WO2021134848A1

WO2021134848A1 - Spline having corrugated end face, and manufacturing method therefor

Info

Publication number: WO2021134848A1
Application number: PCT/CN2020/072963
Authority: WO
Inventors: 王小椿; 帅梅
Original assignee: 北京智能大艾机器人科技有限公司
Priority date: 2020-01-02
Filing date: 2020-01-19
Publication date: 2021-07-08
Also published as: CN113059237B; CN113059237A

Abstract

Disclosed is a spline having a corrugated end face, a surface of the spline being provided with multiple teeth, wherein the surface of the spline is a continuous periodic curved face, which is a first-order continuous corrugated face; and transition curved faces (17, 18) are formed between adjacent working tooth faces (13, 14) of the teeth, and the transition curved faces (17, 18) are single-parameter enveloping faces of cylindrical faces perpendicular to an axis of the spline. A method for manufacturing a spline having a corrugated end face is further provided. The spline having a corrugated end face is light in weight, high in strength, and low in cost, is easy to mount and dismount, and is suitable for connection between rotating parts of a high-speed mechanism.

Description

Spline with wavy end face and manufacturing method thereof

Technical field

This article relates to an end face connecting mechanism of mechanical parts, and particularly to a spline with a wave end face and a method for manufacturing the spline.

Background technique

In mechanical manufacturing, it is often necessary to connect shaft parts, disc parts and sleeve parts to each other in pairs. Commonly used connection methods are: flat keys, splines, semi-circular keys, tangential keys, elastic expansion sleeves, and interference fits. , Face key, mouse tooth plate and arc tooth end tooth connection, among which the most commonly used are flat key, spline and semicircular key connection. The connection of the flat key and the half-round key has a great influence on the fatigue strength of the shaft, and a thicker shaft and a thicker hub have to be used. When the flat key and the half-round key bear large torque, it will also affect the concentricity between the connecting parts, and sometimes have to adopt a tight fit, which greatly increases the workload of assembly and maintenance. In the small batch production of a single piece, the processing cost of the spline is quite high, and it is often necessary to order a special tool. The production cycle is very long, so it is rarely used. The elastic expansion sleeve is usually only suitable for the connection between the shaft and the hub, and is not suitable for the connection between the disc parts and the disc parts. The use of elastic expansion sleeve connection is to rely on friction to transmit torque and axial force, so a large pre-tightening force is required, which will generate a large assembly stress on the shaft and the hub. This connection method is also not suitable for high-speed rotating mechanical parts. Centrifugal force will cause the pre-tightening force on the expansion sleeve to relax. For the interference fit, its use characteristics are basically the same as those of the elastic expansion sleeve, but the requirements for processing accuracy are higher, and assembly and disassembly are more difficult. If the radial size of the workpiece is limited and the bearing capacity of the face key is limited, the face key is basically only used in the machine tool industry, such as the connection of the tool holder, cutter head and chuck packing with the machine tool spindle. For the connection between the squirrel tooth disc and the arc tooth end gear, the processing method is restricted, and no shaft extension is allowed in the middle of the workpiece. Usually it can only be used for the connection between disc parts and disc parts. Special equipment is required, and the processing cost is compared. high.

In order to obtain a light-weight, high-strength, low-cost, easy-to-install and disassemble connection between rotating parts suitable for high-speed machinery, the present invention proposes a wave-shaped end-face combined spline.

Summary of the invention

The purpose of the present invention is to provide a light-weight, high-strength, low-cost, easy-to-install and disassemble connection form between rotating parts suitable for high-speed machinery.

In order to achieve the purpose of the present invention, this article provides a spline with a wave end surface, the surface of the spline has a plurality of teeth, wherein the surface of the spline is a continuous periodic curved surface, and the curved surface is a first-order surface. A continuous wave surface; and a transition curved surface is formed between adjacent working tooth surfaces of the tooth, and the transition curved surface is a single-parameter envelope surface of a cylindrical surface perpendicular to the axis of the spline.

The spline according to one or more embodiments of the present invention, wherein the involute line of the intersection of the transition surface and the inner cylindrical surface of the spline is a circular arc curve.

The spline according to one or more embodiments of the present invention, wherein the involute of the transition curve at the tooth root has a first radius, and the transition curve at the tooth tip has a first radius. The involute has a second radius, and the second radius is greater than the first radius.

The spline according to one or more embodiments of the present invention, wherein the second radius is 1.02 to 1.08 times the first radius.

