CN105784360A - Method for determining gear engagement dynamic stiffness based on engagement contact line length variation - Google Patents
Method for determining gear engagement dynamic stiffness based on engagement contact line length variation Download PDFInfo
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- CN105784360A CN105784360A CN201610316112.7A CN201610316112A CN105784360A CN 105784360 A CN105784360 A CN 105784360A CN 201610316112 A CN201610316112 A CN 201610316112A CN 105784360 A CN105784360 A CN 105784360A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M13/00—Testing of machine parts
- G01M13/02—Gearings; Transmission mechanisms
- G01M13/021—Gearings
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Abstract
The invention relates to a method for determining gear engagement dynamic stiffness based on engagement contact line length variation. The method includes the following steps that: first step, a gear end section unit contact line length engagement stiffness curve is obtained through calculation; second step, gear engagement line length is calculated; third step, a gear rotation angle and contact line length function is calculated; fourth step, the engagement dynamic stiffness of a single pair of teeth of gears is calculated; fifth step, superposition is carried out according to the number of the teeth of the gears; sixth step, the correction of a theoretical value by an experimental value is considered; and seventh step, single-tooth engagement stiffness and the total engagement dynamic stiffness data of the gears are outputted. The method of the invention can satisfy precision and efficiency requirements of engineering design.
Description
Technical field
The present invention relates to automotive transmission, be specifically related to a kind of method determining gear engagement dynamic stiffness based on engagement contact line length change.
Background technology
In automotive power transmission system, gear is one of topmost component.Gear rigidity in engagement process is being continually changing, and this is the one of the main reasons producing transmission noise.Therefore, the NVH of variator is analyzed by gear engagement dynamic stiffness is required and important.Empirical equation is adopted to calculate Gear Meshing Stiffness, although can quickly obtain gear rigidity, but be the meansigma methods of rigidity, it is impossible to obtain stiffness variation curve.The method being additionally based on finite element calculates overlong time, it is impossible to meet the efficiency requirements of engineering design.It is thus desirable to a kind of quickly and the method comparatively accurately calculating Gear Meshing Stiffness.
CN103234021B disclosed " a kind of determine the crin method with Bel's lattice bevel gear time-variant mesh stiffness ", step is as follows: crin is simplified the torsional vibration system model being treated as gear pair by (1) with Bel's lattice bevel gear system；(2) in the torsional vibration system model of gear pair, introduce time-variant mesh stiffness, set up crin with Bel's lattice bevel gear kinetics equation；(3) according to crin with Bel's lattice bevel gear time-variant mesh stiffness principle, the time-variant mesh stiffness equation that crin launches is set up with Bel's lattice bevel gear polynomial function；(4) the time-variant mesh stiffness equation launched with Bel's lattice bevel gear polynomial function according to crin tries to achieve its time-variant mesh stiffness value, carries out theoretical simulation analysis with the crin set up based on traditional method with Bel's lattice bevel gear time-variant mesh stiffness value and compares.The method, for obtaining this kind of gear time-variant mesh stiffness value, lays the first stone for the vibration damping of crin Gen Beierge Bevel Gear Transmission, noise reduction, the research of steady drive dynamics.Certainly, this is the significant trial of one of described technical field.
CN101246083B discloses the measuring method of a kind of dynamic mesh stiffness of straight spur gear.Its process includes: measure geometry size and form and position tolerance the tested gear of mounting and adjusting；Measure output angle and the testboard outfan dynamic friction moment sequence of driving gear and driven gear each point at steady state, define the driving error formula δ of tested gear, and expand into fourier series；Utilize periodic function characteristic, dynamic friction torque Fg fourier series is represented；Fourier series expression-form according to driving error fourier series and dynamic friction torque, obtains gear dynamic mesh stiffness expression；Build gear dynamic mesh stiffness solution formula；Substitute into rigidity solution formula by adopting optimization to calculate the correlation coefficient tried to achieve simultaneously, obtain dynamic mesh stiffness fourier expansion coefficient ak0, aki, bki, draw gear dynamic mesh stiffness K (t).It directly can be measured with to Meshing Stiffness of Spur Gears, and gear-driven design and application are had directive significance.
Summary of the invention
It is an object of the invention to provide a kind of method determining gear engagement dynamic stiffness based on engagement contact line length change, precision and the efficiency requirements of engineering design can be met simultaneously.
