CN107391876A - Helical gear pair time-variant mesh stiffness computational methods - Google Patents
Helical gear pair time-variant mesh stiffness computational methods Download PDFInfo
- Publication number
- CN107391876A CN107391876A CN201710687624.9A CN201710687624A CN107391876A CN 107391876 A CN107391876 A CN 107391876A CN 201710687624 A CN201710687624 A CN 201710687624A CN 107391876 A CN107391876 A CN 107391876A
- Authority
- CN
- China
- Prior art keywords
- mrow
- msub
- engagement
- spur gear
- plate sheet
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Geometry (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- Computer Hardware Design (AREA)
- General Engineering & Computer Science (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Computational Mathematics (AREA)
- Gears, Cams (AREA)
Abstract
The invention belongs to mechanical kinetics technical field, and in particular to helical gear pair time-variant mesh stiffness computational methods.Helical gear pair time-variant mesh stiffness computational methods comprise the following steps：Step S1：Obtain the basic parameter of helical gear pair；Step S2：Along facewidth Directional Decomposition it is N number of independent and uniform thin slice spur gear pair by the wheel tooth model of helical gear pair；Step S3：Determine whether N number of thin slice spur gear participates in engaging in position of engagement j；Step S4：Calculate the time-variant mesh stiffness of each plate sheet spur gear；Step S5：The time-variant mesh stiffness of each plate sheet spur gear is summed, obtains the time-variant mesh stiffness of helical gear pair.Helical gear pair time-variant mesh stiffness computational methods, which consider nonlinear contact, amendment MATRIX STIFFNESS and extend engagement, to be influenceed, and is improved analytic modell analytical model, is improved computational accuracy.
Description
Technical field
The invention belongs to mechanical kinetics technical field, and in particular to helical gear pair time-variant mesh stiffness computational methods.
Background technology
Gear drive is a kind of type of belt drive that mechanical transmission fields are most widely used, this to be widely applied not only
Due to its own transmission precisely, efficiency high, reliable operation, long lifespan the advantages that, also have benefited from gear drive possess it is a set of more
The complete international standard and development of gear transmission technology has reached certain level.
In mechanical field it is indispensable just because of gear drive, attracts increasing domestic and foreign scholars and throw
The gear-driven research of body, it is directed to promoting the development of gear technique.
With the development of gear research with progressive, it is necessary to the practical problem of solution also becomes increasingly complex, gear power transmission
How to improve precision, efficiency, bearing capacity, how vibration and noise reducing, how selection etc. is all urgent problem to be solved.Research direction
Also helical gear progressively is deep into from spur gear, from the research of healthy gear to the research of failure gear, some gear defects (such as flank profils
Error, Shaft misalignment etc.) it is also required to be taken into account.
Although research at present has certain basis, the needs of engineering practice, such as tooth profile error can't be fully met
Influences of factor engagement secondary to actual gear is also studied not deep enough, needs more deep theory in Practical Project is put into practice
Carry out design, reduce the proportion of goods damageds.
Gear time-variant mesh stiffness is the basis for studying gear pair meshing characteristic, gear time-variant mesh stiffness modeling method
Development and the important indicator for weighing gear drive research.
With the gradual perfection of modeling method, substantial amounts of scholar be also dedicated to gear modeling method being generalized to it can be considered that
Factor in more actual engagement situations, such as matrix correction, extends engagement, load distribution, nonlinear contact.
Gear time-variant mesh stiffness has very big influence to gear train vibratory response, how to calculate time-variant mesh stiffness
It is the important process of gear research.
At present, helical gear pair time-variant mesh stiffness, which calculates, mainly several ways：It is empirical formula method, analytic method, limited
First (FE) method and parsing-finite element method.Although empirical formula method calculating is simple and convenient, its computational accuracy is inadequate, can use
In rough calculation.Limitation be present for research profile modifying gear pair in existing analytic method, this limitation be presented as do not account for it is non-
Linear contact, amendment MATRIX STIFFNESS and extension engagement influence.The result of calculation of finite element method and parsing-finite element method more connects
The true engagement process of nearly gear pair, but it the is present shortcoming such as modeling process is more complicated, computational efficiency is low.
The content of the invention
(1) technical problems to be solved
In order to solve the above mentioned problem of prior art, the present invention provides helical gear pair time-variant mesh stiffness computational methods, uses
To solve limitation existing for existing analytic calculation helical gear pair time-variant mesh stiffness, this limitation, which is presented as, not to be accounted for
Nonlinear contact, amendment MATRIX STIFFNESS and extension engagement influence.
(2) technical scheme
In order to achieve the above object, the main technical schemes that the present invention uses include：
Helical gear pair time-variant mesh stiffness computational methods provided by the invention, comprise the following steps：
Step S1：Obtain the basic parameter of helical gear pair；
Step S2：Along facewidth Directional Decomposition it is N number of independent and uniform thin slice spur gear by the wheel tooth model of helical gear pair
It is secondary；
Step S3：Determine whether N number of thin slice spur gear participates in engaging in position of engagement j；
Step S4：Consider nonlinear contact, amendment MATRIX STIFFNESS and extend the gear pair meshing characteristic analysis that engagement influences
Method calculates the time-variant mesh stiffness of each plate sheet spur gear；
Step S5：The time-variant mesh stiffness of each plate sheet spur gear is summed, the time-varying engagement for obtaining helical gear pair is firm
Degree.
Further, step S3 comprises the following steps：
Step S31：Determine the maximum engagement angle α of helical gear pair at the j of the position of engagementmaxWith Minimum Operating Pressure Angle αmin；
Step S32：Determine pressure angle (α of the n-th plate sheet spur gear at the j of the position of engagementn)j；
Step S33：Judge whether the n-th plate sheet spur gear participates in engaging.
