Constant engagement characteristic for externally toothed cylindrical gear pair

Abstract

The application discloses a constant engagement characteristic pair-constructing external engagement cylindrical gear pair, and relates to the technical field of gear transmission, comprising a pair-constructing cylindrical gear I and a pair-constructing cylindrical gear II based on conjugate curves. The normal tooth profile curves of the pair-constructing cylindrical gear I and the pair-constructing cylindrical gear II are continuous combination curves with the same curve shape, facilitating machining with the same cutter; the common normal line at the inflection point or the tangent point of the continuous combination curve passes through the node of the gear pair, and the inflection point or the tangent point position can be adjusted according to actual requirements to adjust the sliding rate of the gear pair; the coincidence degree is designed as an integer, and the engagement stiffness can be kept constant, thereby greatly improving the dynamic engagement performance of the gear pair. In the application, the normal tooth profile of the pair-constructing cylindrical gear I and the pair-constructing cylindrical gear II is the same, the engagement point curvature radius is constant and tends to infinity, the sliding rate is constant, and the engagement stiffness is constant, and the application has the technical characteristics of low manufacturing cost, high bearing capacity, high transmission efficiency, low vibration and noise and the like.

Description

Technical Field

[0001] This invention relates to the field of gear transmission technology, and more particularly to a pair of external meshing cylindrical gears with constant meshing characteristics, specifically a pair of external meshing cylindrical gears consisting of a pair of externally meshing cylindrical gears I and II, having the same normal tooth profile, a constant and infinitumiously curvature radius at the meshing point, a constant sliding rate, and a constant meshing stiffness. Background Technology

[0002] External gear pairs are one of the main forms of mechanical transmission. Their function is to realize the change of rotational motion direction and the transmission of power, as well as to reduce speed and increase torque or increase speed and reduce torque. They are widely used in high-end equipment, aerospace, and precision instruments. Existing external gear pairs are mostly involute gear pairs, which suffer from problems such as high tooth surface sliding rate and time-varying meshing stiffness. This leads to reduced transmission efficiency, shorter service life, and decreased dynamic meshing performance. With the development of technology and the expansion of applications, traditional external gear pairs are struggling to meet the high-performance requirements of defense technology, industrial manufacturing, and daily life.

[0003] Patent CN105202115 A discloses a multi-point contact cylindrical gear meshing pair based on conjugate curves, consisting of convex and concave gears meshing at multiple points. The pair of concave-convex gears requires different cutting tools, increasing the manufacturing cost. The concave-convex tooth shape limits the radius of curvature at the meshing point, thus restricting further improvement in the gear pair's load-bearing capacity. Choosing the contact point at the node causes tooth surface interference, making it difficult to achieve zero slip rate. Patent CN110081148A discloses a convex-convex contact pairing gear based on conjugate curves, consisting of a first and second gear with convex-convex meshing points. The tooth surfaces of the first and second gears are single-parameter spherical family envelope surfaces, resulting in a limited radius of curvature at the meshing point, similarly limiting the gear pair's load-bearing capacity. The uncertainty of the gear pair's overlap ratio and the time-varying meshing stiffness exacerbate vibration and noise. Therefore, there is an urgent need to innovate the tooth profile design based on the existing conjugate curve-based gear design theory, so as to improve the meshing performance of external meshing cylindrical gear pairs and reduce the production cost of gear pairs. Summary of the Invention

[0004] This invention proposes a pair of external meshing cylindrical gears with constant meshing characteristics. The pair consists of a pair of cylindrical gears I and II. The normal tooth profiles of cylindrical gears I and II are the same, the radius of curvature at the meshing point is constant and tends to infinity, the sliding ratio is constant, and the meshing stiffness is constant. It has the technical characteristics of low manufacturing cost, high load-bearing capacity, high transmission efficiency, and low vibration and noise.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] This invention provides a pair of external meshing cylindrical gears with constant meshing characteristics, comprising a pair of opposing cylindrical gears I and II based on a conjugate curve, wherein the normal tooth profile curve Γ of the opposing cylindrical gear I... s1 The normal tooth profile curve Γ of the opposing cylindrical gear II s2 Γ is a continuous combination of curves with the same shape. L The continuous combination curve Γ L Γ is a combination curve of an odd-power function curve and its tangent at its inflection point. L1 The curve Γ is a combination of a sine function curve and its tangent at its inflection point. L2 The combined curve of the epicycloid function curve and its tangent at the inflection point Γ L3 Combination curves of odd-power functions Γ L4 The combination curve of sine functions Γ L5 Or the combined curve Γ of the epicycloid function L6 The continuous combination curve Γ L It consists of two continuous curves, and the connection point between the two continuous curves is the continuous composite curve Γ. L The inflection point or tangent point of the continuous combined curve Γ L The inflection point or tangent point is located at a designated point on the line of action of the constant meshing characteristic on the meshing force of the external meshing cylindrical gear pair; the normal tooth profile curve Γ of the paired cylindrical gear I s1 The tooth surface of the paired cylindrical gear I is obtained by sweeping along a given conjugate curve, and the normal tooth profile curve Γ of the paired cylindrical gear II is obtained. s2 The tooth surface of the paired cylindrical gear II is obtained by sweeping along the given conjugate curve.