The spline according to one or more embodiments of the present invention, wherein the spline is processed on a table perpendicular to the tool axis using a cylindrical end mill, wherein the first radius is the cylindrical 1.02 to 1.08 times the radius of the end mill.

The spline according to one or more embodiments of the present invention, wherein the first radius is 1.05 times the radius of the cylindrical end mill.

The spline according to one or more embodiments of the present invention, wherein the head clearance between the tooth tip and the tooth root is 0.028 to 0.03 times the radius of the cylindrical end mill.

This article also provides a method for processing a spline with a wave-shaped end face, the method includes: placing a workpiece on a worktable perpendicular to the tool axis, and milling the end face of the workpiece with a cylindrical end mill to Forming a spline surface with a plurality of teeth; and using the cylindrical end mill to perform milling at the tooth tip and tooth root to form a transition surface between adjacent working tooth surfaces, the transition surface being and The single-parameter envelope surface of the cylindrical surface with the axis perpendicular to the workpiece. The swing angle of the cylindrical end mill in the swing is determined by a spline curve, the spline curve is a harmonic function composed of a mixture of trigonometric functions and power functions, and wherein the spline surface is continuous Periodic curved surface, the curved surface is a first-order continuous wave surface.

The method according to one or more embodiments of the present invention, wherein the parameter of the harmonic function is the ratio of the first difference and the second difference, wherein the first difference is the difference between the transition surface and the workpiece The difference between the central angle on the line of intersection on the inner cylindrical surface that corresponds to the position being processed and the central angle of the midpoint of the line of intersection, and the second difference is that on the line of intersection corresponds to the transition The difference between the central angle at the position of the starting point of the curve and the central angle of the midpoint of the intersection.

The method according to one or more embodiments of the present invention, wherein the trigonometric function is a cosine function, and the power function is a cubic polynomial function.

The method according to one or more embodiments of the present invention, wherein the involute of the intersection of the transition curved surface and the inner cylindrical surface of the workpiece is a circular arc curve, and the transition curve at the tooth root The involute has a first radius, and the involute of the transition curve at the tooth tip has a second radius.

The method according to one or more embodiments of the present invention, wherein the second radius is 1.02 to 1.08 times the first radius.

The method according to one or more embodiments of the present invention, wherein the head gap between the tooth tip and the tooth root is 0.028 to 0.03 times the radius of the cylindrical end mill.

The method according to one or more embodiments of the present invention, wherein the first radius is 1.02 to 1.08 times the radius of the cylindrical end mill.

This article also provides a shaft-type part, including: a main shaft; and a shaft shoulder surrounding the main shaft, on which a wave-shaped end face coupling spline according to one or more embodiments of the present invention is formed.

This article also provides a disc-like part, comprising: a ring-shaped body having an opening; and a sprocket plate formed on an end surface of the ring-shaped body around the periphery of the opening, wherein the squirrel plate A wave-shaped end face joint spline is formed according to one or more embodiments of the present invention.

This article also provides a sleeve part, including: a cylindrical sleeve; a tooth portion formed on the outer peripheral surface of the sleeve; and a spline formed on the end surface of the sleeve, the spline being The wave-shaped end surface according to one or more embodiments of the present invention is combined with a spline.

Description of the drawings

Fig. 1A is a perspective schematic view of an end spline according to an embodiment of this document.

Fig. 1B is a side view of the end face of Fig. 1A after spline coupling.

Fig. 2 is a perspective schematic view of an end spline according to another embodiment of this document.

FIG. 3 is a schematic diagram showing a method of processing a spline part according to an embodiment of this document.

Fig. 4 is a schematic diagram showing a transition surface of a spline part according to an embodiment of this document.

Fig. 5 is a flowchart of a method of processing a spline part according to an embodiment of this document.

Fig. 6 is a schematic diagram showing the swing of the milling cutter when processing a spline part according to the embodiment of this document.

Fig. 7 is a schematic diagram of a disc component according to an embodiment of this document.

Fig. 8 is a schematic diagram of a kit of parts according to an embodiment of this document.

9A and 9B are schematic diagrams showing how different spline parts are combined with each other.

Detailed ways

The face spline is generally used to connect two rotating parts to each other so that the two rotating parts can be connected to each other as a whole for rotation.

Fig. 1A shows a three-dimensional schematic diagram of two end face splines, and Fig. 1B shows a side view when the two splines are combined with each other.