Further, in step S31：
The maximum engagement angle α of helical gear pair at the j of the position of engagementmaxCalculation formula it is as follows：
The Minimum Operating Pressure Angle α of helical gear pair at the j of the position of engagementminCalculation formula it is as follows：
In formula, rb1For driving wheel base radius；rb2For driven pulley base radius；α0For pressure angle；ra1For driving wheel tooth top
Radius of circle；αa2For pressure angle corresponding to driven pulley tooth top meshing point.
Further, in step s 32：
Pressure angle (α of the n-th plate sheet spur gear at the j of the position of engagementn)jCalculation formula it is as follows：
In formula, (αn)jFor pressure angle of the n-th plate sheet spur gear at the j of the position of engagement；Represent the n-th plate sheet straight-tooth
Take turns intermeshing pressure angle of the driving wheel of i-th pair rodent population at the j of the position of engagement；θb1For the half of driving wheel base tooth angle.
Further, in step S33：
Mesh stiffness judgment expression of the n-th plate sheet spur gear at the j of the position of engagement is as follows：
In formula, (kn)jRepresent time-variant mesh stiffness of the n-th plate sheet spur gear at the j of the position of engagement.
Further, in step s 4：
Time-variant mesh stiffness (k of the n-th plate sheet spur gear at the j of the position of engagementn)jSpecific formula for calculation it is as follows：
In formula,For the revised driving wheel MATRIX STIFFNESS at the j of the position of engagement；For in position of engagement j
Locate revised driven pulley MATRIX STIFFNESS；For the MATRIX STIFFNESS of the n-th plate sheet spur gear driving wheel,It is straight for the n-th plate sheet
The MATRIX STIFFNESS of gear driven wheel；λ1For the matrix correction coefficient of each plate sheet spur gear driving wheel；λ2It is straight for each plate sheet
The matrix correction coefficient of gear driven wheel；Represent all gear teeth pair of the n-th plate sheet spur gear at the j of the position of engagement
Gear tooth rigidity.
Further, in step s 4：
The gear tooth rigidity of all gear teeth pair of the n-th plate sheet spur gear at the j of the position of engagementCalculation formula such as
Under：
Wherein,
In formula, m represents ingear tooth logarithm simultaneously；Represent the gear tooth rigidity of i-th pair engaging tooth；For
Hertzian contact stiffness of the n plate sheet spur gear pair i-th pair engaging tooths at the j of the position of engagement；For the n-th plate sheet spur gear pair
The gear tooth rigidity of driving wheel at the j of the position of engagement；For driven pulley of the n-th plate sheet spur gear pair at the j of the position of engagement
Gear tooth rigidity；EeFor effective modulus of elasticity；L is the facewidth；It is that the n-th plate sheet spur gear i-th pair gear pair is engaging position
Put the engagement force at j；F is total engagement force；For load of the n-th plate sheet spur gear i-th pair gear at the j of the position of engagement
Distribution coefficient.
Further, in step s 4：
Weight distribution factor (lsr of the n-th plate sheet spur gear i-th pair gear at the j of the position of engagementi n)jCalculation formula
It is as follows：
Wherein,
In formula, LsfiFor the i-th pair gear teeth weight distribution factor of n-th spur gear；LsfjPosition is engaged for n-th spur gear
Put weight distribution factor at j；For total gear tooth rigidity of the n-th plate sheet spur gear；For total gear teeth of N plate gears
Rigidity.
Further, in step s 5：
Helical gear pair time-variant mesh stiffness KjCalculation formula it is as follows：
In formula, KjIt is time-variant mesh stiffness of the helical gear pair at the j of the position of engagement；N represents the sum of thin slice.
(3) beneficial effect
The beneficial effects of the invention are as follows：
The helical gear pair time-variant mesh stiffness computational methods of the present invention, first by the wheel tooth model of helical gear pair along facewidth side
To N number of independent and uniform thin slice spur gear pair is decomposed into, secondly determine whether N number of thin slice spur gear participates in position of engagement j
Engagement, then consider nonlinear contact, amendment MATRIX STIFFNESS and extend the time-varying for engaging and influenceing to calculate each plate sheet spur gear
Mesh stiffness, finally the time-variant mesh stiffness of each plate sheet spur gear is summed, obtains the time-variant mesh stiffness of helical gear pair；
The helical gear pair time-variant mesh stiffness computational methods of the present invention, it is firm due to considering nonlinear contact, amendment matrix
Degree and extension engagement influence, to calculate the time-variant mesh stiffness of each plate sheet spur gear, to improve each thin slice spur gear
Computational accuracy, and then the computational accuracy of the time-variant mesh stiffness of helical gear pair is improved.
To sum up, it is firm to consider nonlinear contact, amendment matrix to helical gear pair time-variant mesh stiffness computational methods of the invention
Degree and extension engagement influence, and improve analytic modell analytical model, improve computational accuracy.
Brief description of the drawings
Fig. 1 is embodiment helical gear pair time-variant mesh stiffness computational methods flow chart；
Fig. 2 is embodiment helical gear section schematic diagram；
Fig. 3 is embodiment driving wheel tooth matching angle schematic diagram；
Fig. 4 is the helical gear pair time-variant mesh stiffness figure that different calculation methods obtain when helical angle is 12 ° in embodiment one；
Fig. 5 is the helical gear pair time-variant mesh stiffness figure that different calculation methods obtain when helical angle is 16 ° in embodiment one；
Fig. 6 is the helical gear pair time-variant mesh stiffness figure that different calculation methods obtain when helical angle is 20 ° in embodiment one；
Fig. 7 is the helical gear pair time-variant mesh stiffness figure that different calculation methods obtain when helical angle is 24 ° in embodiment one；
Fig. 8 is the helical angle of embodiment two and registration graph of a relation；
Fig. 9 is that the helical angle of embodiment two fluctuates graph of a relation with mesh stiffness；
Figure 10 is helical gear pair time-variant mesh stiffness figure when the facewidth is 10mm and 15mm in embodiment three；
Figure 11 is helical gear pair time-variant mesh stiffness figure when the facewidth is to 20mm and 25mm in embodiment three；
Figure 12 is the example IV facewidth and registration graph of a relation；
Figure 13 is that the example IV facewidth fluctuates graph of a relation with mesh stiffness；
Figure 14 is helical gear pair time-variant mesh stiffness figure under five different modification coefficients of embodiment；
Figure 15 is the modification coefficient of embodiment six and registration graph of a relation；
Figure 16 is the modification coefficient of embodiment six and mesh stiffness graph of a relation；
Figure 17 is the time-variant mesh stiffness figure under the different coefficients of friction of embodiment seven.
