Design method of cutting teeth and cutting edge curve of tools for chamfering gear tooth profile

Abstract

This invention discloses a method for designing the cutting teeth and their cutting edge curves of a tool for chamfering the tooth profile of a countersunk gear. The tool body is a cylindrical body, with the cutting teeth located on the side of the cylindrical body. Each cutting tooth includes a tooth body, the upper half of which has tooth grooves forming left and right cutting teeth distributed along the axial direction of the cylindrical body. The overall curve of the top of the left cutting tooth and its left profile is denoted as the left cutting edge curve, and the overall curve of the top of the right cutting tooth and its right profile is denoted as the right cutting edge curve. The left and right cutting edge curves are respectively formed by fitting the tooth profile point sets obtained by rotating the left and right tooth profile point sets of the original reference tooth groove of the gear with corresponding offset angles. This invention can effectively solve the problems of negative cutting edge angle, tooth surface interference, and inconsistent chamfering amount in the existing rolling method for machining countersunk gears.

Description

Technical Field

[0001] This invention belongs to the field of gear processing technology, specifically relating to a design method for the cutting teeth and cutting edge curve of a combined tooth profile chamfering tool for countersinking gears, which is particularly suitable for generating cylindrical gears with countersinking structures. Background Technology

[0002] Chamfering of gear teeth (see) Figure 1 This method can significantly reduce residual stress at the edges of gear tooth profiles and improve gear life. Among the methods for chamfering gear tooth profiles, rolling chamfering has gradually become one of the main methods due to its high efficiency, low cost, and integration with gear hobbing machines. However, the traditional rolling chamfering method has the following problems when machining gears with countersinking:

[0003] 1. Due to the influence of the tooth root profile of the countersunk gear, there is a sudden change in slope in the countersunk portion (see...). Figure 2 According to traditional design methods, interference and multiple cuts are almost unavoidable when machining the tooth profile chamfer at the abrupt change point (see...). Figure 3 This causes scratches on the tooth surface, leading to the gear becoming unusable.

[0004] 2. At the same time, a negative angle cutting edge will also appear in the undercut section (see...) Figure 2 This makes it impossible to manufacture the cutting tool, requiring manual adjustment to change the chamfer amount of the countersink, resulting in less cutting of the countersink portion (see...). Figure 4 Inconsistent chamfer dimensions of gear tooth profiles (see...) Figure 5 This affects the effect of gear chamfering.

[0005] The two problems mentioned above cannot be avoided by traditional design methods. Generally, it is only acceptable to reduce the amount of chamfering, which seriously restricts the application and processing quality of countersunk gears.

[0006] Therefore, there is an urgent need to design a tooth profile chamfering tool that can avoid negative cutting edge angles, eliminate tooth surface interference, and ensure consistent chamfer dimensions. Summary of the Invention

[0007] The purpose of this invention is to propose a design method for the cutting teeth and their cutting edge curves of a combined tooth profile chamfering tool for countersinking gears, in order to solve the problems of negative cutting edge angle, tooth surface interference, and inconsistent chamfering amount that exist in the existing rolling method for machining countersinking gears.

[0008] To achieve the above objectives, the present invention employs the following technical solution: In a first aspect, the present invention provides cutting teeth for a tool used for chamfering the profile of countersunk gears, such as... Figures 6-8As shown, the body of the gear tooth profile chamfering tool is a cylindrical body. The cutting teeth are arranged on the side of the cylindrical body. The cutting teeth include a cutting tooth body. The upper half of the cutting tooth body has tooth grooves to form a left cutting tooth and a right cutting tooth distributed along the axial direction of the cylindrical body. The top of the left cutting tooth and the overall curve of the left side profile of the left cutting tooth are denoted as the left cutting edge curve. The top of the right cutting tooth and the overall curve of the right side profile of the right cutting tooth are denoted as the right cutting edge curve.

[0009] The left-side cutting edge curve is formed by the set of left-side tooth profile points P of the original reference tooth groove of the countersunk gear to be machined. L (X i ,Y i ) via left offset angle φ L The tooth profile point set P obtained after rotation L '(X i ',Y i The right-side cutting edge curve is formed by fitting the original reference tooth groove of the countersunk gear to be machined, and is composed of the right-side tooth profile point set P. R (X i ny i (by right offset angle φ) R The tooth profile point set P obtained after rotation R '(X i ',Y i ') Fitted to form.

