CN109190227A - Based on the complicated tooth base Meshing Stiffness of Spur Gears calculation method of parsing-finite element - Google Patents
Based on the complicated tooth base Meshing Stiffness of Spur Gears calculation method of parsing-finite element Download PDFInfo
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Abstract
The invention proposes based on the complicated tooth base Meshing Stiffness of Spur Gears calculation method of parsing-finite element, it is intended to improve the computational efficiency of the Meshing Stiffness of Spur Gears containing complicated tooth base.Realize step are as follows: bending, shearing and radial compression rigidity based on the analytic calculation straight spur gear gear teeth；Calculate contact stiffness；Calculate monodentate mesh stiffness；Establish the finite element model of the straight spur gear pair containing complicated tooth base；Principal mass point is established with Mass21 unit at meshing point, and principal mass point is subjected to rigid coupling with corresponding tooth base portion minute；The gear teeth corresponding principal mass point in meshing state Combin14 unit is connected；Mesh stiffness when calculating.The present invention considers influence of the complicated tooth base containing web and lightening hole to Meshing Stiffness of Spur Gears, using parsing-Finite element arithmetic time-variant mesh stiffness of straight spur gear, computational efficiency is improved, can be used for the Dynamic Performance Analysis and optimization design of straight spur gear.
Description
Technical field
The invention belongs to gear precision drive technology and mechanical analysis field, it is related to based on the complicated tooth of parsing-finite element
Base Meshing Stiffness of Spur Gears calculation method can be used for the Dynamic Performance Analysis and optimization design of straight spur gear.
Background technique
It mainly include a variety of biographies such as Spur Gear Driving, Helical gear Transmission and Worm Wheel System in traditional gear system
Flowing mode, Spur Gear Driving therein can be further divided into spur gear transmission, spur bevel gear transmission and straight-tooth again
The forms such as face gear transmissions, and spur gear transmission be in transmission field with most commonly used driving form it
One, this drive mechanism not only has the features such as stable drive, shock and vibration and smaller noise, is also equipped with small in size, weight
Gently, transmitting torque is big, starts steady and transmission ratio is classified fine advantage, therefore is widely used in high-end numerical control equipment, automatic
Change the fields such as precision machinery and aerospace.
In recent years, high-end numerical control equipment just constantly developed towards high speed, high-precision and the direction of long-life, and to straight-tooth
More stringent requirements are proposed for the kinetic characteristics of this critical component of roller gear.And it is transmission that mesh stiffness, which periodically changes,
One of main exiting form of system, this mesh stiffness periodically change referred to as time-variant mesh stiffness, directly affect
The kinetic characteristics in transmission process.Time-variant mesh stiffness is mainly since the registration of straight spur gear is not generally whole
Number, i.e., it is in caused by cyclically-varying that straight spur gear simultaneously participates in the number of teeth of engagement at any time.In straight spur gear
In actual processing, in order to obtain good mechanical performance, the tooth base of straight spur gear is often processed to web knot with holes
Structure.Therefore accurately can solve this straight spur gear time-variant mesh stiffness containing complicated tooth base is research straight tooth column tooth
Drive train power characteristic is taken turns, the premise of Dynamic Performance Analysis and optimization design is carried out, so research contains complicated tooth base
The calculation method of straight spur gear time-variant mesh stiffness is necessary.
From the point of view of presently disclosed data, in the time-variant mesh stiffness side for calculating the straight spur gear containing complicated tooth base
Face mainly uses FInite Element to carry out simulation calculating.For example, entitled " the Dynamic that Abbes in 2010 is delivered at it
behaviour modelling of a flexible gear system by the elastic foundation
A kind of straight tooth column tooth for considering complicated tooth base is disclosed in the journal article of theory in presence of defects "
The dynamic analysis calculation method of wheel.This method is mainly that the method for using finite element simulation obtains the straight-tooth containing complicated tooth base
The dynamic response of roller gear.But this method needs to establish complete finite element model to simulate true situation, needs
Expend a large amount of computing resource, therefore the deficiency low there is computational efficiency.
Summary of the invention
It is an object of the invention to overcome the problems of the above-mentioned prior art, proposes and answered based on parsing-finite element
Miscellaneous tooth base Meshing Stiffness of Spur Gears calculation method, it is intended to improve the Meshing Stiffness of Spur Gears containing complicated tooth base
Computational efficiency and precision.