Embodiment
In order to preferably explain the present invention, in order to understand, below in conjunction with the accompanying drawings, by embodiment, to this hair
It is bright to be described in detail.
The helical gear pair time-variant mesh stiffness computational methods of the present invention, helical gear model is separated into uniformly along facewidth direction
Thin slice spur gear, by calculating thin slice spur gear time-variant mesh stiffness, and firm by being engaged per a piece of thin slice spur gear time-varying
Degree summation, it is established that helical gear time-variant mesh stiffness solving model, and then pass through the model solution helical gear time-variant mesh stiffness.
Referring to figs. 1 to Fig. 3, helical gear pair time-variant mesh stiffness computational methods, comprise the following steps：
Step S1：Obtain the basic parameter of helical gear pair.
The basic parameter of helical gear pair in the step S1 of the present invention includes：The number of teeth, modulus of elasticity, Poisson's ratio, endoporus half
Footpath, modulus, the facewidth, pressure angle, helical angle, addendum coefficient and tip clearance coefficient.
Step S2：Along facewidth Directional Decomposition it is N number of independent and uniform thin slice spur gear by the wheel tooth model of helical gear pair,
As shown in Figure 2.
Step S3：Determine whether N number of thin slice spur gear participates in engaging in position of engagement j.
Step S31：Shown in reference picture 3, the maximum engagement angle α of helical gear pair at the j of the position of engagement is determinedmaxEngaged with minimum
Angle αmin, specific formula for calculation is as follows：
Wherein, NA=NP-AP=rb1·tanα0-rb2·(tanαa2-tanα0)
r1=mz1/cosβ
r2=mz2/cosβ
rb1=r1cosα0
rb2=r2cosα0
ra1=r1+ham
ra2=r2+ham
αa2=arccos (rb2/ra2)
In formula, r1For the reference radius of driving wheel；r2For the reference radius of driven pulley；M is modulus；z1For driving wheel
The number of teeth；z2For the number of teeth of driven pulley；β is oblique gear spiral angle；rb1For driving wheel base radius；rb2For driven pulley basic circle half
Footpath；α0For pressure angle；ra1For driving wheel radius of addendum；ra2For driven pulley radius of addendum；haFor height of teeth top；αa2For driven pulley
Pressure angle corresponding to tooth top meshing point.
Step S32：Determine pressure angle (α of the n-th plate sheet spur gear at the j of the position of engagementn)j；
In formula, (αn)jFor pressure angle of the n-th plate sheet spur gear at the j of the position of engagement；Represent the n-th plate sheet straight-tooth
Take turns intermeshing pressure angle of the driving wheel of i-th pair rodent population at the j of the position of engagement；θb1For the half of driving wheel base tooth angle.
Wherein, θb1=π/(2z1)+invαt
In formula, αtFor transverse pressure angle；invαtFor infolute function.
Wherein, intermeshing pressure angle of the driving wheel of the n-th plate sheet spur gear i-th pair rodent population at the j of the position of engagementTried to achieve by equation below：
βb1=arctan (rb1tanβ/r1)
In formula,It is minimum roll angle；N is the n-th plate sheet spur gear；Nibbled for the n-th plate sheet spur gear i-th pair
The gear centre of tooth pair and center o' distance (as shown in Figure 2) are closed, its span size is L；βb1For driving wheel
Base spiral angle；L is the facewidth.
Step S33：Judge whether the n-th plate sheet spur gear participates in engaging；
If αmin≤(αn)j≤αmax, then the n-th plate sheet spur gear participation engagement, if (αn)j＜ αminOr (αn)j＞ αmax,
Then the n-th plate sheet spur gear is not involved in engaging, and specifically, mesh stiffness of the n-th plate sheet spur gear at the j of the position of engagement judges
Expression formula is as follows：
Step S4：Calculate the time-variant mesh stiffness of each plate sheet spur gear.
In the present invention, the thin slice spur gear time-variant mesh stiffness for having neither part nor lot in engagement is zero, and participates in the thin slice straight-tooth of engagement
Time-variant mesh stiffness (the k of wheeln)jIt is not zero.
Specifically, the time-variant mesh stiffness for participating in the thin slice spur gear of engagement is repaiied using consideration nonlinear contact, finite element
The gear pair meshing characteristic analysis method that matrix rigidity, extension engagement influence is tried to achieve.
More specifically, in the present invention, before calculating each plate sheet spur gear time-variant mesh stiffness, it is thus necessary to determine that each
Plate sheet spur gear is based on finite element method in bi-tooth gearing and the matrix correction coefficient lambda of three tooth engagement processesi, it is specific to calculate public affairs
Formula is as follows：
λi=1+rkfi
rkfi=(kfAi-kfBi) × 100%/kfBi
In formula, i value is 1 and 2, i.e. λiFor λ1And λ2, λ1For the matrix correction system of each plate sheet spur gear driving wheel
Number；λ2For the matrix correction coefficient of each plate sheet spur gear driven pulley；rkfiFor bi-tooth gearing when MATRIX STIFFNESS relative to monodentate
The variable quantity of MATRIX STIFFNESS during engagement；kfAiThe bidentate area mesh stiffness for being the n-th plate sheet spur gear at the j of the position of engagement；kfBi
The monodentate area mesh stiffness for being the n-th plate sheet spur gear at the j of the position of engagement.
