CN-122020874-A - Method for generating tooth profile shape of high-overlap-ratio straight-tooth cylindrical gear pair

CN122020874ACN 122020874 ACN122020874 ACN 122020874ACN-122020874-A

Abstract

A method for generating the tooth profile of straight-tooth cylindrical gear pair includes such steps as dividing the single tooth of gear into four parts including tooth top arc, involute, transition curve and tooth root arc, drawing the curves of tooth top arc, involute, transition curve and tooth root arc according to the parameters and geometry of gear, sequentially forming a finished tooth, array the shape of single tooth to obtain a complete tooth profile, and translational and rotational regulation of two gears to obtain the tooth profile of gear pair. The method can realize rapid drawing of the tooth profile shape of the gear pair, increases universality and practicability of the method, and is suitable for drawing of the tooth profile shape of the gear pair under various design requirements.

Inventors

SHU RUIZHI
WU NAN
LI FANG
WEI JING
WANG YIFENG
CHEN SONGLIN
WEI HAIBO

Assignees

重庆理工大学
中国航发沈阳发动机研究所
重庆大学

Dates

Publication Date: 20260512
Application Date: 20251229

Claims (10)

1. The method for generating the tooth profile shape of the straight-tooth cylindrical gear pair with high contact ratio is characterized by comprising the following steps of: (1) Inputting macroscopic parameters of a gear, wherein the macroscopic parameters comprise a modulus m, a tooth number Z 1 /Z 2 , a displacement coefficient x, a tooth top coefficient h a * , a top clearance coefficient c * and a cutter fillet radius rho 0 ; (2) Calculating geometric dimensions, namely a reference circle diameter d, a base circle diameter d b , a tooth top circle diameter d a , a tooth root circle diameter d f and an actual center distance A according to the macroscopic parameters; (3) Generating full tooth form coordinate matrixes of the gear 1 and the gear 2 respectively; (4) Judging whether undercut or transition curve interference occurs on the gear pair based on the macroscopic parameters, if so, adjusting the macroscopic parameters and returning to the step (1); (5) Rotating the tooth form coordinate matrix of the gear 1 by 180 degrees; (6) Translating the tooth form coordinate matrix of the gear 2 along the longitudinal direction by a distance A; (7) Rotating the tooth-shaped coordinate matrix of the gear 1 by 2 times of tooth thickness half angle; (8) And outputting tooth profile shapes according to the output layout requirements, namely directly outputting the tooth profile shapes if the tooth profile shapes are in a longitudinal layout, and outputting the tooth profile shapes after rotating the coordinate matrix of the gear 2 by 90 degrees if the tooth profile shapes are in a transverse layout.
2. The method for generating the tooth profile shape of the high-coincidence spur gear pair of claim 1, wherein the method for generating the full-tooth profile coordinate matrix of the single gear in the step (3) comprises the following steps: a. Calculating an involute spread angle theta k from the base circle to the top circle according to the macroscopic parameters; Wherein r a is the radius of the top circle, r b is the radius of the base circle; b. generating a right involute coordinate matrix; wherein, theta is the angular spread parameter corresponding to any point on the involute, and theta is more than or equal to 0 and less than or equal to k ; c. rotating the right involute coordinate matrix to be symmetrical about a Y axis; wherein, theta 1 is the rotation angle, ; Gamma b is the tooth thickness half angle; d. Judging the size relation between the base circle and the root circle, and if the base circle is smaller than the root circle, removing coordinate points smaller than the radius of the root circle in the involute; e. Generating a right transition curve coordinate matrix: Wherein phi is the included angle between the center of the circular angle of the tool top and the center line of the tooth slot of the tool: a 1 is the distance from the center line of the round corner of the cutter to the center line, ; B 1 is the circular distance of the tool fillet distance of cutter tooth slot center: Gamma a is a variable parameter, and gamma a is more than or equal to 0 and less than or equal to 45 degrees; f. removing incompatible coordinate points between the involute and the transition curve; g. Mirroring to obtain left involute and transition curve coordinates; h. Generating coordinates of an addendum arc and a dedendum arc; i. sequentially combining the tooth top arc, the involute, the transition curve and the tooth root arc into a single gear tooth coordinate matrix; j. And generating a full tooth form coordinate matrix according to the tooth number array.