As shown in FIG. 1A, it shows the

spline parts

10 and 20 that can be combined with each other. Teeth are formed on the end surfaces of the

spline parts

10 and 20, respectively. When the

spline parts

10 and 20 are combined with each other, the teeth on the end surfaces thereof mesh with each other, so that the

spline parts

10 and 20 can be combined as a whole and rotate together, as shown in FIG. 1B.

The teeth formed on the end face of the spline part 10 will be described below. It should be noted that the spline part 20 has the same tooth structure as the spline part 10. A plurality of teeth are formed on the end surface of the spline component 10, and these teeth are formed by tooth tops 11 and 15,

tooth roots

12 and 16, and working tooth surfaces 13 and 14 formed at uniform intervals along the circumferential direction of the end surface. The end surface on which the teeth are formed may be referred to as a spline surface. The tooth tops 11, 15, the

tooth roots

12, 16 and the working tooth surfaces 13, 14 are alternately formed on the end surfaces at uniform intervals. As shown in FIG. 1A, the tooth top 11 is formed between the two working tooth surfaces 13 and 14, and the tooth root 12 is also formed between the two working tooth surfaces. Therefore, the spline part 10 has a tooth top and working tooth surface on the end surface. The order of tooth surface, tooth root, working tooth surface, and tooth top is formed on the end surface.

As shown in FIG. 1A, the spline surface of the spline component 10 is a continuous periodic toroidal curved surface, the curved surface is a wavy curved surface and has a first-order continuous geometric feature, that is, the curved surface is a first-order continuous wavy surface. The working tooth surfaces 13 and 14 formed on both sides of the tooth top 11 are formed as inclined planes. The working tooth surface 13 is formed between the tooth top 11 and the tooth root 12 on one side of the tooth top 11, and the working tooth surface 14 is formed between the tooth top 11 and the tooth root 16 on the other side of the tooth top 11. Therefore, the working tooth surfaces 13 and 14 are inclined at complementary angles. The spline component 10 includes two groups of working tooth surfaces, one of which has the same working tooth surface as the working tooth surface 13 and the other group has the same working tooth surface as the working tooth surface 14. Based on the spline parts of the above structure, it can be ensured that two end-face joint spline parts (for example, spline parts 10 and 20) with the same structure can achieve rigidity between the two parts under the action of appropriate axial preload. The connection eliminates all six degrees of freedom. The combined spline parts can not only transmit rotational torque, but also bear radial force and subversion torque.

In the traditional processing method of spline parts, the tooth profile of the end face is processed and manufactured by using a disk-shaped milling cutter with a larger diameter to feed along the direction perpendicular to the rotation axis A of the spline part.

However, traditional processing methods have certain limitations. For example, as shown in FIG. 2, for a spline part 30 having a shaft extension 31. The traditional machining method of milling in the radial direction of the spline part is no longer applicable. To obtain a spline part 30 with a shaft extension 31, it is often necessary to first process the annular spline part 32 separately, and then install fasteners (for example, bolts or pins) on the shoulder of the shaft extension 31 to form the spline Part 30. But in this way, the volume, weight, rigidity and reliability of the entire mechanism will be greatly affected.

Therefore, another milling method can be considered to form spline parts, so that this milling method can be used to manufacture spline parts with shaft extension. According to an embodiment of this article, the teeth on the spline surface can use a cylindrical end mill, which can be used in a machining center (for example, a horizontal machining center, a turning center with a power tool post, or a vertical three-axis machine equipped with a turntable). The machining is completed on the shaft machining center. As shown in FIG. 3, when the cylindrical end mill 50 is used to process the spline part 10, the cylindrical end mill 50 swings in the circumferential direction C around the rotation axis A of the spline part 10, thereby realizing the flower The teeth of the key part 10. In this way, even if the spline part has a shaft extension, the cylindrical end mill 50 has a shorter nose overtravel distance, so the cylindrical end mill 50 swings in the circumferential direction C for milling processing instead of The spline part 10 is milled in the radial direction (for example, the radial direction B in FIG. 1A), so the existence of the shaft extension will not affect the milling processing of the cylindrical end mill 50, so that it can be integrated with a shaft Compared with the formed spline parts, the volume, weight, rigidity and reliability of the whole mechanism have been improved.

