CN103577687B - Time-varying characteristic quantitative calculation method for meshing stiffness of gear with minor defect - Google Patents
Time-varying characteristic quantitative calculation method for meshing stiffness of gear with minor defect Download PDFInfo
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Abstract
The invention relates to a quantitative calculation method for the meshing stiffness of a gear with a minor defect. In order to describe the influence of a typical gear fault on the time-varying stiffness characteristic, a meshing stiffness energy method calculation model is firstly introduced, wherein five kinds of elastic strain energy, which refers to bending, shearing, radial compression, contact and base deformation, are respectively considered, and five corresponding stiffnesses are further formed. The quantitative calculation method is based on the energy method, the influences of case crush, tooth root crack and tooth breakage on the stiffness distribution are discussed one after another. Aiming at spalling defects, the influences of spalling length (in the meshing direction) and spalling width (in the tooth width direction) on a stiffness distribution curve is researched, and the quantitative relationship between the spalling size and the stiffnesses degradation is obtained. In the aspect of flexural fatigue crack, the change rule of the stiffness curve along with the crack depth, and the quantitative relationship between the stiffness curve and the crack depth are discussed. In the aspect of broken gear tooth, the influence of missing of a single tooth on the stiffness distribution is discussed. By adopting the quantitative calculation method, the actual meshing situation can be really reflected, the complexity and computation in the process of solving can be lowered.
Description
Technical field
The present invention relates to a kind of gear rigidity time-varying characteristics quantitative calculation method, belongs to Gear Fault Diagnosis field, especially
It is related to a kind of time-varying characteristics quantitative calculation method of local defect Gear Meshing Stiffness.
Background technology
Time-variant mesh stiffness is one of main driving source of gear train assembly vibratory response, therefore is effectively and accurately calculated
Local defect gear time-variant mesh stiffness has important meaning to studying failure gear vibration Response Mechanism.
At present, mainly there are following 5 kinds of (1) international standard methods to the method for mesh stiffness research both at home and abroad：National Standard Method can have
Effect calculates the average mesh stiffness of gear exactly, but can not calculate time-variant mesh stiffness；(2) laboratory method：The solution of laboratory method
As a result it is relatively accurate, but complex operation and experimental facilitiess are had high demands, therefore, it is difficult to extensively applying；(3) Ishikawa method：Using Ishikawa
It is that gear is reduced to one by the trapezoidal cantilever beam constituted with rectangle that formula calculates mesh stiffness, and does not consider that wheel body deformation is drawn
The rigidity for rising；(4) linear programming method：When linear programming method is solved for normal Gear Meshing Stiffness, result is also relatively accurate, but should
Method is studied seldom to failure Gear Meshing Stiffness, and the reliability of its research and the degree of accuracy for calculating need to be investigated；(5) have
The first method of limit：FInite Element generally by setting up the physical model of gear train assembly, reapplies Finite element arithmetic and goes out the gear
The deflection of transmission, finally obtains the gear-driven time-variant mesh stiffness, and finite element can more really reflect actual engagement
Situation, but solution procedure amount of calculation is relatively large.Sum it up, the mean rigidity that calculated of Ishikawa method compared with National Standard Method gap compared with
Greatly, it is impossible to effectively reflect the practical situation of gear time-variant mesh stiffness；Laboratory method, Finite element arithmetic are complicated；Linear programming
Method is still immature.
The external solution to time-variant mesh stiffness mainly has based on energy method, it is assumed that elastic strain energy is converted into hertz energy entirely
It is several or whole in amount, shear energy, flexional and radial compression energy, but seldom have consideration wheel body elastic deformation.Base
The present invention is analyzed more than and proposes a kind of time-varying characteristics quantitative calculation method of local defect Gear Meshing Stiffness, the method is with energy
It is mensuration for rely on, to peel off gear consider peel off hole along the facewidth and along flank engagement direction two kinds of change in size to it is comprehensive when
Become the impact of mesh stiffness；To Gear with Crack, it is contemplated that different crack depths impact respectively to shear energy and flexional；
Finally, the time-variant mesh stiffness containing local defect gear is quantitatively solved.