[0010] Furthermore, both the left and right edge curves are spline curves. Preferably, they are cubic spline curves or B-spline curves.

[0011] Furthermore, the left offset angle φ L and right offset angle φ R The tooth profile, formed by the left and right cutting edge curves, is determined based on the helix direction of the countersunk gear and the type of tool used, ensuring that there is no negative angle cutting edge and interference with the tooth surface during gear machining. Specifically, the left offset angle φ... L and right offset angle φ R The selection is as follows: φ L = -π / Z1×KL1, φ R = π / Z1×KR1 Where Z1 represents the number of teeth of the undercut gear to be machined; KL1 and KR1 represent the selection parameters of the left offset angle and the right offset angle, respectively, and their values ​​are selected from Table 1 according to the tool type and the direction of rotation of the undercut gear to be machined.

[0012] Table 1. Parameters for Selecting the Bias Angle

[0013] Note: Higher values ​​for KL1 and KR1 result in more precise and consistent chamfers on the gear tooth profile. However, in actual machining, considering the complexity of tool manufacturing and machining costs, the recommended values ​​in Table 1 can be used.

[0014] In a second aspect, the present invention provides a method for designing the cutting edge curve of the cutting tool teeth for chamfering the tooth profile of a countersunk gear as described in the first aspect, comprising the following steps: Step 1: Obtain the reference tooth profile point set. Extract the gear parameters of the countersunk gear to be machined and the left tooth profile point set P of the original reference tooth groove from the gear model. L [X i ,Y i ] and the right tooth profile point set P R [X i ,Y i ], i=1,2,...,N. The point set is evenly distributed on the involute and the countersinking transition curve of the countersinking gear.

[0015] The gear parameters include at least the number of teeth Z1, the number of cutting tool teeth Z0, and the tooth root chamfer angle φ. c Machining center distance a 01 Installation height H and machining axis intersection angle ep.

[0016] Step 2: Calculate the tooth profile offset angle. Determine the left offset angle based on the helix direction of the countersunk gear to be machined and the type of tool used (e.g., tooth thickness tool, tooth groove tool). φ L and right offset angle φ R ; and the offset angle rotation matrix; Step 3: Calculate the set of machining tooth profile points: using the left offset angle rotation matrix M φL And the right offset angle rotation matrix M φR For the left tooth profile point set P respectively L (X i ,Y i ) and the right tooth profile point set P R [X i ,Y i Rotate the tooth profile to obtain the rotated point set P. L '[X i ',Y i '] and P R '[X i ',Y i ']; Step 4: Calculate the set of tooth profile points obtained in Step 3 based on the gear parameters collected in Step 1. The tool rotation angle φ corresponding to each point in the diagram during cutting. ci .

[0017] Step 5: Calculate the left cutting edge point set T of the tool using the results obtained in steps 3 and 4. L [X ti Y ti ] and the right-side cutting edge point set T R [X ti Y ti ].

[0018] Step 6: Perform spline curve fitting on the left and right cutting edge point sets of the tool obtained in Step 5 to obtain the left and right cutting edge curves of the combined tooth profile chamfering tool for countersinking gears.

[0019] Furthermore, in step 2: φ L = -π / Z1×KL1 φ R = π / Z1×KR1 Where Z1 represents the number of teeth of the countersunk gear to be processed; KL1 and KR1 are selected according to Table 1.

[0020]

[0021]

[0022] in, , These represent the left-side offset angle rotation matrix and the right-side offset angle rotation matrix, respectively.

[0023] Furthermore, in step 3: (i=1,2,3……200) (i=1,2,3……200).

[0024] Furthermore, in step 4:

[0025] Among them, a 01 H is the center distance, H is the installation height, ep is the machining axis intersection angle, and φ is the center distance. c This is the chamfer angle at the tooth root.

[0026] Using tooth profile point set Calculated tool rotation angle φ ci Recorded as Using tooth profile point set Calculated tool rotation angle φ ci Recorded as .