To achieve the goals above, the technical solution adopted by the present invention includes the following steps:
(1) it is based on analytic method, calculates separately straight spur gear gear tooth rigidity, including gear teeth bend stiffness kb, shearing
Rigidity value ksWith radial compression rigidity value ka；
(2) it is based on Hertzian contact theory, calculates the contact stiffness value k of the gear teethh；
(3) theoretical in series and parallel based on rigidity, monodentate is calculated to mesh stiffness value kt；
(4) it is established according to the straight spur gear geometric parameter containing complicated tooth base containing the several of complicated tooth base straight spur gear
What model, and it is based on Finite Element, mesh mapping division is carried out using Solid185 unit, forms the straight-tooth containing complicated tooth base
The finite element model of roller gear；
(5) according to gear mesh theory, rigid coupling regime is established；
(5.1) based on the mesh theory of straight spur gear, respectively in the meshing point position of driving gear and driven gear
Place establishes key point, and uses Mass21 dividing elements key point, forms principal mass point；
(5.2) corresponding relationship based on the gear teeth on principal mass point and complicated tooth base, using Mpc184 unit by principal mass point
Rigid coupling is carried out with corresponding tooth base portion point, forms rigid coupling regime；
(6) according to gear mesh theory, judge whether the corresponding gear teeth of principal mass point are in meshing state, if in engagement
State then connects the corresponding principal mass point of the gear teeth in meshing state with Combin14 unit, and by Combin14 unit
Rigidity value be set as k obtained in step (3)tValue；
(7) it is based on static analysis, calculates the mesh stiffness value k of the straight spur gear containing complicated tooth base；
(8) Rigidity Calculation for judging whether one mesh cycle of completion, if not completing the rigidimeter of a mesh cycle
It calculates, then straight spur gear rotates by a certain angle, and repeats step (1) to step (7), if completing the rigidity of a mesh cycle
It calculates, then stops calculating, obtain the time-variant mesh stiffness containing complicated tooth base straight spur gear.
Preferably as one kind of the invention, straight spur gear gear tooth rigidity is calculated separately described in step (1), including
Gear teeth bend stiffness kb, shearing rigidity value ksWith radial compression rigidity value ka, calculation expression is respectively as follows:
Wherein, kbFor the bending stiffness of the gear teeth, ksFor the shearing rigidity of the gear teeth, kaFor the radial compression rigidity of the gear teeth, E is
Elasticity modulus, G are modulus of shearing, For pressure angle of graduated circle, rbFor base radius, τc
=αc-(θb-invαc), For the pressure angle at contact point, θbFor the half of base tooth angle,For addendum coefficient, m is modulus, and γ and τ are limit of integration,
y1For the horizontal coordinate at any point on easement curve, y2For the horizontal coordinate at any point on involute, Iy1For easement curve
The cross sectional moment of inertia of upper any position, Iy2For the cross sectional moment of inertia of any position on involute, Ay1Take up an official post for easement curve
Area of section at meaning position, Ay2For the area of section of any position on involute.
Preferably as one kind of the invention, the contact stiffness value k of the gear teeth is calculated described in step (2)h, calculation expression
Formula are as follows:
Wherein, khContact stiffness between the gear teeth, E are elasticity modulus, and B is the width of slice, and v is the Poisson of slice
Than.
Preferably as one kind of the invention, calculating monodentate described in step (3) is to mesh stiffness kt, calculation expression
Are as follows:
Wherein, ktFor the mesh stiffness of monodentate pair, kb1For the bending stiffness of the driving wheel gear teeth, ks1For cutting for the driving wheel gear teeth
Cut rigidity, ka1For the radial compression rigidity of the driving wheel gear teeth, kb2For the bending stiffness of the driven wheel gear teeth, ks2For the driven wheel gear teeth
Shearing rigidity, ka2For the radial compression rigidity of the driven wheel gear teeth, khContact stiffness between the gear teeth.
Preferably as one kind of the invention, according to the straight spur gear geometry containing complicated tooth base described in step (4)
Parameter establishes the geometrical model containing complicated tooth base straight spur gear, specific establishment process are as follows:
Firstly, straight spur gear is reduced to a cylindrical body, the height of cylindrical body is equal to the tooth of straight spur gear
Width, the radius of cylindrical body are equal to the root radius of straight spur gear；Secondly, according to the parameter of straight spur gear, in circle
The modeling of web part is completed on cylinder；Finally, completing building for lightening hole on web according to the parameter of straight spur gear
Mould, to form the geometrical model of the straight spur gear containing complicated tooth base.
