High load-bearing parabolic tooth profile gear pair

Abstract

This invention provides a high-load-bearing parabolic tooth profile gear pair. The tooth surface equation of the face gear is determined by combining the parabolic tooth profile of the driving gear and the parabolic tooth profile of the face gear. The curvature stability of the parabolic tooth profile makes the curvature change of the face gear tooth profile gradual, so that it is close to the surface contact state in both the tooth height and tooth width directions. This effectively reduces the tooth surface contact stress and equivalent stress, effectively improves the load-bearing capacity of the gear pair, and the smooth change of the sliding rate during meshing is conducive to the formation of a uniform lubricating oil film between the tooth surfaces, reducing friction and wear. At the same time, it can suppress vibration and noise, effectively improve the transmission smoothness, especially suitable for high-speed transmission scenarios, and is easy to manufacture, reducing the processing difficulty.

Description

Technical Field

[0001] This invention relates to a gear pair, and more particularly to a high-load-bearing parabolic tooth profile gear pair. Background Technology

[0002] Face gear transmission, as a highly efficient angle transmission method, is widely used in high-end equipment fields such as aerospace, industrial robots, and precision machine tools due to its advantages such as compact structure, balanced torque distribution, large overlap ratio, and no axial force of spur gears. It is one of the core components of high-end power transmission systems.

[0003] Existing involute gears have the following defects: the principal curvature of the tooth surface changes drastically, local stress concentration is prominent during meshing, and problems such as root undercut and tooth tip sharpening are prone to occur, resulting in limited load-bearing capacity of the gear pair; the tooth profile tangent transition is not smooth, the slip ratio fluctuates greatly during meshing, it is difficult to form a uniform lubricating oil film between the tooth surfaces, and friction and wear are severe; the vibration and noise are large, the transmission stability is poor, and it cannot meet the requirements of high-end equipment such as aerospace and industrial robots for transmission accuracy, load-bearing capacity and operational stability.

[0004] Therefore, in order to solve the above-mentioned technical problems, it is urgent to propose a new technical approach. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a high-load-bearing parabolic tooth profile gear pair. The tooth surface equation of the face gear is determined by combining the parabolic tooth profile of the driving gear and the parabolic tooth profile of the face gear. The curvature stability of the parabolic tooth profile makes the curvature change of the face gear tooth profile gradual, so that it is close to the surface contact state in both the tooth height and tooth width directions. This effectively reduces the tooth surface contact stress and equivalent stress, effectively improves the load-bearing capacity of the gear pair, and the sliding rate changes gradually during meshing, which is conducive to the formation of a uniform lubricating oil film between the tooth surfaces, reducing friction and wear. At the same time, it can suppress vibration and noise, effectively improve the transmission smoothness, especially suitable for high-speed transmission scenarios, and is easy to manufacture, reducing the processing difficulty.

[0006] The present invention provides a high load-bearing parabolic tooth profile gear pair, including a driving gear and a driven gear. The driving gear is a driving gear, and the driven gear is a surface gear. The tooth profiles of the driving gear and the driven gear are parabolic, and the driving gear and the driven gear form an orthogonal spur tooth surface gear pair.

[0007] The tooth surface equations of the driving gear and the driven gear are determined by the following method:

[0008] S1. Construct a coordinate system with the point of maximum curvature of the tooth profile of the driving gear as the origin. And to construct a coordinate system coordinate system The x-axis is the tangent direction of the reference parabola, and the y-axis is the normal direction at the origin;

[0009] S2. Construct the tooth profile equation of the driving gear, and based on the coordinate system. and coordinate system The transformation relationship and tooth profile equation determine the tooth surface equation of the driving gear;

[0010] S3. Construct a static coordinate system S s0 Moving coordinate system S s static coordinate system S 20 And the moving coordinate system S2; where the static coordinate system S s0 It is fixed to the rotation center of the driving gear, and the static coordinate system S s0 The Z-axis coincides with the axis of the driving gear, and the moving coordinate system S... s As the driving gear rotates around its axis and the moving coordinate system S... s At the initial position, relative to the static coordinate system S s0 Coincident, static coordinate system S 20 Fixed to the rotation center of the driven gear, the static coordinate system S 20 The Z-axis of the driven gear coincides with the axis of the driven gear. The moving coordinate system S2 rotates with the driven gear around its axis, and the static coordinate system S... 20 And the moving coordinate system S2 coincides with the initial position;

[0011] S4. Based on static coordinate system S s0 Moving coordinate system S s static coordinate system S 20 The transformation relationship of the moving coordinate system S2 and the tooth surface equation of the driving gear are used to determine the tooth surface equation of the driven gear.