The content of the invention
Object of the present invention is to provide a kind of time-varying characteristics quantitative calculation method of local defect Gear Meshing Stiffness,
In order to systematically inquire into the quantitative Analysis of failure gear time-variant mesh stiffness, it is proposed that a kind of to be stored in meshing gear centering
Elastic strain energy converts the energy of quinquepartite, then obtains corresponding five kinds of rigidity, gained after every kind of rigidity series connection
Result be final gear mesh comprehensive time-variant mesh stiffness method.
To achieve these goals, the technical solution used in the present invention is a kind of time-varying of local defect Gear Meshing Stiffness
Property quantification computational methods, the step of realizing of the method is：Set up Gear Meshing Stiffness computation model；Set up and peel off gear engagement
Rigidity Calculation model；Set up Gear with Crack mesh stiffness computation model；Set up broken teeth Gear Meshing Stiffness computation model；Failure tooth
The calculating of one swing circle internal messing rigidity of wheel.
Compared with existing computational methods, the present invention has advantages below：
1st, the method considers peeling hole along the facewidth and along flank engagement direction to peeling off gear with energy method to rely on
The impact of two kinds of change in size to comprehensive time-variant mesh stiffness.
2nd, to Gear with Crack, it is contemplated that different crack depths impact respectively to shear energy and flexional, effectively
Reflect gear time-variant mesh stiffness practical situation, be more nearly practical situation.
3rd, the time-variant mesh stiffness containing local defect gear is quantitatively solved, is really reflected actual engagement
Situation, reduces the complexity and amount of calculation in solution procedure.
Description of the drawings
Fig. 1 is tooth force figure；
Fig. 2 is peeling gear graph；
Fig. 3 is Gear with Crack figure；
Fig. 4 is broken teeth gear graph；
Fig. 5 is diagram of gears, Basic parameters of gear：Little gear number of teeth z1=22, canine tooth tooth number z2=30, height of teeth top
Coefficient ha*=1, tip clearance coefficient c*=0.25, facewidth L1=L2=20mm, pressure angle of graduated circle a0=20 degree, elastic modulus E=
209MP, Poisson's ratio u=0.269, driving wheel based on little gear, number of teeth z in figure1=22, it is engagement starting point at arrow indication；
Fig. 6 is workflow diagram；
Fig. 7 is the geometric parameter of wheel body deformation；
Fig. 8 is the mesh stiffness of normal gear in two mesh cycles；
Fig. 9 is the contrast that gear and normal gear synthesis mesh stiffness curve are peeled off along facewidth direction different faults size；
Figure 10 is the contrast that gear and normal Gear Meshing Stiffness curve are peeled off along flank engagement direction different faults size；
Figure 11 is Gear with Crack relevant parameter concrete meaning；
Figure 12 is the contrast of the failure gear with normal gear bending stiffness of three kinds of different crackles；
Figure 13 is the contrast of the failure gear with normal gear shearing rigidity of three kinds of different crackles；
Figure 14 is the size that normal gear subtracts Gear with Crack mesh stiffness, normal gear and Gear with Crack mesh stiffness it
Difference；
Figure 15 is the contrast of three kinds of different crack depths failure gears and normal gear synthesis mesh stiffness；
Figure 16 is broken teeth diagram of gears；
Figure 17 is the contrast of broken teeth gear and normal Gear Meshing Stiffness.
Specific embodiment
Below with reference to case-study, the invention will be further described.