[0007] Preferably, when the continuous combination curve Γ L The curve Γ is a combination of the odd-power function curve and its tangent at the inflection point. L1 At that time, the continuous combination curve Γ L Including the tangent line Γ at the inflection point of the odd power function curve. L11 And odd power function curve Γ L12 ; in the continuous combination curve Γ L Establish a rectangular coordinate system at the point of tangency, and define the combined curve Γ of the odd-power function curve and its tangent at the inflection point. L1 The equation is:

[0008]

[0009] In the formula: x 10 and y 10The continuous combination curves Γ are respectively L The coordinates of the x-axis and y-axis in a rectangular coordinate system; parameter t is the independent variable of the equation; t1 and t2 are the continuous combined curves Γ. L The range of values ​​for ; A is the coefficient of the equation; n is the degree of the independent variable and is a positive integer.

[0010] Preferably, when the continuous combination curve Γ L The curve Γ is a combination of the sine function curve and its tangent at the inflection point. L2 At that time, the continuous combination curve Γ L Including the tangent Γ at the inflection point of the sine function curve L21 and the sine function curve Γ L22 ; in the continuous combination curve Γ L Establish a rectangular coordinate system at the point of tangency, and define the combined curve Γ of the sine function curve and its tangent at the inflection point. L2 The equation is:

[0011]

[0012] In the formula: x 20 and y 20 The continuous combination curves Γ are respectively L The coordinates of the x-axis and y-axis in a rectangular coordinate system; parameter t is the independent variable of the equation; t1 and t2 are the continuous combined curves Γ. L The range of values ​​for Γ; k is the tangent line Γ at the inflection point of the sine function curve. L21 The slope of the equation; A and B are the coefficients of the equation.

[0013] Preferably, when the continuous combination curve Γ L Γ is a combination curve of the epicycloid function curve and its tangent at the inflection point. L3 At that time, the continuous combination curve Γ L Including the tangent Γ at the inflection point of the epicycloid function curve L31 and the epicycloid function curve Γ L32 ; in the continuous combination curve Γ L Establish a rectangular coordinate system at the point of tangency, and define the combined curve Γ of the epicycloid function curve and its tangent at the inflection point. L3 The equation is:

[0014]

[0015] In the formula: x 30 and y 30 The continuous combination curves Γ are respectively L The coordinates of the x-axis and y-axis in a rectangular coordinate system; parameter t is the independent variable of the equation; t1 and t2 are the continuous combined curves Γ. LThe range of values ​​for Γ; k is the tangent line Γ at the inflection point of the epicycloid function curve. L31 The slope of the cycloid; R is the radius of the fixed circle; r is the radius of the moving circle; e is the eccentricity.

[0016] Preferably, when the continuous combination curve Γ L The combination curve Γ of odd-power functions L4 At that time, the continuous combination curve Γ L Including the first odd-power function curve Γ L41 Curve of the second odd power function Γ L42 ; in the continuous combination curve Γ L Establish a rectangular coordinate system at the inflection point, and the combined curve Γ of the odd-power function. L4 The equation is:

[0017]

[0018] In the formula: x 40 and y 40 The continuous combination curves Γ are respectively L The coordinates of the x-axis and y-axis in a rectangular coordinate system; parameter t is the independent variable of the equation; t1 and t2 are the continuous combined curves Γ. L The range of values ​​for ; A and B are the coefficients of the equation; n1 and n2 are the degrees of the independent variable and are positive integers.

