Constant engagement characteristic for double helical gear pair

Abstract

The application discloses a constant engagement characteristic pair of double helical gears, and relates to the technical field of gear transmission, comprising a pair of double helical gears I and a pair of double helical gears II based on conjugate curves. In the application, the normal tooth profile curve of the pair of double helical gears is a continuous combination curve with the same curve shape, which is convenient for 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 overlapping degree of the pair of double helical gears is designed as an integer, and the engagement force action line and the engagement stiffness are constant. In the application, the normal tooth profile of the pair of double helical gears I and the pair of double helical gears II is the same, the curvature radius of the engagement point is constant and tends to infinity, the sliding rate is constant, the engagement stiffness is constant, and the direction of the engagement force action line is constant, and the application has the technical characteristics of low manufacturing cost, high bearing capacity, high transmission efficiency and low vibration and noise.

Description

Technical Field

[0001] This invention relates to a pair of herringbone gears with constant meshing characteristics having the same continuous combined curve tooth profile, and more particularly to a pair of herringbone gears consisting of a pair of herringbone gears I and II with the same normal tooth profile, constant and infinitumular radius of curvature at the meshing point, constant slip ratio, constant meshing stiffness, and constant direction of the meshing force line of action. Background Technology

[0002] Herringbone gears are key components for transmitting motion and power, and are used in aerospace, industrial automation equipment, precision instruments, and other fields. Most existing herringbone gear pairs are involute gear pairs, which have inherent characteristics such as high slip ratio between tooth surfaces, time-varying meshing stiffness, and time-varying lines of action of meshing forces. These characteristics limit the potential for improvement in the transmission efficiency, service life, and dynamic meshing performance of herringbone gear pairs.

[0003] Patents with publication numbers 103939575A, 105202115A, and 105114542A disclose point-contact gear meshing pairs based on conjugate curves. The gear pairs constructed in these patents consist of convex and concave gears. Each pair of gears with convex and concave teeth requires different cutting tools, increasing the manufacturing cost of the gear pair. The convex and concave tooth shapes limit the radius of curvature at the meshing point, thus restricting further improvements in the load-bearing capacity of the gear pair. Selecting the contact point at the node causes tooth surface interference, making it difficult to achieve zero slip rate. During meshing, the contact point moves in the tooth width direction, causing time-varying meshing forces. Therefore, there is an urgent need to innovate tooth profile design based on existing spatial conjugate curve gear design theory to improve the meshing performance of paired gear drives and reduce the production cost of paired herringbone gear drives. Summary of the Invention

[0004] The purpose of this invention is to provide a herringbone gear pair with constant meshing characteristics to solve the problems existing in the prior art and achieve 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 discloses a herringbone gear pair with constant meshing characteristics, comprising a herringbone gear I and a herringbone gear II based on a conjugate curve, wherein the normal tooth profile curve Γ of the herringbone gear I in the constant meshing characteristic herringbone gear pair is... s1 and the normal tooth profile curve Γ of the herringbone gear II s2 Γ is a continuous combination of curves with the same shape. L The continuous combination curve Γ L The combined curve Γ, including odd-power function curves and their tangents at inflection points.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 composite curve consists of two continuous curve segments. The connection point of the two continuous curve segments is the inflection point or tangent point of the continuous composite curve. The common normal at the inflection point or tangent point of the continuous composite curve passes through the node of the herringbone gear pair. The normal tooth profile curve is swept along the given conjugate curve to obtain the tooth surfaces of the paired herringbone gear I and the paired herringbone gear II.

[0007] Furthermore, the aforementioned constant meshing characteristic is applicable to a herringbone gear pair, 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 At that time, the continuous combination curve Γ L The tangent line Γ at the inflection point of the odd power function curve L11 And odd power function curve Γ L12 Composition; A rectangular coordinate system is established at the tangent points of the continuous combined curves, and the combined curve Γ of the odd-power function curve and its tangents at the inflection points. L1 The equation is:

[0008]

[0009] In the formula: x 10 and y 10 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of values ​​for the continuous curve; A is the coefficient of the equation; and n is the degree of the independent variable and is a positive integer.

