Cylindrical gear with high contact performance

Abstract

The application discloses a high-contact-performance cylindrical gear. When the high-contact-performance cylindrical gear as a driving gear and the high-contact-performance cylindrical gear as a driven gear mesh and transmit power, the relative curvature k r satisfies k r =|k1-k2|=ar 2 +br+c, r is the distance from the meshing point C to the node P, k1 and k2 are the curvatures of the tooth profile Σ1 of the driving gear and the tooth profile Σ2 of the driven gear at any meshing point C respectively, and a, b and c are the coefficients of the quadratic polynomial. Compared with the prior art, the high-contact-performance cylindrical gear can obtain higher contact, bending, wear and gluing bearing capacity and better lubrication performance.

Description

Technical Field

[0001] This invention relates to the field of gear technology, and in particular to a cylindrical gear with high contact performance. Background Technology

[0002] Gears are essential basic mechanical components. Involute gears, due to their advantages such as constant transmission ratio, high contact ratio, separable transmission, and convenient machining, are widely used in aerospace, rail transportation, engineering machinery, and precision instruments. However, involute gears also have some drawbacks, such as a relatively large tooth profile sliding coefficient, which easily leads to wear and heat generation, affecting transmission smoothness, efficiency, and service life; and a relatively small relative radius of curvature of the meshing tooth profile, limiting the contact load capacity. These drawbacks result in the main failure modes of involute gears under bending fatigue strength conditions being tooth surface pitting, wear, and scuffing. Summary of the Invention

[0003] The purpose of this invention is to provide a cylindrical gear with high contact performance to achieve higher contact, bending, wear, and scuff load-bearing capacity, as well as better lubrication performance.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] This invention discloses a high-contact-performance cylindrical gear. When the high-contact-performance cylindrical gear, serving as the driving gear, meshes with the high-contact-performance cylindrical gear, the relative curvature k... r Satisfying k r =|k1-k2|=ar 2 +br+c, r is the distance from the meshing point C to the node P, k1 and k2 are the curvatures of the tooth profile Σ1 of the driving gear and the tooth profile Σ2 of the driven gear at any meshing point C, respectively, and a, b, and c are the coefficients of the quadratic polynomial.

[0006] Preferably, at the meshing initiation point of the two high-contact cylindrical gears, the relative curvature is less than the relative curvature of the involute gear with the same parameters at the upper boundary point of a single pair of teeth meshing. The same parameters refer to the same module, number of teeth, and addendum coefficient.

[0007] Preferably, at the node of the two meshing high-contact cylindrical gears, the relative curvature is less than the minimum relative curvature of the involute gear with the same parameters, and the derivative of the relative curvature is greater than the derivative of the relative curvature of the involute gear with the same parameters, wherein the same parameters refer to the same module, number of teeth, and addendum coefficient.

[0008] Preferably, when the two high-contact cylindrical gears mesh, the overlap ratio is greater than 1.

[0009] The present invention achieves the following technical effects compared to the prior art:

[0010] The high-contact cylindrical gear of the present invention exhibits a parabolic variation in the relative curvature of the meshing tooth profiles at any meshing point. Under the same module, number of teeth, and addendum coefficient, the gear of the present invention can achieve higher contact, bending, wear, and scuff load-bearing capacity, as well as better lubrication performance, compared to involute gears and gears with equal relative curvature (gears disclosed in CN 109241679 A). Attached Figure Description

[0011] 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.

[0012] Figure 1 A coordinate system required for tooth profile design;

[0013] Figure 2 This is the tooth profile of the high-contact cylindrical gear in this embodiment;

[0014] Figure 3 This is a comparison chart of relative curvature.

[0015] Figure 4 A comparison chart of tooth surface sliding coefficients;

[0016] Figure 5 A comparison chart of minimum oil film thickness on tooth surfaces;

[0017] Figure 6 A comparison diagram of tooth surface wear depth;

[0018] Figure 7 This is a comparison chart of flash temperature rise on the tooth surface; Detailed Implementation

[0019] 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.

[0020] The purpose of this invention is to provide a high-contact cylindrical gear and its design method to achieve higher contact, bending, wear, and scuff load-bearing capacity, as well as better lubrication performance.

[0021] 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. In the drawings, the gear of the present invention refers to the driving gear or the driven gear, gear 1 of the present invention refers to the driving gear, gear 2 of the present invention refers to the driven gear, and the gear with equal relative curvature refers to the gear disclosed in CN 109241679 A.

