Tooth root digging double-arc design method of tooth surface strengthened cylindrical external gear

Abstract

The invention discloses a tooth root digging double-arc design method for a tooth surface strengthened cylindrical external gear. The smooth connection of the tooth root transition curved surface B-C, the tooth profile and the tooth root and the design method of the maximum range of the involute starting circle are ensured. The tooth root transition curved surface design of the tooth surface strengthened cylindrical external gear is carried out, the end point and the curvature extreme value of the tooth root transition curved surface B-C are determined, it is guaranteed that the tooth root transition curved surface B-C is in smooth connection with the tooth profile and the tooth root, and the maximum range of the involute starting circle is guaranteed so that the involute starting circle can be used for rack tool design; and the cutter design and manufacturing and technological machining processes are comprehensively considered, so that the reliability and quality of the gear after forming are improved.

Description

Technical Field

[0001] The present invention relates to a method for designing a double circular arc with root cutting for a tooth surface strengthened cylindrical external gear, belonging to the technical field of gears. Background Art

[0002] The tooth surface A - B and the tooth root surface C - D of the cylindrical gear 1 are connected through the tooth root transition surface B - C, as Figure 1 shown. The tooth root transition surface B - C is generally formed by the involute of the convex angle 3 of the rack cutter 2 ( Figure 2 ), with complex size calculations and great quantification difficulties. In the gear design drawing, the dimensional parameters of this transition surface cannot be directly given. Only the tip fillet radius Ra of the rack cutter 2 or the height of the convex angle 3 (as specified in GB / T 12369 "Basic Tooth Profile of Straight and Helical Bevel Gears": Ra = the root fillet radius of the basic tooth profile = 0.3mn, where mn is the normal module of the gear) is given for the design and manufacture of the gear cutter, and it should be ensured that this fillet Ra or convex angle 3 can generate a transition surface that meets the design requirements.

[0003] To improve the load - bearing capacity of the gear, a strengthening process such as surface carburizing or nitriding of the tooth profile is generally adopted. In addition to increasing the tooth surface hardness, it also generates a certain amount of compressive stress on the strengthened surface (which is beneficial to improving the bending fatigue strength of the gear). After the strengthening process, gear grinding is required to complete the final precision machining of the tooth profile. For the root - cutting tooth profile of the cylindrical gear 1, all the tooth surfaces and the upper part of the tooth root transition surface need to remain concave steps after gear grinding, as Figure 2 B' in. The tooth root surface and the lower part of the tooth root transition surface are not ground, retaining the compressive stress after the surface treatment.

[0004] In engineering, a process of grinding all the tooth surfaces, tooth root transition surfaces, and tooth root surfaces (also known as grinding the whole tooth) is generally not adopted. As can be seen from Figure 2 , during the process of the tooth profile bearing the load, the remaining tooth root transition surface still bears the bending load during operation. The shape mutation (step) or the tooth root transition surface with a smaller curvature at the tooth root transition surface will directly affect the bending fatigue strength of the gear, and thus directly affect the load - bearing capacity of the gear. When the influence is serious, it will cause the tooth profile to fail and break due to bending fatigue, resulting in accidents. Therefore, the precision and accuracy of the dimensional design of the tooth root transition surface are particularly important. Summary of the Invention

[0005] To solve the above - mentioned technical problems, the present invention provides a method for designing a double circular arc with root cutting for a tooth surface strengthened cylindrical external gear.

[0006] The present invention is achieved through the following technical solutions.

[0007] A method for designing a double circular arc with root cutting for a tooth surface strengthened cylindrical external gear provided by the present invention includes;

[0008] It ensures that the tooth root transition surface B-C is smoothly connected to the tooth profile and the tooth root, and a design method for the maximum range of the involute starting circle.

[0009] The design method includes Step 1: Determine the actual center distance of the gear pair, the end face meshing angle of the pitch circle, and the addendum circle pressure angle of the mating gear according to the gear pair parameters.

[0010] The design method further includes Step 2: Determine the maximum starting circle diameter of the involute where point B is located and its tolerance according to the parameters and tolerances of the mating gear:

[0011]

[0012] The design method further includes Step 3: Calculate the end face pressure angle at point B:

[0013]

[0014] The design method further includes Step 4: Calculate the end face arc tooth groove width and tolerance at point B:

[0015]

[0016] The design method further includes Step 5: Calculate the normal arc tooth groove width and tolerance at point B according to the gear parameters.

[0017] The design method further includes Step 6: Draw a normal tooth groove diagram according to Steps 1 to 4 and various gear parameters, and draw the involute tooth profile L1 after gear cutting;

[0018] Calculate the coordinates of point B on the involute tooth profile based on the normal arc tooth groove width and tolerance at point B and the maximum starting circle radius of the involute where point B is located.

[0019] The design method further includes Step 7: In the normal tooth groove diagram, draw the involute tooth profile L2 after gear grinding according to the grinding depth and gear parameters.

[0020] The design method further includes Step 8: In the normal tooth groove diagram, draw an arc with a certain radius that is tangent to the tooth root circle surface of point B, and the size of this radius should be the largest under the condition that the arc is recessed 0.02 mm below the L2 line within each tolerance zone.

