Machining method of high-performance crowned tooth

Abstract

The invention relates to the technical field of coupling crowned teeth, and discloses a high-performance crowned tooth processing method, which comprises the following steps of: 1, processing a conventional crowned tooth by adopting a gear hobbing method, 2, carrying out secondary processing on the conventional crowned tooth by adopting a slotting cutter (3), and 3, calculating the clearance of the crowned tooth. The tooth thickness at the crowned tooth reference circle, the coordinate of the involute on the y axis and the pressure angle at any position on the tooth profile need to be calculated firstly, an involute 10 equation is obtained, an equation of an intersection curve G of the crowned tooth root and the inner tooth crest is obtained according to the crowned tooth surface from the moving track of the involute 10, and finally the tooth thickness of the crowned tooth is calculated on the basis of the maximum coordinate of the curve G on the x axis before and after rotation. And calculating the minimum design clearance of the crowned teeth. Gaps of traditional crowned teeth under the non-centering working condition can be effectively increased, the movement, parallel to the x axis, of the slotting cutter helps the whole crowned tooth surface to obtain parallel involutes, the contact area of the crowned teeth is increased, and the bearing capacity of the crowned teeth is improved.

Description

Technical Field

[0001] The invention relates to the technical field of coupling drum gears, in particular to a high-performance drum gear processing method. Background Art

[0002] Gear couplings are widely used in various mechanical industries such as metallurgy, mining, lifting and transportation, petroleum and shipbuilding due to their compact structure, large load-bearing capacity, wide operating speed range and reliable operation. Drum gear couplings are often processed by gear hobbing, which causes the drum gear heel and the inner tooth top to contact first under misalignment conditions, thereby restricting the misalignment angle of the drum gear coupling. For example, the allowable misalignment angle of metallurgical drum gear couplings is usually less than 1.5°, and generally does not exceed 2.5° under extreme conditions, which seriously affects the expanded application of drum gear couplings in transmission systems. Summary of the invention

[0003] The object of the present invention is to provide a high-performance drum-shaped tooth processing method to solve the problems raised in the above background technology.

[0004] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0005] A high-performance drum-shaped gear processing method, the specific steps are as follows:

[0006] Step 1: Use gear hobbing to produce conventional drum gears:

[0007] ① Determine the radius of the hobbing cutter's travel circle:

[0008] R1=(0.5~2.0)mz,

[0009] Among them: m is the module, mm; z is the number of teeth; R1 is the arc radius, mm.

[0010] ② Define the machining path of the gear hobbing cutter on the roller teeth:

[0011] x 2 +y 2 =R1 2 .

[0012] Step 2: Use a gear shaping cutter to perform secondary processing on conventional drum gears:

[0013] ①Define the motion trajectory of the gear shaping cutter:

[0014] x 2 +y 2 =(R1-0.1) 2 .

[0015] ②The gear shaping cutter always keeps a posture parallel to the y-axis.

[0016] Step 3: Calculate the clearance of the drum-shaped gear of the present invention:

[0017] ① Calculate the tooth thickness at the pitch circle of the drum gear:

[0018]

[0019] ② Calculate the tip circle diameter of the drum gear and the internal gear to determine the coordinate of the involute on the y-axis:

[0020]

[0021] Among them: f is the tooth top height coefficient; C1 and C2 are the displacement coefficients of the drum tooth and the internal tooth; p1 is the tooth height variation coefficient.

[0022] ③Calculate the pressure angle at any position on the tooth profile:

[0023]

[0024] Where: r is the distance between the center of the coordinate system and any point on the involute.

[0025] ④ Calculate the angle θ between the point on the involute and the center point of the drum gear ring and the y-axis:

[0026]

[0027] Where: α is the standard pressure angle;

[0028] ⑤ Get the equation of the involute l0 at z=0:

[0029]

[0030] ⑥ Since the root of the drum tooth contacts the inner tooth top first, the minimum design clearance should be designed based on the curve G where the root of the drum tooth intersects the inner tooth top.

[0031] ⑦ The drum-shaped tooth surface of the present invention is obtained by moving the involute l0 along the running track of the gear shaping cutter for a distance, and the equation of the intersection curve G of the drum-shaped tooth root and the inner tooth top is obtained:

[0032]

[0033] ⑧ Define the drum gear to rotate along the y-axis by an angle of α to be equivalent to the actual misalignment condition, and obtain the coordinate of the x-axis after rotation:

[0034]

[0035] ⑨ Based on the maximum coordinate of the curve G on the x-axis before and after the rotation, calculate the minimum design clearance of the drum gear:

[0036] e=2(X 2max-x max ).