More specifically, time-variant mesh stiffness (k of the n-th plate sheet spur gear at the j of the position of engagementn)jSpecific formula for calculation
It is as follows：
In formula, (kn)jRepresent time-variant mesh stiffness of the n-th plate sheet spur gear at the j of the position of engagement；To nibble
Close revised driving wheel MATRIX STIFFNESS at the j of position；For the revised driven pulley MATRIX STIFFNESS at the j of the position of engagement；For the MATRIX STIFFNESS of the n-th plate sheet spur gear driving wheel,For the MATRIX STIFFNESS of the n-th plate sheet spur gear driven pulley；λ1For
The matrix correction coefficient of each plate sheet spur gear driving wheel；λ2For the matrix correction system of each plate sheet spur gear driven pulley
Number；Represent the gear tooth rigidity of all gear teeth pair of the n-th plate sheet spur gear at the j of the position of engagement.
Wherein,Calculation formula it is as follows：
In formula, m represents ingear tooth logarithm simultaneously；Represent the gear tooth rigidity of i-th pair engaging tooth；For
Hertzian contact stiffness of the n plate sheet spur gear pair i-th pair engaging tooths at the j of the position of engagement；For the n-th plate sheet spur gear pair
The gear tooth rigidity of driving wheel at the j of the position of engagement；For driven pulley of the n-th plate sheet spur gear pair at the j of the position of engagement
Gear tooth rigidity；EeFor effective modulus of elasticity；For the n-th plate sheet spur gear i-th pair gear pair nibbling at the j of the position of engagement
With joint efforts；For the gear teeth bending stiffness of driving wheel of the n-th plate sheet spur gear at the j of the position of engagement；It is thin for n-th
The gear teeth shearing rigidity of driving wheel of the piece spur gear at the j of the position of engagement；It is the n-th plate sheet spur gear in position of engagement j
The driving wheel at place is compressed axially rigidity；The gear teeth for driven pulley of the n-th plate sheet spur gear at the j of the position of engagement are curved
Stiffness；For the gear teeth shearing rigidity of driven pulley of the n-th plate sheet spur gear at the j of the position of engagement；For n-th
Driven pulley of the thin slice spur gear at the j of the position of engagement is compressed axially rigidity.
More specifically, be wide tooth (plane strain) or narrow tooth (plane stress) according to the gear teeth, effective modulus of elasticity EeMeter
It is as follows to calculate formula：
R=L/HP
HP=π m/2
In formula, E is modulus of elasticity；ν is Poisson's ratio；Flakiness ratio R is used to judge that the gear teeth are wide tooth or are narrow tooth；HPTo divide
It is thick to spend knuckle-tooth.
More specifically,Calculation formula it is as follows：
In formula, F is total engagement force；For the n-th plate sheet spur gear i-th pair gear load at the j of the position of engagement point
Distribution coefficient.
Wherein, weight distribution factor of the n-th plate sheet spur gear i-th pair gear at the j of the position of engagementCalculating it is public
Formula is as follows：
In formula, LsfiFor the i-th pair gear teeth weight distribution factor of n-th spur gear；LsfjPosition is engaged for n-th spur gear
Put weight distribution factor at j；For total gear tooth rigidity of the n-th plate sheet spur gear；It is firm for total gear teeth of N plate gears
Degree.
Wherein, total engagement force F calculation formula is as follows：
In formula, T is the moment of torsion that the driving wheel of helical gear pair is subject to.
Step S5：The time-variant mesh stiffness of each plate sheet spur gear is summed, the time-varying engagement for obtaining helical gear pair is firm
Degree.
The time-variant mesh stiffness calculation formula of helical gear pair is as follows：
In formula, KjIt is time-variant mesh stiffness of the helical gear pair at the j of the position of engagement；N represents the sum of thin slice.
The helical gear pair time-variant mesh stiffness computational methods of the present invention, both ensure that certain computational accuracy, in turn ensure that
Certain computational efficiency.
Illustrate the helical gear pair time-variant mesh stiffness computational methods of the present invention below by embodiment one to embodiment seven.Its
The validity of the helical gear pair time-variant mesh stiffness computational methods of middle contrast verification the present embodiment of embodiment one, embodiment two to reality
Apply example seven and illustrate specific influence of the different gear pair basic parameters on time-variant mesh stiffness.
Embodiment one
In the present embodiment, the basic parameter of helical gear pair is as shown in table 1：
The helical gear pair basic parameter of table 1
Specifically, helical angle is respectively 12 °, 16 °, 20 °, 24 °, when whole tooth participates in engaging, the facewidth L values 60mm, R
For 12.738>5, EeFor 230.769GPa.
In the present embodiment, Fig. 4 is that helical angle is 12 °, registration be 3.0614 when, using analytic method, FInite Element,
The helical gear time-variant mesh stiffness figure that ISO6336 or document 1 obtain；Fig. 5 is that helical angle is 16 °, when registration is 3.4472,
The helical gear time-variant mesh stiffness figure obtained using analytic method, FInite Element, ISO6336 or document 1；Fig. 6 is that helical angle is
20 °, when registration is 3.8124, the helical gear time-varying obtained using analytic method, FInite Element, ISO6336 or document 1 is engaged
Rigidity figure；Fig. 7 is that helical angle is 24 °, when registration is 4.1588, is obtained using analytic method, FInite Element, ISO6336 or document 1
The helical gear time-variant mesh stiffness figure arrived.
Wherein, document 1 is Chang L H, Liu G, Wu L Y.A robust model for determining the
mesh stiffness of cylindrical gears[J].Mechanism and Machine Theory,2015,87:
93-114。
It can be seen that what the helical gear pair time-variant mesh stiffness that the present embodiment obtains obtained with FInite Element from Fig. 4-Fig. 7
Helical gear pair time-variant mesh stiffness coincide very well, and the helical gear pair time-variant mesh stiffness computational methods of the present embodiment are effective.
