Constant engagement characteristic for internal engagement cylindrical gear pair

Abstract

The application discloses a constant engagement characteristic pair-constructive internal engagement cylindrical gear pair and relates to the technical field of gear transmission, comprising a pair-constructive external cylindrical gear and a pair-constructive internal cylindrical gear based on conjugate curves. In the application, the normal tooth profile curves of the pair-constructive external cylindrical gear and the pair-constructive internal cylindrical gear 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 sliding ratio of the gear pair can be adjusted according to the requirement by adjusting the position of the inflection point or the tangent point; the coincidence degree is designed as an integer, and the constant engagement stiffness can be realized, thereby greatly improving the dynamic engagement performance of the gear pair. In the application, the normal tooth profile of the pair-constructive external cylindrical gear and the pair-constructive internal cylindrical gear is the same, the curvature radius of the engagement point is constant and tends to infinity, the sliding ratio 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 in particular to a pair of internally meshing cylindrical gears with constant meshing characteristics. More specifically, it relates to a pair of internally meshing cylindrical gears consisting of a pair of external cylindrical gears and a pair of internal cylindrical gears, with identical normal tooth profiles, a constant and infinitumiously curvature radius at the meshing point, a constant sliding rate, and a constant meshing stiffness. Background Technology

[0002] Internal gear pairs are one of the main forms of mechanical transmission. Their function is to maintain the same direction of mechanical rotation and transmit 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, precision instruments, and other fields. Existing internal 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 internal gear pairs are struggling to meet the high-performance requirements of defense technology, industrial manufacturing, and daily life.

[0003] The paper "Basic Theoretical Research on Internal Meshing Curve Pair Gear Transmission" further applies the basic theory of conjugate curve meshing to paired internal meshing gears, establishing the fundamental principle of convex-concave internal meshing curve paired gears. The convex and concave internal meshing gear pairs constructed in this paper require different cutting tools, increasing the manufacturing cost of the gear pairs. The concave-convex tooth profile limits the radius of curvature at the meshing point, thus restricting further improvement in the load-bearing capacity of the gear pairs. Selecting the contact point at the node causes tooth surface interference, making it difficult to achieve zero slip rate. Therefore, there is an urgent need for innovative tooth profile design based on the existing conjugate curve paired gear design theory, thereby improving the meshing performance of paired internal meshing cylindrical gear pairs and reducing the production cost of the gear pairs. Summary of the Invention

[0004] The purpose of this invention is to provide a pair of internally meshing cylindrical gears with constant meshing characteristics to solve the problems existing in the prior art. The gear pair consists of an external cylindrical gear and an internal cylindrical gear. The normal tooth profiles of the external cylindrical gear and the internal cylindrical gear are the same. The radius of curvature at the meshing point is constant and tends to infinity. The sliding rate 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 internally meshing cylindrical gears with constant meshing characteristics, comprising a pair of external cylindrical gears and an internal cylindrical gear based on a conjugate curve; characterized in that: the normal tooth profile curve Γ of the external cylindrical gears... s1 And the normal tooth profile curve Γ of the internal cylindrical gear s2 Γ is a continuous combination of curves with the same shape. L The continuous combination curve Γ L The combined curve Γ, which includes 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 of the epicycloid function Γ L6 The continuous combination 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 combination curve. 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 meshing cylindrical gear pair in the structure. The normal tooth profile curve is swept along the given conjugate curve to obtain the tooth surface of the external cylindrical gear and the internal cylindrical gear in the structure.

[0007] Preferably, when the continuous combined curve ΓL is a combined curve of an odd-power function curve and its tangent at the inflection point Γ 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] Where, parameter t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; a is the coefficient of the equation; n is the degree of the independent variable and is a positive integer; x 10 and y 10 These are the x and y coordinates of the composite curve in the rectangular coordinate system, respectively.

[0010] Preferably, 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 L21It is composed of the sine function curve ΓL22; a rectangular coordinate system is established at the tangent points of the continuous combined curves, and the equation of the combined curve ΓL2 of the sine function curve and its tangent at the inflection points is:

[0011]

[0012] Where, parameter 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; x 20 and y 20 , respectively, are the x and y coordinates of the composite curve in the rectangular coordinate system; k is the slope of the tangent line at the inflection point of the sine function curve.

