Staggered axis involute cylindrical gear and variable thickness gear transmission mechanism

Abstract

The present invention provides a staggered-axis involute cylindrical gear and variable-thickness gear transmission mechanism, comprising a variable-thickness gear I and an involute cylindrical gear II. The variable-thickness gear I and the involute cylindrical gear II form a mutually meshing gear transmission mechanism, with the axes of the variable-thickness gear I and the involute cylindrical gear II spatially staggered. The geometric design parameters of the involute cylindrical gear and variable-thickness gear transmission are derived based on gear geometry and the principle of spatial gear meshing. The present invention reduces and eliminates meshing interference and jamming caused by large axial motion.

Description

Technical Field

[0001] The present invention relates to the technical field of gear transmission, and in particular to a staggered axis involute cylindrical gear and variable thickness gear transmission mechanism. Background Art

[0002] Currently, involute variable-thickness gear transmissions are widely used in power transmission applications such as automotive transmissions and precision transmissions due to their advantages such as easy processing, compact structure, and high precision. However, while variable-thickness gear pairs can achieve precision transmission through axial play, they are highly sensitive to installation errors. Excessive axial play can lead to meshing interference and seizure, restricting their application in power transmission.

[0003] The meshing of involute cylindrical gears and variable thickness gears can avoid this phenomenon. It is only necessary to replace the variable thickness gear on the output shaft of the gearbox with an involute cylindrical gear, and form a staggered axis involute cylindrical gear and variable thickness gear transmission with the variable thickness gear on the input shaft, so that the output shaft can move axially within a larger range without causing meshing interference, jamming, etc.

[0004] The involute cylindrical gear is a general form of variable thickness gear. Through geometric parameter design, it can form any form of transmission mode with the variable thickness gear in space. Summary of the Invention

[0005] In view of the deficiencies in the prior art, the present invention provides a staggered axis involute cylindrical gear and thickened gear transmission mechanism, which solves the problems of meshing interference, jamming and the like caused by large axial movement in the prior art.

[0006] According to an embodiment of the present invention, a staggered axis involute cylindrical gear and thickened gear transmission mechanism includes a thickened gear I and an involute cylindrical gear II; the thickened gear I and the involute cylindrical gear II constitute a set of mutually meshing gear transmission mechanisms, and the axes of the thickened gear I and the involute cylindrical gear II are spatially staggered.

[0007] The meshing of the staggered axis involute cylindrical gear and the variable thickness gear can be regarded as the meshing between the working pitch cylinder and the working pitch cone. A meshing model of the spatial pitch cylinder and the pitch cone is established based on the spatial geometric relationship. During the gear meshing process, the two contacting tooth surfaces are in a continuous contact state. At any time, the two gears have a common contact point and a common normal at this point. The contact equation can be expressed as:

[0008]

[0009]

[0010] Where l1 and u1 represent the parameters of the thickened gear along the tooth profile and tooth width respectively; l2 and u2 represent the parameters of the cylindrical gear along the tooth profile and tooth width respectively. and are the rotation angles of the two gears respectively.

[0011] The position coordinates of any contact point P between the variable thickness gear I and the involute cylindrical gear II are:

[0012]

[0013] In the formula

[0014] x j ,y j ,z j (j=1,2)——Coordinates of the tangent contact point P on the pitch cone (cylinder);

[0015] θ j (j=1,2)——point P and point o j x j z j The expansion angle of the (j=1,2) plane.

[0016] The unit normal vector of the variable thickness gear I and the involute cylindrical gear II at the contact point P is:

[0017] n1=[cosγ w1 cosθ1 cosγ w1 sinθ1 -sinγ w1 ] T

[0018] n2=[cosθ2 sinθ2 0] T

[0019] When the axes of the variable thickness gear I and the involute cylindrical gear II are spatially staggered, the following relationship exists:

[0020] d1=r w1 (cotγ w1 -cot 2 δtanγ w1 )+r w2 (cot 2 δsinγ w1 +sinγ w1 )

[0021] d2=d1cosδ+r w1 cotγ w1 cosδ+r w1 tanγ w1 cosδ

[0022]

[0023] Where:

[0024] d j (j=1,2) are the installation distances between the variable thickness gear I and the involute cylindrical gear II respectively;

[0025] r wj (j=1,2) are the working pitch radius of the variable thickness gear I and the involute cylindrical gear II respectively;

[0026] β wj (j=1,2) are the working helix angles of variable thickness gear I and involute cylindrical gear II respectively;

[0027] γ w1 is the working pitch cone angle of thickened gear Ⅰ;

[0028] E is the shortest distance between the axis of the variable thickness gear I and the involute cylindrical gear II.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] 1. This invention proposes a new gear transmission method, which breaks through the traditional transmission method of a pair of thickened gears. When the gear pair has a large amount of movement, it will produce meshing interference, jamming and other phenomena.