[0022] This embodiment provides a high-contact-performance cylindrical gear. When the high-contact-performance cylindrical gear, serving as the driving gear, meshes with the high-contact-performance cylindrical gear, the relative curvature k... r Should meet

[0023] k r =|k1-k2|=ar 2 +br+c (1)

[0024] In the formula, r is the distance from the meshing point C to the node P, k1 and k2 are the curvatures of the tooth profile Σ1 of the driving gear and the tooth profile Σ2 of the driven gear at any meshing point C, respectively, and a, b, and c are the coefficients of the quadratic polynomial.

[0025] Let the pitch circle radius of Σ1 be r1, and the pitch circle radius of Σ2 be r2. The line connecting the rotation centers of Σ1 and Σ2 coincides with the y-axis of the fixed coordinate system Oxy. Let the counterclockwise rotation angle of PC relative to the positive x-axis of the fixed coordinate system Oxy be α. Then, when the meshing point is in the first quadrant, according to differential geometry theory, we have...

[0026]

[0027] The power series solution to the above differential equation for sinα is:

[0028]

[0029] In the formula, n is the highest degree of the polynomial; a n a n-1 ..., a0 are the coefficients of each term.

[0030] According to the principle of planar tooth profile meshing, in the moving coordinate system O3x3y3 (where the origin of the moving coordinate system O3x3y3 coincides with node P), the equation of the tooth profile Σ3 of the producing rack is:

[0031]

[0032] In the coordinate system Oxy, the equation of the meshing line is:

[0033]

[0034] The equation of Σ1 in the rotating coordinate system O1x1y1 is:

[0035]

[0036] Similarly, the equation of Σ2 in the rotating coordinate system O2x2y2 is:

[0037]

[0038] In the above formula, These are the rotation angles of the driving gear and the driven gear about their centers of rotation.

[0039]

[0040]

[0041] The equation for the tooth root transition curve corresponding to Σ1 is as follows:

[0042]

[0043] The equation for the tooth root transition curve corresponding to Σ2 is as follows:

[0044]

[0045] In the formula, (x i * ,y i * ), (i=1,2) are the coordinates of the vertices of the tooth profiles of Σ1 and Σ2 respectively; α1 * α2 * These are the angles between the normals to the vertices of the tooth profiles of Σ1 and Σ2, respectively, and the positive x-axis; α f1 α f2 θ1 and θ2 are the angle variables corresponding to the tooth tip arcs of the tooth profiles of the Σ1 and Σ2 producing racks, respectively; θ1 and θ2 are the intermediate angle variables corresponding to the tooth tip arcs of the tooth profiles of the Σ1 and Σ2 producing racks, respectively; ρ is the radius of curvature of the tooth tip arc of the tooth profile of the producing rack.

[0046] Thus, by solving the above equations, we can obtain the equations for Σ1 and Σ2, as well as the equations for the tooth root transition curves corresponding to Σ1 and Σ2, and thereby process the driving gear and the driven gear.

[0047] It should be noted that, in order to achieve a comprehensive improvement in gear contact performance (contact, wear and scuff load-bearing capacity, lubrication performance), the following conditions should be met:

[0048] 1. At the meshing initiation point of two high-contact cylindrical gears, the relative curvature is less than the relative curvature of an involute gear with the same parameters at the upper boundary point of a single pair of teeth meshing. The same parameters refer to the same module, number of teeth, and tooth addendum coefficient.

[0049] 2. At the node of two meshing high-contact cylindrical gears, the relative curvature is less than the minimum relative curvature of an involute gear with the same parameters, and the derivative of the relative curvature is greater than the derivative of the relative curvature of an involute gear with the same parameters. The same parameters refer to the same module, number of teeth, and addendum coefficient.

[0050] 3. When two high-contact cylindrical gears mesh, the overlap ratio is greater than 1.

[0051] If Z1 is taken as the number of teeth of the driving gear, These represent the angles the driving gear rotates from the starting point of engagement to the pitch point, and the angles it rotates from the pitch point to the ending point of engagement, respectively. k rB2 Let be the relative curvature of the driving gear and the driven gear at the initial point of meshing, and m be the module of the driving gear and the driven gear. For involute gears with identical parameters, the distance from the meshing termination point to the peg is given by the following equation.

[0052]

[0053] The following is an illustration using a specific case.