3. The method for generating a tooth profile of a high overlap ratio spur gear set according to claim 1, wherein said step of removing a portion having an involute smaller than a root circle in step d comprises: Calculating the distance S (i) from each point of the involute to the original point, if S (i) ≥ R f (tooth root circle radius), reserving the coordinates of the point, otherwise, eliminating the point; The specific method comprises the following steps: calculating the radius of each point in the involute coordinate matrix by using Pythagorean theorem, namely the distance S (i) between each point and the origin; The calculation formula is as follows: Judging the size relation between the distance S (i) and the root radius R f , if the distance S (i) is larger than or equal to the root radius R f , storing the point coordinates to a new involute coordinate matrix W, starting a new cycle, if the distance S (i) is smaller than the root radius R f , starting the new cycle, and until all the points are screened.
4. The method for generating a tooth profile shape of a high-overlap spur-gear set according to claim 1, wherein the step of removing the incompatible coordinate point in the step f comprises: The distance G from the starting point to the origin of the involute is calculated, and the distance S (j) from each point to the origin of the involute is calculated, wherein the calculation modes of G and S (j) are as follows: calculating the radius of a first point in the involute coordinate matrix, namely the distance G from an origin by using Pythagorean theorem; the calculation formula is as follows: Calculating the radius of each point in the involute coordinate matrix by using Pythagorean theorem, namely the distance S (j) between each point and the origin; the calculation formula is as follows: and judging that if S (j) is less than or equal to G, reserving the coordinates of the point, otherwise, eliminating the point.
5. The method for generating the tooth profile of the high-coincidence spur gear pair according to claim 1, wherein the condition for judging the undercut in the step (4) is as follows: Constraint of number of teeth: Constraint of displacement coefficient: The lead-in judgment is rewritten as follows: the judgment formula is obtained by rewriting: In the formula, if the maximum value is greater than zero, the two decision formulas must have terms greater than zero, i.e. radical cutting occurs, whereas if the maximum value is less than or equal to 0, both are less than or equal to 0, i.e. radical cutting does not occur.
6. The method for generating the tooth profile of the high-coincidence spur gear pair according to claim 1, wherein the condition for judging the transition curve interference in the step (4) is as follows: The lead-in judgment is rewritten as follows: the judgment formula is obtained by rewriting: In the formula, Is the engagement angle; If the maximum pressure angle is greater than zero, the two decision formulas must have terms greater than zero, i.e., interference occurs, whereas if the maximum pressure angle is less than or equal to 0, both are less than or equal to 0, i.e., no interference occurs.
7. The method of generating a tooth profile for a high overlap spur gear set as defined in claim 1, wherein the gear is a spur-external gear and the transition curve is formed by machining with a rack-type cutter, and the root portion has two root fillet radii.
8. The method for generating the tooth profile shape of the high-contact-ratio spur gear pair according to claim 1, wherein the single-gear full-tooth-form coordinate matrix generated in the step (3) has a coordinate origin coincident with an absolute coordinate system origin.
9. A storage medium having stored thereon a computer readable program, wherein the program when executed implements the high-overlap spur gear set tooth profile shape generation method according to any one of claims 1 to 8.
10. An electronic device comprising a processor and a memory, the memory storing a computer program, wherein the processor, when executing the program, implements the high-overlap spur gear pair tooth profile shape generation method according to any one of claims 1 to 8.