The method realizes that step is as follows：
1st, set up Gear Meshing Stiffness computation model
1.1 basic parameters for determining gear mesh
1.2 determine that gear mesh list bi-tooth gearing is interval
1.3 five kinds of rigidity for calculating meshing gear respectively
Tooth force figure is illustrated in figure 1, when gear pair is acted on by engagement F, F is decomposed into and gear teeth centerline parallel
With two vertical power FaAnd Fb.Because gear pair has linear contact lay, therefore there is Hertzian contact stiffness；By parallel to gear teeth centrage
Power FaEffect, there is radial compression in gear, therefore there is radial compression rigidity；By perpendicular to gear teeth centrage FbEffect, because of Fb
It is equal to shearing and makes wheel body bear moment of flexure relative to gear centre, therefore there is shearing rigidity and bending stiffness；Finally because of the gear teeth
There is elastic deformation in stress, basis, therefore there is wheel body deformation rigidity.Will be stored in meshing gear centering strain energy be converted into it is conspicuous
Hereby energy Uh, flexional Ub, radial compression energy Ua, shear energy UsWith wheel body strain energy of distortion Uf, just can be counted by preservation of energy
Calculate corresponding hertz rigidity kh, bending stiffness kb, radial compression rigidity ka, shearing rigidity ksWith wheel body deformation rigidity
kf。
The calculating of 1.4 global stiffnesses
Normal spur gear synthesis time-variant mesh stiffness will be just obtained after five kinds of rigidity series connection of gained in 1.3：
Wherein, subscript 1,2 represent driving and driven gear respectively.
2nd, peel off the foundation of Gear Meshing Stiffness computation model
Peeling gear graph is illustrated in figure 2, when gear pair is acted on by engagement F, F is decomposed into and gear teeth centerline parallel
With two vertical power FaAnd Fb.By power F parallel to gear teeth centrageaEffect, there is radial compression in gear, because of FaIt is constant,
Therefore radial compression rigidity is constant；By perpendicular to gear teeth centrage FbEffect, because of FbIt is equal to shearing and makes relative to gear centre
Wheel body bears moment of flexure, FbIt is constant, therefore shearing rigidity and bending stiffness are also constant；Finally because of tooth force, there is elasticity and become in basis
Shape, because overall stress F is constant, therefore it is also constant to there is wheel body deformation rigidity.The last contact line length because of gear engagement occurs to become
Change, and hertz rigidity is mainly relevant with contact line length, therefore when having peeling, mainly consider the change of hertz rigidity, now normally
Hertz rigidity k during gearhHertz rigidity k for being changed into peeling off during gearhchip.Wherein, it is considered to peel off hole size along facewidth direction
Change and along flank engagement direction change when, khchipIt is with regard to peeling off hole size w respectivelysAnd αsFunction.
The comprehensive time-varying engagement for peeling off gear has been obtained final product after gear hertz rigidity substitutes normal gear hertz rigidity just by peeling off
Degree：
3rd, the foundation of Gear with Crack mesh stiffness computation model
Gear with Crack figure is illustrated in figure 3, because of contact surface area and component FaIt is unchanged, therefore hertz rigidity and radial compression
Rigidity is constant；Overall stress F is also constant again, therefore the rigidity of wheel body deformation is also constant；Mainly consider when having crackle bending stiffness and
The change of shearing rigidity.With step 2：The bending stiffness of normal gear is by kbWith shearing rigidity ksIt is changed into the curved of Gear with Crack respectively
Bent kbcrackWith shearing rigidity kscrack.Now kbcrackAnd kscrackAll it is with regard to crack depth q and crackle and gear teeth center wire clamp
The function of angle v, finally obtaining Gear with Crack synthesis time-variant mesh stiffness is：
4th, the foundation of broken teeth Gear Meshing Stiffness computation model
Broken teeth gear graph being illustrated in figure 4, contact being lost in the position of gear tooth breakage, original double-teeth toothing region is changed into single
Tooth is engaged.Therefore, only by monodentate to constituting, broken teeth Gear Meshing Stiffness computing formula is comprehensive mesh stiffness：
Wherein comma presubscript 1,2 represents driving and driven gear；The gear on left side when subscript 1 represents bi-tooth gearing after comma
It is secondary.
5th, the calculating of one swing circle internal messing rigidity of failure gear
Diagram of gears is illustrated in figure 5, if meshing gear centering little gear is drivewheel, with initial two pairs of gears simultaneously
During engagement on the basis of the gear mesh on the left side.If the failure gear teeth are first teeth of rotate counterclockwise in little gear, little gear rotation
When one week, gear pair has z1(z1For the little gear number of teeth) individual mesh cycle.[3, z1] individual mesh cycle mesh stiffness with it is normal
Gear is identical.Within first and second mesh cycle, the size of failure gear tooth rigidity value is obtained by step 2～4.So far, you can
Obtain the mesh stiffness in one swing circle of failure gear.
