Involute nonlinear displacement and tooth thickness variable gear transmission mechanism

Abstract

The present invention provides an involute nonlinear displacement and variable tooth thickness gear transmission mechanism, comprising an involute nonlinear displacement and variable thickness gear I and an involute nonlinear displacement and variable thickness gear II. The involute nonlinear displacement and variable thickness gear I and the involute nonlinear displacement and variable thickness gear II form a mutually meshing nonlinear gear transmission mechanism. Both the involute nonlinear displacement and variable thickness gear I and the involute nonlinear displacement and variable thickness gear II are machined using parabolic curves to form the nonlinear gears. By adjusting the machining path to achieve a nonlinear variation in the displacement coefficient along the axis while retaining the characteristics of a gear with variable tooth thickness along the axis, a flexible creation method for nonlinear displacement gears based on hobbing machining theory is established. Secondly, the staggered axis transmission characteristics of the nonlinear displacement and variable thickness gears are studied.

Description

Technical Field

[0001] The invention belongs to the technical field of gear transmission, and in particular relates to an involute nonlinear displacement and tooth thickness variable gear transmission mechanism. Background Art

[0002] Currently, involute variable-thickness gear transmissions are widely used in power transmission applications such as high-speed ships, precision robots, and all-wheel drive vehicles due to their advantages such as easy processing, compact structure, and high precision. However, due to their theoretical point contact, the sliding velocity between the gear tooth surfaces is high, resulting in low load-bearing capacity, easy wear of the gear pairs, and high vibration noise, which reduces the gear life and reliability. Furthermore, the linear variation of the processing parameter u causes the gear's large end to become pointed, severely restricting the widespread application and development of variable-thickness gear transmissions in the power transmission field.

[0003] Involute variable-thickness gears are a general form of involute nonlinear variable-thickness gears. Theoretically, the two gears can form transmissions at any angle about their axes, enabling power transmission in parallel, intersecting, and staggered axis configurations. In particular, meshing performance in small-angle power transmission configurations offers advantages such as high strength, excellent rigidity, and ease of fabrication.

[0004] The involute nonlinear displacement and thickness gear can adjust the processing path curve of the imaginary rack tool to realize the creation process of nonlinear displacement and thickness gear. j ) is a function of the machining parameter u, which can realize the modification of the tooth profile. Summary of the Invention

[0005] In view of this, the present invention aims to explore and provide an involute nonlinear displacement and variable tooth thickness gear transmission mechanism. One of the key technical problems to be solved is to break through the bottleneck of linear change of the previous linear displacement gear processing path along the axis. By adjusting the processing path, the displacement coefficient along the axis direction changes nonlinearly, and at the same time retains the characteristics of the variable tooth thickness gear along the axis direction, a nonlinear displacement gear flexible creation method based on the rolling processing theory is established; the second is to study the staggered axis transmission characteristics of the thickened gear after nonlinear displacement, so as to have a deeper understanding of the law of change of the variable tooth thickness gear coefficient.

[0006] In order to achieve the above technical features, the purpose of the present invention is achieved as follows: an involute nonlinear displacement and tooth thickness variable gear transmission mechanism, characterized in that it includes an involute nonlinear displacement and thickness variable gear I and an involute nonlinear displacement and thickness variable gear II; the involute nonlinear displacement and thickness variable gear I and the involute nonlinear displacement and thickness variable gear II constitute a set of mutually meshing nonlinear gear transmission mechanisms;

[0007] The involute nonlinear displacement and thickness gear I and the involute nonlinear displacement and thickness gear II are both processed using parabolic curves to form nonlinear gears.

[0008] The parabolic curves of the involute nonlinear displacement and thickness gear I and the involute nonlinear displacement and thickness gear II are determined by the function y, wherein:

[0009] y=Au 2 +Bu+C (1)

[0010] Where: A, B, C are coefficients, and different coefficients correspond to different nonlinear thickening gears; u is the processing parameter; y is the processing curve function.

[0011] The axes of the involute nonlinear displacement and thickness changing gear I and the involute nonlinear displacement and thickness changing gear II are spatially staggered.

[0012] The axis intersection angle between the involute nonlinear displacement and thickness changing gear I and the involute nonlinear displacement and thickness changing gear II is less than 45°.