Description

Method for generating tooth profile shape of high-overlap-ratio straight-tooth cylindrical gear pair Technical Field The invention relates to the technical field of gear transmission, in particular to a method for generating a tooth profile shape of a straight-tooth cylindrical gear pair with high contact ratio. Background In the field of gear transmission, a high-contact ratio (HCR) gear pair has the outstanding advantages of excellent transmission stability, high bearing capacity, low vibration noise and the like because of multiple tooth pairs which participate in meshing simultaneously and large contact ratio, and becomes a key component of a high-speed heavy-load high-precision transmission system. However, the superior performance of HCR gears is highly dependent on their precise tooth profile geometry. Especially when the nonstandard gear is required to be adopted in the face of special working conditions and personalized design requirements, whether the tooth profile curve of the nonstandard gear can be accurately drawn and defined becomes a foundation stone in the whole design, analysis and manufacturing flow. In the transmission design level, accurate drawing of the tooth profile shape of the HCR gear is a fundamental premise for accurate meshing interference analysis, slip ratio calculation, load distribution prediction and transmission efficiency optimization. Only on the basis of the accurate tooth profile can the dynamic meshing process of the gear pair be truly simulated, so that the theoretical advantage of the HCR gear is converted into a practical and reliable transmission scheme. More importantly, minor variations in tooth profile shape, particularly in the root transition curve, can significantly affect the stress concentrating effect at the root in terms of root bending strength calculation. The adoption of the approximate or simplified tooth profile model for calculation may cause serious deviation between the strength prediction result and the actual situation, or increase the manufacturing cost and weight due to over conservation, or cause fatal faults such as early fatigue fracture due to insufficient prediction. Therefore, a set of accurate HCR gear pair tooth profile shape drawing method is researched and established, so that not only is a direct means for realizing nonstandard design from the geometric configuration, but also a core link for deeply influencing the accuracy of transmission performance prediction and the calculation reliability of the tooth root intensity. The method has very obvious and indispensable theoretical value and engineering significance for improving the design quality of the HCR gear, ensuring the operation safety of the HCR gear and fully playing the technical potential of the HCR gear. Disclosure of Invention In view of the above, the present invention aims to provide a method for generating a tooth profile of a spur gear pair with high contact ratio, so as to solve the problems in the prior art. The invention is realized by the following technical scheme: a method for generating tooth profile shape of a straight tooth cylindrical gear pair with high contact ratio comprises the following steps: (1) Inputting macroscopic parameters of a gear, wherein the macroscopic parameters comprise a modulus m, a tooth number Z 1/Z2, a displacement coefficient x, a tooth top coefficient h a*, a top clearance coefficient c * and a cutter fillet radius rho 0; (2) Calculating geometric dimensions, namely a reference circle diameter d, a base circle diameter d b, a tooth top circle diameter d a, a tooth root circle diameter d f and an actual center distance A according to the macroscopic parameters; (3) Generating full tooth form coordinate matrixes of the gear 1 and the gear 2 respectively; (4) Judging whether undercut or transition curve interference occurs on the gear pair based on the macroscopic parameters, if so, adjusting the macroscopic parameters and returning to the step (1); (5) Rotating the tooth form coordinate matrix of the gear 1 by 180 degrees; (6) Translating the tooth form coordinate matrix of the gear 2 along the longitudinal direction by a distance A; (7) Rotating the tooth-shaped coordinate matrix of the gear 1 by 2 times of tooth thickness half angle; (8) And outputting tooth profile shapes according to the output layout requirements, namely directly outputting the tooth profile shapes if the tooth profile shapes are in a longitudinal layout, and outputting the tooth profile shapes after rotating the coordinate matrix of the gear 2 by 90 degrees if the tooth profile shapes are in a transverse layout. Further defined, the method of generating the single gear full tooth form coordinate matrix in step (3) includes: a. Calculating an involute spread angle theta k from the base circle to the top circle according to the macroscopic parameters; Wherein r a is the radius of the top circle, r b is the radius of the base circle; b. generating a right involu