FIG. 4 depicts a schematic diagram of the transition surface of the spline part 10. As described above, the teeth on the end surface of the spline component 10 include the tooth top 11, the tooth root 12, and the working tooth surfaces 13 and 14. Among them, the working tooth surfaces 13 and 14 are inclined planes. A transition surface 17 is formed between the working tooth surfaces 13 and 14 to transition from the working tooth surface 13 to the working tooth surface 14, and between the working tooth surface 14 and another working tooth surface, a transition from the working tooth surface 14 to another is formed. The transition surface of the working tooth surface 18. The tooth top 11 is formed in the transition surface 17, and the tooth root 12 is formed in the transition surface 18. In the embodiment herein, the transition surfaces 17 and 18 of the spline part 10 are formed as single-parameter envelope surfaces of a cylindrical surface perpendicular to the rotation axis of the spline part 10 (for example, the axis A in FIG. 1A). The entire spline surface of the key part 10 can be processed by a cylindrical end mill 50 swinging in the circumferential direction of the spline part for milling processing.

Although the existing cylindrical end mills and processing platforms can be used to process spline parts, there is no technical difficulty, but the processing can smoothly transition with two adjacent

inclined planes

13 and 14 at the full tooth width, and is inclined The smooth transition between the

planes

13 and 14 does not produce any interference or creases, and the smooth transition surfaces 17 and 18 between the

inclined planes

13 and 14 need to be specially designed.

As shown in the left part of FIG. 4, the inner diameter of the spline component 10 is taken as the radius, and the axis of rotation of the spline component 10 is taken as the axis to form a cylindrical surface 60, which is called the inner cylindrical surface of the spline. It should be noted that the cylindrical surface 60 is a virtual shape and does not physically exist. It can be seen that the teeth of the spline component 10 will intersect the outer peripheral surface of the cylindrical surface 60 to form a line of intersection showing the contour of the teeth of the spline component 10. For example, FIG. 5 shows that the profile of the teeth of the spline component 10 is a progressive wavy line. Imagine winding a piece of paper with a thickness of 0 on the cylindrical surface 60, and copying the intersection line between the teeth of the spline part 10 and the inner cylindrical surface 60 on this paper. When the paper is unfolded into a plane, the intersection The copied figure of the line stretches into a plane curve, and the plane curve is the involute 61 of the above-mentioned intersection line, as shown in the right part of FIG. 4.

The involute corresponding to the transition curved surface 17 is the section 62 on the involute 61, and the involute corresponding to the transition curved surface 18 is the section 63 on the involute 61, which corresponds to the involute of the working tooth surface 13 It is the section 64 on the involute 61, and the involute corresponding to the working tooth surface 14 is the section 65 on the involute 61. The

sections

64 and 65 are also inclined planes, and the

sections

62 and 63 are circular arcs. Section 62 is tangent to

sections

64 and 65 at two end points 66, and section 63 is tangent to section 65 at two end points 67 and a section corresponding to the involute of another working tooth surface. The radius of curvature of the involute (ie, section 62) of the transition surface including the tooth tip 11 (ie, the transition surface 17) is slightly larger than the involute of the transition surface (ie, the transition surface 18) including the tooth root 12 (Ie, the section 62) has a radius of curvature to ensure that a certain head gap is maintained between the tooth tip transition surface 17 and the tooth root transition surface 18. The head clearance refers to the distance between the tooth root of one spline part and the corresponding tooth tip of the other spline part when two spline parts of the same structure are combined. In some embodiments, the radius of curvature of the involute of the tooth tip transition surface (section 62) is 1.02 to 1.08 times the radius of curvature of the involute of the tooth root transition surface (section 63).

As shown above, the spline part 10 shown in FIG. 4 can be processed using a cylindrical end mill 50. In some embodiments, the radius of curvature of the involute (section 63) of the tooth root transition surface is 1.02 to 1.08 times the radius of the cylindrical end mill 50, preferably 1.05 times. In some embodiments, the radius of curvature of the involute of the tooth tip transition surface (section 62) and the radius of curvature of the involute of the tooth root transition surface (section 63) are designed such that the tooth tip transition surface 17 is in line with the tooth The top clearance between the root transition surfaces 18 is between 0.028 and 0.030 times the diameter of the cylindrical end mill 50.

By forming the above-mentioned tooth tip transition surface 17 and tooth root transition surface 18, it is possible to smoothly transition to the adjacent working tooth surface over the full tooth width without any interference or crease.

Fig. 5 shows a flowchart of a method of processing a spline part. In box 110, first place the workpiece on a worktable perpendicular to the tool axis (for example, a horizontal machining center, a turning center with a powered tool post, or a vertical three-axis machining center equipped with a turntable), using a cylindrical shape The end mill is milled on the end face of the workpiece to form multiple tooth tops, multiple tooth roots, and working tooth surfaces between the tooth tops and the tooth roots. Each of these working tooth surfaces is an inclined plane. For example, a cylindrical end mill 50 can be used to perform milling processing along the tangential direction of the spline tooth surface on the end face of the key part 10 to form the tooth top 11, the tooth root 12, and the working tooth surfaces 13,14. At this time, the transitional curved surface has not been processed between adjacent working tooth surfaces.