[0027] Furthermore, in step 5: The calculation formula is as follows: (i=1,2,3……200) (i=1,2,3……200).

[0028] Thirdly, the present invention provides a tool for chamfering the profile of countersunk gears, comprising a cylindrical tool body, wherein a plurality of cutting teeth (2 to 6, preferably 4) are evenly arranged around the cylindrical side of the tool body. These cutting teeth employ the countersunk gear tooth profile chamfering cutting teeth described in the first and second aspects above. The countersunk gear tooth profile chamfering tool is used to be mounted on a gear hobbing machine to perform the chamfering of the gear tooth profile.

[0029] Compared with the prior art, the present invention has the following technical effects: 1. This invention selects the tooth profile of the countersinking gear with no negative angle and small abrupt change as the benchmark for calculating the tooth profile, and obtains the tooth profile cutting edge shape by offsetting it with an offset angle. This avoids the problem of negative angle of the cutting edge shape caused by the abrupt change of the tangent in the countersinking part in the traditional method, so that the cutting tool can be manufactured normally.

[0030] Meanwhile, in the traditional method for designing large-angle helical directions on the tooth profile, the transition curve of the tooth profile cannot be accurately solved. The present invention further eliminates the negative angle of the cutting edge by designing the left and right tooth profiles, and can accurately solve the left and right tooth profiles. Therefore, the design of the present invention has strong versatility and is applicable to the design of tools with different helical directions and reference types. It is easy to implement on existing gear hobbing machines and has low modification costs.

[0031] 2. The tool employs a combined tooth profile design, with the left and right cutting edges each undergoing rotational fitting based on independent offset angles. This effectively eliminates tooth surface interference during machining, preventing tooth surface scratches and improving yield. By eliminating tooth surface interference, the consistency of the chamfer dimensions in the undercut section is ensured, eliminating the need to manually reduce the chamfer amount and improving gear chamfer quality and gear life. After being put into use, the tool of this invention has been successfully applied to gears in new energy vehicle reducers, achieving consistent chamfer amounts in the undercut section without overcutting or undercutting, thus improving the uniformity of gear strength. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of gear tooth profile chamfering; Figure 2 It is a tooth profile with undercutting processed by traditional methods, which has abrupt change points and negative tooth angles; Figure 3 The experiment showed that the large negative angle in the tool tooth profile designed according to the original reference tooth profile caused excessive interference and cutting of the gear tooth surface. Figure 4 This shows that manually adjusting the tool teeth to the correct angle will inevitably result in less cutting of the undercut portion and a smaller chamfering amount. Figure 5 The diagram shows a conventional cutting tool machining process, which exhibits serious overcutting, undercutting, and inconsistent chamfering amounts.

[0033] Figure 6 This is a schematic diagram of the structure of the gear tooth profile chamfering tool and cutting teeth of the present invention; Figure 7 for Figure 6 The right view; Figure 8 This is a perspective view of the gear tooth profile chamfering tool and cutting teeth of the present invention; Figure 9 This is a schematic diagram of the chamfering process designed for an embodiment of the present invention, showing no overcutting or undercutting, and consistent chamfering amount; Figure 10 This is a schematic diagram of the cutting edge profile of the tool used for chamfering the gear tooth profile obtained in the example.

[0034] The present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. Detailed Implementation

[0035] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, but the implementation of the present invention is not limited thereto.

[0036] This embodiment takes a right-hand helical cylindrical gear as an example, and uses a tooth groove reference type hobbing cutter to perform tooth profile chamfering. The basic parameters of the gear are shown in Table 1.

[0037] Table 2 Basic Gear Parameters (Example)

[0038] The specific implementation steps of the design method according to the present invention are as follows (due to the large number of calculation points, only one point is taken as an example in the implementation process): Step 1: Obtain the reference tooth profile point set.

[0039] Extract the left tooth profile point set P from the gear design model. L (X i ,Y i ) and the right tooth profile point set P R (X i ,Y i ), i=1,2,...,N. In this embodiment, N is taken as 200, and the point set is evenly distributed on the involute and the shear transition curve. When N=1, P on the left reference tooth profile L (X1,Y1)=(14.4753,104.2404).

[0040] Step 2: Determine the offset angle φ L .