[0019] Preferably, when the continuous combination curve Γ L The combination curve Γ of the sine function L5 At that time, the continuous combination curve Γ L Including the first sine function curve Γ L51 The second sine function curve Γ L52 ; in the continuous combination curve Γ L Establish a rectangular coordinate system at the inflection point, and the combined curve Γ of the sine function. L5 The equation is:

[0020]

[0021] In the formula: x 50 and y 50 The continuous combination curves Γ are respectively L The coordinates of the x-axis and y-axis in a rectangular coordinate system; parameter t is the independent variable of the equation; t1 and t2 are the continuous combined curves Γ. L The range of values ​​for ; A1, B1, A2, and B2 are the coefficients of the equation.

[0022] Preferably, when the continuous combination curve Γ L The combined curve Γ of the epicycloid function L6At that time, the continuous combination curve Γ L Including the first epicycloid function curve Γ L61 Second epicycloid function curve Γ L62 ; in the continuous combination curve Γ L Establish a rectangular coordinate system at the inflection point, and the combined curve Γ of the epicycloid function. L6 The equation is:

[0023]

[0024] In the formula: parameter t is the independent variable of the equation; t1 and t2 are the continuous combination curves Γ. L The range of values ​​for ; R1 and r1 are the radii of the moving and fixed circles of the first epicycloid, respectively; R2 and r2 are the radii of the moving and fixed circles of the second epicycloid, respectively; e is the eccentricity; x 60 and y 60 The continuous combination curves Γ are respectively L The coordinates of the x-axis and y-axis in a rectangular coordinate system.

[0025] Preferably, the continuous combination curve Γ L The normal tooth profile curve Γ of the paired cylindrical gear I is obtained by rotating it by an angle α1 about the origin of the rectangular coordinate system. s1 The equation of the curve is:

[0026]

[0027] In the formula: x 01 and y 01 These are the x-axis and y-axis coordinates of the normal tooth profile curve of the paired cylindrical gear I in a rectangular coordinate system.

[0028] Preferably, the normal tooth profile curve Γ of the paired cylindrical gear II is obtained by rotating the normal tooth profile curve Γs1 of the paired cylindrical gear I by 180° around the origin of the rectangular coordinate system. s2 The equation of the curve is:

[0029]

[0030] In the formula: x 02 and y 02 These are the x-axis and y-axis coordinates of the normal tooth profile curve of the paired cylindrical gear II in a rectangular coordinate system.

[0031] Preferably, the normal tooth profile curve Γ of the paired cylindrical gear I is... s1 The tooth surface Σ1 of the paired cylindrical gear I is obtained by sweeping along a given helix, and the tooth surface equation is:

[0032]

[0033] In the formula: x Σ1 y Σ1 and z Σ1 β is the coordinate value of the tooth surface of the paired cylindrical gear I; θ is the gear pair helix angle; θ is the angle of the given contact line; and r is the pitch circle radius of the paired cylindrical gear I.

[0034] Preferably, the normal tooth profile curve Γ of the paired cylindrical gear II is... s2 The tooth surface Σ2 of the paired cylindrical gear II is obtained by sweeping along a given helix, and the tooth surface equation is:

[0035]

[0036] In the formula: x Σ2 y Σ2 and z Σ2 , respectively, are the coordinate values ​​of the tooth surface of the paired cylindrical gear II; a is the center distance of the paired external meshing cylindrical gear pair.

[0037] Preferably, the constant meshing characteristic is designed to have an integer overlap ratio for the external meshing cylindrical gear pair.

[0038] The present invention achieves the following technical effects compared to the prior art:

[0039] In this invention, the normal tooth profiles of the opposing cylindrical gear I and the opposing cylindrical gear II are the same, and can be machined with the same cutting tool, reducing manufacturing costs; the radius of curvature at the meshing point is constant and tends to infinity, improving the load-bearing capacity of the gear pair; the slip ratio during meshing is constant and can be designed as zero slip ratio, improving the transmission efficiency of the gear pair and reducing wear during transmission; the overlap ratio of the opposing external meshing cylindrical gear pair is designed to be an integer, which can achieve constant meshing stiffness, thereby greatly reducing the vibration and noise of the gear pair. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 A schematic diagram of a curve combining an odd-power function curve and its tangent at its inflection point, provided as an embodiment of the present invention;

[0042] Figure 2A schematic diagram of the formation of the normal tooth profile of a pair of external meshing cylindrical gears, provided by an embodiment of the present invention, using a combination curve of an odd power function curve and the tangent at its inflection point as the tooth profile curve.