[0021] The beneficial effects of the present invention are as follows: In this application, the root transition surface design of the tooth surface strengthened cylindrical external gear is carried out, the end point and curvature extreme value of the root transition surface B-C are determined, ensuring that the root transition surface B-C is smoothly connected to the tooth profile and the tooth root, and ensuring the maximum range of the involute starting circle for the design of the rack cutter; and comprehensively considering the tool design and manufacturing and the process machining process, the design of the gear root transition curve is applicable to the complex working conditions of the high-speed and heavy-load gears of aero-engines compared with the recommended values of the rack cutter given by the standard, improving the reliability and quality of the formed gear. Description of the Drawings

[0022] Figure 1 is a schematic diagram of the root-cut tooth profile (after gear cutting) of a cylindrical gear;

[0023] Figure 2 is a structural schematic diagram of the root-cut tooth profile (after gear grinding) of a cylindrical gear; Detailed Embodiments

[0024] The technical solution of the present invention will be further described below, but the scope of protection is not limited thereto.

[0025] Step 1: According to the parameters of the gear pair, determine the actual center distance of the gear pair, the pitch circle end face engagement angle, and the addendum circle pressure angle of the mating gear.

[0026] Step 2: According to the parameters and tolerances of the mating gear, determine the maximum starting circle diameter and its tolerance of the involute where point B is located:

[0027]

[0028] Among them:

[0029] r B1 ——The maximum starting circle radius of the involute where point B is located, unit: millimeter.

[0030] r2——The pitch circle radius of the mating gear, unit: millimeter.

[0031] a sj ——The actual center distance of the gear pair (including tolerance), unit: millimeter.

[0032] α a2 ——The addendum circle pressure angle of the mating gear (including tolerance), unit: degree.

[0033] α jt ——The pitch circle end face engagement angle, unit: degree.

[0034] Step 3: Calculate the end face pressure angle of point B:

[0035]

[0036] Among them:

[0037] d b1 —— Base circle diameter of the gear, unit: millimeter.

[0038] Step 4, calculate the face arc tooth space width and tolerance at point B:

[0039]

[0040] Where:

[0041] S cBt1 —— Face arc tooth space width at point B except, unit: millimeter.

[0042] Z1 —— Number of teeth of the gear.

[0043] S ft —— Face arc tooth thickness of the gear pitch circle, unit: millimeter.

[0044] d f1 —— Pitch circle diameter of the gear, unit: millimeter.

[0045] ɑ ft —— Face pressure angle of the gear pitch circle, unit: degree.

[0046] Step 5, calculate the normal arc tooth space width and tolerance at point B according to the gear parameters.

[0047] Step ⑥, according to Steps 1 to 4 and the various gear parameters, draw the normal tooth space diagram in mechanical drawing software, and draw the involute tooth profile L1 after gear cutting. According to the normal arc tooth space width and tolerance at point B and the maximum starting circle radius of the involute where point B is located, calculate the coordinates of point B on the involute tooth profile.

[0048] Step 7, in the normal tooth space diagram, draw the involute tooth profile L2 after gear grinding according to the grinding depth specified by the process specification (generally 0.2 millimeters) and the gear parameters.

[0049] Step 8, in the normal tooth space diagram, draw an arc with a certain radius that is tangent to the tooth root circle surface of point B. The radius should ensure that the arc is recessed 0.02 mm below the L2 line and is the largest in each tolerance zone. This radius is the maximum radius of the tooth root transition surface and can be directly marked in the gear design drawing, providing a basis for the design of the gear cutter.

Claims

1. A design method of a tooth root-digging double arc for a cylindrical external gear with tooth surface strengthening, characterized in that, It ensures the smooth connection between the tooth root transition surface B-C and the tooth profile and tooth root, and the design method for the maximum range of the involute starting circle.

2. The tooth root digging double-arc design method for the tooth surface strengthened cylindrical external gear according to claim 1, characterized in that, The design method includes Step 1: Determine the actual center distance of the gear pair, the meshing angle of the pitch circle end face, and the addendum circle pressure angle of the mating gear according to the gear pair parameters.

3. The tooth root digging double arc design method for the tooth surface strengthened cylindrical external gear as described in claim 2, characterized in that, The design method further includes Step 2: Determine the maximum starting circle diameter of the involute where point B is located and its tolerance according to the parameters and tolerances of the mating gear.

4. The tooth root digging double arc design method for the tooth surface strengthened cylindrical external gear according to claim 3, characterized in that: The design method further includes Step 3: Calculate the end face pressure angle at point B.

5. The tooth root digging double arc design method for the tooth surface strengthened cylindrical external gear according to claim 4, characterized in that, The design method further includes Step 4: Calculate the end face arc tooth groove width and tolerance at point B.

6. The tooth root digging double arc design method for the tooth surface strengthened cylindrical external gear according to claim 5, characterized in that, The design method further includes Step 5: Calculate the normal arc tooth groove width and tolerance at point B according to the gear parameters.

7. The tooth root cutting double-arc design method for the tooth surface strengthened cylindrical external gear according to claim 6, characterized in that, The design method further includes Step 6: Draw the normal tooth groove diagram according to Step 1 to Step 4 and various gear parameters, and draw the involute tooth profile L1 after gear cutting. Calculate the coordinates of point B on the involute tooth profile based on the normal arc tooth groove width and tolerance at point B and the maximum starting circle radius of the involute where point B is located.

8. The tooth root digging double arc design method for the tooth surface strengthened cylindrical external gear according to claim 7, characterized in that, The design method further includes Step 7: In the normal tooth groove diagram, draw the involute tooth profile L2 after gear grinding according to the grinding depth and gear parameters.

9. The tooth root cutting double arc design method for the tooth surface strengthened cylindrical external gear according to claim 8, characterized in that, The design method further includes Step 8: In the normal tooth groove diagram, draw an arc with a certain radius to be tangent to the tooth root circle surface of point B, and the radius should ensure the maximum size under the condition that the arc is recessed 0.02 mm below the L2 line within each tolerance zone.

Images