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] The present invention can effectively improve the clearance of traditional drum teeth under misalignment conditions. The movement of the gear shaping cutter parallel to the x-axis helps the entire drum tooth surface obtain mutually parallel involutes, which helps to increase the contact area of ​​the drum teeth and improve their load-bearing capacity. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a travel route diagram of the gear hobbing cutter and the gear shaping cutter of the present invention;

[0040] Figure 2 It is a forming principle diagram of the drum-shaped tooth of the present invention.

[0041] In the figure: 1—gear hobbing cutter; 2—roller teeth; 3—gear shaping cutter; 4—involute. DETAILED DESCRIPTION

[0042] The following is combined with Figure 1 -2 and Examples describe the present invention in detail.

[0043] In the first embodiment, the calculation and analysis are carried out using a drum-shaped tooth with a module of 5 mm, a number of teeth of 50, a pressure angle of 20°, and a misalignment angle of 1.5°.

[0044] 1) Use the gear hobbing method to produce conventional drum-shaped teeth:

[0045] ① Determine the radius of the travel circle of the gear hobbing cutter 1:

[0046] R1=(0.5~2.0)mz=250mm (1)

[0047] ② Define the processing path of gear hobbing cutter 1 on roller tooth 2:

[0048] x 2 +y 2 =250 2 (2)

[0049] 2) Use gear shaping cutter 3 to perform secondary processing on conventional drum gear:

[0050] ①Define the motion trajectory of the gear shaping cutter 3:

[0051] x 2 +y 2 =249.9 2 (3)

[0052] ② If Figure 1 As shown, the gear shaping cutter 3 always maintains a posture parallel to the y-axis to obtain a high-performance crown-shaped tooth.

[0053] 3) Calculate the clearance of the drum-shaped teeth of the present invention:

[0054] ① Calculate the tooth thickness at the pitch circle of the drum gear:

[0055]

[0056] ② Take f as 1.0, C1, C2 as 0, and p1 as 0. Calculate the addendum diameter of the drum gear and the internal gear to determine the coordinate of the involute 4 on the y-axis:

[0057]

[0058] Among them: f is the tooth top height coefficient; is the displacement coefficient of the drum tooth and the internal tooth; p1 is the tooth height variation coefficient.

[0059] ③ According to the value of y1, the range of r is initially selected as [118,132]. A point is selected every 0.5 mm to calculate the pressure angle at any position on the involute 4:

[0060]

[0061] α y / °: 5.475, 7.591, 9.223, 10.598, 11.806, 12.894, 13.89, 14.814, 15.677, 16.49, 17.259, 17.991, 18.689, 19.358, 20, 20.618, 21.214, 21.79, 22.348, 22.888, 23.412, 23.922, 24.418, 24.901, 25.371, 25.83, 26.278, 26.716, 27.144.

[0062] ④ Calculate the angle θ between the point on involute 4 and the center point of the drum gear ring and the y-axis:

[0063]

[0064] θ / °: 2.637, 2.609, 2.573, 2.531, 2.484, 2.432, 2.375, 2.315, 2.251, 2.183, 2.112, 2.038, 1.962, 1.882 , 1.8, 1.715, 1.628, 1.539, 1.447, 1.353, 1.258, 1.16, 1.06, 0.958, 0.854, 0.749, 0.642, 0.533, 0.423.

[0065] ⑤ Calculate the tooth surface coordinates according to the involute l0 equation at z = 0:

[0066]

[0067] Table 1 Involute coordinates

[0068] NO. x / mm y / mm z / mm NO. x / mm y / mm z / mm 1 5.11059 120.285 0 11 3.75533 125.3952 0 2 5.01272 120.7995 0 12 3.57892 125.904 0 3 4.90543 121.3126 0 13 3.39586 126.4126 0 4 4.78925 121.8246 0 14 3.20626 126.9208 0 5 4.66459 122.336 0 15 3.01025 127.4287 0 6 4.53181 122.8468 0 16 2.80793 127.9363 0 7 4.39121 123.3571 0 17 2.59939 128.4436 0 8 4.24305 123.8671 0 18 2.38474 128.9506 0 9 4.08756 124.3768 0 19 2.16404 129.4572 0 10 3.92492 124.8862 0 20 1.93739 129.9634 0