[0043] Figure 3 A schematic diagram of the construction of the tooth surface of a pair of external meshing cylindrical gears using a combination curve of an odd power function curve and its tangent at the inflection point as a tooth profile curve, provided in an embodiment of the present invention.

[0044] Figure 4 A schematic diagram of an external meshing cylindrical gear pair, which is a combination curve of an odd power function curve and its tangent at the inflection point, provided as an embodiment of the present invention;

[0045] Figure 5 A schematic diagram of the radius of curvature at the meshing point of an external meshing cylindrical gear pair, provided by an embodiment of the present invention, showing a combination curve of an odd power function curve and its tangent at the inflection point as a tooth profile curve;

[0046] Figure 6 A schematic diagram of a designated point on the line of action of the meshing force of an external meshing cylindrical gear pair provided in an embodiment of the present invention;

[0047] Figure 7 This invention provides a schematic diagram of the slip ratio at the meshing point of an external meshing cylindrical gear pair, which is a combination curve of an odd-power function curve and its tangent at the inflection point, as a tooth profile curve.

[0048] Wherein: 1-paired cylindrical gear I, 2-paired cylindrical gear II. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] This invention proposes a pair of external meshing cylindrical gears with constant meshing characteristics. The pair consists of a pair of cylindrical gears I1 and II2. The normal tooth profiles of the pair of cylindrical gears I1 and II2 are the same, the radius of curvature at the meshing point is constant and tends to infinity, the sliding ratio is constant, and the meshing stiffness is constant. It has the technical characteristics of low manufacturing cost, high load-bearing capacity, high transmission efficiency, and low vibration and noise.

[0051] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0052] like Figures 1 to 7 As shown: This embodiment provides a constant meshing characteristic paired external meshing cylindrical gear pair, in which the normal tooth profile curves of paired cylindrical gear I1 and paired cylindrical gear II2 are continuous combination curves with the same curve shape Γ. L The meshing point of the opposing cylindrical gear I1 and the opposing cylindrical gear II2 is on the continuous combination curve Γ L The inflection point or tangent point.

[0053] In this embodiment, the constant meshing characteristics affect the basic parameters of the external meshing cylindrical gear pair: normal module m. n =8mm, number of teeth Z1 of the paired cylindrical gear I1 = 20, number of teeth Z2 of the paired cylindrical gear II2 = 30, addendum coefficient h a * =0.5, tooth root height coefficient h f * =0.5, porosity coefficient c * =0.2, tooth tip height h a =4mm, tooth root height h f =5.6mm, the teeth of the opposing cylindrical gear I1 are left-handed, the teeth of the opposing cylindrical gear II2 are right-handed, the helix angle β = 15°, and the tooth width w = 50mm.

[0054] The curve Γ is a combination of the curve of an odd power function and the tangent at its inflection point. L1 For example, plot the curve of the odd-power function and the combined curve Γ of the tangent at its inflection point on the rectangular coordinate system σ1(O1-x1,y1). L1 ,like Figure 1 As shown. Taking coefficients A = 1.2 and n = 2, the combined curve Γ of the odd-power function curve and its tangent at the inflection point is... L1 (including the tangent line at the inflection point of the odd power function curve) L11 And odd power function curve Γ L12 The equation for is:

[0055]

[0056] In the formula: x 10 and y 10 These are continuous combination curves Γ L The coordinates of the x and y axes in the rectangular coordinate system σ1; the parameter t is the independent variable of the equation; t1 and t2 are the continuous combination curves Γ. L The range of values ​​for .

[0057] This embodiment provides a combined curve Γ of an odd-power function curve and its tangent at the inflection point. L1This diagram illustrates the formation of the normal tooth profile of a pair of meshing external cylindrical gears, with the inflection point P being the meshing point. Figure 2 As shown. Figure 2 The tooth roots of both the paired cylindrical gear I1 and the paired cylindrical gear II2 are tangent segments, while the tooth tips of both the paired cylindrical gear I1 and the paired cylindrical gear II2 are cubic power function curve segments. When the continuous combined curve Γ... L Rotating the cylindrical gear I1 about the origin of the rectangular coordinate system by an angle α1 yields the normal tooth profile curve Γ. s1 When rotating, the value of the rotation angle α1 needs to be determined based on the specific parameters of the gear pair, and the general range is: 0° < α1 < 180°. The specific formation process and tooth profile curve equation of the external meshing cylindrical gear pair are as follows:

[0058] The curve Γ is a combination of the curve of an odd power function and the tangent at its inflection point. L1 Rotating the gear I1 about the origin of the rectangular coordinate system σ1 by an angle α1 = 120°, we obtain the normal tooth profile curve Γ of the paired cylindrical gear I1. s1 The equation of the curve is:

[0059]

[0060] In the formula: x 01 and y 01 These are the x-axis and y-axis coordinates of the normal tooth profile curve of the paired cylindrical gear I1 in the rectangular coordinate system σ1.