Preferably as one kind of the invention, straight spur gear of the calculating described in step (7) containing complicated tooth base is nibbled
Close rigidity value k, calculation expression are as follows:
Wherein, T is the torque for being applied to driving wheel central hole, rb1For driving wheel centre bore radius, Δ θ is in driving wheel
The deformation in heart hole.
Compared with the prior art, the invention has the following advantages:
The present invention calculates the straight tooth column tooth containing complicated tooth base in such a way that analytic method is combined with FInite Element
The time-variant mesh stiffness of wheel, and use Combin14 unit in the connection type of principal mass point and be attached, compared to existing
Some only calculates the time-variant mesh stiffness of the straight spur gear containing complicated tooth base by FInite Element, and the present invention is calculating
It is greatly improved in efficiency, is foreshortened to 2-3 minutes from original or so 10 hours.
Detailed description of the invention
Fig. 1 is implementation flow chart of the invention；
Fig. 2 is the schematic diagram of the straight spur gear stress of the embodiment of the present invention；
Fig. 3 is the schematic diagram of the straight tooth column tooth entity tooth based structures of the embodiment of the present invention；
Fig. 4 is the schematic diagram that the straight tooth column tooth of the embodiment of the present invention contains only the tooth based structures of web；
Fig. 5 is the schematic diagram for the complicated tooth base that the straight tooth column tooth of the embodiment of the present invention contains web and web hole；
Fig. 6 is the schematic diagram of the straight spur gear finite element model containing complicated tooth base of the embodiment of the present invention；
Fig. 7 is schematic diagram of the tooth to active line of the embodiment of the present invention；
Fig. 8 is the time-variant mesh stiffness comparative result figure of the embodiment of the present invention.
Specific embodiment
With reference to the accompanying drawing, and for the straight cylindrical gear design parameters shown in the table 1, the present invention is made further detailed
It describes in detail bright.
Table 1
With reference to Fig. 1, based on the complicated tooth base Meshing Stiffness of Spur Gears calculation method of parsing-finite element, including such as
Lower step:
Step 1) is based on analytic method, calculates separately straight spur gear gear tooth rigidity, including gear teeth bend stiffness kb, cut
Cut rigidity value ksWith radial compression rigidity value ka；
With reference to Fig. 2, the schematic diagram of a tooth is given, by engagement force FtOrthogonal Decomposition is carried out, the axial direction on the gear teeth is obtained
Power FtaWith radial force Ftb, whereinFor the pressure angle at contact point, rbFor base radius, CD sections are negotiating curved sections, and BC is
Involute curve part.
Since function and effect of the power to driving gear with driven gear are identical, therefore one of gear is only taken to be divided
Analysis, with reference to Fig. 2, radial force FtbBending and shear action, axial force F can be generated to the gear teethtaRadial compression can be generated to the gear teeth to make
With, utilize " mechanics of materials " in ENERGY METHOD, calculate the corresponding bend stiffness k of the gear teethb, shearing rigidity value ksWith radial pressure
Contracting rigidity value ka, specific formula for calculation expression formula are as follows:
Wherein, kbFor the bending stiffness of the gear teeth, ksFor the shearing rigidity of the gear teeth, kaFor the radial compression rigidity of the gear teeth, E is
Elasticity modulus, G are modulus of shearing, For pressure angle of graduated circle, rbFor base radius, τc
=αc-(θb-invαc), For the pressure angle at contact point, θbFor the half of base tooth angle,For addendum coefficient, m is modulus, and γ and τ are limit of integration,
y1For the horizontal coordinate at any point on easement curve, y2For the horizontal coordinate at any point on involute, Iy1For easement curve
The cross sectional moment of inertia of upper any position, Iy2For the cross sectional moment of inertia of any position on involute, Ay1Take up an official post for easement curve
Area of section at meaning position, Ay2For the area of section of any position on involute.
Step 2) is based on Hertzian contact theory, calculates the contact stiffness value k of the gear teethh；
It is contacted since active straight spur gear exists in transmission process each other with driven straight spur gear, because
There are contact stiffness for this, are calculated using Hertz formula and energy method, the expression formula of contact stiffness are as follows:
Wherein, khContact stiffness between the gear teeth, E are elasticity modulus, and B is the width of slice, and v is the Poisson of slice
Than.