[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 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 combined curves, and the combined curve Γ of the epicycloid function curve and its tangents at inflection points. L3 The equation is:

[0014]

[0015] Where, parameter t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; R and r are the radii of the moving and fixed circles of the cycloid, respectively; e is the eccentricity; x 30 and y 30 , respectively, are the x and y coordinates of the composite curve in the rectangular coordinate system; k is the slope of the tangent line at the inflection point of the epicycloid function curve.

[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 From the curve Γ of the first odd power function L41 Curve of the second odd power function Γ L42 Composition; a rectangular coordinate system is established at the inflection points of the continuous combined curve, and the combined curve Γ of the odd-power function is... L4 The equation is:

[0017]

[0018] Where, parameter 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; x 40 and y40 These are the x and y coordinates of the composite curve in a rectangular coordinate system.

[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 From the first sine function curve Γ L51 The second sine function curve Γ L52 Composition; a rectangular coordinate system is established at the inflection points of the continuous combined curve, and the combined curve Γ of the sine function is... L5 The equation is:

[0020]

[0021] Where, parameter t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; a1, b1, a2, and b2 are the coefficients of the equation; x 50 and y 50 These are the x and y coordinates of the composite curve in a rectangular coordinate system.

[0022] Preferably, 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 point of the continuous combined curve, and the combined curve Γ of the epicycloid function is... L6 The equation is:

[0023]

[0024] Where, 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, and 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] Preferably, the continuous combination curve Γ L Rotating the gear by an angle α1 about the origin of the rectangular coordinate system yields the normal tooth profile curve Γ of the external cylindrical gear. s1 The equation of the curve is:

[0026]

[0027] Where, x 01 and y 01These are the x and y coordinates of the normal tooth profile curve of the external cylindrical gear in a rectangular coordinate system.

[0028] Preferably, the normal tooth profile curve Γ of the paired external cylindrical gears s1 Rotating the gear by 180° around the origin of the rectangular coordinate system yields the normal tooth profile curve Γ of the internal cylindrical gear. s2 The equation of the curve is:

[0029]

[0030] Where, x 02 and y 02 These are the x and y coordinates of the normal tooth profile curve of the internal cylindrical gear in a rectangular coordinate system.

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

[0032]

[0033] Where, x Σ1 y Σ1 and z Σ1 These are the coordinate values ​​of the tooth surface of the external cylindrical gear; β is the helix angle of the gear pair; φ1 is the angle of the given contact line; r 01 Let be the pitch circle radius of the external cylindrical gear.

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

[0035]

[0036] Where xΣ2, yΣ2 and zΣ2 are the coordinate values ​​of the tooth surface of the cylindrical gear in the pair, and r02 is the pitch circle radius of the cylindrical gear in the pair.

[0037] Preferably, the overlap ratio of the meshing cylindrical gear pair within the structure is designed to be an integer to achieve constant meshing stiffness transmission.

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

[0039] In this invention, the normal tooth profile of the internal cylindrical gear is the same as that of the external cylindrical gear, allowing it to be machined with the same tool, thus 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 to be zero, improving the transmission efficiency of the gear pair and reducing wear during transmission. The overlap ratio of the internal meshing cylindrical gear pair is designed to be an integer, enabling 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 This invention provides a schematic diagram of a curve combining an odd-power function curve and its tangent at its inflection point;

[0042] Figure 2 A schematic diagram of the formation of the normal tooth profile of a meshing cylindrical gear pair in a structured configuration, 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.

[0043] Figure 3 A schematic diagram of the construction of the tooth surface of a pair of 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 for an embodiment of the present invention.

[0044] Figure 4 A schematic diagram of an internal meshing cylindrical gear pair, provided as a tooth profile curve, using a combination curve of an odd power function curve and its tangent at the inflection point as an embodiment of the present invention.

[0045] Figure 5 A schematic diagram of the radius of curvature at the meshing point of an internal meshing cylindrical gear pair, provided as an embodiment of the present invention, showing a combined 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 internal 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 internal 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] In the diagram: 1 - a pair of external cylindrical gears, 2 - a pair of internal cylindrical gears. 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] 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.

[0051] like Figures 1-7 As shown, in a constant meshing characteristic internal meshing cylindrical gear pair disclosed in this invention, the normal tooth profile curve of the external cylindrical gear 1 and the normal tooth profile curve of the internal cylindrical gear 2 are continuous combination curves with the same curve shape, and the meshing point of the external cylindrical gear 1 and the internal cylindrical gear 2 is at the inflection point or tangent point of the continuous combination curve.