[0069] ⑥ Calculate the coordinates based on the equation of the intersection curve G between the root of the drum tooth and the inner tooth top:

[0070]

[0071] Table 2 Coordinates of points on curve G

[0072]

[0073]

[0074] ⑦ Define the drum gear to rotate along the y-axis by an angle of α (1.5°) to be equivalent to the actual misalignment condition, and calculate the coordinate of the x-axis after rotation:

[0075]

[0076] Table 3 Coordinates of points on curve G after rotation 1.5° along the y axis

[0077] NO. 1 2 3 4 5 6 7 <![CDATA[X2 / mm]]> 5.32546 5.37421 5.36962 5.33747 5.28581 5.21853 5.13792 NO. 8 9 10 11 12 13 14 <![CDATA[X2 / mm]]> 5.04547 4.94226 4.82907 4.70653 4.57511 4.43525 4.28728 NO. 15 16 17 18 19 20 <![CDATA[X2 / mm]]> 4.1315 3.96815 3.79744 3.61959 3.43474 3.24308

[0078] ⑧ Obtain X through Table 3 and Table 2 2max 5.37421mm and x max is 5.11059 mm, calculate the minimum design clearance of the drum gear:

[0079] e=2(X 2max -x max )=0.52724mm (11)

[0080] In the second embodiment, the calculation and analysis are carried out using a drum-shaped tooth with a module of 2 mm, a number of teeth of 30, a pressure angle of 20°, and a misalignment angle of 1.5°.

[0081] 1) Use the gear hobbing method to produce conventional drum-shaped teeth:

[0082] ① Determine the radius of the travel circle of the gear hobbing cutter 1:

[0083] R1=(0.5~2.0)mz=60mm (12)

[0084] ② Define the processing path of gear hobbing cutter 1 on roller tooth 2:

[0085] x 2 +y 2 =60 2 (13)

[0086] 2) Use gear shaping cutter 3 to perform secondary processing on conventional drum gear:

[0087] ①Define the motion trajectory of the gear shaping cutter 3:

[0088] x 2 +y 2 =59.9 2 (14)

[0089] ② If Figure 1 As shown, the gear shaping cutter 3 always maintains a posture parallel to the y-axis to obtain a high-performance crown-shaped tooth.

[0090] 3) Calculate the clearance of the drum-shaped teeth of the present invention:

[0091] ① Calculate the tooth thickness at the pitch circle of the drum gear:

[0092]

[0093] ② Take f as 1.0, C1, C2 as 0, and p1 as 0. Calculate the addendum diameter of the drum gear and the internal gear to determine the coordinate of the involute 4 on the y-axis:

[0094]

[0095] Among them: f is the tooth top height coefficient; is the displacement coefficient of the drum tooth and the internal tooth; p1 is the tooth height variation coefficient.

[0096] ③ According to the value of y1, the range of r is initially selected as [28,33]. A point is selected every 0.2 mm to calculate the pressure angle at any position on the involute 4:

[0097]

[0098] α y / °: 1.465, 6.959, 9.704, 11.806, 13.567, 15.108, 16.49, 17.751, 18.915, 20, 21.018, 21.978, 22.888, 23.754, 24.58, 25.371, 26.13, 26.86, 27.563, 28.241, 28.897, 29.531, 30.146, 30.742, 31.321.

[0099] ④ Calculate the angle θ between the point on involute 4 and the center point of the drum gear ring and the y-axis:

[0100]

[0101] θ / °: 3.854, 3.82, 3.76, 3.684, 3.595, 3.494, 3.383, 3.263, 3.135, 3, 2.858, 2.709, 2.5 53, 2.392, 2.226, 2.054, 1.878, 1.696, 1.511, 1.32, 1.126, 0.928, 0.725, 0.519, 0.31.

[0102] ⑤ Calculate the tooth surface coordinates according to the involute l0 equation at z = 0:

[0103]

[0104] Table 4 Involute coordinates

[0105]

[0106]

[0107] ⑥ Calculate the coordinates based on the equation of the intersection curve G between the root of the drum tooth and the inner tooth top:

[0108]