[0054] The number of teeth of the driving gear and driven gear are Z1 = 23 and Z2 = 47 respectively, the module of the driving gear and driven gear is m = 3mm, and the addendum coefficient of the driving gear and driven gear is... The radius of curvature of the tooth tip arc of the gear rack is ρ = 0.76 m. Establish the following... Figure 1 The coordinate system shown is: coordinate system Oxy is a fixed coordinate system with its origin at node P, and O1x1y1 and O2x2y2 are rotating coordinate systems with their origins at the rotation centers O1 and O2 of the driving gear, respectively. The polynomial coefficients of the relative curvature are a = 0.0011, b = 0, and c = 0.087. Taking n = 3, we solve equation (3) to obtain the equations of tooth profile Σ1 and tooth profile Σ2 in their respective rotating coordinate systems, as well as the transition curve equations, and generate the complete tooth profile curve, such as Figure 2 As shown.

[0055] Table 1 Comparison of Gear Performance Indicators

[0056]

[0057] Assuming the driving torque of the driving gear is 50 N·m, the constant speed is 3000 rpm, and the operating time is 100 h, the calculated performance indicators of three gears with the same design parameters (module, number of teeth, and addendum coefficient) are shown in Table 1. Figure 3 The relative curvatures of three types of gears during one meshing cycle are given. Figures 4-7 Performance indicators for three types of gears within one meshing cycle are given.

[0058] Through this specific case comparison, the following conclusions can be drawn easily. Compared with involute gears and gears with equal relative curvature and the same design parameters, the high-contact-performance cylindrical gear of this embodiment achieves improvements in the following performance aspects:

[0059] (1) Since the relative curvature of the meshing point is less than that of the involute gear and the gear with equal relative curvature in the single pair of teeth meshing area, the maximum contact stress of the gear tooth surface in this embodiment is less than that of the involute gear and the gear with equal relative curvature, and the contact bearing capacity is higher.

[0060] (2) Since the sliding coefficient (absolute value) is significantly lower than that of involute gears and gears with equal relative curvature, especially at the meshing start and end points, the wear depth of the gear tooth surface in this embodiment is smaller than that of involute gears and gears with equal relative curvature, and the wear bearing capacity is higher.

[0061] (3) Since the relative curvature of the meshing point is smaller than that of the involute gear and the gear with equal relative curvature in most areas, that is, the relative curvature radius is larger and the contact half width is larger. At the same time, the smaller sliding coefficient (absolute value) results in a sliding speed that is smaller than that of the involute gear and the gear with equal relative curvature. Therefore, the flash temperature rise of the gear tooth surface in this embodiment is lower than that of the involute gear and the gear with equal relative curvature, and the bearing capacity of the adhesive is higher.

[0062] (4) Since the relative curvature of the meshing point is smaller than that of the involute gear and the gear with equal relative curvature in most areas, that is, the relative curvature radius is larger, the average minimum oil film thickness of the gear tooth surface in this embodiment is greater than that of the involute gear and the gear with equal relative curvature, resulting in better lubrication performance.

[0063] (5) Because the thickness of the tooth root is greater, the maximum bending stress of the gear tooth root in this embodiment is less than that of the involute gear and the gear with equal relative curvature, and the bending load capacity is higher.

[0064] Based on the above comparison, it can be seen that the "high contact performance" in the high contact performance cylindrical gear of this embodiment refers to the fact that, under the same module, number of teeth and tooth tip height coefficient, the gear of this embodiment can obtain better contact, bending, wear, scuffing load-bearing capacity and lubrication performance parameters than the involute gear.

[0065] 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 high contact performance cylindrical gear characterized by, When the high-contact-performance cylindrical gear as the driving gear meshes with the high-contact-performance cylindrical gear as the driven gear, the relative curvature of the tooth profiles of the two gears at any meshing point varies as a parabola, and the relative curvature k r satisfies k r = |k1-k2| = ar 2 +br+c, r is the distance from the meshing point C to the node P, k1 and k2 are the curvatures of the tooth profile Σ1 of the driving gear and the tooth profile Σ2 of the driven gear at any meshing point C, respectively, and a, b, and c are the coefficients of the quadratic polynomial.

2. The high contact performance spur gear of claim 1, wherein, At the meshing start point of two said high contact performance cylindrical gears, the relative curvature is less than the relative curvature of involute gears with the same parameters at the single pair of tooth meshing upper limit point, said same parameters refer to the same modulus, the same number of teeth and the same addendum coefficient.

3. The high contact performance spur gear of claim 1, wherein, At the node of two said high contact performance cylindrical gears in mutual meshing, the relative curvature is less than the minimum relative curvature of involute gears with the same parameters, and the derivative of the relative curvature is greater than the derivative of the relative curvature of involute gears with the same parameters, said same parameters refer to the same modulus, the same number of teeth and the same addendum coefficient.

4. The high contact performance spur gear of claim 1, wherein, When two said high contact performance cylindrical gears mesh and drive, the coincidence degree is greater than 1.

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