Embodiment two
In the present embodiment, the basic parameter of helical gear pair is as embodiment one.
In the present embodiment, time-variant mesh stiffness fluctuation is weighed using parameter η, and its expression formula is as follows：
In formula, Δ K represents the difference of time-variant mesh stiffness maxima and minima in a mesh cycle, KmeanRepresent one
The mean rigidity of mesh cycle, the two unit is identical, and parameter η is a dimensionless ratio value, for weighing mesh stiffness
Fluctuation.
Specifically, the computational accuracy of " section thought " can be affected after helical angle is more than 30 °, therefore, the present embodiment
It is 3 °, 5 °, 8 °, 10 °, 13 °, 15 °, 18 °, 20 °, 23 °, 25 °, 28 °, 30 ° to choose helical angle, L=60mm.
In the present embodiment, Fig. 8 represents helical angle and the relation of registration, and Fig. 9 represents helical angle and time-variant mesh stiffness ripple
Dynamic relation.
The 1, increase with helical angle is can be seen that from Fig. 8 and Fig. 9, registration increases therewith, and registration is different right
Mesh stiffness fluctuation has a great influence, and when registration is integer, the fluctuation of mesh stiffness is smaller；2nd, gear pair Face contact ratio
Excursion be more than the excursion of transverse contact ratio, can reduce mesh stiffness by controlling Face contact ratio for integer
Fluctuation.
Embodiment three
In the present embodiment, the basic parameter of helical gear pair in addition to the facewidth and embodiment one are different, other specification and
As embodiment one.
In the present embodiment, it is respectively 10mm, 15mm, 20mm, 25mm to take facewidth L.
In the present embodiment, Figure 10 represents helical gear pair time-variant mesh stiffness figure when the facewidth is 10mm and 15mm, and Figure 11 is tooth
Helical gear pair time-variant mesh stiffness figure during a width of 20mm and 25mm.Wherein, for L=10mm operating mode, monodentate area and double be present
Tooth area, monodentate area (monodentate area ratio is only the 2.05% of a cycle) do not mark in figure.
Can be seen that time-variant mesh stiffness from Figure 10 and Figure 11 increases with the increase of the facewidth, and when the facewidth is by 10mm
25mm is increased to, average time-variant mesh stiffness increase by 5%.
Example IV
In the present embodiment, the basic parameter of helical gear pair in addition to the facewidth and embodiment one are different, other specification and
As embodiment one.
In the present embodiment, facewidth L span is in the range of 30-85mm, and value gap is 5mm.
In the present embodiment, Figure 12 represents the facewidth and the relation of registration, and Figure 13 represents the facewidth and the pass of mesh stiffness fluctuation
System.
The change of the facewidth is can be seen that from Figure 12 and Figure 13 does not influence transverse contact ratio, as the facewidth increases Total contact ratio
Increase therewith with overlap ratio, when overlap ratio is closer to integer, mesh stiffness, which fluctuates, reaches minimum.
Embodiment five
In the present embodiment, the basic parameter of helical gear pair is as embodiment one.
In the present embodiment, according to the difference of modification coefficient, there is positive drive, Zero-drive Chain and negative transmission in gear modification transmission
Distinguish.
In the present embodiment, Figure 14 represents the time-variant mesh stiffness figure under different modification coefficients.
It is seen from figure 14 that modification coefficient influences the trend and numerical value of time-variant mesh stiffness, modification coefficient influences engagement
The engaging tooth area distribution of rigidity.
Embodiment six
In the present embodiment, the basic parameter of helical gear pair is as embodiment one.
In the present embodiment, according to the difference of modification coefficient, there is positive drive, Zero-drive Chain and negative transmission in gear modification transmission
Distinguish.
In the present embodiment, Figure 15 represents the relation of modification coefficient and registration, and Figure 16 represents that modification coefficient engages with average
The relation of rigidity.
Can be seen that modification coefficient from Figure 15 and Figure 16 does not influence on overlap ratio, and opposite end is towards registration and always
For registration, as the increase of driving wheel modification coefficient is first increases and then decreases, the influence for average mesh stiffness is also
First increases and then decreases.
Embodiment seven
In the present embodiment, the basic parameter of helical gear pair is as embodiment one.
In the present embodiment, friction coefficient μ=0,0.01,0.02,0.03,0.04,0.05,0.06.
In the present embodiment, Figure 17 is time-variant mesh stiffness figure under different coefficients of friction.
As can be seen from Figure 17, the average mesh stiffness of helical gear pair increases with the increase of coefficient of friction, further, since
The change of gear tooth friction force direction, occurs a turning point in the double-teeth toothing region of time-variant mesh stiffness.
Above content is only presently preferred embodiments of the present invention, for one of ordinary skill in the art, according to the present invention's
Thought, there will be changes, this specification content should not be construed as to the present invention in specific embodiments and applications
Limitation.
Claims (9)
1. a kind of helical gear pair time-variant mesh stiffness computational methods, it is characterised in that comprise the following steps：
Step S1：Obtain the basic parameter of helical gear pair；
Step S2：Along facewidth Directional Decomposition it is N number of independent and uniform thin slice spur gear pair by the wheel tooth model of helical gear pair；
Step S3：Determine whether N number of thin slice spur gear participates in engaging in position of engagement j；
Step S4：Consider nonlinear contact, amendment MATRIX STIFFNESS and extend the gear pair meshing characteristic analysis method that engagement influences
Calculate the time-variant mesh stiffness of each plate sheet spur gear；
Step S5：The time-variant mesh stiffness of each plate sheet spur gear is summed, obtains the time-variant mesh stiffness of helical gear pair.