[0109] Table 5 Coordinates of points on curve G

[0110] NO. x / mm y / mm z / mm NO. x / mm y / mm z / mm 1 1.89438 28 3.04319 14 1.28562 28 12.76863 2 1.89161 28 4.37269 15 1.20399 28 13.25134 3 1.87537 28 5.52694 16 1.11836 28 13.71985 4 1.85034 28 6.48887 17 1.02879 28 14.17543 5 1.81803 28 7.33317 18 0.93537 28 14.61926 6 1.77933 28 8.09626 19 0.83816 28 15.05230 7 1.7348 28 8.79894 20 0.73722 28 15.47536 8 1.68486 28 9.45456 21 0.6326 28 15.88919 9 1.62983 28 10.07214 22 0.52436 28 16.29439 10 1.56996 28 10.65818 23 0.41253 28 16.69154 11 1.50544 28 11.21751 24 0.29715 28 17.08112 12 1.43646 28 11.75384 25 0.17827 28 17.46355 13 1.36314 28 12.27008

[0111] ⑦ Define the drum gear to rotate along the y-axis by an angle of α (1.5°) to be equivalent to the actual misalignment condition, and calculate the coordinate of the x-axis after rotation:

[0112]

[0113] Table 6 Coordinates of points on curve G after rotation 1.5° along the y axis

[0114] NO. 1 2 3 4 5 6 7 8 <![CDATA[X2 / mm]]> 1.973 2.005 2.019 2.020 2.009 1.991 1.965 1.932 NO. 9 10 11 12 13 14 15 16 <![CDATA[X2 / mm]]> 1.893 1.848 1.799 1.744 1.684 1.619 1.550 1.477 NO. 17 18 19 20 21 22 23 <![CDATA[X2 / mm]]> 1.400 1.318 1.232 1.142 1.048 0.951 0.849

[0115] ⑧ Obtain X through Table 3 and Table 2 2max 2.020mm and x max is 1.894 mm, calculate the minimum design clearance of the crown gear:

[0116] e=2(X 2max -x max )=0.252mm (22)

[0117] In the above two groups of embodiments, the movement of the gear cutter parallel to the x-axis helps the entire drum tooth surface to obtain mutually parallel involutes, which helps to increase the contact area of ​​the drum tooth, improve its load-bearing capacity, and strengthen the application of the drum tooth coupling in the transmission system. The minimum design clearance of the drum tooth coupling of the present invention is calculated, and then the key design parameters of the drum tooth of the present invention are determined. At the same time, it can ensure the reasonable distribution of the load-bearing performance of each circumferential tooth pair, greatly improving the load-bearing performance of the drum tooth coupling.

[0118] What is described above is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for processing high-performance drum-shaped teeth, characterized in that: The following steps are involved: Step 1: Use gear hobbing to produce conventional drum gears: ① Determine the radius of the travel circle of the gear hobbing cutter (1): R1=(0.5~2.0)mz, Among them: m is the module, mm; z is the number of teeth; R1 is the arc radius, mm. ② Define the machining path of the gear hobbing cutter (1) on the roller teeth (2): Step 2: Use the gear shaping cutter (3) to perform secondary processing on the conventional drum gear: ① Define the motion trajectory of the gear shaping cutter (3): x 2 +y 2 =(R1-0.1) 2 。 ②The gear shaping cutter always keeps a posture parallel to the y-axis. Step 3: Calculate the clearance of the drum-shaped gear of the present invention: ① Calculate the tooth thickness at the pitch circle of the drum gear: ② Calculate the tip circle diameter of the drum gear and the internal gear to determine the coordinate of the involute on the y-axis: Among them: f is the tooth top height coefficient; C1 and C2 are the displacement coefficients of the drum tooth and the internal tooth; p1 is the tooth height variation coefficient. ③Calculate the pressure angle at any position on the tooth profile: Where: r is the distance between the center of the coordinate system and any point on the involute. ④ Calculate the angle θ between the point on the involute and the center point of the drum gear ring and the y-axis: Where: α is the standard pressure angle; ⑤ Get the equation of the involute l0 at z=0: ⑥ Since the root of the drum tooth contacts the inner tooth top first, the minimum design clearance should be designed based on the curve G where the root of the drum tooth intersects the inner tooth top. ⑦ The drum-shaped tooth surface of the present invention is moved along the running track of the gear shaping cutter by the involute l0 for a distance to obtain the equation of the intersection curve G between the root of the drum-shaped tooth and the inner tooth top: ⑧ Define the drum gear to rotate along the y-axis by an angle of α to be equivalent to the actual misalignment condition, and obtain the coordinate of the x-axis after rotation: ⑨ Based on the maximum coordinate of the curve G on the x-axis before and after the rotation, calculate the minimum design clearance of the drum gear: e=2(X 2max -x max )。

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