internal gear to determine whether the tooth root fillet radius R has reached the maximum value; When the maximum radius R of the tooth root fillet is obtained by progressive calculation, first set R=R0 and judge whether R+Rr is less than Rcg; if not, judge whether the tooth root fillet radius R has reached the maximum value; if so, assign R+r as the new value of R, and judge again whether R+Rr is less than Rcg, and repeat this cycle until R+Rr is less than Rcg.

2. The internal gear tooth root fillet evaluation method according to claim 1, wherein: Calculating the position (x1, y1) of the end point of the tooth profile termination circle in the coordinate system based on the radius Rz of the tooth profile termination circle at the tooth root means: calculating based on the radius Rz of the tooth profile termination circle and the angle Az between the radius Rz of the tooth profile termination circle and the X-axis, x1=Rz*cosAz, y1=Rz*sin Az.

3. The method for evaluating the root fillet angle of an internal gear according to claim 2, wherein: Az is calculated as follows: based on half of the arc tooth thickness center angle As, the pitch circle involute function angle inv(A1) and the termination circle involute function angle inv(A2), Az=As+inv(A1)-inv(A2), where A1 is the pitch circle end face pressure angle and A2 is the tooth profile termination circle end face pressure angle.

4. The method for evaluating the root fillet angle of an internal gear according to claim 3, wherein: The calculation of half of the arc tooth thickness center angle As is: As=SS / (2*Rd), where SS is the arc tooth thickness and Rd is the pitch circle radius.

5. The method for evaluating the root fillet angle of an internal gear according to claim 3, wherein: The calculation of A1 in inv(A1) is: A1=arcos(Rb / Rd), where Rb is the base circle radius; the calculation of A2 in inv(A2) is: A2=arcos(Rb / Rz).

6. The internal gear tooth root fillet evaluation method according to claim 3, wherein: The position of the center of the root fillet in the coordinate system (x0, y0) is calculated based on the point (x1, y1) and R as follows: x0 = x1-R*sin Ax, y0 = y1-R*cos Ax, where Ax is the angle between the normal on the involute at the point (x1, y1) and the Y axis; The calculation of the point (x2, y2) corresponding to the point (x1, y1) on the root fillet diameter where the point (x1, y1) is located is: x2 = x1-2R*sin Ax, y2 = y1-2R*cos Ax.

7. The method for evaluating the root fillet angle of an internal gear according to claim 6, wherein: The angle Ax is calculated as: Ax=A2-arctan(y1 / x1).

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