It is illustrated in figure 6 workflow of the present invention to local defect Gear Meshing Stiffness time-varying characteristics quantitative calculation method
Figure.Specific implementation process is as follows：
1st, the calculating of healthy Meshing Stiffness of Spur Gears
1.1 basic parameters for determining gear mesh
The parameter and material behavior of selected standard involute spur, by taking Fig. 5 as an example.The tooth of driving and driven gear
Number is respectively z1=22, z2=30；Addendum coefficient ha*=1；Tip clearance coefficient c*=0.25；Facewidth L1=L2=20mm；Reference circle
Pressure angle α0=20.；Elastic modulus E=2.09*1011；Poisson's ratio u=0.269.
1.2 determine a mesh cycle
By the fundamental formular of gear, obtain：
θ1∈[0,θd] when be double-teeth toothing region,When be monodentate region of engagement.It is computed：θd=10.2 °, i.e.,
This pair of gear belongs to double-teeth toothing region at [0,10.2 °], belongs to monodentate region of engagement at [10.2 °, 16.4 °].
1.3 calculate the hertz rigidity of normal gear engagement, bending stiffness, shearing rigidity, footpath in a mesh cycle respectively
To the rigidity that compression stiffness and wheel body deform.
Can be obtained by mechanics ABC
Hertz rigidity：
Bending stiffness：
Shearing rigidity：
Radial compression rigidity：
In each formula, i=1,2 represent two pairs of gear pairs during bi-tooth gearing respectively, and
Wheel body deformation rigidity：
Wherein coefficient L*, M*, P* and Q* can be expressed as by polynomial function：
X*Represent coefficient L*, M*, P*And Q*。hf=rf/ r, rfFor root radius, uf, θfAnd sfMeaning it is as shown in Figure 7.
The value of A, B, C, D, E and F is as shown in following table one.
Parameter A, B, the value of C, D, E, F in one formula of table (19)
| L* | M* | P* | Q* | |
| A | -5.574×10-5 | 60.111×10-5 | -50.952×10-5 | -6.2042×10-5 |
| B | -1.9986×10-3 | 28.100×10-3 | 185.50×10-3 | 9.0889×10-3 |
| C | -2.3015×10-4 | -83.431×10-4 | 0.0538×10-4 | -4.0964×10-4 |
| D | 4.7702×10-3 | -9.9256×10-3 | 53.300×10-3 | 7.8297×10-3 |
| E | 0.0271 | 0.1624 | 0.2895 | -0.1472 |
| F | 6.8045 | 0.9086 | 0.9236 | 0.6904 |
1.4 comprehensive mesh stiffness are calculated
kt,1, kt,2The mesh stiffness of the right and left, comprehensive mesh stiffness k when representing bi-tooth gearing respectivelyt=kt,1+kt,2。
Stiffness curve is as shown in Figure 8.With the alternate that Dan Shuan is engaged to tooth in Meshing Process of Spur Gear, mesh stiffness also cycle therewith
The change of property.
2nd, peel off the calculating of Gear Meshing Stiffness
In Meshing Process of Spur Gear, it is assumed that peel off hole position and be present near reference circle.If peel off hole is shaped as rectangle, tooth
When face has peeling, because mainly gear pair contact length there occurs change, therefore bending stiffness, shearing rigidity, radial compression are firm
The rigidity of degree and wheel body deformation keeps constant, now mainly considers the change of hertz rigidity.By：There is stripping
When falling, facewidth W will be changed into actual engagement facewidth Wc, now Wc=W-ws, wherein wsTo peel off size of the hole in facewidth direction,Global stiffness is changed into：
Now, the solution of the failure gear time-variant mesh stiffness point peels off hole size only along facewidth direction change and only along tooth
Engage two kinds of situations of direction change in face：
2.1 peel off the change that hole size is only considered along facewidth direction
By taking Fig. 2 as an example, normal gear tooth width W=20mm, whole depth h=11.25mm.If along the size in flank engagement direction
αs=4mm be certain value, facewidth direction ws3mm, tetra- groups of different values of 6mm, 9mm, 12mm, w are taken respectivelysFour values shared by
The ratio of the facewidth is respectively 15%, 30%, 45%, 60%.Finally give peeling gear synthesis mesh stiffness as shown in figure 9, by
Fig. 9 is apparent from：Peel off size w in facewidth directionsBigger, rigidity is less.