[0041] Since it is a toothed cutting tool and the gear to be machined has a left-hand helix direction, KL1=0 is selected according to the recommended value, φ L = -π / Z1×KL1=-3.1416 / 71 0 = 0.

[0042] Step 3: Calculate the corresponding coordinates on the machined tooth profile.

[0043]

[0044] Step 4: Solve for the workpiece rotation angle φ Lc1 .

[0045]

[0046] Solve using numerical methods (such as Newton's iteration). =0.0077.

[0047] Step 5: Switch to the tool coordinate system.

[0048]

[0049] Substitute the data to get .

[0050] Further calculations yielded the coordinates of all tool cutting edges on both the left and right sides.

[0051] Step 6: Spline curve fitting.

[0052] For T L and T R Perform cubic B-spline curve fitting on the point set, with 20 control points, and the curve should be C. 2 Continuous. The two fitted curves represent the profiles of the left and right cutting edges of the tool.

[0053] Step 7: Tool Structure Design. Based on the fitted tooth profile curve and the hob design method, design the hob's outer diameter, inner diameter, keyway dimensions, and other parameters.

[0054] The final cutter tooth profile obtained in this embodiment is as follows: Figure 9As shown, compared with conventionally designed tools, this invention utilizes the periodic rotational change of gear tooth profiles. By selecting different periodic angles and applying them to the hobbing cutter tooth profile, it causes positive rotational deformation, completely eliminating the problem of negative angle cutting edges that is unavoidable in traditional designs. Through data analysis and visual inspection, the angle between the cutting edge tangent and the vertical direction has been improved from -6° to over +10°, significantly enhancing the manufacturability of the hobbing cutter tooth profile. This avoids the problem of manually adjusting and reducing the tooth profile shape due to the inability to manufacture with a negative tangent angle. The tool is manufactured directly using the theoretical hobbing cutter tooth profile curve, and the chamfer size of the machined gear is consistent with the theoretical design. Therefore, the chamfer amount of the gear tooth profile is completely and uniformly distributed on the involute and transition curves, resulting in smooth, interference-free chamfers on the machined gears, with no overcutting or undercutting (see...). Figure 10 ).

Claims

1. A cutting tooth for a tool used in chamfering the profile of countersunk gears, characterized in that, The body of the gear tooth profile chamfering tool is a cylindrical body. The cutting tooth (1) is set on the side of the cylindrical body. The cutting tooth includes a cutting tooth body (1-1). The upper half of the cutting tooth body (1-1) has a tooth groove (1-2) to form a left cutting tooth (1-3) and a right cutting tooth (1-4) distributed along the axial direction of the cylindrical body. The overall curve of the top of the left cutting tooth (1-3) and the left side profile of the left cutting tooth (1-3) is called the left cutting edge curve. The overall curve of the top of the right cutting tooth (1-4) and the right side profile of the right cutting tooth (1-3) is called the right cutting edge curve. The left-side cutting edge curve is formed by the set of left-side tooth profile points P of the original reference tooth groove of the countersunk gear to be machined. L (X i ,Y i ) via left offset angle φ L The tooth profile point set P obtained after rotation L '(X i ',Y i The right-side cutting edge curve is formed by fitting the original reference tooth groove of the countersunk gear to be machined, and is composed of the right-side tooth profile point set P. R (X i ny i (by right offset angle φ) R The tooth profile point set P obtained after rotation R '(X i ',Y i ') Fitted to form.

2. The cutting teeth of the gear tooth profile chamfering tool as described in claim 1, characterized in that, Both the left and right edge curves are spline curves.

3. The cutting teeth of the gear tooth profile chamfering tool as described in claim 1, characterized in that, The left offset angle φ L and right offset angle φ R The selection is as follows: f L = -π / Z1×KL1,φ R = π / Z1×KR1 Where Z1 represents the number of teeth of the countersunk gear to be machined; KL1 and KR1 represent the selection parameters for the left offset angle and the right offset angle, respectively, and the selection method is as follows: (1) For tooth thickness type tools: when the helix direction of the countersunk gear being machined is left-handed, KL1 is 1, 3 or 5, and KR1 is 1 or 3; when the helix direction of the countersunk gear being machined is right-handed, KL1 is 1 or 3, and KR1 is 1, 3 or 5. (2) For toothed cutting tools: When the direction of the countersunk gear being machined is left-handed, KL1 is 2, 4 or 6, and KR1 is 0 or 2; when the direction of the countersunk gear being machined is right-handed, KL1 is 0 or 2, and KR1 is 2, 4 or 6.