2. helical gear pair time-variant mesh stiffness computational methods according to claim 1, it is characterised in that
Step S3 comprises the following steps：
Step S31：Determine the maximum engagement angle α of helical gear pair at the j of the position of engagementmaxWith Minimum Operating Pressure Angle αmin；
Step S32：Determine pressure angle (α of the n-th plate sheet spur gear at the j of the position of engagementn)j；
Step S33：Judge whether the n-th plate sheet spur gear participates in engaging.
3. helical gear pair time-variant mesh stiffness computational methods according to claim 2, it is characterised in that
In step S31：
The maximum engagement angle α of helical gear pair at the j of the position of engagementmaxCalculation formula it is as follows：
<mrow>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>=</mo>
<mo>&angle;</mo>
<mi>N</mi>
<mi>O</mi>
<mi>D</mi>
<mo>=</mo>
<mi>arctan</mi>
<mfrac>
<msub>
<mi>r</mi>
<mrow>
<mi>a</mi>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>r</mi>
<mrow>
<mi>b</mi>
<mn>1</mn>
</mrow>
</msub>
</mfrac>
</mrow>
The Minimum Operating Pressure Angle α of helical gear pair at the j of the position of engagementminCalculation formula it is as follows：
<mrow>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msub>
<mo>=</mo>
<mo>&angle;</mo>
<mi>N</mi>
<mi>O</mi>
<mi>A</mi>
<mo>=</mo>
<mi>arctan</mi>
<mfrac>
<mrow>
<msub>
<mi>r</mi>
<mrow>
<mi>b</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msub>
<mi>tan&alpha;</mi>
<mn>0</mn>
</msub>
<mo>-</mo>
<msub>
<mi>r</mi>
<mrow>
<mi>b</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>tan&alpha;</mi>
<mrow>
<mi>a</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>tan&alpha;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<msub>
<mi>r</mi>
<mrow>
<mi>b</mi>
<mn>1</mn>
</mrow>
</msub>
</mfrac>
</mrow>
In formula, rb1For driving wheel base radius；rb2For driven pulley base radius；α0For pressure angle；ra1For driving wheel outside circle half
Footpath；αa2For pressure angle corresponding to driven pulley tooth top meshing point.
4. helical gear pair time-variant mesh stiffness computational methods according to claim 2, it is characterised in that
In step s 32：
Pressure angle (α of the n-th plate sheet spur gear at the j of the position of engagementn)jCalculation formula it is as follows：
<mrow>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mo>=</mo>
<mi>arctan</mi>
<mrow>
<mo>(</mo>
<msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&tau;</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>i</mi>
</mrow>
<mi>n</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&theta;</mi>
<mrow>
<mi>b</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
In formula, (αn)jFor pressure angle of the n-th plate sheet spur gear at the j of the position of engagement；Represent the n-th plate sheet spur gear
Intermeshing pressure angles of the i to the driving wheel of rodent population at the j of the position of engagement；θb1For the half of driving wheel base tooth angle.
5. helical gear pair time-variant mesh stiffness computational methods according to claim 2, it is characterised in that
In step S33：
Mesh stiffness judgment expression of the n-th plate sheet spur gear at the j of the position of engagement is as follows：
<mrow>
<msub>
<mrow>
<mo>(</mo>
<msup>
<mi>k</mi>
<mi>n</mi>
</msup>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mrow>
<mo>(</mo>
<msup>
<mi>k</mi>
<mi>n</mi>
</msup>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mi>min</mi>
</msub>
<mo>&le;</mo>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mo>&le;</mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>0</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mo><</mo>
<msub>
<mi>&alpha;</mi>
<mi>min</mi>
</msub>
<mi>o</mi>
<mi>r</mi>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mo>></mo>
<msub>
<mi>&alpha;</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
In formula, (kn)jRepresent time-variant mesh stiffness of the n-th plate sheet spur gear at the j of the position of engagement.
6. helical gear pair time-variant mesh stiffness computational methods according to claim 5, it is characterised in that
In step s 4：
Time-variant mesh stiffness (k of the n-th plate sheet spur gear at the j of the position of engagementn)jSpecific formula for calculation it is as follows：
<mrow>
<msub>
<mrow>
<mo>(</mo>
<msup>
<mi>k</mi>
<mi>n</mi>
</msup>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>/</mo>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<msubsup>
<mi>k</mi>
<mrow>
<mi>f</mi>
<mn>1</mn>
</mrow>
<mi>n</mi>
</msubsup>
</mrow>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>k</mi>
<mrow>
<mi>t</mi>
<mi>o</mi>
<mi>o</mi>
<mi>t</mi>
<mi>h</mi>
</mrow>
<mi>n</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<msubsup>
<mi>k</mi>
<mrow>
<mi>f</mi>
<mn>2</mn>
</mrow>
<mi>n</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
In formula,For the revised driving wheel MATRIX STIFFNESS at the j of the position of engagement；To be repaiied at the j of the position of engagement
Driven pulley MATRIX STIFFNESS after just；For the MATRIX STIFFNESS of the n-th plate sheet spur gear driving wheel；For the n-th plate sheet spur gear
The MATRIX STIFFNESS of driven pulley；λ1For the matrix correction coefficient of each plate sheet spur gear driving wheel；λ2For each plate sheet spur gear
The matrix correction coefficient of driven pulley；Represent the gear teeth of all gear teeth pair of the n-th plate sheet spur gear at the j of the position of engagement
Rigidity.