[0010] Furthermore, the aforementioned constant meshing characteristic is applicable to a herringbone gear pair, 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 The tangent Γ at the inflection point of the sine function curve L21 and the sine function curve Γ L22 Composition; A rectangular coordinate system is established at the tangent points of the continuous composite curves, and the composite curve Γ of the sine function curve and its tangents at the inflection points. L2 The equation is:

[0011]

[0012] In the formula: x 20and y 20 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; k is the slope of the tangent line at the inflection point of the sine function curve; A and B are the coefficients of the equation.

[0013] Furthermore, the aforementioned constant meshing characteristic is applicable to a herringbone gear pair, 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 The tangent Γ at the inflection point of the epicycloid function curve L31 and the epicycloid function curve Γ L32 Composition; A rectangular coordinate system is established at the tangent points of the continuous composite curves, and the composite curve Γ of the epicycloid function curve and its tangents at the inflection points. L3 The equation is:

[0014]

[0015] In the formula: x 30 and y 30 t1 and t2 are the x and y coordinates of the composite curve in the rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; k is the slope of the tangent at the inflection point of the epicycloid function curve; R1, r1, R2, and r2 are the radii of the moving and fixed circles of the cycloid, respectively; e is the eccentricity.

[0016] Furthermore, the aforementioned constant meshing characteristic is applicable to a herringbone gear pair, 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 From the curve Γ of the first odd power function L41 Curve of the second odd power function Γ L42 Composition; Establish a rectangular coordinate system at the inflection points of the continuous combination curve, the combination curve Γ of the odd power function. L4 The equation is:

[0017]

[0018] In the formula: x 40 and y 40 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; A and B are the coefficients of the equation; n1 and n2 are the degrees of the independent variable and are positive integers.

[0019] Furthermore, the aforementioned constant meshing characteristic is applicable to a herringbone gear pair, when the continuous combination curve Γ LThe combination curve Γ of the sine function L5 At that time, the continuous combination curve Γ L From the first sine function curve Γ L51 The second sine function curve Γ L52 Composition; Establish a rectangular coordinate system at the inflection points of the continuous combination curve, the combination curve Γ of the sine function L5 The equation is:

[0020]

[0021] In the formula: x 50 and y 50 t1 and t2 are the x and y coordinates of the composite curve in the rectangular coordinate system, respectively; parameter t is the independent variable of the equation; t1 and t2 are the range of values ​​for the continuous curve; A1, B1, A2, and B2 are the coefficients of the equation.

[0022] Furthermore, the aforementioned constant meshing characteristic is applicable to a herringbone gear pair, 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 From the first epicycloid function curve Γ L61 Second epicycloid function curve Γ L62 Composition; a rectangular coordinate system is established at the inflection points of the continuous composite curve, and the composite curve Γ of the epicycloid function is... L6 The equation is:

[0023]

[0024] In the formula: parameter t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; 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 the x and y coordinates of the composite curve in a rectangular coordinate system.

[0025] Furthermore, the aforementioned constant meshing characteristic configuration for a herringbone gear pair is based on the continuous combination curve Γ. L The normal tooth profile curve Γ of the herringbone 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 and y coordinates of the normal tooth profile curve of the herringbone gear I in the rectangular coordinate system.

[0028] Furthermore, the constant meshing characteristic of the herringbone gear pair is determined by the normal tooth profile curve Γ of the herringbone gear I. s1 The normal tooth profile curve Γ of the herringbone gear II is obtained by rotating it 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 and y coordinates of the normal tooth profile curve of the herringbone gear II in the rectangular coordinate system.

[0031] Furthermore, the constant meshing characteristic of the herringbone gear pair is determined by the normal tooth profile curve Γ of the herringbone gear I. s1 The tooth surface Σ1 of the paired herringbone 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 , respectively, are the coordinate values ​​of the tooth surface of the herringbone gear I; β is the gear pair helix angle, parameter m is the independent variable of the equation, m1 and m2 are the range of tooth width values, and in the symbol “±”, “+” indicates the left tooth surface of the herringbone gear and “-” indicates the right tooth surface of the herringbone gear.

