Sprocket Design Method

Abstract

The present invention discloses a sprocket design method, including: selecting a chain model and determining the number of sprocket teeth; determining a chain link according to the number of sprocket teeth and the chain model, the chain link being a closed ring composed of multiple flat chains and multiple vertical chains arranged alternately, and the number of flat chains and vertical chains being the same as the number of sprocket teeth; determining the overall contour of the sprocket according to the selected chain; determining the external tooth profile of the sprocket according to the chain link; and determining the internal tooth profile according to the chain link and the external tooth profile of the sprocket. The sprocket design method of the present invention adopts a reverse design idea, breaks out of the empirical formula for sprocket design, can effectively reduce the design error, improve the design accuracy of the sprocket, so that the chain and the sprocket are nearly perfectly matched, and greatly reduces the quality problems such as chain mismatch, tooth jamming, tooth skipping or severe wear.

Description

Technical Field

[0001] The present invention relates to the field of mechanical technology, and particularly to a method for designing a sprocket wheel. Background Art

[0002] Chain drive is a transmission method that transmits the motion and power of a driving sprocket wheel with a special tooth profile to a driven sprocket wheel with a special tooth profile through a chain. Chain drive has the advantages of no elastic sliding and slipping phenomenon, accurate average transmission ratio, reliable operation, high efficiency; large transmission power, strong overload capacity, and smaller transmission size under the same working conditions; small required tension force and small pressure acting on the shaft; and can work in harsh environments such as high temperature, humidity, dust, and pollution, etc., and is widely used in mechanical equipment. As the main component of chain drive, the sprocket wheel plays a very important role in the operation of chain drive.

[0003] Currently, the design of the sprocket wheel is to calculate parameters such as the pitch diameter, outer diameter, and chain socket of the sprocket wheel through theoretical empirical formulas after determining the number of teeth of the sprocket wheel, the pitch of the chain, and the diameter. This design method belongs to an empirical and normal theoretical forward design method. There will inevitably be a large error between the sprocket wheel designed by this theoretical empirical formula and the actual model, and generally there are the following problems: 1. Too empirical; 2. The error of the sprocket wheel designed purely by the empirical formula is large, and there is a large deviation from the actual sprocket wheel model; 3. There is a high probability that the sprocket wheel designed purely by the empirical formula does not match the chain, and there are quality problems such as tooth jamming, tooth skipping, or severe wear. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for designing a sprocket wheel that can break out of the empirical formula, reduce the design error to a small extent, and improve the design accuracy of the sprocket wheel.

[0005] The present invention provides a method for designing a sprocket wheel, including:

[0006] Select a chain model and determine the number of teeth of the sprocket wheel;

[0007] Determine a chain link according to the number of teeth of the sprocket wheel and the chain model. The chain link is a closed ring composed of multiple flat chains and multiple vertical chains arranged alternately. The number of the flat chains and the vertical chains is the same as the number of teeth of the sprocket wheel;

[0008] Determine the overall contour of the sprocket wheel according to the selected chain;

[0009] Determine the outer tooth profile of the sprocket wheel according to the chain link;

[0010] Determine the inner tooth profile according to the chain link and the outer tooth profile of the sprocket wheel.

[0011] In one embodiment, the method for designing the sprocket wheel further includes the step of determining the inner hole diameter and the length of the sprocket wheel according to the size of the sprocket wheel shaft.

[0012] In one embodiment, when determining the chain link according to the number of teeth of the sprocket and the chain model, the flat chain and the vertical chain of the chain link have the same structure as the flat chain and the vertical chain of the selected chain, and the pitch circle radius of the chain link is determined according to the number of teeth of the sprocket and the chain model.

[0013] In one embodiment, the specific steps of determining the pitch circle radius of the chain link include:

[0014] Obtaining half of the pitch circle angle corresponding to one flat chain in the chain link;

[0015] According to half of the pitch circle angle corresponding to the flat chain;

[0016] Obtaining the actual pitch circle radius of the chain link according to the theoretical pitch circle radius of the chain link and the error coefficient.