The width W that actual participation is engagedcHertz rigidity formula is substituted into, is obtained：IfTo a pair of the gears for determining, E, L, μ are constant, therefore λ, A are constant.If ws
For m, khchipFor n, it is a letter with regard to peeling size m along facewidth direction change to finally give and peel off gear hertz rigidity n
Count, its expression formula is：λ m+n-A=0.Again to a pair of the gears for determining, bending stiffness, shearing rigidity, radial compression rigidity and wheel
At a time rigidity value does not change body deformation rigidity with the change of x, therefore sets B is not also changed with the change of u.Peeling gear synthesis mesh stiffness can now be directly obtained
ktchipWith the relation that size u is peeled off along the facewidth it is：Thus formula calculates the value that can be directly obtained as u
Respectively 3mm, 6mm, 9mm and 12mm when, peel off mean rigidity of the gear within a mesh cycle and be respectively normal gear and put down
The 99.60%, 99.06%, 98.26% and 96.98% of equal mesh stiffness.
2.2 peel off hole size is only considered along flank engagement direction change
If along facewidth direction ws=10mm is certain value, and the size in flank engagement direction takes α respectivelys1=1.5mm, αs2=
3mm, αs3=4.5mm, αs4Tetra- groups of different values of=6mm, obtain peeling off gear synthesis along flank engagement direction different faults size
Mesh stiffness and correlation curve such as Figure 10 of normal Gear Meshing Stiffness, can be obtained by Figure 10：Facewidth direction size wsWhen constant, therefore
Barrier Gear Meshing Stiffness is identical in the minima of synchronization；αsAlong flank engagement direction change when, mesh stiffness value reduce
Angle range also respective change.Work as αsValue when being respectively 1.5mm, 3mm, 4.5mm and 6mm, determine that what rigidity value reduced turns
After angle range, mean rigidity of the failure gear within a mesh cycle respectively normal gear is tried to achieve by formula (22) averagely firm
The 99.26%, 98.44%, 97.63% and 96.70% of degree.
3rd, the calculating of Gear with Crack time-variant mesh stiffness
When gear has crackle, because of contact surface area and component FaIt is unchanged, therefore hertz rigidity and radial compression rigidity are not
Become；Overall stress F is also constant again, therefore the rigidity of wheel body deformation is also constant；Now mainly consider bending stiffness and shearing rigidity
Change.There is the failure gear relevant parameter concrete meaning of crackle as shown in figure 11.Wherein, hc, hrRespectively tooth root crackle is to the gear teeth
The half of chordal tooth thickness at the distance and outside circle of centrage；α1, αgRespectively the complementary angle of path of contact and gear teeth centerlines and nibble
The complementary angle of path of contact and gear teeth centerlines when chalaza is at outside circle.
Work as hc＜ hrOr hc≥hrAnd α1≤αgWhen,
Work as hc≥hrAnd α1＞ αgWhen,
For the ease of calculate, it is assumed that crackle on tooth root and with v=45 ° of the angle of gear teeth centrage at, such as Fig. 3 institutes
Show.Transverse tooth thickness of the gear teeth at root circle is 13.92mm, now considers that different crack depths q are respectively 2mm, 4mm, 6mm.Now
The correlation curve of the failure gear of three kinds of different crack depths and the bending stiffness and shearing rigidity of normal gear can be respectively obtained,
As shown in figure 12 and shown in Figure 13.