[0034] Furthermore, the constant meshing characteristic herringbone gear pair is characterized by: the normal tooth profile curve Γ of the herringbone gear II s2 The tooth surface Σ2 of the paired herringbone 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 θ represents the coordinate values ​​of the tooth surface of the herringbone gear II; r is the pitch circle radius of the herringbone gear pair with constant meshing characteristics; θ is the angle of the given contact line; in the symbol “±”, “+” indicates the left tooth surface of the herringbone gear and “-” indicates the right tooth surface of the herringbone gear.

[0037] Furthermore, the constant meshing characteristic pair of the herringbone gear pair is designed with an integer overlap ratio to achieve constant stiffness meshing transmission.

[0038] Furthermore, in the aforementioned constant meshing characteristic herringbone gear pair, the herringbone gear I and the herringbone gear II are designed to be symmetrical along the tooth width, thereby achieving a constant line of action of the meshing force of the gear pair.

[0039] The present invention achieves the following technical effects compared to the prior art:

[0040] The constant meshing characteristic herringbone gear pair provided by this invention has the same normal tooth profile for herringbone gear I and herringbone gear II, which can be machined with the same tool, reducing manufacturing costs; the radius of curvature at the meshing point is constant and tends to infinity, improving the overall load-bearing capacity; the slip ratio is constant during meshing and can be designed to be zero, improving the overall transmission efficiency and reducing wear during transmission; the herringbone gear I and herringbone gear II are designed to be symmetrical along the tooth width, which can achieve a constant line of action of the meshing force; the overlap ratio of the constant meshing characteristic herringbone gear pair is designed to be an integer, which can achieve constant meshing stiffness, thereby greatly reducing the vibration and noise of the constant meshing characteristic herringbone gear pair. Attached Figure Description

[0041] 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.

[0042] Figure 1 A schematic diagram of a curve combining an odd-power function curve and its tangent at its inflection point, provided by the present invention;

[0043] Figure 2 A schematic diagram illustrating the formation of the normal tooth profile of a herringbone gear pair using a combination curve of an odd power function curve and its tangent at the inflection point as a constant meshing characteristic of the tooth profile curve provided by the present invention.

[0044] Figure 3 A schematic diagram illustrating the construction of the tooth surface of a herringbone gear pair using a combination curve of an odd power function curve and its tangent at the inflection point as a constant meshing characteristic of the tooth profile curve, provided by the present invention.

[0045] Figure 4 A schematic diagram of a herringbone gear pair, showing a combination curve of an odd power function curve and its tangent at the inflection point as a constant meshing characteristic of the tooth profile curve, provided by the present invention.

[0046] Figure 5 A schematic diagram of the radius of curvature at the meshing point of a herringbone gear pair, showing a combination curve of an odd power function curve and its tangent at the inflection point as a constant meshing characteristic of the tooth profile curve.

[0047] Figure 6 A schematic diagram of a designated point on the line of action of the meshing force of a herringbone gear pair with constant meshing characteristics provided by the present invention;

[0048] Figure 7 A schematic diagram of the slip ratio at the meshing point of a herringbone gear pair, showing a combination curve of an odd power function curve and its tangent at the inflection point as a constant meshing characteristic of the tooth profile curve.

[0049] Figure 8 A schematic diagram of the meshing force of a herringbone gear pair based on the constant meshing characteristics provided by the present invention.

[0050] In the diagram: 1 - Herringbone gear I, 2 - Herringbone gear II. Detailed Implementation

[0051] 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.

[0052] The purpose of this invention is to provide a herringbone gear pair with constant meshing characteristics to solve the technical problems in the prior art, such as the need for different cutting tools to process the gears in the gear pair, high manufacturing cost, large vibration and noise, and low transmission efficiency.

[0053] 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.

[0054] like Figures 1-8 As shown, this embodiment provides a herringbone gear pair with constant meshing characteristics. The basic parameters of the herringbone gear pair with constant meshing characteristics are: module m = 8, number of teeth of the first pair of gears z1 = 20, number of teeth of the second pair of gears z2 = 85, and addendum coefficient h. a * =0.5, porosity coefficient c * =0.2, tooth tip height h a =4mm, tooth root height h f =5.6mm, helix angle β=35°, tooth width w=80mm.