[0017] In one embodiment, the specific method of obtaining half of the pitch circle angle corresponding to one flat chain in the chain link is: According to Calculating to obtain half of the pitch circle angle corresponding to one flat chain in the chain link;

[0018] The specific steps of obtaining the theoretical pitch circle radius of the chain link include: According to the formula Calculating to obtain the theoretical pitch circle radius of the chain link;

[0019] The specific steps of obtaining the actual pitch circle radius of the chain link include: According to Calculating to obtain the actual pitch circle radius of the chain link, where , where is the error coefficient, r is the theoretical pitch circle radius, 2α is the pitch circle angle corresponding to the flat chain, d is the chain diameter and p is the chain pitch, R is the actual pitch circle radius of the chain link, z is the determined number of teeth of the sprocket, and n is the total number of the flat chain and the vertical chain of the chain link.

[0020] In one embodiment, the specific steps of determining the overall profile of the sprocket according to the selected chain include: Determining the sprocket pitch angle, sprocket pitch circle diameter, sprocket outer diameter, sprocket vertical ring vertical groove diameter and short tooth thickness according to the selected chain and the determined number of teeth of the sprocket.

[0021] In one embodiment, determining the external tooth profile of the sprocket according to the link specifically includes: determining the external diameter of the external tooth profile according to the outer diameter of the sprocket, determining the internal diameter of the external tooth profile according to the diameter of the vertical groove of the vertical link of the sprocket, determining the standard opening angle and the maximum opening angle of the external tooth profile according to the pitch angle of the sprocket, and determining the position of the outline edge line of the standard opening angle of the external tooth profile of the corresponding sprocket tooth according to the short tooth thickness and the center line of the vertical chain of the link.

[0022] In one embodiment, the external diameter of the external tooth profile is equal to the outer diameter of the sprocket, the internal diameter of the external tooth profile is equal to the diameter of the vertical groove of the vertical link of the sprocket, the standard opening angle of the external tooth profile is equal to twice the pitch angle of the sprocket, the maximum opening angle of the external tooth profile is less than or equal to three times the pitch angle of the sprocket and greater than the standard opening angle of the external tooth profile, and the distance from the outline edge line of the standard opening angle of the external tooth profile of the sprocket tooth to the center line of the vertical chain of the corresponding link is half of the short tooth thickness; the external tooth profile includes the outline edge line of the standard opening angle of the external tooth profile and the outline line of the maximum opening angle of the external tooth profile, one end of the outline edge line of the standard opening angle of the external tooth profile is located on the circumference of the internal diameter of the external tooth profile, the other end is connected to the outline line of the maximum opening angle of the external tooth profile, and one end of the outline line of the maximum opening angle of the external tooth profile is located on the circumference of the external diameter of the external tooth profile.

[0023] In one embodiment, determining the internal tooth profile according to the link and the external tooth profile of the sprocket specifically includes: determining the external diameter and the internal diameter of the internal tooth profile according to the external diameter and the internal diameter of the external tooth profile, determining the standard opening angle of the internal tooth profile according to the standard opening angle of the external tooth profile, determining the outline edge line of the standard opening angle of the internal tooth profile according to the outline edge line of the standard opening angle of the external tooth profile, determining the tooth running edge line of the internal tooth profile according to the link, determining the small diameter of the tooth running of the internal tooth profile according to the diameter of the chain, and determining the external diameter of the tooth running of the internal tooth profile according to the link and the small diameter of the tooth running of the internal tooth profile.

[0024] In one embodiment, the external diameter and the internal diameter of the internal tooth profile are respectively equal to the external diameter and the internal diameter of the external tooth profile, the standard opening angle of the internal tooth profile is equal to the standard opening angle of the external tooth profile, and the outline edge line of the standard opening angle of the internal tooth profile is the same as the outline edge line of the standard opening angle of the external tooth profile. The outermost contour line of the flat chain of the link is mapped as the tooth running edge line of the internal tooth profile. The diameter of the small diameter of the tooth running of the internal tooth profile is equal to the diameter of the chain. An auxiliary circle is made with the center of the distal center point of the adjacent vertical chains of the link corresponding to the internal tooth being tangent to the small diameter of the tooth running of the internal tooth profile, and the external diameter of the tooth running of the internal tooth profile intersects with the auxiliary circle; the internal tooth profile includes the tooth running edge line of the internal tooth profile, the small diameter of the tooth running of the internal tooth profile, and the external diameter of the tooth running of the internal tooth profile. The two ends of the small diameter of the tooth running of the internal tooth profile are respectively connected to the tooth running edge line of the internal tooth profile and the external diameter of the tooth running of the internal tooth profile, and one end of the tooth running edge line of the internal tooth profile is located on the circumference of the external diameter of the internal tooth profile.