[0052] In this embodiment of the invention, the constant meshing characteristics are applied to the following basic parameters of the internal meshing cylindrical gear pair: normal module m = 8, number of teeth for external cylindrical gear 1 is z1 = 20, number of teeth for internal cylindrical gear 2 is z2 = 82, and 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 hf =5.6mm, helix angle β =15°, tooth width w =40mm.

[0053] Taking the curve of an odd-power function and the combination curve of its tangent at its inflection point as an example, draw the curve of the odd-power function and the combination curve of its tangent at its inflection point on the rectangular coordinate system σ1(O1-x1, y1), as follows. 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 The equation of (composed of the tangent line ΓL11 at the inflection point of the odd power function curve and the odd power function curve ΓL12) is:

[0054]

[0055] Where x 10 and y 10t1 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.

[0056] This invention provides a schematic diagram of the formation of the normal tooth profile of a gear pair using a combination curve of an odd-power function curve and its tangent at the inflection point as the tooth profile curve. Figure 2 As shown, the inflection point P is the meshing point, Ⅰ is the pitch circle of the external cylindrical gear, and Ⅱ is the pitch circle of the internal cylindrical gear. In the figure, the tooth roots of both the external cylindrical gear 1 and the internal cylindrical gear 2 are tangent segments, while the tooth tips of both the external cylindrical gear 1 and the internal cylindrical gear 2 are cubic power function curve segments. When the continuous combined curve Γ... L Rotating the cylindrical gear I about the origin of the rectangular coordinate system by an angle α1 yields the normal tooth profile curve Γ. s1 The value of the rotation angle α1 needs to be determined based on the specific parameters of the gear pair, and generally the range is: 0° < α1 < 180°. The specific formation process and tooth profile curve equation of the internal meshing cylindrical gear pair are as follows:

[0057] The curve Γ is a combination of the curve of an odd power function and the tangent at its inflection point. L1 Rotating the external cylindrical gear 1 about the origin of the rectangular coordinate system σ1 by an angle α1 = 120°, we obtain the normal tooth profile curve Γ. s1 The equation of the curve is:

[0058]

[0059] Where, x 01 and y 01 The normal tooth profile curves Γ of the external cylindrical gear 1 are respectively. s1 The x and y coordinates in the rectangular coordinate system σ1.

[0060] The normal tooth profile curve Γ of the external cylindrical gear 1 s1 The normal tooth profile curve Γ of the internal cylindrical gear 2 is obtained by rotating it by 180° around the origin σ1 of the rectangular coordinate system. s2 The equation of the curve is:

[0061]

[0062] Where, x 02 and y 02 The normal tooth profile curves Γ of the internal cylindrical gear 2 are respectively. s2 The x and y coordinates in the rectangular coordinate system σ1.

[0063] Figure 3This invention provides a schematic diagram of the construction of the tooth surface of an internal meshing cylindrical gear pair using a combination curve of an odd-power function curve and its tangent at the inflection point as the tooth profile curve. In the diagram, A represents the conjugate curve, B represents the tooth profile sweep direction, and C represents the sweeping tooth surface of the normal tooth profile curve family. The specific construction process and tooth surface equation of the tooth surface of the internal meshing cylindrical gear pair are as follows:

[0064] The normal tooth profile curve Γ of the external cylindrical gear 1 s1 The tooth surface Σ1 of the external cylindrical gear 1 is obtained by sweeping along a given helix. The equation of Σ1 is:

[0065]

[0066] Where, x Σ1 y Σ1 and z Σ1 φ1 represents the coordinates of the tooth surface of the external cylindrical gear 1; φ1 represents the angle of the given contact line.

[0067] Similarly, the normal tooth profile curve Γ of the internal cylindrical gear 2 is described above. s2 The tooth surface Σ2 of the internal cylindrical gear 2 is obtained by sweeping along a given helix, and the tooth surface equation is:

[0068]

[0069] Where, x Σ2 yΣ2 and zΣ2 are the coordinate values ​​of the tooth surface of the cylindrical gear 2 in the structure.

[0070] Figure 4 The present invention provides a schematic diagram of an internal meshing cylindrical gear pair using an odd power function curve and a combination curve of the tangent at the inflection point as the tooth profile curve. The tooth tip circle and tooth root circle are generated by extrusion, and the tooth surfaces of the external cylindrical gear 1 and the internal cylindrical gear 2 are trimmed, stitched, and filled with fillets to obtain a solid model of an internal meshing cylindrical gear pair with constant meshing characteristics.