7. helical gear pair time-variant mesh stiffness computational methods as claimed in claim 6, it is characterised in that
In step s 4：
The gear tooth rigidity of all gear teeth pair of the n-th plate sheet spur gear at the j of the position of engagementCalculation formula it is as follows：
<mrow>
<msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>k</mi>
<mrow>
<mi>t</mi>
<mi>o</mi>
<mi>o</mi>
<mi>t</mi>
<mi>h</mi>
</mrow>
<mi>n</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msubsup>
<mi>k</mi>
<mrow>
<mi>t</mi>
<mi>o</mi>
<mi>o</mi>
<mi>t</mi>
<mi>h</mi>
</mrow>
<mi>i</mi>
</msubsup>
</mrow>
Wherein,
<mrow>
<msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>k</mi>
<mrow>
<mi>h</mi>
<mi>i</mi>
</mrow>
<mi>n</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msup>
<msub>
<mi>E</mi>
<mi>e</mi>
</msub>
<mn>0.9</mn>
</msup>
<msup>
<mi>L</mi>
<mn>0.8</mn>
</msup>
<msup>
<msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>F</mi>
<mi>i</mi>
<mi>n</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mn>0.1</mn>
</msup>
</mrow>
<mn>1.275</mn>
</mfrac>
</mrow>
<mrow>
<msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>F</mi>
<mi>i</mi>
<mi>n</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mo>=</mo>
<mi>F</mi>
<mo>&CenterDot;</mo>
<msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>lsr</mi>
<mi>i</mi>
<mi>n</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
</mrow>
In formula, m represents ingear tooth logarithm simultaneously；Represent the gear tooth rigidity of i-th pair engaging tooth；For n-th
Hertzian contact stiffness of the thin slice spur gear pair i-th pair engaging tooth at the j of the position of engagement；Exist for the n-th plate sheet spur gear pair
The gear tooth rigidity of driving wheel at the j of the position of engagement；For driven pulley of the n-th plate sheet spur gear pair at the j of the position of engagement
Gear tooth rigidity；EeFor effective modulus of elasticity；L is the facewidth；It is the n-th plate sheet spur gear i-th pair gear pair in position of engagement j
The engagement force at place；F is total engagement force；For load distribution of the n-th plate sheet spur gear i-th pair gear at the j of the position of engagement
Coefficient.
8. helical gear pair time-variant mesh stiffness computational methods as claimed in claim 7, it is characterised in that
In step s 4：
Weight distribution factor (lsr of the n-th plate sheet spur gear i-th pair gear at the j of the position of engagementi n)jCalculation formula it is as follows
It is shown：
<mrow>
<msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>lsr</mi>
<mi>i</mi>
<mi>n</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mo>=</mo>
<msup>
<mi>Lsf</mi>
<mi>i</mi>
</msup>
<mo>&times;</mo>
<msub>
<mi>Lsf</mi>
<mi>j</mi>
</msub>
</mrow>
Wherein,
<mrow>
<msub>
<mi>Lsf</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfrac>
<msubsup>
<mi>K</mi>
<mrow>
<mi>t</mi>
<mi>o</mi>
<mi>o</mi>
<mi>t</mi>
<mi>h</mi>
</mrow>
<mi>n</mi>
</msubsup>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msubsup>
<mi>K</mi>
<mrow>
<mi>t</mi>
<mi>o</mi>
<mi>o</mi>
<mi>t</mi>
<mi>h</mi>
</mrow>
<mi>n</mi>
</msubsup>
</mrow>
</mfrac>
</mrow>
In formula, LsfiFor the i-th pair gear teeth weight distribution factor of n-th spur gear；LsfjAt n-th spur gear position of engagement j
Weight distribution factor；For total gear tooth rigidity of the n-th plate sheet spur gear；For total gear tooth rigidity of N plate gears.
9. helical gear pair time-variant mesh stiffness computational methods as claimed in claim 6, it is characterised in that
In step s 5：
Helical gear pair time-variant mesh stiffness KjCalculation formula it is as follows：
<mrow>
<msub>
<mi>K</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mrow>
<mo>(</mo>
<msup>
<mi>k</mi>
<mi>n</mi>
</msup>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
</mrow>
In formula, KjIt is time-variant mesh stiffness of the helical gear pair at the j of the position of engagement；N represents the sum of thin slice.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710687624.9A CN107391876A (en) | 2017-08-11 | 2017-08-11 | Helical gear pair time-variant mesh stiffness computational methods |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710687624.9A CN107391876A (en) | 2017-08-11 | 2017-08-11 | Helical gear pair time-variant mesh stiffness computational methods |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN107391876A true CN107391876A (en) | 2017-11-24 |
Family
ID=60354620
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710687624.9A Pending CN107391876A (en) | 2017-08-11 | 2017-08-11 | Helical gear pair time-variant mesh stiffness computational methods |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107391876A (en) |
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108416120A (en) * | 2018-02-12 | 2018-08-17 | 武汉理工大学 | A kind of determination method of straight spur gear double-teeth toothing region weight-distribution factor |
| CN109871652A (en) * | 2019-03-14 | 2019-06-11 | 东北大学 | A kind of gear pair Abrasion prediction method based on dynamic engagement power |
| CN110059287A (en) * | 2019-04-16 | 2019-07-26 | 江苏省金象传动设备股份有限公司 | Consider to extend engagement and gear ring internal gear pair mesh stiffness calculation method flexible |
| CN111488682A (en) * | 2020-04-09 | 2020-08-04 | 北京理工大学 | Involute helical gear pair tooth width modification dynamic model establishing 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 |
| CN112507485A (en) * | 2020-11-27 | 2021-03-16 | 江苏省金象传动设备股份有限公司 | Bevel gear time-varying meshing stiffness analysis method based on slice coupling theory |
| CN113051682A (en) * | 2021-03-25 | 2021-06-29 | 天津职业技术师范大学(中国职业培训指导教师进修中心) | Method and device for calculating thermal elastic meshing stiffness of helical gear pair |
| CN113378312A (en) * | 2021-05-25 | 2021-09-10 | 武汉理工大学 | Helical gear time-varying meshing stiffness calculation method considering relative positions of base circle and root circle |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20020170374A1 (en) * | 2001-05-21 | 2002-11-21 | Stewart David A. | Energy saving gear system |