Principles of the invention is: first obtain the mesh stiffness K of single pair of tooth contact unit line lengthi(θ), then calculate the length of line of action l in single pair of tooth engagement processi(θ), both are multiplied and can obtain the engagement dynamic stiffness of single pair of tooth, finally consider registration, obtain the engagement dynamic stiffness that gear is total
A kind of method determining gear engagement dynamic stiffness based on engagement contact line length change of the present invention, comprises the following steps:
The first step, calculates and obtains gear end cross-sectional unit contact line length mesh stiffness curve KEnd=f (θ)；θ is the corner of little gear, and the smallest cross-sectional of helical gear teeth is normal section, and normal section contact unit line length mesh stiffness is KMethod=KEnd·(cosβ)2, β is helical angle, and when gear is spur gear, its helical angle is 0；
Second step, calculates gear length of line of action；When spur gear engages, the contact wire of the flank of tooth is each parallel to Gear axis, and its length of line of action is equal to working gear facewidth B；Helical gear is when engaged transmission, no matter flank profil in what position engages, its contact wire is all the straight line tilted with axis, the length of face line is gradually increased by zero, arrives maximum, then is gradually shortened, until disengaging, its length of line of action maximum is: B/cos βb, βbFor Base spiral angle；
3rd step, calculates gear corner and contact line length function；According to gear meshing geometry shape (see Fig. 1), the corresponding relation that can derive gear corner and contact line length is:For the average corner of little gear per tooth (deg)；εβFor Face contact ratio；dlFor the Small variables on contact line length, dθFor Small variables relevant with gear corner on flank profil direction；
4th step, by the contact unit line length mesh stiffness in the first step and the contact line length integration in the 3rd step, the computing formula of the engagement dynamic stiffness that can obtain gear single pair of tooth is:
Wherein, θ1And θ2The little gear corner that respectively beginning and end of contact wire is corresponding；
5th step, is overlapped further according to number of gear teeth, calculates the dynamic stiffness of gear pair engagement process；This engagement dynamic stiffness is the curve of mechanical periodicity, and the cycle is the average corner of gear per tooth；
6th step, according to GBT_3480-1997, it is considered to the experiment value correction to theoretical value；Engagement dynamic stiffness is multiplied by theoretical correction coefficient；
The engagement dynamic stiffness data that 7th step, output monodentate engagement dynamic stiffness and gear are total.
The present invention compared with prior art has the great advantage that
(1) having considered the change of single pair of gear rigidity and length of line of action, result is more accurate.
(2) the gear engagement variation rigidity with corner change can be obtained, be applied in gear dynamic analysis and variator NVH analysis, and design of gears is had important directive significance.
(3) drastically reduce the area the calculating time, be more suitable for engineer applied.
Accompanying drawing explanation
Fig. 1 gear meshing geometry shape graph；
Fig. 2 gear engagement dynamic stiffness defining method flow chart of the present invention；
The end section contact unit line length mesh stiffness curve chart of Fig. 3 gear；
Fig. 4 gear length of line of action curve chart；
The engagement dynamic stiffness curve figure of Fig. 5 gear single pair of tooth；
The engagement dynamic stiffness curve figure of Fig. 6 gear teeth superposition；
Fig. 7 gear always engages dynamic stiffness fair curve figure.
Detailed description of the invention
Below in conjunction with the drawings and specific embodiments, describe the present invention:
The flow process of these computational methods such as Fig. 2, implements step as follows:
The first step, calculates single pair of tooth contact unit line length mesh stiffness curve；
Second step, calculates gear length of line of action；
3rd step, calculates gear corner and contact line length function；
4th step, calculates the engagement dynamic stiffness of gear single pair of tooth；
5th step, is overlapped according to number of gear teeth, calculates the dynamic stiffness of gear pair engagement process；
6th step, it is considered to the experiment value correction to theoretical value；
The engagement dynamic stiffness data that 7th step, output monodentate engagement dynamic stiffness and gear are total.
Embodiment:
The third gear gear of certain variator is helical gear, its design parameter such as table 1, and this end section contact unit line length mesh stiffness curve to gear, referring to Fig. 3.
Certain variator third gear shifting gear parameter of table 1
It is embodied as step, referring to Fig. 2.