[0055] Taking the combined curve of an odd-power function curve and its tangent at the inflection point as an example, the normal tooth profile is described. Figure 1This embodiment provides a schematic diagram of a combined curve of an odd-power function curve and its tangent at the inflection point. A local Cartesian coordinate system σ1(O1-x1,y1) is established at the inflection point of the continuous curve, with 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 then obtained. L1 (The tangent line Γ at the inflection point of the odd power function curve) L11 And odd power function curve Γ L12 The equation for the composition is:

[0056]

[0057] In the formula: x 10 and y 10 t1 and t2 are the x and y coordinates of the composite curve in the rectangular coordinate system σ1, respectively; parameter t is the independent variable of the equation; t1 and t2 are the ranges of values ​​for the continuous curve.

[0058] Figure 2 This embodiment provides a schematic diagram of the formation of the normal tooth profile of a herringbone gear pair using a combination curve of an odd-power function curve and its tangent at the inflection point as a constant meshing characteristic of the tooth profile curve. The inflection point P is the meshing point. When the continuous combination curve Γ L Rotating the sun gear by an angle α1 about the origin of the rectangular coordinate system yields the normal tooth profile curve Γ. s1 When the rotation angle α1 is used, the value needs to be determined based on the specific parameters of the gear pair, and the general range is: 0° < α1 < 180°. The specific constant meshing characteristics affect the formation process of the normal tooth profile and the tooth profile curve equation of the herringbone gear pair as follows:

[0059] The curve Γ is a combination of the curve of an odd power function and the tangent at its inflection point. L1 Rotating the herringbone gear I1 by an angle α1 = 120° around the origin of the rectangular coordinate system σ1 yields the normal tooth profile curve Γ. s1 The equation of the curve is:

[0060]

[0061] In the formula: x 01 and y 01 These are the x and y coordinates of the normal tooth profile curve of the herringbone gear I1 in the rectangular coordinate system σ1.

[0062] The normal tooth profile curve Γ of the herringbone gear I1 s1 The normal tooth profile curve Γ of the herringbone 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:

[0063]

[0064] In the formula: x 02 and y 02 These are the x and y coordinates of the normal tooth profile curve of the herringbone gear II2 in the rectangular coordinate system σ1.

[0065] Figure 3 This embodiment provides a schematic diagram of the construction of the herringbone gear tooth surface using a combination curve of an odd-power function curve and its tangent at the inflection point as a constant meshing characteristic of the tooth profile curve. The specific construction process and tooth surface equation of the herringbone gear tooth surface using the constant meshing characteristic are as follows:

[0066] The normal tooth profile curve Γ of the herringbone gear I1 s1 The tooth surface Σ1 of the herringbone gear I1 is obtained by sweeping along a given helix, and the tooth surface equation is:

[0067]

[0068] In the formula: x Σ1 y Σ1 and z Σ1 Let m be the coordinate value of the tooth surface of the herringbone gear I1. The parameter m is the independent variable of the equation, and m1 and m2 are the range of tooth width values. In the symbol "±", "+" indicates the left tooth surface of the herringbone gear, and "-" indicates the right tooth surface of the herringbone gear.

[0069] Similarly, the normal tooth profile curve Γ of the herringbone gear II2 s2 The tooth surface Σ2 of the herringbone gear II2 is obtained by sweeping along a given helix, and the tooth surface equation is:

[0070]

[0071] In the formula: x Σ2 y Σ2 and z Σ2 θ represents the coordinates of the tooth surface of the herringbone gear II2; θ is the angle of the given contact line. In the symbol “±”, “+” indicates the left tooth surface of the herringbone gear and “-” indicates the right tooth surface of the herringbone gear.

[0072] Figure 4 This embodiment provides a schematic diagram of a herringbone gear pair with constant meshing characteristics, using a combination curve of an odd-power function curve and its tangent at the inflection point as the tooth profile curve. By defining the addendum circle and dedendum circle dimensions of the herringbone gear I1 and the herringbone gear II2 respectively, and performing operations such as trimming, stitching, and filleting on the tooth surface, a herringbone gear pair with constant meshing characteristics and tooth profiles having the same continuous combination curve is obtained.