In order to systematically analyze bending stiffness and shearing rigidity influence degree respectively to comprehensive time-variant mesh stiffness, it is considered to
During crack depth q=6mm, calculate respectively normal gear in a mesh cycle, only consider bending, only consider shearing and while
After comprehensive time-variant mesh stiffness in the case of considering shearing and bending these four, normal gear time-variant mesh stiffness is individually subtracted
Only consider bending, only consider shearing, while consider bending and shear the time-variant mesh stiffness in the case of these three, it is poor by these three
The defecation of value (being referred to as bending difference, shearing difference and total difference) is obtained because of bending, shearing or while considers bending
With impact of the shearing to comprehensive time-variant mesh stiffness, corresponding curve is as shown in figure 14.Impact with shearing by bending, it is poor to bend
Value, shearing difference and total difference are increasing when all moving from tooth root to tooth top with the position of engagement；Bending difference mainly receives tooth
Impact of the wheel set to tooth root displacement, when drivewheel drives driven pulley to rotate, gear pair increases more and more faster to tooth root displacement,
Therefore bending difference also increases also rapid with the rotation of gear；Shearing difference mainly with by gear pair and in the gear teeth
The cross-sectional sizes of heart line are relevant, and so that with the change of the position of engagement, shearing difference increase is more steady, approximately linear relation；
But to after 26.5 ° (i.e. one mesh cycle adds latter bi-tooth gearing), the gear teeth for having crackle will be no longer participate in engagement, and engagement is firm
The size of degree no longer will be affected by shearing and bend.In order to more specifically analyze bending and shear which kind of factor to comprehensive time-varying
The impact of mesh stiffness is bigger, the bending difference from Figure 14 and shearing difference can be seen that when little gear corner [0,
21.7 °] (i.e. from just start to be engaged to 1.533 times of bi-tooth gearing cycles) when, mesh stiffness value is affected larger by shearing；When turn
Angle (adds 0.533 times of bi-tooth gearing cycle to add one to first mesh cycle from a mesh cycle at [21.7 °, 26.5 °]
The bi-tooth gearing cycle) when, the impact by bending of mesh stiffness value is larger.
As seen from Figure 12, it is apparent due to there is impact of the crackle to tooth bending rigidity at tooth root.By scheming
13 as can be seen that tooth root crackle also has a certain impact to gear shearing rigidity.The crack depth different to three kinds, can be obvious
Find out that impact of the crackle to rigidity is increased with the increase of depth.Within a mesh cycle, when crack depth q is respectively
When 2mm, 4mm, 6mm, the meansigma methodss of shearing rigidity are respectively the 86.22% of the meansigma methodss of healthy gear shearing rigidity,
69.94%, 52.38%.It is last to consider bending simultaneously and shear the impact to mesh stiffness, obtain three kinds of different crack depths
Gear with Crack is as shown in figure 15 with normal gear synthesis time-variant mesh stiffness correlation curve.
4th, the calculating of broken teeth gear time-variant mesh stiffness
During gear tooth breakage, contact is lost in the position of broken teeth, as shown in figure 16.Original double-teeth toothing region is changed into monodentate and nibbles
Close.Therefore, only by monodentate to constituting, its computing formula is changed into total mesh stiffness：
Final broken teeth gear is as shown in figure 17 with the correlation curve of normal Gear Meshing Stiffness.Broken teeth gear is only monodentate pair
Engagement, mesh stiffness reduce two mesh cycles in broken teeth gear mean rigidity value be the one of normal gear mean rigidity value
Half left and right.
Comprehensive all of the above research contents, the present invention are based on energy method, right to study with standard straight spur geer
As systematically discussing the quantitative Analysis of mesh stiffness when single gear has peeling, crackle, three kinds of difference local defects of broken teeth.
But when multipair gear is engaged jointly, time-variant mesh stiffness is not the simple addition of single pair of Gear Meshing Stiffness, will also in practice
Distributed by wheel Transverse Load, and then also affected by profile error.
