CN-115034007-B - Method for obtaining comprehensive meshing rigidity of spiral bevel gear

CN115034007BCN 115034007 BCN115034007 BCN 115034007BCN-115034007-B

Abstract

The invention relates to a method for acquiring comprehensive meshing stiffness of a spiral bevel gear, which comprises the following steps of S1, acquiring single tooth pairs which are in contact based on multi-tooth pair and meshing state analysis by combining a displacement rotation angle of a given gear and a rotation angle of a target tooth pair at a theoretical meshing position, S2, acquiring distribution loads of all tooth pairs which are in contact based on penetration quantity between the single tooth pairs and meshing stiffness between the single tooth pairs, and S3, acquiring comprehensive meshing stiffness under the multi-tooth meshing state based on deformation quantity and distribution loads between the single tooth pairs. The invention combines the penetration quantity between the tooth pairs and is more close to the actual situation, thereby obtaining reduced and actual errors.

Inventors

ZHANG WEIQING
GUO RUIQI
GUO XIAODONG
TAN RULONG

Assignees

重庆理工大学
重庆理工大学

Dates

Publication Date: 20260421
Application Date: 20220531
Priority Date: 20220531

Claims (2)

1. A method for obtaining comprehensive meshing rigidity of a spiral bevel gear is characterized by comprising the following steps: S1, based on multi-tooth pair and meshing state analysis, combining a displacement rotation angle of a given gear and a rotation angle of a target tooth pair at a theoretical meshing position to obtain a single tooth pair generating contact; S2, based on the penetration amount between single tooth pairs and the meshing stiffness between the single tooth pairs, obtaining the distribution load of all the tooth pairs which generate contact; S3, acquiring comprehensive meshing stiffness in a multi-tooth meshing state based on deformation and distribution load between single-tooth pairs; the S1 specifically comprises selecting a tooth pair meeting the following formula; Wherein, the ; Representing the displacement angle of a given gear; Representing transmission errors, where ; Representing the rotation angle of a given target tooth pair at a theoretical meshing position; the angle of normal vector to circumferential tangential direction at the meshing point is expressed, Representing the radius of the circumference of the meshing point; Wherein, the 、 And The following relationship exists: For the number of teeth of the big wheel or the small wheel, Representing the angle of rotation of the front in order of age pair of a given target tooth pair, Representing the angle of rotation of the trailing in order of age pair of a given target tooth pair; The step S2 is specifically as follows: S21, judging If it is greater than 0, then enter S22, otherwise, let =0, Proceed to S24; s22, giving initial distribution load And iterative step size ; S23 based on S22 Obtaining single tooth meshing stiffness Then judge If yes, S24 is performed, otherwise, the following formula is satisfied = + S22, carrying out again; representing the meshing stiffness of a single tooth, Represents penetration; S24, output ; S25, judging output If the following formula is satisfied, entering into the step S3, otherwise, reselecting the displacement rotation angle of the gear and the rotation angle of the target tooth pair at the theoretical meshing position, and repeating the step S1 until the output Satisfies the following formula: ; Wherein the method comprises the steps of Torque for selecting a large wheel or a small wheel; Wherein, the Is the angle between the normal vector of the curved surface at the meshing point of the ith pair of teeth and the circumferential tangential vector direction; is the radius of the circumference where the meshing point of the ith pair of teeth is located.
2. The method for obtaining the integrated engagement stiffness of a spiral bevel gear according to claim 1, wherein the method for obtaining the integrated engagement stiffness in the multi-tooth engaged state is represented by the following formula: ; wherein: Represent the first As to the amount of deformation of the meshing gear teeth, 。

Description

Method for obtaining comprehensive meshing rigidity of spiral bevel gear Technical Field The invention relates to the technical field of gear design, in particular to contact analysis of a spiral bevel gear. Background In the actual transmission process, the spiral bevel gear is usually in a state of alternately meshing single teeth with multiple teeth due to high overlap ratio. The overall stiffness of the gear in the multi-tooth meshing state cannot be simply directly derived from the single-tooth meshing stiffness. The most common comprehensive rigidity solving method at present is to take the influence of the contact ratio under the meshing state of multiple teeth into consideration, and obtain the single tooth rigidity by superposition. In an actual multi-tooth engagement state, load is distributed among the engaged tooth pairs, the distributed load among the tooth pairs changes along with the change of the rotation angle, and the rigidity also changes along with the change of the load, so that the single-tooth engagement rigidity in the multi-tooth engagement state is lower than the single-tooth engagement rigidity in consideration. Therefore, the simple rigidity superposition calculation is carried out only according to the theoretical overlap ratio, the deformation coordination principle of multi-tooth meshing is not satisfied, and the calculation result deviation is larger. Disclosure of Invention The invention aims to provide a method for acquiring comprehensive meshing rigidity of a spiral bevel gear, which aims to solve the problem that the prior art cannot meet the deformation coordination principle of multi-tooth meshing and can cause larger deviation of calculation results. In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: a method for obtaining comprehensive meshing rigidity of a spiral bevel gear comprises the following steps: S1, based on multi-tooth pair and meshing state analysis, combining a displacement rotation angle of a given gear and a rotation angle of a target tooth pair at a theoretical meshing position to obtain a single tooth pair generating contact; S2, based on the penetration amount between single tooth pairs and the meshing stiffness between the single tooth pairs, obtaining the distribution load of all the tooth pairs which generate contact; and S3, acquiring comprehensive meshing stiffness in a multi-tooth meshing state based on deformation and distribution load between single-tooth pairs. Further, the S1 specifically comprises selecting a tooth pair satisfying the following formula; ; Wherein, the ;Representing the displacement angle of a given gear; Representing transmission errors, where ;Representing the rotation angle of a given target tooth pair at a theoretical meshing position; the angle of normal vector to circumferential tangential direction at the meshing point is expressed, Representing the radius of the circumference of the meshing point; Wherein, the 、AndThe following relationship exists: , For the number of teeth of the big wheel or the small wheel, Representing the angle of rotation of the front in order of age pair of a given target tooth pair,Representing the angle of rotation of the trailing in order of age pair of a given target tooth pair. Further, the S2 specifically is: S21, judging If it is greater than 0, then enter S22, otherwise, let=0, Proceed to S24; s22, giving initial distribution load And iterative step size; S23 based on S22Obtaining single tooth meshing stiffnessThen judgeIf yes, S24 is performed, otherwise, the following formula is satisfied=+S22, carrying out again; ; representing the meshing stiffness of a single tooth, Represents penetration; S24, output ; S25, judging outputIf the following formula is satisfied, entering into the step S3, otherwise, reselecting the displacement rotation angle of the gear and the rotation angle of the target tooth pair at the theoretical meshing position, and repeating the step S1 until the outputThe following formula is satisfied. ; Wherein the method comprises the steps ofTorque for selecting a large wheel or a small wheel; Further, the method for obtaining the comprehensive meshing stiffness in the multi-tooth meshing state is as follows: ; wherein: Represent the first As to the amount of deformation of the meshing gear teeth,。 The invention has the beneficial effects that: Starting from the state of multi-tooth pair engagement analysis, the invention obtains the distribution load generated by gear engagement by combining the penetration quantity of the target tooth pair, the front in order of age pair and the rear in order of age pair at the displacement rotation angle of the given gear and the rotation angle of the target tooth pair at the theoretical engagement position, obtains the comprehensive engagement rigidity based on the distribution load and rigidity among different tooth pairs, and combines the penetration quantity among the tooth p