4. A method for designing the cutting edge curve of a tool for chamfering the profile of countersunk gears, comprising the following steps: Step 1: Obtain the reference tooth profile point set: Extract the gear parameters of the countersunk gear to be machined and the left tooth profile point set P of the original reference tooth groove from the gear model. L [X i ,Y i ] and the right tooth profile point set P R [X i ,Y i ], i=1,2,...,N; the point set is uniformly distributed on the involute and the undercut transition curve of the undercut gear; The gear parameters include at least the number of teeth Z1, the number of cutting tool teeth Z0, and the tooth root chamfer angle φ. c Machining center distance a 01 Installation height H and machining axis intersection angle ep; Step 2: Calculate the tooth profile offset angle: Determine the left offset angle based on the helix direction of the countersunk gear to be machined and the tool reference type used. φ L and right offset angle φ R ; and the offset angle rotation matrix; Step 3: Calculate the set of machining tooth profile points: using the left offset angle rotation matrix M φL And the right offset angle rotation matrix M φR For the left tooth profile point set P respectively L (X i ,Y i ) and the right tooth profile point set P R [X i ,Y i Rotate the tooth profile to obtain the rotated point set P. L '[X i ',Y i '] and P R '[X i ',Y i ']; Step 4: Calculate the set of tooth profile points obtained in Step 3 based on the gear parameters collected in Step 1. The tool rotation angle φ corresponding to each point in the diagram during cutting. ci ; Step 5: Calculate the left cutting edge point set T of the tool using the results obtained in steps 3 and 4. L [X ti Y ti ] and the right-side cutting edge point set T R [X ti Y ti ]; Step 6: Perform spline curve fitting on the left and right cutting edge point sets of the tool obtained in Step 5 to obtain the left and right cutting edge curves of the combined tooth profile chamfering tool for countersinking gears.

5. The method as described in claim 4, characterized in that, In step 2: f L = -π / Z1×KL1 f R = π / Z1×KR1 Where Z1 represents the number of teeth of the countersunk gear to be processed; KL1 and KR1 are selected according to the following method: (1) For tooth thickness type tools: when the helix direction of the countersunk gear being machined is left-handed, KL1 is 1, 3 or 5, and KR1 is 1 or 3; when the helix direction of the countersunk gear being machined is right-handed, KL1 is 1 or 3, and KR1 is 1, 3 or 5. (2) For toothed cutting tools: When the helix direction of the countersunk gear being machined is left-handed, KL1 is 2, 4 or 6, and KR1 is 0 or 2; when the helix direction of the countersunk gear being machined is right-handed, KL1 is 0 or 2, and KR1 is 2, 4 or 6. in, , These represent the left offset angle rotation matrix and the right offset angle rotation matrix, respectively.

6. The method as described in claim 5, characterized in that, In step 3: (i=1,2,3……200) (i=1,2,3……200)。 7. The method as described in claim 6, characterized in that, In step 4: Among them, a 01 H is the center distance, H is the installation height, ep is the machining axis intersection angle, and φ is the center distance. c This refers to the chamfer angle at the tooth root; Using tooth profile point set Calculated tool rotation angle φ ci Recorded as Using tooth profile point set Calculated tool rotation angle φ ci Recorded as .

8. The method as described in claim 7, characterized in that, In step 5: The calculation formula is as follows: (i=1,2,3……200) (i=1,2,3……200)。 9. A tool for chamfering the profile of countersunk gear teeth, characterized in that, The tool body (2) is cylindrical, and a plurality of cutting teeth (1) are evenly arranged around the cylindrical side of the tool body (2). The cutting teeth are made using the chamfering cutting teeth of the gear profile as described in any one of claims 1 to 8.

10. The gear tooth profile chamfering tool as described in claim 9, characterized in that, Two to six cutting teeth (1) are evenly arranged around the cylindrical side of the cutter body (2).

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