Step 3) is theoretical in series and parallel based on rigidity, calculates monodentate to mesh stiffness value kt；
When calculating the mesh stiffness of monodentate pair, need to calculate separately the bending stiffness k of the driving gear gear teethb1, shearing it is rigid
Spend ks1, radial compression rigidity ka1With the bending stiffness k of the driven gear gear teethb2, shearing rigidity ks2, radial compression rigidity ka2And
Contact stiffness k between the gear teethh, so the mesh stiffness k of monodentate pairtIt is rigidity by the driving gear gear teeth, the driven gear gear teeth
Rigidity and the gear teeth between contact stiffness khIn series, according to the series-parallel relationship of rigidity, the engagement for obtaining monodentate pair is rigid
Angle value kt, calculation expression are as follows:
Wherein, ktFor the mesh stiffness of monodentate pair, kb1For the bending stiffness of the driving wheel gear teeth, ks1For cutting for the driving wheel gear teeth
Cut rigidity, ka1For the radial compression rigidity of the driving wheel gear teeth, kb2For the bending stiffness of the driven wheel gear teeth, ks2For the driven wheel gear teeth
Shearing rigidity, ka2For the radial compression rigidity of the driven wheel gear teeth, khContact stiffness between the gear teeth.
Step 4) is established according to the straight spur gear geometric parameter containing complicated tooth base containing complicated tooth base straight spur gear
Geometrical model, and be based on Finite Element, using in ANSYS software Solid185 unit carry out mesh mapping division, shape
At the finite element model of the straight spur gear containing complicated tooth base；
Referring to figs. 3 to Fig. 5, common gear matrix mainly has 3 kinds of structures, Fig. 3 presentation-entity tooth base, Fig. 4 indicate containing only
Have a tooth base of web, Fig. 5 indicate the complicated tooth base containing web and web hole and the present invention towards the case where.With reference to Fig. 6,
Straight spur gear is reduced to a cylindrical body, the height of cylindrical body is equal to the facewidth of straight spur gear, and the half of cylindrical body
Diameter is equal to the root radius of straight spur gear, and according to the parameter of straight spur gear, completes web portion on the cylinder
Point modeling and on web complete lightening hole modeling, thus formed the straight spur gear containing complicated tooth base geometry mould
Type, and mesh mapping division is carried out using Solid185 unit, the elasticity modulus for being provided with unit is 2.1 × 1011Pa, Poisson
Than being 0.3.
Step 5) establishes rigid coupling regime according to gear mesh theory；
Mesh theory of the step 5.1) based on straight spur gear, respectively in the engagement point of driving gear and driven gear
The place of setting establishes key point, and uses Mass21 dividing elements key point, forms principal mass point；
The engagement point of driving gear and driven gear is calculated according to the mesh theory of straight spur gear with reference to Fig. 6
It sets, and establishes key point respectively at position, and using the 21 dividing elements key point of Mass in ANSYS software, form parenchyma
Amount point.
Corresponding relationship of the step 5.2) based on the gear teeth on principal mass point and complicated tooth base, using Mpc184 unit by principal mass
Point carries out rigid coupling with corresponding tooth base portion minute, forms rigid coupling regime；
With reference to Fig. 6, using the Mpc184 unit in ANSYS software, the principal mass point and step that will be established in step 5.1)
4) node of corresponding teeth base portion point is attached in the complicated tooth basic mode type established in, rigid coupling regime is formed, to simulate
The gear tooth portions of straight spur gear.
Step 6) judges whether the corresponding gear teeth of principal mass point are in meshing state according to gear mesh theory, if being in
Meshing state then connects Combin14 unit of the gear teeth corresponding principal mass point in meshing state in ANSYS software,
And k obtained in step 3) is set by the rigidity value of the Combin14 unit in ANSYS softwaretValue；
First determine whether the principal mass point established in step 5.1) is in engagement shape according to mesh theory with reference to Fig. 7
State, N1N2For theory activity line, B1B2For actual activity line, C1C2For the principal mass point of foundation.N1C1And N2C2It calculates as follows:
Wherein, mod function is mod, z1For the parameter of driving gear, Ω1T is the rotation angle of driving gear,rb1For the driving wheel center pore radius of driving gear.
If principal mass point is in meshing state, with reference to Fig. 6, using the Combin14 unit in ANSYS software by driving tooth
Corresponding principal mass point is attached on wheel and driven gear, and the rigidity value of the Combin14 unit in ANSYS software is set
It is set to k obtained in step 3)tValue；
Step 7) is based on static analysis, calculates the time-variant mesh stiffness value k of straight spur gear.