[0012] Furthermore, the tooth profile equation of the driving gear is:

[0013] (1);

[0014] in: This represents the parabola parameter, which is a multiple of the module n1 of the driving gear. The base profile deviation distance, which is n² times the modulus; This represents the offset distance from the origin of the coordinate system, and its value is n³ times the modulus. The pressure angle of the tooth profile is 20°. 。 .

[0015] Furthermore, based on the coordinate system and coordinate system The transformation relationship and the tooth profile equation are used to determine the tooth surface equation of the driving gear, specifically including:

[0016] Establish coordinate transformation equations:

[0017] (2);

[0018] The tooth profile equation r t Transform to coordinate system using formula (2) The equation for the normal tooth profile of the driving gear is obtained below:

[0019] (3);

[0020] Construct coordinate system S s and coordinate system Transformation equation:

[0021] (4);

[0022] Multiply the tooth profile equation (3) of the driving gear normal surface tooth profile by the coordinate system S s and coordinate system Equation (4) transforms to obtain the tooth surface equation of the driving gear:

[0023] (5);

[0024] in: Represents the vertical axis (i.e., y). f The angular parameter from the axis of symmetry line to the starting point of the tooth profile of the driving gear; h represents the distance from the center of the normal tooth profile circle to the center of the end face tooth profile circle of the driving gear, μ s Indicates the tooth width of the driving gear;

[0025] N s Indicates the number of teeth on the driving gear;

[0026] in: (6), The radius of the base circle, , , The tooth offset constant is... The value is n4 times the modulus. The value is n = 5 times the modulus;

[0027] So, It can be represented as .

[0028] Furthermore, based on the static coordinate system S s0 Moving coordinate system S s static coordinate system S 20 The transformation relationship of the moving coordinate system S2 and the determination of the tooth surface equation of the driving gear specifically include:

[0029] Determine the moving coordinate system S s To static coordinate system S s0 Matrix expression:

[0030] ;

[0031] Where: φ s Indicates the rotation angle of the driving gear;

[0032] static coordinate system S s0 To static coordinate system S 20 The matrix expression is:

[0033] ;

[0034] From the static coordinate system S 20 The matrix expression for the moving coordinate system S2 is:

[0035] ;

[0036] but:

[0037] ;

[0038] Then, the moving coordinate system S s The matrix expression for the moving coordinate system S2 is:

[0039] ;

[0040] Where: φ2 represents the rotation angle of the large gear;

[0041] If the normal vectors of the tooth surfaces of the driving gear and the driven gear at the contact point are perpendicular to the velocity vector, then: ;

[0042] in: Let be the unit normal vector of the tooth surface of the driving gear at the contact point. The velocity vector of the driven gear relative to the driving gear;

[0043] Find x using formula (5) s y s The partial derivatives of the derivatives yield the two tangent vectors of the tooth surface of the driving gear, and then the unit normal vector is obtained. for:

[0044] (13);

[0045] in: ; This represents an auxiliary angle, typically taken as 16°.

[0046] The relative velocity vector of the driven gear with respect to the driving gear is:

[0047] (14);

[0048] in: Let be the angular velocity of the driving gear. Let be the angular velocity of the driven gear, and the number of teeth of the driving gear and the driven gear are respectively... and Then the gear ratio of the driving gear to the driven gear is:

[0049] (15);

[0050] Substituting formulas (15) and (5) into formula (14) yields:

[0051] (16);

[0052] Substituting formulas (16) and (13) into formula (12) yields the following solution:

[0053] (17);

[0054] in: It is the engagement angle of the driving gear; for Take the partial derivative with respect to t; for Take the partial derivative with respect to t

[0055] The equation for the tooth surface of the driven gear is expressed as: (18);

[0056] Substituting equations (5) and (17) into equation (18), we obtain the final tooth surface equation of the driven gear as follows:

[0057] (19).

[0058] The beneficial effects of this invention are as follows: The tooth surface equation of the face gear is determined by combining the parabolic tooth profile of the driving gear and the parabolic tooth profile of the face gear. The curvature stability of the parabolic tooth profile makes the curvature change of the face gear tooth profile gradual, so that it is close to the surface contact state in both the tooth height and tooth width directions. This effectively reduces the tooth surface contact stress and equivalent stress, effectively improves the load-bearing capacity of the gear pair, and the sliding rate changes gradually during meshing, which is conducive to the formation of a uniform lubricating oil film between the tooth surfaces, reducing friction and wear. At the same time, it can suppress vibration and noise, effectively improve the transmission smoothness, especially suitable for high-speed transmission scenarios, and is easy to manufacture, reducing the processing difficulty. Attached Figure Description

[0059] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0060] Figure 1 This is a schematic diagram of the gear pair meshing structure of the present invention.