[0061] The normal tooth profile curve Γ of the paired cylindrical gear I1 s1 The normal tooth profile curve Γ of the paired cylindrical gear II2 is obtained by rotating it by 180° around the origin of the rectangular coordinate system σ1. s2 The equation of the curve is:

[0062]

[0063] In the formula: x 02 and y 02 These are the x-axis and y-axis coordinates of the normal tooth profile curve of the paired cylindrical gear II2 in the rectangular coordinate system σ1.

[0064] Figure 3 This embodiment provides a combined curve Γ of an odd-power function curve and its tangent at the inflection point. L1 The schematic diagram of the tooth surface construction of the paired external meshing cylindrical gear pair is shown below. The specific construction process and tooth surface equation of the paired external meshing cylindrical gear pair are as follows:

[0065] The normal tooth profile curve Γ of the paired cylindrical gear I1 s1 The tooth surface Σ1 of the paired cylindrical gear I is obtained by sweeping along a given helix, and the tooth surface equation is:

[0066]

[0067] In the formula: x Σ1 y Σ1 and z Σ1 These are the coordinate values ​​of the tooth surface of the cylindrical gear I1.

[0068] Similarly, the normal tooth profile curve Γ of the paired cylindrical gear II2 s2 The tooth surface Σ2 of the paired cylindrical gear II2 is obtained by sweeping along a given helix, and the tooth surface equation is:

[0069]

[0070] In the formula: x Σ2 y Σ2 and z Σ2 θ represents the coordinates of the tooth surface of the cylindrical gear II2; θ is the angle of the given contact line.

[0071] Figure 4 This embodiment provides a combined curve Γ of an odd-power function curve and its tangent at the inflection point. L1 As a schematic diagram of the external meshing cylindrical gear pair with tooth profile curves, the addendum circle and root circle are generated by extrudement, and the tooth surfaces of the external meshing cylindrical gears I1 and II2 are trimmed, stitched, and filled to obtain a solid model of the external meshing cylindrical gear pair with constant meshing characteristics.

[0072] In this embodiment, the normal tooth profile curves of the opposing cylindrical gears I1 and II2 can also be a combination curve Γ of a sine function curve and its tangent at the inflection point. L2 The combined curve of the epicycloid function curve and its tangent at the inflection point Γ L3 Combination curves of odd-power functions Γ L4 The combination curve of sine functions Γ L5 Or the combined curve Γ of the epicycloid function L6 The curve formulas are as follows:

[0073] When the continuous combination curve Γ L Γ is a combination curve of a sine function curve and its tangents at inflection points. L2 At that time, the continuous combination curve Γ L Including the tangent Γ at the inflection point of the sine function curve L21 and the sine function curve Γ L22 ; in the continuous combination curve Γ L Establish a rectangular coordinate system at the point of tangency, and form the combined curve Γ of the sine function curve and the tangent at its inflection point. L2 The equation is:

[0074]

[0075] In the formula: x 20 and y 20 These are continuous combination curves Γ L The coordinates of the x and y axes in a rectangular coordinate system; the parameter t is the independent variable of the equation; t1 and t2 are the continuous combination curves Γ. L The range of values ​​for Γ; k is the tangent line Γ at the inflection point of the sine function curve. L21 The slope of the equation; A and B are the coefficients of the equation.

[0076] When the continuous combination curve Γ L Γ is a combination curve of the epicycloid function curve and its tangent at the inflection point. L3 At that time, the continuous combination curve Γ L Including the tangent Γ at the inflection point of the epicycloid function curve L31 and the epicycloid function curve Γ L32 ; in the continuous combination curve Γ L Establish a rectangular coordinate system at the point of tangency, and form the combined curve Γ of the epicycloid function curve and the tangent at its inflection point. L3 The equation is:

[0077]

[0078] In the formula: x 30 and y 30 These are continuous combination curves Γ L The coordinates of the x and y axes in a rectangular coordinate system; the parameter t is the independent variable of the equation; t1 and t2 are the continuous combination curves Γ. L The range of values ​​for Γ; k is the tangent line Γ at the inflection point of the epicycloid function curve. L31 The slope of the cycloid; R is the radius of the fixed circle of the cycloid, r is the radius of the moving circle; e is the eccentricity.