[0013] When the axis planes of the involute nonlinear displacement and thickness gear I and the involute nonlinear displacement and thickness gear II are parallel or intersecting, the following relationship exists:

[0014] cos(β1+β2)=tanγ w1 tanγ w2 +cos(γ w1 +γ w2 ) / cosγ w1 cosγ w2 (2)

[0015] Where: β1 is the helix angle on the first pitch plane of the involute nonlinear displacement and thickness gear;

[0016] β2 is the helix angle on the plane of pitch II of the involute nonlinear displacement and thickening gear;

[0017] γ w1 is the working pitch cone angle of the involute nonlinear displacement and thickness gear Ⅰ;

[0018] γ w2 is the working pitch cone angle of the involute nonlinear displacement and thickness gear II;

[0019] When β1 and β2 are positive, it is right-handed, and when they are negative, it is left-handed.

[0020] When the axes of the involute nonlinear displacement and thickness gear I and the involute nonlinear displacement and thickness gear II are spatially staggered, the following relationship exists:

[0021] d1=-r pw2 / sinγw1 cosγ w2 +E(sin 2 (γ w1 +γ w2 )-sin 2 γ w1 -sinγ w1 sinγ w2 cos(γ w1 +γ w2 )) / sinγ w1 sin(γ w1 +γ w2 )(sin 2 (γ w1 +γ w2 )-sin 2 γ w1 -sin 2 γ w2 -2sinγ w1 sinγ w2 cos(γ w1 +γ w2 )) 1 / 2 (3)

[0022] d2=-r pw2 / sinγ w2 cosγ w2 -E(sinγ w1 cos(γ w1 +γ w2 )+sinγ w2 ) / (sin 2 (γ w1 +γ w2 )-sin 2 γ w1 -sin 2 γ w2 -2sinγ w1 sinγ w2 cos(γ w1 +γ w2 )) 1 / 2 (4)

[0023] E=(r pw1 cosγ w2 +r pw1 cosγ w2 )sin(β1 + β2) / sin(γ w1 +γ w2 ) (5)

[0024] Where: d1 is the mounting distance of the involute non-linear modified thickening gear I;

[0025] d2 is the installation distance of the involute nonlinear displacement and thickness gear II;

[0026] r pw1 The distance from the pitch cone contact point of the involute nonlinear displacement and thickness gear transmission to the axis of the involute nonlinear displacement and thickness gear I;

[0027] r pw2 The distance from the pitch taper contact point of the involute nonlinear displacement and thickening gear transmission to the axis of the involute nonlinear displacement and thickening gear II;

[0028] β1 is the helix angle on the plane of pitch I of the involute nonlinear displacement and thickness gear;

[0029] β2 is the helix angle on the plane of pitch II of the involute nonlinear displacement and thickening gear;

[0030] E is the shortest distance between the axis of the involute nonlinear displacement and thickness gear I and the axis of the involute nonlinear displacement and thickness gear II.

[0031] The present invention has the following beneficial effects:

[0032] 1. The present invention proposes a nonlinear change in the gear processing path, which breaks through the traditional processing method and provides a new direction for the morphology design and optimization of thickened gears.

[0033] 2. The present invention can generate different nonlinear displacement and thickening gears through different processing path curves, so that the gear tooth profile is changed while ensuring that the tooth profile direction is an involute, which will effectively avoid the phenomenon of heel cutting after the large end of the linear displacement and thickening gear becomes pointed.

[0034] 3. The involute gear transmission mechanism of the present invention adopts nonlinear displacement theory to perform different treatments on the tooth surface of conventional variable thickness gears, breaking through the limitation that the coefficient of the variable thickness gear changes linearly, and providing a deeper understanding of the law of the change of the coefficient of the variable thickness gear. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The present invention will be further described below with reference to the accompanying drawings and examples.

[0036] Figure 1 , Figure 2 This is a machining curve for modifying the shape of the nonlinear gear at both ends and a comparison diagram with the linear machining method, which is proposed for the linear machining of the gear. Figure 2 The middle contour line A is a simplified diagram of the nonlinear gear tooth profile.

[0037] Figure 3 , Figure 4This is a nonlinear gear proposed by the present invention for the linear processing of the gear with a sharp end. It only modifies the big end of the processing path curve and the comparison diagram with the linear processing method. Figure 4 The middle contour line B is a simplified diagram of the nonlinear gear tooth profile.