[0073] In this embodiment, the normal tooth profile curves of the herringbone gear I1 and the herringbone gear 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:

[0074] 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 L2 The tangent Γ at the inflection point of the sine function curve L21 and the sine function curve Γ L22 Composition; Establish a rectangular coordinate system at the tangent points of the continuous composite curves, and form the composite curve Γ of the sine function curve and its tangents at the inflection points. L2 The equation is:

[0075]

[0076] In the formula: x 20 and y 20 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; k is the slope of the tangent line at the inflection point of the sine function curve; A and B are the coefficients of the equation.

[0077] 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 L3 The tangent Γ at the inflection point of the epicycloid function curve L31 and the epicycloid function curve Γ L32 Composition; Establish a rectangular coordinate system at the tangent points of the continuous composite curves, and form the composite curve Γ of the epicycloid function curve and its tangents at the inflection points. L3 The equation is:

[0078]

[0079] In the formula: x 30 and y 30 t1 and t2 are the x and y coordinates of the composite curve in the rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; k is the slope of the tangent at the inflection point of the epicycloid function curve; R1, r1, R2, and r2 are the radii of the moving and fixed circles of the cycloid, respectively; e is the eccentricity.

[0080] When the continuous combination curve Γ L The combination curve Γ of odd-power functions L4 At that time, the continuous combination curve Γ L4 From the odd power function curve Γ L41 Curve of the second odd power function Γ L42 Composition; Establish a rectangular coordinate system at the inflection points of continuous combination curves, and the combination curve Γ of odd-power functions. L4 The equation is:

[0081]

[0082] In the formula: x 40 and y 40 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; A and B are the coefficients of the equation; n1 and n2 are the positive integers of the degree of the independent variable.

[0083] When the continuous combination curve Γ L The combination curve Γ of the sine function L5 At that time, the continuous combination curve Γ L5 From the sine function curve Γ L51 The second sine function curve Γ L52 Composition; Establish a rectangular coordinate system at the inflection points of the continuous composite curve, and the composite curve Γ of the sine function. L5 The equation is:

[0084]

[0085] In the formula: x 50 and y 50 t1 and t2 are the x and y coordinates of the composite curve in the rectangular coordinate system, respectively; parameter t is the independent variable of the equation; t1 and t2 are the range of values ​​for the continuous curve; A1, B1, A2, and B2 are the coefficients of the equation.

[0086] When the continuous combination curve Γ L The combined curve Γ of the epicycloid function L6 At that time, the continuous combination curve Γ L6 From the epicycloid function curve Γ L61 Second epicycloid function curve Γ L62 Composition; Establish a rectangular coordinate system at the inflection points of the continuous composite curve, and the composite curve Γ of the epicycloid function. L6 The equation is:

[0087]

[0088] In the formula: parameter t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; 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 the x and y coordinates of the composite curve in the rectangular coordinate system, respectively.

[0089] In a constant meshing characteristic herringbone gear pair disclosed in this embodiment, the normal tooth profile curves of the herringbone gear I1 and the herringbone gear II2 are continuous combination curves with the same curve shape, and the meshing point of the herringbone gear I1 and the herringbone gear II2 is at the inflection point or tangent point of the continuous combination curve.

[0090] In this embodiment, the inflection point or tangent point of the continuous composite curve is:

[0091] ① When the continuous combination curve is a combination curve of odd power functions, a combination curve of sine functions, or a combination curve of epicycloid functions, the connection point of the continuous combination curve is the inflection point, that is, the boundary between 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.

[0092] ② When the combined curve is a combination of an odd power function curve and its tangent at the inflection point, a sine function curve and its tangent at the inflection point, or an epicycloid and its tangent at the inflection point, the connection point of the combined curve is the inflection point of the odd power function curve, sine function curve, or epicycloid (meaning the same as ①), and is also the tangent point of the tangent of the odd power function curve, sine function curve, or epicycloid at that point.

[0093] At the inflection points or tangent points of a continuous composite curve, the curvature is zero, and the radius of curvature tends to infinity. Specifically, when the continuous composite curve is a composite curve of odd-power functions, sine functions, or epicycloid functions, the radii of curvature on both sides of the inflection point tend to infinity. When the continuous composite curve is a composite curve of an odd-power function curve and its tangent at the inflection point, the radius of curvature on the odd-power function side tends to infinity, and the radius of curvature on the tangent side is infinite.