With reference to Fig. 6, model is applied and is constrained, applies torque T in driving gear central hole first；Secondly in driving gear
Principal mass point is established at center, and the principal mass point and driving gear inner hole is carried out Degree-of-freedom Coupling, while constraining the principal mass
Point is except remaining freedom degree around own axis；Then principal mass point is established at driven gear center using identical method,
And the inner hole of the principal mass point and driven gear is subjected to Degree-of-freedom Coupling, while constraining whole freedom degrees of the principal mass point；
Finally model is calculated using the static analysis of ANSYS, obtains the deformation result of model, by extracting driving gear center
Principal mass point around the rotational deformation amount Δ θ of axis, obtain the time-variant mesh stiffness value k of straight spur gear, calculation expression
Formula are as follows:
Wherein, T is the torque for being applied to driving wheel central hole, rb1For driving wheel centre bore radius, Δ θ is in driving wheel
The deformation in heart hole.
Step 8) judges whether to complete the Rigidity Calculation of a mesh cycle, if not completing the rigidity of a mesh cycle
It calculates, then straight spur gear rotates by a certain angle, and repeats step 1) to step 7), if completing the rigidity of a mesh cycle
It calculates, then stops calculating, obtain the time-variant mesh stiffness containing complicated tooth base straight spur gear.
It based on above-mentioned steps, is calculated in conjunction with the design parameter of the embodiment of the present invention, with reference to Fig. 8, solid line is indicated in figure
The straight spur gear time-variant mesh stiffness curve being calculated according to the method for the invention, dotted line are indicated only with finite element
The straight spur gear time-variant mesh stiffness curve that method is simulated, obtains the time-variant mesh stiffness of the embodiment of the present invention
Maximum relative error is 2.03%, and calculates the time and by the 10h or so of conventional method foreshorten to 2-3min, compared to only with having
The prior art of first method simulation is limited, computational efficiency is largely increased.
Claims (6)
1. based on the complicated tooth base Meshing Stiffness of Spur Gears calculation method of parsing-finite element, which is characterized in that including such as
Lower step:
(1) it is based on analytic method, calculates separately straight spur gear gear tooth rigidity, including gear teeth bend stiffness kb, shearing rigidity value
ksWith radial compression rigidity value ka；
(2) it is based on Hertzian contact theory, calculates the contact stiffness value k of the gear teethh；
(3) theoretical in series and parallel based on rigidity, monodentate is calculated to mesh stiffness value kt；
(4) the geometry mould containing complicated tooth base straight spur gear is established according to the straight spur gear geometric parameter containing complicated tooth base
Type, and it is based on Finite Element, mesh mapping division is carried out using Solid185 unit, forms the straight tooth column containing complicated tooth base
The finite element model of gear；
(5) according to gear mesh theory, rigid coupling regime: the mesh theory based on straight spur gear is established, respectively in master
Key point is established at the meshing point position of moving gear and driven gear, and uses Mass21 dividing elements key point, forms parenchyma
Amount point；Based on the corresponding relationship of the gear teeth on principal mass point and complicated tooth base, using Mpc184 unit by principal mass point with it is corresponding
Tooth base portion point carries out rigid coupling, forms rigid coupling regime；
(6) according to gear mesh theory, judge whether the corresponding gear teeth of principal mass point are in meshing state, if in engagement shape
State then connects the corresponding principal mass point of the gear teeth in meshing state with Combin14 unit, and by Combin14 unit
Rigidity value is set as k obtained in step (3)tValue；
(7) it is based on static analysis, calculates the mesh stiffness value k of the straight spur gear containing complicated tooth base；
(8) Rigidity Calculation for judging whether one mesh cycle of completion, if not completing the Rigidity Calculation of a mesh cycle,
Straight spur gear rotates by a certain angle, and repeats step (1) to step (7), if completing the Rigidity Calculation of a mesh cycle,
Then stop calculating, obtains the time-variant mesh stiffness containing complicated tooth base straight spur gear.