[0025] The sprocket design method of the present invention adopts a reverse design concept, breaks away from the empirical formula for sprocket design, can effectively reduce the design error, improve the design accuracy of the sprocket, so that the chain and the sprocket are nearly perfectly matched, and greatly reduces the quality problems such as chain mismatch, tooth jamming, tooth skipping or severe wear. Brief Description of the Drawings

[0026] Figure 1 It is a schematic structural diagram of the sprocket to be designed according to the present invention.

[0027] Figure 2 It is a schematic flow diagram of the sprocket design method according to an embodiment of the present invention.

[0028] Figure 3 is Figure 2 A schematic structural diagram of the link involved in the sprocket design method shown.

[0029] Figure 4 is Figure 2 A schematic structural diagram of the outer tooth profile of the sprocket in the sprocket design method shown.

[0030] Figure 5 is Figure 2 A schematic structural diagram of the inner tooth profile of the sprocket in the sprocket design method shown. Detailed Description of the Invention

[0031] To further elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following combines the drawings and embodiments to detail the specific implementation manner, structure, features and effects of the present invention as follows.

[0032] The present invention provides a sprocket design method for designing a sprocket. As Figure 1 shown, the sprocket generally includes a main body portion 11 and a plurality of teeth 13 provided on the outer peripheral edge of the main body portion 11. The teeth 13 include an outer tooth portion 132 and an inner tooth portion 134. For a sprocket, the design difficulties lie in the tooth profiles of the outer tooth portion and the inner tooth portion, as well as the design of the chain socket.

[0033] As Figure 2 shown, the sprocket design method according to an embodiment of the present invention includes the following steps:

[0034] S11, select the chain model and determine the number of teeth z of the sprocket. Usually, the chain model can be selected according to needs in the national standard or design manual.

[0035] S13, determine the link 10 according to the number of teeth z of the sprocket and the chain model, as Figure 3As shown in the figure, the link 10 is a closed ring composed of multiple flat chains 12 and multiple vertical chains 14 arranged alternately. The number of flat chains 12 and vertical chains 14 is the same as the number of teeth z of the sprocket. Among them, the link 10 is an intermediate component determined for the design of the sprocket. The link is a closed ring composed of an equal number of vertical chains and flat chains arranged alternately. In theory, the flat chain just meshes with the tooth profile of the sprocket, that is, the number of chains n of the link 10 is twice the number of teeth z of the sprocket, that is . Figure 3 The schematic diagram of the link structure when the number of teeth z of the sprocket is 5 is shown in the figure.

[0036] Specifically, the flat chains 12 and vertical chains 14 of the link 10 have the same structure as the flat chains and vertical chains of the selected chain, and the pitch circle radius R of the link is determined according to the number of teeth z of the sprocket and the chain model. In this way, the structure of the link 10 is determined.

[0037] Determining the pitch circle radius R of the link 10 includes the following steps:

[0038] S131, obtain half α of the pitch circle angle corresponding to a flat chain in the link. Specifically,

[0039] , where 2α is the pitch circle angle corresponding to a flat chain in the link, d is the chain diameter, p is the chain pitch, and z is the number of teeth of the sprocket.

[0040] S133, obtain the theoretical pitch circle radius r of the link according to half α of the pitch circle angle corresponding to the flat chain, d as the chain diameter, and p as the chain pitch. Specifically, .

[0041] S135, obtain the actual pitch circle radius R of the link according to the theoretical pitch circle radius r of the link 10 and the error coefficient .

[0042] Specifically, due to the error existing when the polygon approximates the ring, there is also an error in the theoretically calculated pitch circle radius r. Through comparison and calculation with the actual model, it can be known that when the number of teeth is 5, the error is only 0.75%, and the error decreases with the increase of the number of teeth. When the number of teeth is 36, the error is 0.016%, which can be completely ignored. When the number of teeth is greater than 36, it can be considered that the actual pitch circle radius R is equal to the theoretical pitch circle radius r. Then the number of teeth z and the error coefficient approximately have the following linear relationship:

[0043] .

[0044] The actual pitch circle radius R of the link is:

[0045] .

[0046] S15. Determine the overall contour of the sprocket according to the selected chain.