[0061] Figure 2 This is a schematic diagram of the tooth profile of the driving gear of the present invention.

[0062] Figure 3 This is a schematic diagram of the tooth profile of the drive gear end face of the present invention. Detailed Implementation

[0063] The present invention will be further described in detail below:

[0064] The present invention provides a high load-bearing parabolic tooth profile gear pair, including a driving gear and a driven gear. The driving gear is a driving gear, and the driven gear is a surface gear. The tooth profiles of the driving gear and the driven gear are parabolic, and the driving gear and the driven gear form an orthogonal spur tooth surface gear pair.

[0065] The tooth surface equations of the driving gear and the driven gear are determined by the following method:

[0066] S1. Construct a coordinate system with the point of maximum curvature of the tooth profile of the driving gear as the origin. And to construct a coordinate system coordinate system The x-axis is the tangent direction of the reference parabola, and the y-axis is the normal direction at the origin; where, for example... Figure 2 As shown, coordinate system The origin is determined by parameters L, l, and α, which are determined in advance based on actual working conditions during the design and manufacturing process.

[0067] S2. Construct the tooth profile equation of the driving gear, and based on the coordinate system. and coordinate system The transformation relationship and tooth profile equation determine the tooth surface equation of the driving gear;

[0068] S3. Construct a static coordinate system S s0 Moving coordinate system S s static coordinate system S 20 And the moving coordinate system S2; where the static coordinate system S s0 It is fixed to the rotation center of the driving gear, and the static coordinate system S s0 The Z-axis coincides with the axis of the driving gear, and the moving coordinate system S... s As the driving gear rotates around its axis and the moving coordinate system S... s At the initial position, relative to the static coordinate system S s0 Coincident, static coordinate system S 20Fixed to the rotation center of the driven gear, the static coordinate system S 20 The Z-axis of the driven gear coincides with the axis of the driven gear. The moving coordinate system S2 rotates with the driven gear around its axis, and the static coordinate system S... 20 And the moving coordinate system S2 coincides with the initial position;

[0069] S4. Based on static coordinate system S s0 Moving coordinate system S s static coordinate system S 20 The transformation relationship of the moving coordinate system S2 and the tooth surface equation of the driving gear are used to determine the tooth surface equation of the driven gear.

[0070] Specifically, the tooth profile equation of the driving gear is:

[0071] (1);

[0072] in: Let represent the parabola parameters, which are multiples of the module n1 of the driving gear. The value of n1 is generally 1.48. The value of t is in the range of [t1, t2], where t1 = -1.65*m*sin(19*π / 180), m represents the module of the driving gear, and t2 = 1.65*m*sin(30.1*π / 180). The base profile deviation distance is n² times the modulus, where n² is typically 6.67. This represents the offset distance from the origin of the coordinate system, and its value is n3 times the modulus, where n3 is typically 1.5. The pressure angle of the tooth profile is 20°. 。 .

[0073] Based on coordinate system and coordinate system The transformation relationship and the tooth profile equation are used to determine the tooth surface equation of the driving gear, specifically including:

[0074] Establish coordinate transformation equations:

[0075] (2);

[0076] The tooth profile equation r t Transform to coordinate system using formula (2) The equation for the normal tooth profile of the driving gear is obtained below:

[0077] (3);

[0078] Construct coordinate system S s and coordinate system Transformation equation:

[0079] (4);

[0080] Multiply the tooth profile equation (3) of the driving gear normal surface tooth profile by the coordinate system S s and coordinate system Equation (4) transforms to obtain the tooth surface equation of the driving gear:

[0081] (5);

[0082] in: Represents the vertical axis (i.e., y). f The angular parameter from the axis of symmetry line to the starting point of the tooth profile of the driving gear; h represents the distance from the center of the normal tooth profile circle to the center of the end face tooth profile circle of the driving gear, μ s Indicates the tooth width of the driving gear; N s Indicates the number of teeth on the driving gear;

[0083] in: (6), The radius of the base circle, , , The tooth offset constant is... The value is n4 times the modulus, and the value of n4 is generally 0.94. The value of is n5 times the modulus, and the value of n5 is generally 0.11.

[0084] So, It can be represented as .