[0038] Figure 5 It is a schematic diagram of the working pitch cone of the involute nonlinear displacement and thickness gear staggered shaft transmission of the present invention.

[0039] Figure 6 This is a diagram of the involute nonlinear displacement and thickening gear hobbing process of the present invention.

[0040] Figure 7 This is the first three-dimensional diagram of the involute nonlinear displacement and thickness gear staggered axis transmission meshing model of the present invention.

[0041] Figure 8 This is the second three-dimensional diagram of the involute nonlinear displacement and thickness gear staggered axis transmission meshing model of the present invention.

[0042] Figure 9 This is the third three-dimensional diagram of the involute nonlinear displacement and thickness gear staggered axis transmission meshing model of the present invention. DETAILED DESCRIPTION

[0043] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0044] Example 1:

[0045] like Figure 1 , its processing curve f(uj) is given by the equation group:

[0046] a)k1*(u min ) 2 +k2*(u min )+k3+2=0

[0047] b)k1*(u mid ) 2 +k2*(u mid )+k3=0

[0048] c)k1*(u max ) 2 +k2*u max +k3+2=0

[0049] Three equations are obtained, where k1, k2, k3 are coefficients, and u min is the machining parameter of the small end of the gear, u mid is the machining parameter of the gear middle plane, u max These are the machining parameters for the big end of the gear.

[0050] like Figure 5The figure shows a schematic diagram of a staggered axis variable thickness gear transmission pitch cone. An involute nonlinear variable thickness gear I and an involute nonlinear variable thickness gear II are generated along the obtained parabolic curve by gear hobbing. In this embodiment, the axis of the involute nonlinear variable thickness gear I and the axis of the involute nonlinear variable thickness gear II are spatially staggered, and:

[0051] cos(β1+β2)=tanγ w1 tanγ w2 +cos(γ w1 +γ w2 ) / cosγ w1 cosγ w2

[0052] Where β1 is the helix angle on the plane of pitch I of the involute nonlinear displacement and thickness gear;

[0053] β2 is the helix angle on the plane of pitch II of the involute nonlinear displacement and thickening gear;

[0054] γ w1 is the working pitch cone angle of the involute nonlinear displacement and thickness gear Ⅰ;

[0055] γ w2 is the working pitch cone angle of the involute nonlinear displacement and thickness gear II;

[0056] When β1 and β2 are positive, it is right-handed, and when they are negative, it is left-handed.

[0057] The involute nonlinear displacement and thickness changing gear pair transmission of this embodiment also needs to meet the following conditions:

[0058] d1=-r pw2 / sinγ w1 cosγ w2 +E(sin 2 (γ w1 +γ w2 )-sin 2 γ w1 -sinγ w1 sinγ w2 cos(γ w1 +γ w2 )) / sinγ w1 sin(γ w1 +γ w2 )(sin 2 (γ w1 +γ w2 )-sin 2 γ w1 -sin 2 γ w2 -2sinγ w1 sinγw2 cos(γ w1 +γ w2 )) 1 / 2

[0059] d2=-r pw2 / sinγ w2 cosγ w2 -E(sinγ w1 cos(γ w1 +γ w2 )+sinγ w2 ) / (sin 2 (γ w1 +γ w2 )-sin 2 γ w1 -sin 2 γ w2 -2sinγ w1 sinγ w2 cos(γ w1 +γ w2 )) 1 / 2

[0060] E=(r pw1 cosγ w2 +r pw1 cosγ w2 )sin(β1+β2) / sin(γ w1 +γ w2 )

[0061] Wherein, d1 is the installation distance of the involute nonlinear displacement and thickness gear Ⅰ;

[0062] d2 is the installation distance of the involute nonlinear displacement and thickness gear II;

[0063] r pw1 The distance from the pitch cone contact point of the involute nonlinear displacement and thickness gear transmission to the axis of the involute nonlinear displacement and thickness gear I;

[0064] r pw2 The distance from the pitch taper contact point of the involute nonlinear displacement and thickening gear transmission to the axis of the involute nonlinear displacement and thickening gear II;

[0065] E is the shortest distance between the axis of the involute nonlinear displacement and thickness gear I and the axis of the involute nonlinear displacement and thickness gear II.