[0079] When the continuous combination curve Γ L The combination curve Γ of odd-power functions L4 At that time, the continuous combination curve Γ L Including the first odd-power function curve Γ L41 Curve of the second odd power function Γ L42 Composition; in the continuous combination curve Γ L Establish a rectangular coordinate system at the inflection point, and the combination curve Γ of the odd-power function. L4 The equation is:

[0080]

[0081] In the formula: x 40 and y 40 These are continuous combination curves Γ LThe coordinates of the x and y axes in a rectangular coordinate system; the parameter t is the independent variable of the equation; t1 and t2 are the continuous combination curves Γ. L The range of values ​​for ; A and B are the coefficients of the equation; n1 and n2 are the degrees of the independent variable and are positive integers.

[0082] When the continuous combination curve Γ L The combination curve Γ of the sine function L5 At that time, the continuous combination curve Γ L Including the first sine function curve Γ L51 The second sine function curve Γ L52 Composition; in the continuous combination curve Γ L Establish a rectangular coordinate system at the inflection point, and the combination curve Γ of the sine function. L5 The equation is:

[0083]

[0084] In the formula: x 50 and y 50 These are continuous combination curves Γ L The coordinates of the x and y axes in a rectangular coordinate system; the parameter t is the independent variable of the equation; t1 and t2 are the continuous combination curves Γ. L The range of values ​​for ; A1, B1, A2, and B2 are the coefficients of the equation.

[0085] When the continuous combination curve Γ L The combined curve Γ of the epicycloid function L6 At that time, the continuous combination curve Γ L Including the first epicycloid function curve Γ L61 Second epicycloid function curve Γ L62 Composition; in the continuous combination curve Γ L Establish a rectangular coordinate system at the inflection point, and the combined curve Γ of the epicycloid function. L6 The equation is:

[0086]

[0087] In the formula: parameter t is the independent variable of the equation; t1 and t2 are continuous combination curves Γ. L The range of values ​​for ; R1 and r1 are the radii of the moving and fixed circles of the first epicycloid, respectively; R2 and r2 are the radii of the moving and fixed circles of the second epicycloid, respectively; e is the eccentricity; x 60 and y 60 These are continuous combination curves Γ L The coordinates of the x-axis and y-axis in a rectangular coordinate system.

[0088] In this embodiment, the continuous combination curve Γ L The inflection point or tangent point is:

[0089] ① When the continuous combination curve Γ L The combination curve Γ of odd-power functions L4 The combination curve of sine functions Γ L5 Or the combined curve Γ of the epicycloid function L6 At that time, the continuous combination curve Γ L The connection point is the inflection point, that is, the boundary between the concavity and convexity of the curve. The second derivative of the curve is zero at this point, and the signs of the second derivatives on both sides of this point are opposite.

[0090] ② When the continuous combination curve Γ L Γ is a combination curve of an odd-power function curve and its tangent at its inflection point. L1 The curve Γ is a combination of a sine function curve and its tangent at its inflection point. L2 Or a combination curve of the epicycloid function curve and its tangent at the inflection point Γ L3 At that time, the continuous combination curve Γ L The connection point is an odd-power function curve Γ L12 , Sine function curve Γ L22 Or the epicycloid function curve Γ L32 The inflection point (meaning the same as ①) is also the curve Γ of the odd-power function. L12 , Sine function curve Γ L22 Or the epicycloid function curve Γ L32 The point of tangency of the tangent line at that point.