In block 120, a cylindrical end mill is used to further mill the tooth tip and the tooth root to form a transition surface between adjacent working tooth surfaces. Specifically, as shown in FIG. 3, a cylindrical end mill 50 is used to swing the cylindrical end mill 50 from a position parallel to the working tooth surface 13 on a plane perpendicular to the axis A along the circumferential direction C to A position parallel to the working tooth surface 14 on the other side to form a transitional curved surface.

6 illustrates the swing of the cylindrical end mill 50 when the cylindrical end mill 50 is used to process the transition surface. 6 shows a schematic diagram of using a cylindrical end mill 50 to process the transition surface 18. When the milling cutter 50 processes the transition surface 18 at the position D1, the center line 51 of the milling cutter 50 is not aligned with the position D1 and the center of the spline part. The radial lines between O overlap, but deviate toward the end 18' of the transition surface 18 by an angle α, which is the swing angle of the milling cutter 50 at the processing position D1. As the milling cutter moves along the circumferential direction C to continue the milling process, the swing angle gradually decreases. Until the milling cutter 50 processes the tooth root 12 in the center of the transition surface 18, the swing angle of the milling cutter 50 is 0, that is, the center line of the milling cutter 50 overlaps the radial line connecting the tooth root 12 and the center O of the spline part. . As the milling cutter 50 further moves along the circumferential direction C to process the transition surface 18, the milling cutter 50 starts to deviate toward the other end 18" of the transition surface 18, for example, when the milling cutter 50 performs milling processing at the position D2, There is an angle β between the center line 52 of the milling cutter 50 and the radial line between the position D1 and the center O of the spline part. At this time, the angle β is the swing angle when the milling cutter 50 reprocesses the D2 position.

In some embodiments, the swing process of the cylindrical end mill 5 will have a significant impact on the shape of the transition surface. In order to process a transition surface without interference and creases, this patent uses a special spline curve to control the swing angle of the milling cutter 50. The spline curve is a harmonic function composed of a mixture of trigonometric functions and power functions. The parameter of the harmonic function is the difference between the central angle corresponding to the current processing position on the intersection line of the transition surface to be processed and the inner cylindrical surface and the central angle of the midpoint of the intersection, and the intersection line with the transition surface corresponds to the starting point position The ratio of the difference between the central angle and the central angle of the midpoint of the intersection. For example, as shown in Figure 6, the milling cutter 50 moves along the circumferential direction C from the end 18' to the end 18" to process the transition surface 18. When the milling cutter 50 is processing at the position D1, the transition surface and the inner The difference between the central angle of the cylindrical surface corresponding to the current machining position and the central angle of the midpoint of the intersection refers to the radial connection between the position D1 and the center O of the spline part and the tooth root 12 and the flower The angle γ1 between the radial connecting line of the center O of the key part, and the difference between the central angle corresponding to the starting position on the intersection of the transition surface and the central angle of the midpoint of the intersection refers to the starting end 18' and the flower The angle γ2 between the radial line between the center O of the key part and the radial line between the tooth root 12 and the center O of the spline part. The parameter of the harmonic function is the ratio of the angle γ1 and the angle γ2. In some implementations In the method, the trigonometric function in the harmonic function is a cosine function, which is used to control the basic law of tool swing angle, and the power function in the harmonic function is a cubic polynomial function, which is used to control the rate of change of the tool swing angle at the start and end points.

The transition surface is processed by using the above-described harmonic function to control the swing angle of the milling cutter. And the transition surface is processed so that the radius of curvature and the top clearance of the transition surface conform to the relationship described above with reference to FIG. 4, and a transition surface without interference and creases can be obtained.

The spline parts described in this article can be used for a variety of rotating parts.

For example, FIG. 2 has shown a shaft part 30 having a shaft extension 31 (or referred to as a main shaft), in which a spline portion 32 is formed around the shoulder of the main shaft 31.

FIG. 7 shows a schematic diagram of a disc part 70, wherein the disc part 70 has a ring-shaped main body 71 and a squirrel disc 72. The ring main body 71 has an opening 72, and the squirrel disk 72 is formed on the end surface of the ring main body 71 around the periphery of the opening 73, wherein the squirrel disk 72 is formed as a spline part as described herein.