[0094] The radius of curvature of the composite curve is calculated based on the parameters given in the embodiment, such as... Figure 5 As shown. Figure 5 In the composite curve, the radius of curvature of the straight line segment is infinite; 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 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.

[0095] In this embodiment, the inflection point or tangent point of the continuous combination curve is located at a designated point on the line of action of the meshing force of the gear pair. The designated point is specifically defined as: the line of action of the meshing force of the herringbone gear pair with constant meshing characteristics 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 point on the line of action of the meshing force of a herringbone gear pair with constant meshing characteristics. In the diagram: P is the designated point on the line of action of the meshing force; P1 and P2 are the line lines representing the positional limits of the designated point; N1 and N2 are the lines of action of the meshing force; α k The pressure angle is O1, which is the center point of the herringbone gear II2. O1-x1y1 and O2-x2y2 are the local rectangular coordinate systems of the herringbone gear I1 and the herringbone gear II2, respectively; r1 and r2, r a1 and r a2 r f1 and r f2 These are the pitch circle radius, addendum circle radius, and dedendum circle radius of the herringbone gears I1 and II2, respectively. The specified point P is usually located at the node, but can also be a given point near either side of the node. The variation range of the specified point does not exceed half the tooth height.

[0096] According to the gear meshing principle, a constant meshing characteristic means that there is no relative sliding between the tooth surfaces when a herringbone gear pair meshes at the pitch point. Figure 7 This embodiment provides a schematic diagram of the slip ratio at the meshing point of a herringbone gear pair, illustrating the constant meshing characteristic of a tooth profile curve and its combination curve with the tangent at its inflection point. Since the herringbone gear pair with the same continuous combined curve tooth profile in this embodiment meshes at the node at any given time, this constant meshing characteristic can achieve zero-slip meshing. When the inflection point or tangent point of the combined curve does not coincide with the node, the slip ratio of the herringbone gear pair with the constant meshing characteristic remains constant but not zero. The closer the inflection point or tangent point of the continuous curve is to the node, the smaller the slip ratio of the herringbone gear pair with the constant meshing characteristic, and vice versa. When the inflection point or tangent point coincides with the node, the herringbone gear pair with the constant meshing characteristic can achieve zero-slip meshing transmission, reducing wear between tooth surfaces and improving the transmission efficiency of the herringbone gear pair with the constant meshing characteristic.

[0097] Furthermore, when the overlap ratio of the herringbone gear pair is designed to be an integer in the constant meshing characteristics of the embodiment, the meshing stiffness is constant. At this time, the magnitude of the meshing force of the herringbone gear pair at any meshing position is determined, and the position and direction of the meshing force at any time are also determined. Therefore, the meshing state of the herringbone gear pair is constant at any time, which effectively ensures the stability of the dynamic meshing performance of the herringbone gear pair and can effectively reduce the vibration noise of the herringbone gear pair.

[0098] Taking the constant meshing characteristics of the herringbone gear pair in the embodiment as an example, a schematic diagram of the meshing force of the herringbone gear pair is established, as follows. Figure 8 As shown. For the right side of the herringbone gear pair with constant meshing characteristics, the meshing force F on the herringbone cylindrical gear is... n1 It can be decomposed into axial force F a1 Radial force F r1 and circumferential force F t1 The herringbone teeth on the left side of the herringbone gear pair correspond to the meshing force F on the herringbone cylindrical gear. n2 It can be decomposed into axial force F a2 Radial force F r2 and circumferential force F t2 When considering only the right side of the herringbone gear pair, during meshing, as the meshing point moves in the tooth width direction, the meshing force F... n1 The shift in the tooth width direction and the change in force state cause periodic changes in the excitation factors of the herringbone gear pair, severely affecting its dynamic meshing performance. When considering both sides of the herringbone gear pair simultaneously, due to the perfect symmetry of the left and right teeth, the axial force F on both tooth surfaces... a1 and F a2 The radial forces F on both sides cancel each other out. r1 and F r2 Simplifying to the center position of the herringbone gear along the tooth width direction, the circumferential force F on both sides t1 and F t2 Similarly, simplifying to the center position along the tooth width direction of the herringbone cylindrical gear, the meshing force F at any given time is... n1 and F n2 Resultant force F n The determination of the position and direction of the line of action improves the stability of the meshing process of the herringbone gear pair due to constant meshing characteristics.