[0091] In the continuous combination curve Γ L At the inflection point or tangent point, the continuous combination curve Γ L The curvature is zero, meaning the radius of curvature approaches infinity. Among these, when the continuous composite curve Γ... L The combination curve Γ of odd-power functions L4 The combination curve of sine functions Γ L5 Or the combined curve Γ of the epicycloid function L6 When the inflection point is reached, the radii of curvature on both sides tend to infinity; when the continuous composite curve Γ L Γ is a combination curve of an odd-power function curve and its tangent at its inflection point. L1 The curve Γ is a combination of a sine function curve and its tangent at its inflection point. L2 Or a combination curve of the epicycloid function curve and its tangent at the inflection point Γ L3 At the inflection point, the odd-power function curve Γ L12 , Sine function curve Γ L22 Or the epicycloid function curve Γ L32 The radius of curvature on one side tends to infinity, and the radius of curvature on the tangent side is infinite. The continuous composite curve Γ is calculated based on the parameters given in the embodiment. L The radius of curvature, such as Figure 5As shown. Figure 5 Γ continuous combination curve L The radius of curvature of the straight line segment is infinite, and the radius of curvature at the inflection point tends to be infinite. The radius of curvature of the cubic power function curve segment gradually decreases and then increases, but it is still much smaller than the radius of curvature at the inflection point. This means that the radius of curvature at the contact point of the gear pair tends to be infinite, which improves the load-bearing capacity of the gear pair.

[0092] In this embodiment, the continuous combination curve Γ L The inflection point or tangent point is located at a designated point on the line of action of the meshing force of the gear pair. Specifically, the designated point is defined as follows: the line of action of the meshing force of the external meshing cylindrical gear pair is a straight line passing through the node and forming a certain angle (pressure angle) with the horizontal axis, and a given point on or near the node on this straight line. Figure 6 This diagram illustrates a designated point on the line of action of the meshing force of a gear pair. In the diagram: P is the designated point on the line of action of the meshing force of the gear pair; P1 and P2 are the extreme points within the position range of the designated point; the straight lines N1N2 represent the line of action of the meshing force of the gear pair; α k The pressure angle is denoted by O1-x1y1, which is the local rectangular coordinate system of the paired cylindrical gear I1, and O2-x2y2, which is the local rectangular coordinate system of the paired cylindrical gear II2; r1 is the pitch circle radius of the paired cylindrical gear I1, r2 is the pitch circle radius of the paired cylindrical gear II2, and r a1 Let r be the addendum circle radius of the cylindrical gear I1. a2 Let r be the addendum circle radius of the cylindrical gear II2. f1 Let r be the root circle radius of the cylindrical gear I1. f2 Let P be the root circle radius of the cylindrical gear II2. The specified point P is usually located at the pitch point, but it can also be a given point near both sides of the pitch point. The variation area of ​​the specified point does not exceed half of the tooth height.

[0093] According to the gear meshing principle, there is no relative sliding between the tooth surfaces when the external meshing cylindrical gear pairs mesh at the pitch point. Figure 7 This embodiment provides a combined curve Γ of an odd-power function curve and its tangent at the inflection point. L1 As a schematic diagram of the slip ratio at the meshing point of the paired external meshing cylindrical gear pair, which serves as the tooth profile curve, the paired external meshing cylindrical gear pair in the embodiment is meshed at the node at any time due to the constant meshing characteristics. Therefore, this paired external meshing cylindrical gear pair can achieve zero-slip meshing. When the continuous combined curve Γ L When the inflection point or tangent point does not coincide with the node, the slip ratio of the external meshing cylindrical gear pair remains constant but is not zero. (Continuous combination curve Γ) LThe closer the inflection point or tangent point is to the node, the smaller the sliding rate of the external meshing cylindrical gear pair, and vice versa. When the inflection point or tangent point coincides with the node, the external meshing cylindrical gear pair can achieve zero-slip meshing transmission, which reduces the wear between the tooth surfaces and helps to improve the transmission efficiency of the gear pair.

[0094] Furthermore, when the contact ratio of the constant meshing characteristic external meshing cylindrical gear pair is designed to be an integer, the meshing stiffness of the external meshing cylindrical gear pair is constant. At this point, the magnitude of the meshing force at any meshing position is determined. Therefore, when the contact ratio is designed to be an integer, the meshing state of the constant meshing characteristic external meshing cylindrical gear pair remains constant at any given time, effectively ensuring the stability of the dynamic meshing performance of the external meshing cylindrical gear pair and significantly reducing its vibration and noise.