FIG. 8 shows a schematic diagram of the kit part 80. The sleeve part 80 includes a cylindrical sleeve 81 and a spline formed on the end surface of the sleeve 81, and teeth are also formed on the outer peripheral surface of the sleeve 81.

Various rotating parts can be combined with each other as required. For example, FIG. 9A shows a schematic diagram of the disc part 70 and the shaft part 30 being combined with each other, and FIG. 9B shows a schematic diagram of the sleeve part 80 and the shaft part 30 being combined with each other.

The foregoing content is directed to the embodiments of the present disclosure, and other and further embodiments of the present disclosure can be modified without departing from the scope of protection thereof, and the scope of protection is determined by the appended claims.

Claims

A spline with a wavy end face, the surface of the spline has a plurality of teeth, wherein,

The surface of the spline is a continuous periodic curved surface, and the curved surface is a first-order continuous wave surface; and

A transition curved surface is formed between adjacent working tooth surfaces of the tooth, and the transition curved surface is a single-parameter envelope surface of a cylindrical surface perpendicular to the axis of the spline.
The spline according to claim 1, wherein the involute of the intersection of the transition surface and the inner cylindrical surface of the spline is a circular arc curve.
The spline according to claim 2, wherein the involute of the transition curve at the root of the tooth has a first radius, and the transition curve at the top of the tooth has a first radius. The involute has a second radius, and the second radius is greater than the first radius.
The spline according to claim 3, wherein the second radius is 1.02 to 1.08 times the first radius.
The spline according to claim 3, wherein the spline is processed on a table perpendicular to the tool axis using a cylindrical end mill, and wherein the first radius is that of the cylindrical end mill 1.02 to 1.08 times the radius.
The spline according to claim 5, wherein the first radius is 1.05 times the radius of the cylindrical end mill.
The spline according to claim 5, wherein the head gap between the tooth top and the tooth root is 0.028 to 0.03 times the radius of the cylindrical end mill.
A method for processing a spline with a wavy end face, the method comprising:

Place the workpiece on a worktable perpendicular to the axis of the tool, and use a cylindrical end mill to mill the end face of the workpiece to form a spline surface with multiple teeth; and

Use the cylindrical end mill to perform milling at the tooth tip and tooth root to form a transition surface between adjacent working tooth surfaces, the transition surface being a single cylindrical surface perpendicular to the axis of the workpiece Parameter envelope surface,

The swing angle of the cylindrical end mill in the swing is determined by a spline curve, and the spline curve is a harmonic function composed of a mixture of a trigonometric function and a power function, and

The spline surface is a continuous periodic curved surface, and the curved surface is a first-order continuous wave surface.
The method according to claim 8, wherein the parameter of the harmonic function is the ratio of the first difference and the second difference, wherein

The first difference is the difference between the central angle corresponding to the position being processed on the intersection of the transition curved surface and the inner cylindrical surface of the workpiece and the central angle of the midpoint of the intersection,

The second difference is the difference between the central angle at the position corresponding to the starting point of the transition curve on the line of intersection and the central angle of the midpoint of the line of intersection.
The method according to claim 8 or 9, wherein the trigonometric function is a cosine function, and the power function is a cubic polynomial function.
The method according to claim 8, wherein the involute of the intersection of the transitional curved surface and the inner cylindrical surface of the workpiece is a circular arc curve, and the involute of the transitional curve located at the tooth root The line has a first radius, and the involute line of the transition curve at the tooth tip has a second radius.
The method of claim 11, wherein the second radius is 1.02 to 1.08 times the first radius.
The method according to claim 11, wherein the head gap between the tooth top and the tooth root is 0.028 to 0.03 times the radius of the cylindrical end mill.
The method according to claim 11, wherein the first radius is 1.02 to 1.08 times the radius of the cylindrical end mill.
A shaft part, including:

Spindle; and

Around the shaft shoulder of the main shaft, the spline according to any one of claims 1-7 is formed on the shaft shoulder.
A kind of disc parts, including:

A ring-shaped body with an opening; and

A squirrel disk, which is formed on the end surface of the annular body around the periphery of the opening, wherein the squirrel disk is formed as a spline according to any one of claims 1-7.
A set of parts, including:

Cylindrical shaft sleeve;

The teeth are formed on the outer peripheral surface of the sleeve; and

The spline formed on the end surface of the sleeve is the spline according to any one of claims 1-7.