The first step, if the curvilinear function in Fig. 3 is KEnd=f (θ), then smallest cross-sectional is normal section, and normal section contact unit line length mesh stiffness is:
KMethod=KEnd·(cosβ)2=f (θ) (cos β)2=0.703 × f (θ)
Second step, gear length of line of action curve, referring to Fig. 4；
The average rotational angle theta of its medium and small gear0=360 °/Z1=11.613 °；Single pair of tooth flank engagement line greatest length isεβ·θ0=13.471 °；εα·θ0=17.652 °；εAlways·θ0=31.123 °；
3rd step, gear corner and contact line length function areReferring to Fig. 1；
4th step, the engagement dynamic stiffness curve of gear single pair of tooth；Referring to Fig. 5:
5th step: the single pair of tooth dynamic stiffness curve in the 4th step be overlapped according to number of gear teeth, calculates the dynamic stiffness of gear pair engagement process, referring to Fig. 6.
6th step: considering the experiment value correction to theoretical value, engagement dynamic stiffness is multiplied by theoretical correction coefficient 0.8, and result is referring to Fig. 7；
The engagement dynamic stiffness data that 7th step, output monodentate engagement dynamic stiffness and gear are total.
From the above, it is seen that the present invention calculates gear engagement dynamic stiffness simply, fast, efficiency can be substantially improved, save human cost.
Claims (1)
1. the method determining gear engagement dynamic stiffness based on engagement contact line length change, comprises the following steps:
The first step, calculates and obtains gear end cross-sectional unit contact line length mesh stiffness curve KEnd=f (θ)；θ is the corner of little gear, and the smallest cross-sectional of helical gear teeth is normal section, and normal section contact unit line length mesh stiffness is KMethod=KEnd·(cosβ)2, β is helical angle, and when gear is spur gear, its helical angle is 0；
Second step, calculates gear length of line of action；When spur gear engages, the contact wire of the flank of tooth is each parallel to Gear axis, and its length of line of action is equal to working gear facewidth B；Helical gear is when engaged transmission, no matter flank profil in what position engages, its contact wire is all the straight line tilted with axis, the length of face line is gradually increased by zero, arrives maximum, then is gradually shortened, until disengaging, its length of line of action maximum is: B/cos βb, βbFor Base spiral angle；
3rd step, calculates gear corner and contact line length function；According to gear meshing geometry shape, the corresponding relation that can derive gear corner and contact line length is:θ0For the average corner of little gear per tooth (deg)；εβFor Face contact ratio；dlFor the Small variables on contact line length, dθFor Small variables relevant with gear corner on flank profil direction；
4th step, by the contact unit line length mesh stiffness in the first step and the contact line length integration in the 3rd step, the computing formula of the engagement dynamic stiffness that can obtain gear single pair of tooth is:
Wherein, θ1And θ2The little gear corner that respectively beginning and end of contact wire is corresponding；
5th step, is overlapped further according to number of gear teeth, calculates the dynamic stiffness of gear pair engagement process；This engagement dynamic stiffness is the curve of mechanical periodicity, and the cycle is the average corner of gear per tooth；
6th step, according to GBT_3480-1997, it is considered to the experiment value correction to theoretical value；Engagement dynamic stiffness is multiplied by theoretical correction coefficient；
The engagement dynamic stiffness data that 7th step, output monodentate engagement dynamic stiffness and gear are total.
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Cited By (3)
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| CN106568597A (en) * | 2016-11-08 | 2017-04-19 | 江苏大学 | High precision measurement method for roller gear tooth surface comprehensive meshing rigidity |
| CN108534966A (en) * | 2017-03-02 | 2018-09-14 | 武汉理工大学 | A kind of gear time-variant mesh stiffness survey calculation method |
| CN112036049A (en) * | 2020-09-15 | 2020-12-04 | 株洲齿轮有限责任公司 | Rapid calculation method for time-varying meshing stiffness of bevel gear pair under actual working condition |
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|---|---|---|---|---|
| CN106568597A (en) * | 2016-11-08 | 2017-04-19 | 江苏大学 | High precision measurement method for roller gear tooth surface comprehensive meshing rigidity |
| CN108534966A (en) * | 2017-03-02 | 2018-09-14 | 武汉理工大学 | A kind of gear time-variant mesh stiffness survey calculation method |
| CN112036049A (en) * | 2020-09-15 | 2020-12-04 | 株洲齿轮有限责任公司 | Rapid calculation method for time-varying meshing stiffness of bevel gear pair under actual working condition |
| CN112036049B (en) * | 2020-09-15 | 2024-04-23 | 株洲齿轮有限责任公司 | Rapid calculation method for time-varying meshing stiffness of helical gear pair under actual working condition |
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