[0047] Specifically, determine the sprocket pitch angle according to the selected chain and the determined number of teeth of the sprocket , the sprocket pitch diameter , the outer diameter Dg of the sprocket, the diameter of the vertical groove of the sprocket's vertical ring , parameters such as the thickness W of the short tooth, etc.

[0048] The sprocket pitch angle Specifically:

[0049] , where z is the determined number of teeth of the sprocket.

[0050] The sprocket pitch diameter Specifically:

[0051] , where d is the chain diameter and p is the chain pitch.

[0052] The outer diameter Dg of the sprocket is specifically: . Since there is wear in the actual operation of the chain and sprocket, it is necessary to round the sprocket pitch circles to obtain the outer diameter Dg of the sprocket.

[0053] The diameter of the vertical groove of the sprocket's vertical ring Specifically: , where b is the maximum outer width of the chain, is the corresponding value of the chain, which can be queried by referring to the corresponding table.

[0054] The thickness W of the short tooth is specifically: , where , .

[0055] S17. Determine the external tooth profile of the sprocket according to the chain link 10.

[0056] Specifically, please refer to Figure 4 , determine the external tooth profile outer diameter Dw1 according to the sprocket outer diameter Dg, and determine the external tooth profile inner diameter Dn1 according to the diameter of the vertical groove of the sprocket's vertical ring , determine the standard opening angle β and the maximum opening angle δ of the external tooth profile according to the sprocket pitch angle , and determine the position of the standard opening angle contour line 31 of the external tooth profile of the corresponding sprocket tooth according to the thickness W of the short tooth and the vertical chain center line of the chain link.

[0057] Specifically, the external tooth profile outer diameter Dw1 is equal to the sprocket outer diameter Dg, the external tooth profile inner diameter Dn1 is equal to the diameter of the vertical groove of the sprocket's vertical ring , the standard opening angle β of the external tooth profile is equal to the sprocket pitch angle Twice that, the maximum opening angle δ of the external tooth profile is less than or equal to the sprocket pitch angle Three times that, and greater than the standard opening angle β of the external tooth profile. The distance L from the standard opening angle profile side line 31 of the external tooth profile of the sprocket tooth to the vertical chain center line of the corresponding chain link is half of the short tooth thickness W. Among them, the external tooth profile includes two parts: the standard opening angle profile side line 31 of the external tooth profile and the maximum opening angle profile line 33 of the external tooth profile. One end of the standard opening angle profile side line 31 of the external tooth profile is located on the inner diameter circumference of the external tooth profile, and the other end is connected to the maximum opening angle profile line 33 of the external tooth profile. One end of the maximum opening angle profile line 33 of the external tooth profile is located on the outer diameter circumference of the external tooth profile.

[0058] S19. Determine the internal tooth profile according to the chain link 10 and the external tooth profile of the sprocket.

[0059] Specifically, please refer to Figure 5 , determine the external diameter Dw2 and the internal diameter Dn2 of the internal tooth profile according to the external diameter Dw1 and the internal diameter Dn1 of the external tooth profile, determine the standard opening angle βn of the internal tooth profile according to the standard opening angle β of the external tooth profile, determine the standard opening angle profile side line 50 of the internal tooth profile according to the standard opening angle profile side line 31 of the external tooth profile, determine the tooth running side line 51 of the internal tooth profile according to the chain link 10, determine the tooth running minor diameter 53 of the internal tooth profile according to the chain diameter d, and determine the tooth running major diameter 55 of the internal tooth profile according to the chain link 10 and the tooth running minor diameter 53 of the internal tooth profile.

[0060] Specifically, the external diameter Dw2 and the internal diameter Dn2 of the internal tooth profile are respectively equal to the external diameter Dw1 and the internal diameter Dn1 of the external tooth profile. The standard opening angle βn of the internal tooth profile is equal to the standard opening angle β of the external tooth profile, and the standard opening angle profile side line 50 of the internal tooth profile is the same as the standard opening angle profile side line 31 of the external tooth profile. Map the outermost contour line of the flat chain 12 of the chain link 10 as the tooth running side line 51 of the internal tooth profile. The diameter dm of the tooth running minor diameter 53 of the internal tooth profile is equal to the chain diameter d. Make an auxiliary circle with the center at the far-end center point A of the adjacent vertical chain of the corresponding internal tooth. The auxiliary circle is tangent to the tooth running minor diameter 53 of the internal tooth profile, and the tooth running major diameter 55 of the internal tooth profile intersects with the auxiliary circle. Among them, the internal tooth profile includes the tooth running side line 51, the tooth running minor diameter 53, and the tooth running major diameter 55 of the internal tooth profile. The two ends of the tooth running minor diameter 53 of the internal tooth profile are respectively connected to the tooth running side line 51 and the tooth running major diameter 55 of the internal tooth profile. One end of the tooth running side line 51 of the internal tooth profile is located on the outer diameter circumference of the internal tooth profile.