[0085] Furthermore, based on the static coordinate system S s0 Moving coordinate system S s static coordinate system S 20 The transformation relationship of the moving coordinate system S2 and the determination of the tooth surface equation of the driving gear specifically include:

[0086] Determine the moving coordinate system S s To static coordinate system S s0 Matrix expression:

[0087] ;

[0088] Where: φ s Indicates the rotation angle of the driving gear;

[0089] static coordinate system S s0 To static coordinate system S 20 The matrix expression is:

[0090] ;

[0091] From the static coordinate system S 20The matrix expression for the moving coordinate system S2 is:

[0092] ;

[0093] but:

[0094] ;

[0095] Then, the moving coordinate system S s The matrix expression for the moving coordinate system S2 is:

[0096] ;

[0097] Where: φ2 represents the face gear rotation angle;

[0098] According to the meshing principle of face gears, the contact point between the tooth surfaces of the two gears during meshing satisfies the meshing equation, that is: the normal vectors of the tooth surfaces of the driving gear and the driven gear at the contact point are perpendicular to the relative velocity vectors, therefore: ;

[0099] in: Let be the unit normal vector of the tooth surface of the driving gear at the contact point. The velocity vector of the driven gear relative to the driving gear;

[0100] Find x using formula (5) s y s The partial derivatives of the derivatives yield the two tangent vectors of the tooth surface of the driving gear, and then the unit normal vector is obtained. for:

[0101] (13);

[0102] in: ; This represents an auxiliary angle, typically taken as 16°.

[0103] The relative velocity vector of the driven gear with respect to the driving gear is:

[0104] (14);

[0105] in: Let be the angular velocity of the driving gear. Let be the angular velocity of the driven gear, and the number of teeth of the driving gear and the driven gear are respectively... and Then the gear ratio of the driving gear to the driven gear is:

[0106] (15);

[0107] Substituting formulas (15) and (5) into formula (14) yields:

[0108] (16);

[0109] Substituting formulas (16) and (13) into formula (12) yields the following solution:

[0110] (17);

[0111] in: It is the engagement angle of the driving gear; for Take the partial derivative with respect to t; for Take the partial derivative with respect to t;

[0112] The equation for the tooth surface of the driven gear is expressed as: (18); among which, That is, it can be obtained by formula (11);

[0113] Substituting equations (5) and (17) into equation (18), we obtain the final tooth surface equation of the driven gear as follows:

[0114] (19).

[0115] Of course, in practice, it is also necessary to first determine the basic parameters of the gear pair, including the number of teeth, tooth width, module, pitch circle pressure angle, addendum coefficient, tooth profile center offset, and radius of the parabola of the tooth profile of the driving gear, as well as the number of teeth, outer radius, and addendum coefficient of the face gear, etc. These parameters are substituted into the equation to determine the final tooth surface structure. Through this invention, the tooth surface equation of the face gear is determined by combining the parabola tooth profile of the driving gear and the parabola tooth profile of the face gear. The curvature stability of the parabola tooth profile makes the curvature change of the face gear tooth profile gradual, thus approaching a surface contact state in both the tooth height and tooth width directions. It effectively reduces tooth surface contact stress and equivalent stress, effectively improves the load-bearing capacity of the gear pair, and the sliding rate changes smoothly during meshing, which is conducive to the formation of a uniform lubricating oil film between the tooth surfaces, reducing friction and wear. At the same time, it can suppress vibration and noise, effectively improve transmission smoothness, especially suitable for high-speed transmission scenarios, and is easy to process and manufacture, reducing processing difficulty. Moreover, based on the gear pair structure determined by this invention, the working tooth surfaces of the driving gear tooth profile and the driven gear tooth profile form line contact, the principal curvature changes smoothly during meshing, the meshing backlash is small, and the tooth surface contact line is a non-equidistant oblique line distribution, covering a wide range of tooth width.