[0031] 2. This invention establishes a spatial working pitch cone-pitch cylinder meshing model based on gear tooth geometry design and conjugate pitch cone meshing theory. This model then derives the relationship between the mounting parameters, center distance E, axis angle, and helix angle of variable-thickness gears and involute cylindrical gears. Based on the mounting parameters and tooth surface equations, a meshing model for a staggered-axis involute cylindrical gear and variable-thickness gear transmission mechanism is further established. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Schematic diagram of the meshing of the working pitch cone and pitch cylinder of the staggered axis involute cylindrical gear and the variable thickness gear transmission;

[0033] Figure 2 A three-dimensional diagram of the meshing model of the staggered axis involute cylindrical gear and the variable thickness gear transmission mechanism of the present invention;

[0034] Figure 1 (a) is a schematic diagram of the pitch cone model;

[0035] Figure 1 (b) is a schematic diagram of the segmented cylinder model;

[0036] Figure 1 (c) is a schematic diagram of the pitch cone-pitch cylinder meshing model. DETAILED DESCRIPTION

[0037] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0038] like Figure 1 (a) The coordinates of the contact point P on the working pitch cone of the thickened gear I are:

[0039]

[0040] In the formula

[0041] x1, y1, z1——coordinates of the tangent contact point P on the pitch cone;

[0042] u1——the distance from point P to the top of the cone along the generatrix of the pitch cone;

[0043] θ1——the expansion angle between point P and the o1x1z1 plane.

[0044] The normal vector of the contact point P on the working segment cone of the thickened gear I can be expressed as:

[0045]

[0046] n1=[cosγ w1 cosθ1 cosγ w1 sinθ1 -sinγ w1 ] T

[0047] like Figure 1 (b) The coordinates of the contact point P on the working cylinder of the involute cylindrical gear II are:

[0048]

[0049] The normal vector of the tangential contact point P on the working cylinder of the involute cylindrical gear II can be expressed as

[0050] n2=[cosθ2 sinθ2 0] T

[0051] like Figure 1 (c) In the pitch cone-pitch cylinder meshing model, at any moment, the two gears have a common contact point and a common normal at that point. The contact equation can be expressed as:

[0052]

[0053]

[0054] Expand as follows:

[0055]

[0056] Where l1 and u1 represent the parameters of the thickened gear along the tooth profile and width direction, respectively. l2 and u2 represent the parameters of the involute cylindrical gear along the tooth profile and width direction, respectively. and are the rotation angles of the two gears respectively.

[0057] When the axes of the variable thickness gear I and the involute cylindrical gear II are spatially staggered, the relationship is as follows:

[0058] d1=r w1 (cotγ w1 -cot 2 δtanγ w1 )+r w2 (cot 2 δsinγ w1 +sinγ w1 )

[0059] d2=d1cosδ+r w1 cotγ w1 cosδ+r w1 tanγ w1 cosδ

[0060]

[0061] Where:

[0062] d j (j=1,2) are the installation distances between the variable thickness gear I and the involute cylindrical gear II;

[0063] r wj (j=1,2) are the working pitch radius of the variable thickness gear I and the involute cylindrical gear II respectively;

[0064] β wj (j=1,2) are the working helix angles of variable thickness gear I and involute cylindrical gear II respectively;

[0065] γ w1 is the working pitch cone angle of thickened gear Ⅰ;

[0066] E is the shortest distance between the axis of the variable thickness gear I and the involute cylindrical gear II.

[0067] The meshing common rack pressure angle is:

[0068] α nw =arccos(ξ n ·cosα n )

[0069] Where:

[0070] ξ nare the normal tooth profile angle coefficients of variable thickness gear I and involute cylindrical gear II respectively;

[0071] α n is the pressure angle between the variable thickness gear I and the involute cylindrical gear II;

[0072] The working pitch cone angle of the thickened gear I is:

[0073]

[0074] The working helix angles of the variable thickness gear I and the involute cylindrical gear II are:

[0075]

[0076]

[0077] Where:

[0078] γ1 is the pitch cone angle of the thickened gear I;

[0079] The working pitch radius of the variable thickness gear I and the involute cylindrical gear II is:

[0080]

[0081]

[0082] Where:

[0083] ξ tj (j=1,2) are the end face tooth profile coefficients of variable thickness gear I and involute cylindrical gear II respectively;

[0084] β j (j=1,2) are the helix angles of the variable thickness gear I and the involute cylindrical gear II respectively.

Claims

1. Staggered axis involute cylindrical gear and variable thickness gear transmission mechanism, characterized by: The invention comprises a variable thickness gear I and an involute cylindrical gear II; the variable thickness gear I and the involute cylindrical gear II form a set of mutually meshing gear transmission mechanisms, and the axes of the variable thickness gear I and the involute cylindrical gear II are spatially staggered; The basic equations of the variable thickness gear I and the involute cylindrical gear II are as follows: ; Where, and represent the parameters of the thickened gear along the tooth profile and width directions respectively; and represent the parameters of the involute cylindrical gear along the tooth profile and width directions respectively; and are the rotation angles of the two gears respectively; The relationship between the variable thickness gear I and the involute cylindrical gear II is as follows: Where: are the installation distances of variable thickness gear Ⅰ and involute cylindrical gear Ⅱ respectively; are the working pitch circle radii of the variable thickness gear Ⅰ and the involute cylindrical gear Ⅱ respectively; are the working helix angles of variable thickness gear Ⅰ and involute cylindrical gear Ⅱ respectively; is the working pitch cone angle of thickened gear Ⅰ; E It is the shortest distance between the axis of the variable thickness gear I and the involute cylindrical gear II.

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