[0061] In this embodiment, the sprocket design method further includes the steps:

[0062] Determine the inner hole diameter Dm of the sprocket and the length of the sprocket according to the size of the sprocket shaft.

[0063] When designing a sprocket, the model of the chain link can be drawn in a drawing software according to step S13, and then the overall contour of the sprocket can be drawn according to the parameters in step S15. Then, the contour lines of the outer tooth profile and the inner tooth profile of the sprocket can be drawn according to steps S17 and S19 respectively, and the 3D model of the sprocket can be obtained, thus completing the structural design of the sprocket. In steps S17 and S19, it is actually to make the chain link 10 just wrap around the designed sprocket, so that the designed sprocket can cooperate better with the selected chain.

[0064] In the sprocket design method of the embodiment of the present invention, the reverse design idea is adopted to jump out of the empirical formula for sprocket design, which can effectively reduce the design error and improve the design accuracy of the sprocket, so that the chain and the sprocket are almost perfectly matched, greatly reducing the quality problems such as chain mismatch, tooth jamming, tooth skipping or severe wear.

[0065] The above are only the preferred embodiments of the present invention, and there is no limitation to the present invention in any form. Although the present invention has been disclosed above with the preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the above-disclosed technical content to be equivalent embodiments within the scope of the technical solution of the present invention. However, as long as it does not depart from the content of the technical solution of the present invention, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A method for sprocket design, characterized in that, comprising: selecting a chain model and determining the number of teeth z of the sprocket; determining a chain link (10) according to the number of teeth z of the sprocket and the chain model, the chain link (10) being a closed ring formed by alternating a plurality of flat chains (12) and a plurality of vertical chains (14), the number of the flat chains (12) and the vertical chains (14) being the same as the number of teeth z of the sprocket; determining the overall contour of the sprocket according to the selected chain; determining the outer tooth profile of the sprocket according to the chain link; determining the inner tooth profile according to the chain link and the outer tooth profile of the sprocket; Determining the overall contour of the sprocket according to the selected chain specifically includes: determining the sprocket pitch angle according to the selected chain and the number of teeth of the determined sprocket , the sprocket pitch diameter D 0 , the sprocket outer diameter Dg, the diameter of the vertical groove of the sprocket vertical ring and the short tooth thickness W; Determining the specific outer tooth profile of the sprocket according to the link ring specifically includes: determining the outer tooth profile outer diameter (Dw1) according to the sprocket outer diameter Dg, and determining the outer tooth profile inner diameter (Dn1) according to the vertical groove diameter of the sprocket vertical ring Determining the standard opening angle (β) and the maximum opening angle (δ) of the outer tooth profile according to the sprocket pitch angle Determining the position of the outer tooth profile standard opening angle contour line (31) of the corresponding sprocket tooth according to the short tooth thickness W and the vertical chain center line of the link ring; determining the inner tooth profile according to the chain link and the outer tooth profile of the sprocket specifically includes: determining the outer diameter (Dw2) and the inner diameter (Dn2) of the inner tooth profile according to the outer diameter (Dw1) and the inner diameter (Dn1) of the outer tooth profile, determining the standard opening angle (βn) of the inner tooth profile according to the standard opening angle (β) of the outer tooth profile, determining the contour line (50) of the standard opening angle of the inner tooth profile according to the contour line (31) of the standard opening angle of the outer tooth profile, determining the tooth running line (51) of the inner tooth profile according to the chain link (10), determining the minor diameter (53) of the tooth running of the inner tooth profile according to the chain diameter d, and determining the outer diameter (55) of the tooth running of the inner tooth profile according to the chain link (10) and the minor diameter (53) of the tooth running of the inner tooth profile.

2. The sprocket design method according to claim 1, characterized in that, the sprocket design method further includes the step of: determining the inner hole diameter (Dm) of the sprocket and the length of the sprocket according to the size of the sprocket shaft.