[0066] This embodiment is an involute nonlinear displacement and thickening gear transmission. By setting the axis of the involute nonlinear displacement and thickening gear I and the axis of the involute nonlinear displacement and thickening gear II to be staggered, and setting parameters such as the helix angle, it inherits the advantages of the spatial staggered axis involute thickening gear, such as strong transmission capacity, good rigidity, and easy processing and manufacturing. It can also improve the situation where the big end becomes pointed after displacement, which will effectively avoid the root cutting of the thickening gear during transmission.

[0067] Example 2:

[0068] like Figure 3 As shown, the processing curve f(u j )From the equations:

[0069] a)k1*(2u min -u max ) 2 +k2*(2u min -u max )+k3+2=0

[0070] b)k1*(u min ) 2 +k2*(u min )+k3=0

[0071] c)k1*(u max ) 2 +k2*u max +k3+2=0

[0072] Three equations are obtained, where k1, k2, k3 are coefficients, and u min is the machining parameter of the small end of the gear, u max These are the machining parameters for the big end of the gear.

[0073] Except for the gear processing curve of Example 2, which is different from that of Example 1, other implementation steps are the same as those of Example 1 and will not be repeated here.

Claims

1. Involute nonlinear displacement and tooth thickness variable gear transmission mechanism, characterized by: It includes an involute nonlinear displacement and thickness changing gear I and an involute nonlinear displacement and thickness changing gear II; the involute nonlinear displacement and thickness changing gear I and the involute nonlinear displacement and thickness changing gear II form a set of mutually meshing nonlinear gear transmission mechanisms; The involute nonlinear displacement and thickness gear I and the involute nonlinear displacement and thickness gear II are both processed using parabolic curves to form nonlinear gears; The parabolic curves of the involute nonlinear displacement and thickness gear I and the involute nonlinear displacement and thickness gear II are obtained by the function y Determine, where: y = Au 2 + Bu + C （1） Where: A 、 B 、 C is the coefficient, and different coefficients correspond to different nonlinear thickening gears; u is the processing parameter; y is the processing curve function; When the axis planes of the involute nonlinear displacement and thickness gear I and the involute nonlinear displacement and thickness gear II are parallel or intersecting, the following relationship exists: （2） Where: is the helix angle on the plane of pitch I of the involute nonlinear displacement and thickening gear; is the helix angle on the plane of pitch II of the involute nonlinear displacement and thickening gear; is the working pitch cone angle of the involute nonlinear displacement and thickness gear Ⅰ; is the working pitch cone angle of the involute nonlinear displacement and thickness gear II; and When it is positive, it is right-handed, and when it is negative, it is left-handed; When the axes of the involute nonlinear displacement and thickness gear I and the involute nonlinear displacement and thickness gear II are spatially staggered, the following relationship exists: （3） （4） （5） Where: d 1 is the installation distance of the involute nonlinear displacement and thickness gear Ⅰ; d 2 is the installation distance of the involute nonlinear displacement and thickness gear II; r pw1 The distance from the pitch cone contact point of the involute nonlinear displacement and thickness gear transmission to the axis of the involute nonlinear displacement and thickness gear I; r pw2 is the distance from the pitch cone contact point of the involute nonlinear displacement and thickness gear transmission to the axis of the involute nonlinear displacement and thickness gear II; β 1 is the helix angle on the plane of pitch I of the involute nonlinear displacement and thickening gear; β 2 is the helix angle on the plane of pitch II of the involute nonlinear displacement and thickening gear; E It is the shortest distance between the axis of the involute nonlinear displacement and thickening gear I and the axis of the involute nonlinear displacement and thickening gear II.

2. The involute nonlinear displacement and tooth thickness variable gear transmission mechanism according to claim 1, characterized in that: The axes of the involute nonlinear displacement and thickness changing gear I and the involute nonlinear displacement and thickness changing gear II are spatially staggered.

3. The involute nonlinear displacement and tooth thickness variable gear transmission mechanism according to claim 2, characterized in that: The axis intersection angle between the involute nonlinear displacement and thickness changing gear I and the involute nonlinear displacement and thickness changing gear II is less than 45°.

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