[0095] This specification uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A pair of external meshing cylindrical gears with constant meshing characteristics, characterized in that: It includes a pair of opposing cylindrical gears I and II based on conjugate curves, wherein the normal tooth profile curve Γ of the opposing cylindrical gear I is... s1 The normal tooth profile curve Γ of the opposing cylindrical gear II s2 Γ is a continuous combination of curves with the same shape. L The continuous combination curve Γ L Γ is a combination curve of an odd-power function curve and its tangent at its inflection point. L1 Combination curves of odd-power functions Γ L4 The continuous combination curve Γ L It consists of two continuous curves, and the connection point between the two continuous curves is the continuous composite curve Γ. L The inflection point or tangent point of the continuous combined curve Γ L The inflection point or tangent point is located at a designated point on the line of action of the constant meshing characteristic on the meshing force of the external meshing cylindrical gear pair; the normal tooth profile curve Γ of the paired cylindrical gear I s1 The tooth surface of the paired cylindrical gear I is obtained by sweeping along a given conjugate curve, and the normal tooth profile curve Γ of the paired cylindrical gear II is obtained. s2 The tooth surface of the paired cylindrical gear II is obtained by sweeping along the given conjugate curve; When the continuous combination curve Γ L The curve Γ is a combination of the odd-power function curve and its tangent at the inflection point. L1 At that time, the continuous combination curve Γ L Including the tangent line Γ at the inflection point of the odd power function curve. L11 And odd power function curve Γ L12 ; in the continuous combination curve Γ L Establish a rectangular coordinate system at the point of tangency, and define the combined curve Γ of the odd-power function curve and its tangent at the inflection point. L1 The equation is: In the formula: x 10 and y 10 The continuous combination curves Γ are respectively L The coordinates of the x-axis and y-axis in a rectangular coordinate system; parameter t is the independent variable of the equation; t1 and t2 are the continuous combined curves Γ. L The range of values ​​for ; A is the coefficient of the equation; n is the degree of the independent variable and is a positive integer; When the continuous combination curve Γ L The combination curve Γ of odd-power functions L4 At that time, the continuous combination curve Γ L Including the first odd-power function curve Γ L41 Curve of the second odd power function Γ L42 ; in the continuous combination curve Γ L Establish a rectangular coordinate system at the inflection point, and the combined curve Γ of the odd-power function. L4 The equation is: In the formula: x 40 and y 40 The continuous combination curves Γ are respectively L The coordinates of the x-axis and y-axis in a rectangular coordinate system; parameter t is the independent variable of the equation; t1 and t2 are the continuous combined curves Γ. L The range of values ​​for ; A and B are the coefficients of the equation; n1 and n2 are the degrees of the independent variable and are positive integers; The continuous combination curve Γ L The normal tooth profile curve Γ of the paired cylindrical gear I is obtained by rotating it by an angle α1 about the origin of the rectangular coordinate system. s1 The equation of the curve is: In the formula: x 01 and y 01 These are the x-axis and y-axis coordinates of the normal tooth profile curve of the paired cylindrical gear I in a rectangular coordinate system.

2. The constant meshing characteristic external meshing cylindrical gear pair according to claim 1, characterized in that: The normal tooth profile curve Γ of the paired cylindrical gear I is obtained by rotating the normal tooth profile curve Γs1 of the paired cylindrical gear I by 180° around the origin of the rectangular coordinate system. s2 The equation of the curve is: In the formula: x 02 and y 02 These are the x-axis and y-axis coordinates of the normal tooth profile curve of the paired cylindrical gear II in a rectangular coordinate system.

3. The constant meshing characteristic external meshing cylindrical gear pair according to claim 2, characterized in that: The normal tooth profile curve Γ of the paired cylindrical gear I s1 The tooth surface Σ1 of the paired cylindrical gear I is obtained by sweeping along a given helix, and the tooth surface equation is: In the formula: x Σ1 y Σ1 and z Σ1 β is the coordinate value of the tooth surface of the paired cylindrical gear I; θ is the gear pair helix angle; θ is the angle of the given contact line; and r is the pitch circle radius of the paired cylindrical gear I.

4. The constant meshing characteristic external meshing cylindrical gear pair according to claim 3, characterized in that: The normal tooth profile curve Γ of the paired cylindrical gear II s2 The tooth surface Σ2 of the paired cylindrical gear II is obtained by sweeping along a given helix, and the tooth surface equation is: In the formula: x Σ2 y Σ2 and z Σ2 , respectively, are the coordinate values ​​of the tooth surface of the paired cylindrical gear II; a is the center distance of the paired external meshing cylindrical gear pair.

5. The constant meshing characteristic external meshing cylindrical gear pair according to claim 4, characterized in that: The constant meshing characteristics require the overlap ratio of the external meshing cylindrical gear pair to be designed as an integer.

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