[0099] 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. At the same time, 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. In summary, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A herringbone gear pair with constant meshing characteristics, comprising a herringbone gear I based on a conjugate curve and a herringbone gear II based on a conjugate curve, characterized in that, The normal tooth profile curve Γ of the herringbone gear I s1 and the normal tooth profile curve Γ of the herringbone gear II s2 Γ is a continuous combination of curves with the same shape. L The continuous combination curve Γ L The combined curve Γ, including odd-power function curves and their tangents at inflection points. L1 Or the combination curve of odd-power functions Γ L4 The continuous composite curve consists of two continuous curve segments. The connection point of the two continuous curve segments is the inflection point or tangent point of the continuous composite curve. The common normal at the inflection point or tangent point of the continuous composite curve passes through the node of the herringbone gear pair. The normal tooth profile curve is swept along the given conjugate curve to obtain the tooth surfaces of the paired herringbone gear I and the paired herringbone gear II. 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 At that time, the continuous combination curve Γ L The tangent line Γ at the inflection point of the odd power function curve L11 And odd power function curve Γ L12 Composition; A rectangular coordinate system is established at the tangent points of the continuous combined curves, and the combined curve Γ of the odd-power function curve and its tangents at the inflection points. L1 The equation is: In the formula: x 10 and y 10 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of values ​​for the continuous curve; 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 From the curve Γ of the first odd power function L41 Curve of the second odd power function Γ L42 Composition; Establish a rectangular coordinate system at the inflection points of the continuous combination curve, the combination curve Γ of the odd power function. L4 The equation is: In the formula: x 40 and y 40 t1 and t2 are the x and y coordinates of the composite curve in a rectangular coordinate system, respectively; t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; 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 herringbone 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 and y coordinates of the normal tooth profile curve of the herringbone gear I in the rectangular coordinate system.

2. A herringbone gear pair with constant meshing characteristics according to claim 1, characterized in that: The normal tooth profile curve Γ of the herringbone gear I s1 The normal tooth profile curve Γ of the herringbone gear II is obtained by rotating it 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 and y coordinates of the normal tooth profile curve of the herringbone gear II in the rectangular coordinate system.

3. A herringbone gear pair with constant meshing characteristics according to claim 2, characterized in that: The normal tooth profile curve Γ of the herringbone gear II s2 The tooth surface Σ2 of the paired herringbone 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 These are the coordinate values ​​of the tooth surfaces of the herringbone gear II, respectively; β is the helix angle of the gear pair, r is the pitch circle radius of the herringbone gear pair with constant meshing characteristics, θ is the angle of the given contact line, and in the symbol "±", "+" indicates the left tooth surface of the herringbone gear and "-" indicates the right tooth surface of the herringbone gear.

4. A herringbone gear pair with constant meshing characteristics according to claim 1, characterized in that: The normal tooth profile curve Γ of the herringbone gear I s1 The tooth surface Σ1 of the paired herringbone 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 , respectively, are the coordinate values ​​of the tooth surface of the herringbone gear I; β is the gear pair helix angle, parameter m is the independent variable of the equation, m1 and m2 are the range of tooth width values, and in the symbol "±", "+" indicates the left tooth surface of the herringbone gear and "-" indicates the right tooth surface of the herringbone gear.

5. A herringbone gear pair with constant meshing characteristics according to claim 1, characterized in that: The constant meshing characteristic design ensures that the overlap ratio of the herringbone gear pair is an integer, thereby achieving constant stiffness meshing transmission.

6. A herringbone gear pair with constant meshing characteristics according to claim 1, characterized in that: The paired herringbone gears I and II are designed to be symmetrical along the tooth width, so as to achieve a constant line of action of the meshing force of the herringbone gear pair.

Images