[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A high-load-bearing parabolic tooth profile gear pair, characterized in that: It includes a driving gear and a driven gear, wherein the driving gear is a driving gear and the driven gear is a face gear, the tooth profiles of the driving gear and the driven gear are parabolic, and the driving gear and the driven gear form an orthogonal spur tooth face gear pair; The tooth surface equations of the driving gear and the driven gear are determined by the following method: S1. Construct a coordinate system with the point of maximum curvature of the tooth profile of the driving gear as the origin. And to construct a coordinate system coordinate system The x-axis is the tangent direction of the reference parabola, and the y-axis is the normal direction at the origin; S2. Construct the tooth profile equation of the driving gear, and based on the coordinate system. and coordinate system The transformation relationship and tooth profile equation determine the tooth surface equation of the driving gear; S3. Construct a static coordinate system S s0 Moving coordinate system S s static coordinate system S 20 And the moving coordinate system S2; where the static coordinate system S s0 It is fixed to the rotation center of the driving gear, and the static coordinate system S s0 The Z-axis coincides with the axis of the driving gear, and the moving coordinate system S... s As the driving gear rotates around its axis and the moving coordinate system S... s At the initial position, relative to the static coordinate system S s0 Coincident, static coordinate system S 20 Fixed to the rotation center of the driven gear, the static coordinate system S 20 The Z-axis of the driven gear coincides with the axis of the driven gear. The moving coordinate system S2 rotates with the driven gear around its axis, and the static coordinate system S... 20 And the moving coordinate system S2 coincides with the initial position; S4. Based on static coordinate system S s0 Moving coordinate system S s static coordinate system S 20 The transformation relationship of the moving coordinate system S2 and the tooth surface equation of the driving gear are used to determine the tooth surface equation of the driven gear.

2. The high-load-bearing parabolic tooth profile gear pair according to claim 1, characterized in that: The tooth profile equation of the driving gear is: （1）； in: This represents the parabola parameter, which is a multiple of the module n1 of the driving gear. The base profile deviation distance, which is n² times the modulus; This represents the offset distance from the origin of the coordinate system, and its value is n³ times the modulus. The pressure angle of the tooth profile is 20°. 。 .

3. The high-load-bearing parabolic tooth profile gear pair according to claim 2, characterized in that: Based on coordinate system and coordinate system The transformation relationship and the tooth profile equation are used to determine the tooth surface equation of the driving gear, specifically including: Establish coordinate transformation equations: （2）； The tooth profile equation r t Transform to coordinate system using formula (2) The equation for the normal tooth profile of the driving gear is obtained below: （3）； Construct coordinate system S s and coordinate system Transformation equation: （4）； Multiply the tooth profile equation (3) of the driving gear normal surface tooth profile by the coordinate system S s and coordinate system Equation (4) transforms to obtain the tooth surface equation of the driving gear: （5）； in: The angle parameter represents the vertical axis of symmetry line to the starting point of the tooth profile of the driving gear; h represents the distance from the center of the normal tooth profile to the center of the end tooth profile of the driving gear; μ represents the distance from the vertical axis of symmetry line to the starting point of the tooth profile of the driving gear. s Indicates the tooth width of the driving gear; N s Indicates the number of teeth on the driving gear; in: (6), where rbs represents the base circle radius; , This is the tooth profile offset constant. The value is n4 times the modulus. The value is n = 5 times the modulus.

4. The high-load-bearing parabolic tooth profile gear pair according to claim 3, characterized in that: Based on the static coordinate system S s0 Moving coordinate system S s static coordinate system S 20 The transformation relationship of the moving coordinate system S2 and the determination of the tooth surface equation of the driven gear by the tooth surface equation of the driving gear specifically include: Determine the moving coordinate system S s To static coordinate system S s0 Matrix expression: ； Where: φ s Indicates the rotation angle of the driving gear; static coordinate system S s0 To static coordinate system S 20 The matrix expression is: ； From the static coordinate system S 20 The matrix expression for the moving coordinate system S2 is: ； but: ； Then, the moving coordinate system S s The matrix expression for the moving coordinate system S2 is: ； Where: φ2 represents the rotation angle of the large gear; If the normal vectors of the tooth surfaces of the driving gear and the driven gear at the contact point are perpendicular to the velocity vector, then: ; in: Let be the unit normal vector of the tooth surface of the driving gear at the contact point. The velocity vector of the driven gear relative to the driving gear; Find x using formula (5) s y s The partial derivatives of the derivatives yield the two tangent vectors of the tooth surface of the driving gear, and then the unit normal vector is obtained. for: （13）； in: ; This represents an auxiliary angle, typically taken as 16°. The relative velocity vector of the driven gear with respect to the driving gear is: （14）； in: Let be the angular velocity of the driving gear. Let be the angular velocity of the driven gear, and the number of teeth of the driving gear and the driven gear are respectively... and Then the gear ratio of the driving gear to the driven gear is: （15）； Substituting formulas (15) and (5) into formula (14) yields: (16)； Substituting formulas (16) and (13) into formula (12) yields the following solution: (17); in: It is the engagement angle of the driving gear; for Take the partial derivative with respect to t; for Take the partial derivative with respect to t; The equation for the tooth surface of the driven gear is expressed as: (18); Substituting equations (5) and (17) into equation (18), we obtain the final tooth surface equation of the driven gear as follows: (19)。

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