[0071] In this embodiment of the invention, the normal tooth profile curves of the external cylindrical gear 1 and the internal cylindrical gear 2 can also be a combination curve ΓL2 of a sine function curve and its tangent at the inflection point, a combination curve ΓL3 of an epicycloid function curve and its tangent at the inflection point, a combination curve ΓL4 of an odd power function, a combination curve ΓL5 of a sine function, or a combination curve ΓL6 of an epicycloid function. The curve formulas are as follows:

[0072] When the continuous combination curve ΓL is a combination curve ΓL2 of the sine function curve and its tangent at the inflection point, the continuous combination curve ΓL2 is formed by the tangent at the inflection point of the sine function curve Γ L21 and the sine function curve Γ L22Composition; Establish a rectangular coordinate system at the tangent points of the continuous composite curve, and form the composite curve Γ of the sine function curve and its tangents at the inflection points. L2 The equation is:

[0073]

[0074] Where, parameter 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; x 20 and y 20 , respectively, are the x and y coordinates of the composite curve in the rectangular coordinate system; k is the slope of the tangent line at the inflection point of the sine function curve.

[0075] 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:

[0076]

[0077] Where, parameter t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; R and r are the radii of the moving and fixed circles of the cycloid, respectively; e is the eccentricity; x 30 and y 30 , respectively, are the x and y coordinates of the composite curve in the rectangular coordinate system; k is the slope of the tangent line at the inflection point of the epicycloid function curve.

[0078] 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 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 continuous combination curves, and the combination curve Γ of odd-power functions. L4 The equation is:

[0079]

[0080] In the formula: parameter 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; x 40 and y 40These are the x and y coordinates of the composite curve in a rectangular coordinate system.

[0081] 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 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 composite curve, and the composite curve Γ of the sine function. L5 The equation is:

[0082]

[0083] Where, parameter t is the independent variable of the equation; t1 and t2 are the ranges of the continuous curve; a1, b1, a2, and b2 are the coefficients of the equation; x 50 and y 50 These are the x and y coordinates of the composite curve in a rectangular coordinate system.

[0084] 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 first 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:

[0085]

[0086] Where, 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, and 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.

[0087] In this invention, the inflection point or tangent point of the continuous composite curve is:

[0088] 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.

[0089] 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.

[0090] At the inflection points or tangent points of a continuous composite curve, the curvature of the curve is zero, meaning the radius of curvature tends to infinity. Specifically, when the continuous composite curve is a combination 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 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 function curve and its tangent at the inflection point, the radius of curvature on the side of the odd-power function curve, sine function curve, or epicycloid function curve at the inflection point tends to infinity, and the radius of curvature on the side of the tangent is infinite. The radius of curvature of the composite curve is calculated according to the parameters given in the embodiment, such as... Figure 5 As shown. Figure 5 The radius of curvature of the straight line segment in the composite curve 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 meshing cylindrical gear pair in the structure tends to be infinite, which improves the load-bearing capacity of the meshing cylindrical gear pair in the structure.

[0091] In this invention, 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 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 the 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 O1-x1y1 and O2-x2y2, which are the local rectangular coordinate systems of the external cylindrical gear 1 and the internal cylindrical gear 2, respectively; r1 and r2, r f1 and r f2 These are the pitch circle radius and root circle radius of the external cylindrical gear 1 and the internal cylindrical gear 2, respectively; w1 and w2 are the angular velocities of the external cylindrical gear 1 and the internal cylindrical gear 2, respectively. The specified point P is usually located at the node, but can also be a given point near both sides of the node. The variation area of ​​the specified point does not exceed half of the tooth height.

[0092] According to the gear meshing principle, when a pair of meshing cylindrical gears meshes at the pitch point, there is no relative sliding between the tooth surfaces. Figure 7 This invention provides a schematic diagram of the slip ratio at the meshing point of an internal meshing cylindrical gear pair, using a combination curve of an odd-power function curve and its tangent at the inflection point as a tooth profile curve. Because the constant meshing characteristics in this embodiment ensure that the internal meshing cylindrical gear pair meshes at the node at any given time, this pair 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 internal meshing cylindrical gear pair remains constant but is 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 internal meshing cylindrical gear pair, and vice versa. When the inflection point or tangent point coincides with the node, the internal meshing cylindrical gear pair can achieve zero-slip meshing transmission, reducing wear between tooth surfaces and improving the transmission efficiency of the internal meshing cylindrical gear pair.