3. The sprocket design method according to claim 1, characterized in that, when determining the chain link according to the number of teeth z of the sprocket and the chain model, the flat chains and the vertical chains of the chain link have the same structure as the flat chains and the vertical chains of the selected chain, and determining the pitch circle radius of the chain link according to the number of teeth z of the sprocket and the chain model.

4. The sprocket design method according to claim 3, characterized in that, the determining the pitch circle radius of the chain link specifically includes: obtaining half of the pitch circle angle corresponding to one of the flat chains in the chain link; obtaining the theoretical pitch circle radius of the chain link according to half of the pitch circle angle corresponding to the flat chain; obtaining the actual pitch circle radius of the chain link according to the theoretical pitch circle radius of the chain link and the error coefficient.

5. The sprocket design method according to claim 4, characterized in that, Specifically, half of the indexing circle angle corresponding to a flat link in the obtained link chain is: According to Half of the indexing circle angle corresponding to a flat link in the link chain is calculated; Obtaining the theoretical pitch circle radius of the link specifically includes: According to the formula Calculating the theoretical pitch circle radius of the link; Obtaining the actual pitch circle radius of the link specifically includes: According to Calculating to obtain the actual pitch circle radius R of the link, where , where is the error coefficient, r is the theoretical pitch circle radius, 2α is the pitch circle angle corresponding to the flat chain, d is the chain diameter, p is the chain pitch, R is the actual pitch circle radius of the link, z is the determined number of teeth of the sprocket, and n is the total number of the flat chain and the vertical chain of the link.

6. The sprocket design method according to claim 1, characterized in that, The outer tooth profile outer diameter (Dw1) is equal to the sprocket outer diameter Dg, and the outer tooth profile inner diameter (Dn1) is equal to the diameter of the vertical groove of the sprocket vertical ring. , the standard opening angle (β) of the outer tooth profile is equal to twice the pitch angle of the sprocket , the maximum opening angle (δ) of the outer tooth profile is less than or equal to three times the pitch angle of the sprocket , and greater than the standard opening angle (β) of the outer tooth profile. The distance (L) from the standard opening angle profile side line (31) of the outer tooth profile of the sprocket tooth to the center line of the vertical chain of the corresponding chain link is half of the short tooth thickness W; the outer tooth profile includes the standard opening angle profile side line (31) of the outer tooth profile and the maximum opening angle profile line (33) of the outer tooth profile. One end of the standard opening angle profile side line (31) of the outer tooth profile is located on the inner diameter circumference of the outer tooth profile, and the other end is connected to the maximum opening angle profile line (33) of the outer tooth profile. One end of the maximum opening angle profile line (33) of the outer tooth profile is located on the outer diameter circumference of the outer tooth profile.

7. The sprocket design method according to claim 1, characterized in that, The outer diameter (Dw2) and the inner diameter (Dn2) of the internal tooth profile are respectively equal to the outer diameter (Dw1) and the inner diameter (Dn1) of the external tooth profile. The standard opening angle (βn) of the internal tooth profile is equal to the standard opening angle (β) of the external tooth profile, and the contour line (50) of the standard opening angle of the internal tooth profile is the same as the contour line (31) of the standard opening angle of the external tooth profile. The outermost contour line of the flat chain (12) of the chain link (10) is mapped as the tooth running edge line (51) of the internal tooth profile. The diameter (dm) of the minor diameter (53) of the tooth running of the internal tooth profile is equal to the chain diameter d. An auxiliary circle is drawn with the center at the center point (A) of the distal end of the adjacent vertical chain of the chain link corresponding to the internal tooth. The auxiliary circle is tangent to the minor diameter (53) of the tooth running of the internal tooth profile, and the outer diameter (55) of the tooth running of the internal tooth profile intersects with the auxiliary circle. The internal tooth profile includes the tooth running edge line (51) of the internal tooth profile, the minor diameter (53) of the tooth running of the internal tooth profile, and the outer diameter (55) of the tooth running of the internal tooth profile. The two ends of the minor diameter (53) of the tooth running of the internal tooth profile are respectively connected to the tooth running edge line (51) of the internal tooth profile and the outer diameter (55) of the tooth running of the internal tooth profile. One end of the tooth running edge line (51) of the internal tooth profile is located on the circumference of the outer diameter of the internal tooth profile.

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