Claims (4)
1. a kind of time-varying characteristics quantitative calculation method of local defect Gear Meshing Stiffness, it is characterised in that：The realization of the method
Step is to set up Gear Meshing Stiffness computation model；Set up and peel off Gear Meshing Stiffness computation model；Set up Gear with Crack engagement
Rigidity Calculation model；Set up broken teeth Gear Meshing Stiffness computation model；The meter of one swing circle internal messing rigidity of failure gear
Calculate；When gear pair is acted on by engagement F, F can be decomposed into and gear teeth centerline parallel and two vertical power FaAnd Fb；Because of tooth
There is contact in wheel set, therefore have Hertzian contact stiffness；By power F parallel to gear teeth centrageaEffect, gear is present radially presses
Contracting, therefore there is radial compression rigidity；By perpendicular to gear teeth centrage FbEffect, because of FbIt is equal to shearing and relative in gear
The heart makes wheel body bear moment of flexure, therefore there is shearing rigidity and bending stiffness；Finally because of tooth force, there is elastic deformation, therefore exist
Wheel body deformation rigidity；The strain energy that will be stored in meshing gear centering is converted into a hertz energy Uh, flexional Ub, radial compression
Energy Ua, shear energy UsWith wheel body strain energy of distortion Uf, corresponding hertz rigidity k just can be calculated by preservation of energyh、
Bending stiffness kb, radial compression rigidity ka, shearing rigidity ksWith wheel body deformation rigidity kf；
For the foundation for peeling off Gear Meshing Stiffness computation model, when gear pair is acted on by engagement F, F is decomposed into and the gear teeth
Centerline parallel and two vertical power FaAnd Fb；By power F parallel to gear teeth centrageaEffect, gear is present radially presses
Contracting, because of FaIt is constant, therefore radial compression rigidity is constant；By perpendicular to gear teeth centrage FbEffect, because of FbIt is equal to and shears and relative
Wheel body is made to bear moment of flexure, F in gear centrebIt is constant, therefore shearing rigidity and bending stiffness are also constant；Finally because of tooth force, deposit
In elastic deformation, because overall stress F is constant, therefore it is also constant to there is wheel body deformation rigidity；Finally because of the contact line length of gear engagement
Degree changes, and hertz rigidity is relevant with contact line length, therefore the change of hertz rigidity is considered when having peeling, now normally
Hertz rigidity k during gearhHertz rigidity k for being changed into peeling off during gearhchip；Wherein, it is considered to peel off hole size along facewidth direction
Change and along flank engagement direction change when, khchipIt is with regard to peeling off hole size w respectivelysAnd αsFunction, wsTo peel off the length in hole
Degree, αsTo peel off the height in hole.
2. the time-varying characteristics quantitative calculation method of a kind of local defect Gear Meshing Stiffness according to claim 1, which is special
Levy and be：Contact surface area and component FaIt is unchanged, therefore hertz rigidity and radial compression rigidity are constant；Again overall stress F is not yet
Become, therefore the rigidity of wheel body deformation is also constant；The change of bending stiffness and shearing rigidity is considered when having crackle；The bending of normal gear
Rigidity is by kbWith shearing rigidity ksIt is changed into the bending k of Gear with Crack respectivelybcrackWith shearing rigidity kscrack；Now kbcrackWith
kscrackAll it is, with regard to crack depth q and crackle and the function of gear teeth centerlines v, finally to obtain Gear with Crack synthesis time-varying and nibble
Close rigidity.
3. the time-varying characteristics quantitative calculation method of a kind of local defect Gear Meshing Stiffness according to claim 1, which is special
Levy and be：Contact is lost in the position of gear tooth breakage, original double-teeth toothing region is changed into monodentate engagement；Comprehensive mesh stiffness only by
Monodentate can be calculated to composition, broken teeth Gear Meshing Stiffness.
4. the time-varying characteristics quantitative calculation method of a kind of local defect Gear Meshing Stiffness according to claim 1, which is special
Levy and be：If the failure gear teeth are first teeth of rotate counterclockwise on gear, when gear rotates a circle, gear pair has z1Individual engagement
Cycle, z1For the little gear number of teeth；[3, z1] individual mesh cycle mesh stiffness it is identical with normal gear；Engage at first and second
The size of failure gear tooth rigidity value in cycle, is obtained, the mesh stiffness in one swing circle of failure gear is thus obtained.
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| CN105181327B (en) * | 2015-08-26 | 2018-05-08 | 北京工业大学 | A kind of method of crackle gear teeth meshing Rigidity Calculation |
| CN105224744B (en) * | 2015-09-29 | 2018-03-16 | 西安交通大学 | A kind of method for peeling off gear engagement modeling based on mesh stiffness |
| CN108225762B (en) * | 2016-12-15 | 2019-09-20 | 唐智科技湖南发展有限公司 | A kind of single gear tooth crackle broken teeth fault identification diagnostic method |
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