[0093] Furthermore, when the contact ratio of the meshing cylindrical gear pairs with the same continuous combined curve tooth profile is designed to be an integer, the meshing stiffness of the meshing cylindrical gear pairs 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 meshing cylindrical gear pairs with the same continuous combined curve tooth profile is constant at any time, effectively ensuring the stability of the dynamic meshing performance of the meshing cylindrical gear pairs and effectively reducing the vibration and noise of the meshing cylindrical gear pairs.

[0094] Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. Furthermore, those skilled in the art will recognize that, based on the ideas of this 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 this invention.

Claims

1. A constant meshing characteristic internal meshing cylindrical gear pair, characterized in that: It includes a pair of opposing external cylindrical gears and opposing internal cylindrical gears based on conjugate curves; characterized in that: the normal tooth profile curve Γ of the opposing external cylindrical gears s1 And the normal tooth profile curve Γ of the internal cylindrical gear 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 combined 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 combined curve. The inflection point or tangent point of the continuous combined curve is located at a designated point on the line of action of the meshing force of the meshing cylindrical gear pair in the structure. The normal tooth profile curve is swept along the given conjugate curve to obtain the tooth surface of the external cylindrical gear and the internal cylindrical gear in the structure. 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: Among them, parameters t is the independent variable of the equation; t 1 and t 2 represents the range of values ​​for the continuous curve; a The coefficients of the equation; n The degree of the independent variable is a positive integer; x 10 and y 10 These are the composite curves in the rectangular coordinate system. x and y Axis coordinate values; 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; a rectangular coordinate system is established at the inflection points of the continuous combined curve, and the combined curve Γ of the odd-power function is... L4 The equation is: Among them, parameters t is the independent variable of the equation; t 1 and t 2 represents the range of values ​​for the continuous curve; a、b The coefficients of the equation; n 1 and n 2 represents the degree of the independent variable and is a positive integer; x 40 and y 40 These are the composite curves in the rectangular coordinate system. x and y Axis coordinate values; The continuous combination curve Γ L Rotation angle around the origin of the rectangular coordinate system α 1. Obtain the normal tooth profile curve Γ of the external cylindrical gear. s1 The equation of the curve is: in, x 01 and y 01 The normal tooth profile curves of the external cylindrical gears in the rectangular coordinate system are respectively... x and y Axis coordinate values.

2. The constant meshing characteristic internal meshing cylindrical gear pair according to claim 1, characterized in that: The normal tooth profile curve Γ of the aforementioned external cylindrical gear s1 Rotating the gear by 180° around the origin of the rectangular coordinate system yields the normal tooth profile curve Γ of the internal cylindrical gear. s2 The equation of the curve is: in, x 02 and y 02 These are the normal tooth profile curves of the internal cylindrical gears in a rectangular coordinate system. x and y Axis coordinate values.

3. The constant meshing characteristic internal meshing cylindrical gear pair according to claim 2, characterized in that: The normal tooth profile curve Γ of the aforementioned external cylindrical gear s1 The tooth surface Σ1 of the paired external cylindrical gear is obtained by sweeping along a given helix, and the tooth surface equation is: in, x Σ1 , y Σ1 and z Σ1 These are the coordinate values ​​of the tooth surface of the external cylindrical gear; β The helix angle of the gear pair; Given the angle of the contact line; r 01 Let be the pitch circle radius of the external cylindrical gear.

4. The constant meshing characteristic internal meshing cylindrical gear pair according to claim 3, characterized in that: The normal tooth profile curve Γ of the internal cylindrical gear s2 The tooth surface Σ2 of the internal cylindrical gear is obtained by sweeping along a given helix, and the tooth surface equation is: in, x Σ2 , y Σ2 and z Σ2 These are the coordinate values ​​of the tooth surface of the cylindrical gear within the structure. r 02 Let be the pitch circle radius of the cylindrical gear within the structure.

5. The constant meshing characteristic internal meshing cylindrical gear pair according to claim 1, characterized in that: The overlap ratio of the meshing cylindrical gear pair within the structure is designed to be an integer to achieve constant meshing stiffness transmission.

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