2. according to claim 1 based on the complicated tooth base Meshing Stiffness of Spur Gears calculating side of parsing-finite element
Method, it is characterised in that: straight spur gear gear tooth rigidity, including gear teeth bend stiffness are calculated separately described in step (1)
kb, shearing rigidity value ksWith radial compression rigidity value ka, calculation expression is respectively as follows:
Wherein, kbFor the bending stiffness of the gear teeth, ksFor the shearing rigidity of the gear teeth, kaFor the radial compression rigidity of the gear teeth, E is elasticity
Modulus, G are modulus of shearing, For pressure angle of graduated circle, rbFor base radius, τc=
αc-(θb-invαc),
For the pressure angle at contact point, θbFor the half of base tooth angle,For addendum coefficient, m is modulus, and γ and τ are limit of integration, y1
For the horizontal coordinate at any point on easement curve, y2For the horizontal coordinate at any point on involute,For on easement curve
The cross sectional moment of inertia of any position,For the cross sectional moment of inertia of any position on involute,It is any on easement curve
Area of section at position,For the area of section of any position on involute.
3. according to claim 1 based on the complicated tooth base Meshing Stiffness of Spur Gears calculating side of parsing-finite element
Method, it is characterised in that: the contact stiffness value k of the gear teeth is calculated described in step (2)h, calculation expression are as follows:
Wherein, khContact stiffness between the gear teeth, E are elasticity modulus, and B is the width of slice, and v is the Poisson's ratio of slice.
4. according to claim 1 based on the complicated tooth base Meshing Stiffness of Spur Gears calculating side of parsing-finite element
Method, it is characterised in that: calculating monodentate described in step (3) is to mesh stiffness kt, calculation expression are as follows:
Wherein, ktFor the mesh stiffness of monodentate pair, kb1For the bending stiffness of the driving wheel gear teeth, ks1Shearing for the driving wheel gear teeth is rigid
Degree, ka1For the radial compression rigidity of the driving wheel gear teeth, kb2For the bending stiffness of the driven wheel gear teeth, ks2For cutting for the driven wheel gear teeth
Cut rigidity, ka2For the radial compression rigidity of the driven wheel gear teeth, khContact stiffness between the gear teeth.
5. according to claim 1 based on the complicated tooth base Meshing Stiffness of Spur Gears calculating side of parsing-finite element
Method, it is characterised in that: established according to the straight spur gear geometric parameter containing complicated tooth base containing complicated tooth described in step (4)
The geometrical model of base straight spur gear, specific establishment process are as follows:
Firstly, straight spur gear is reduced to a cylindrical body, the height of cylindrical body is equal to the facewidth of straight spur gear, circle
The radius of cylinder is equal to the root radius of straight spur gear；Secondly, according to the parameter of straight spur gear, on the cylinder
Complete the modeling of web part；Finally, the modeling of lightening hole is completed on web according to the parameter of straight spur gear, thus
Form the geometrical model of the straight spur gear containing complicated tooth base.
6. according to claim 1 based on the complicated tooth base Meshing Stiffness of Spur Gears calculating side of parsing-finite element
Method, it is characterised in that: the mesh stiffness value k of straight spur gear of the calculating described in step (7) containing complicated tooth base is calculated
Expression formula are as follows:
Wherein, T is the torque for being applied to driving wheel central hole, rb1For driving wheel centre bore radius, Δ θ is driving wheel centre bore
Deformation.
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110334460A (en) * | 2019-07-11 | 2019-10-15 | 西北工业大学 | Roller gear mesh stiffness calculation method |
| CN111079300A (en) * | 2019-12-23 | 2020-04-28 | 西安电子科技大学 | Straight gear meshing rigidity calculation method considering tooth direction error |
| CN111396507A (en) * | 2020-04-24 | 2020-07-10 | 芜湖蓓慈电器有限公司 | Design method of worm and helical gear transmission pair |
| CN111783258A (en) * | 2020-07-29 | 2020-10-16 | 江苏省金象传动设备股份有限公司 | Estimation method for inherent characteristics and pitch diameter vibration of thin rim gear system |
| CN112434432A (en) * | 2020-11-27 | 2021-03-02 | 西安交通大学 | Modeling method for meshing stiffness under external meshing straight gear abrasion |
| CN114689313A (en) * | 2021-11-26 | 2022-07-01 | 哈尔滨理工大学 | On-line detection device for gear meshing stiffness of nine-gear automatic transmission and multi-signal fusion detection method |
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| CN112434432B (en) * | 2020-11-27 | 2024-04-05 | 西安交通大学 | Modeling method for engagement rigidity of externally engaged spur gear under abrasion |
| CN114689313A (en) * | 2021-11-26 | 2022-07-01 | 哈尔滨理工大学 | On-line detection device for gear meshing stiffness of nine-gear automatic transmission and multi-signal fusion detection method |
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