| CN104573196A (en) * | 2014-12-18 | 2015-04-29 | 西安交通大学 | Analytic calculation method for time-varying meshing stiffness of helical-spur gear |
| CN104820756A (en) * | 2015-05-18 | 2015-08-05 | 东北大学 | Kinetic parameter determination method of extended tooth contact considered crack gear rotor system |
-
2017
- 2017-08-11 CN CN201710687624.9A patent/CN107391876A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20020170374A1 (en) * | 2001-05-21 | 2002-11-21 | Stewart David A. | Energy saving gear system |
| CN104573196A (en) * | 2014-12-18 | 2015-04-29 | 西安交通大学 | Analytic calculation method for time-varying meshing stiffness of helical-spur gear |
| CN104820756A (en) * | 2015-05-18 | 2015-08-05 | 东北大学 | Kinetic parameter determination method of extended tooth contact considered crack gear rotor system |
Non-Patent Citations (2)
| Title |
|---|
| HUI MA ET AL.: "An improved analytical method for mesh stiffness calculation of spur gears with tip relief", 《MECHANISM AND MACHINE THEORY》 * |
| HUI MA ET AL.: "Fault features analysis of cracked gear considering the effects of the extended tooth contact", 《ENGINEERING FAILURE ANALYSIS》 * |
Cited By (14)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108416120A (en) * | 2018-02-12 | 2018-08-17 | 武汉理工大学 | A kind of determination method of straight spur gear double-teeth toothing region weight-distribution factor |
| CN108416120B (en) * | 2018-02-12 | 2021-10-22 | 武汉理工大学 | Method for determining load distribution rate of double-tooth meshing area of straight-toothed spur gear |
| CN109871652A (en) * | 2019-03-14 | 2019-06-11 | 东北大学 | A kind of gear pair Abrasion prediction method based on dynamic engagement power |
| CN109871652B (en) * | 2019-03-14 | 2022-10-04 | 东北大学 | Gear pair wear loss prediction method based on dynamic meshing force |
| CN110059287A (en) * | 2019-04-16 | 2019-07-26 | 江苏省金象传动设备股份有限公司 | Consider to extend engagement and gear ring internal gear pair mesh stiffness calculation method flexible |
| CN110059287B (en) * | 2019-04-16 | 2023-01-24 | 江苏省金象传动设备股份有限公司 | Method for calculating meshing stiffness of internal gear pair by considering prolonged meshing and gear ring flexibility |
| CN111488682B (en) * | 2020-04-09 | 2022-11-08 | 北京理工大学 | Involute helical gear pair tooth width modification dynamic model establishing method |
| CN111488682A (en) * | 2020-04-09 | 2020-08-04 | 北京理工大学 | Involute helical gear pair tooth width modification dynamic model establishing 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 |
| CN112507485A (en) * | 2020-11-27 | 2021-03-16 | 江苏省金象传动设备股份有限公司 | Bevel gear time-varying meshing stiffness analysis method based on slice coupling theory |
| CN113051682A (en) * | 2021-03-25 | 2021-06-29 | 天津职业技术师范大学(中国职业培训指导教师进修中心) | Method and device for calculating thermal elastic meshing stiffness of helical gear pair |
| CN113051682B (en) * | 2021-03-25 | 2022-08-12 | 天津职业技术师范大学(中国职业培训指导教师进修中心) | Method and device for calculating thermal elastic meshing stiffness of helical gear pair |
| CN113378312A (en) * | 2021-05-25 | 2021-09-10 | 武汉理工大学 | Helical gear time-varying meshing stiffness calculation method considering relative positions of base circle and root circle |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107391876A (en) | Helical gear pair time-variant mesh stiffness computational methods | |
| CN104573196B (en) | A kind of helical gears time-variant mesh stiffness Analytic Calculation Method | |
| CN103577687B (en) | Time-varying characteristic quantitative calculation method for meshing stiffness of gear with minor defect | |
| Pedrero et al. | Load distribution model along the line of contact for involute external gears | |
| Yu et al. | A new model for the single mesh stiffness calculation of helical gears using the slicing principle | |
| CN101937211B (en) | Involute straight tooth cone gear trimming method | |
| CN107247856B (en) | A kind of list roller enveloping enveloping worm pair time-variant mesh stiffness analytic method | |
| CN107763173B (en) | Finite element analysis-based helical gear time-varying meshing stiffness calculation method | |
| Sánchez et al. | Strength model for bending and pitting calculations of internal spur gears | |
| Yan et al. | Optimization of distributed axial dynamic modification based on the dynamic characteristics of a helical gear pair and a test verification | |
| CN109918691B (en) | Method for dynamically correcting and calculating meshing stiffness of straight gear under fluctuating load working condition | |
| CN104889505A (en) | Asymmetrical hob and design method thereof | |
| CN111488682B (en) | Involute helical gear pair tooth width modification dynamic model establishing method | |
| He et al. | Study on the optimum standard parameters of hob optimization for reducing gear tooth root stress | |
| CN111079300B (en) | Straight gear meshing rigidity calculation method considering tooth direction error | |
| CN108846189B (en) | Gear pair meshing characteristic analysis method | |
| Li et al. | Meshing theory and simulation of noninvolute beveloid gears | |
| CN110188409A (en) | Torsional spring loads clearance elimination gear tooth surface abrasion amount computation model | |
| CN110443001A (en) | A kind of coalcutter permanent magnetism half is straight to drive cutting transmission system dynamic reliability prediction technique | |
| Vereš et al. | Theoretical and experimental research of the HCR gear’s contact strength | |
| CN103307211A (en) | Non-symmetric involute worm and gear pair | |
| CN110399662A (en) | A kind of Cycloid tooth profile correction method | |
| CN109340346A (en) | Metal worm screw and the helical gear unequal blade spacing structure of plastic cement | |
| Rajesh et al. | Design and Testing of Gears Operating between a Specified Center Distance Using Altered Tooth-sum Gearing (Z±Gearing) | |
| CN107420523A (en) | A kind of helical gear pair mesh stiffness computational methods with cracks in tooth surface defect |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20171124 |
|
| WD01 | Invention patent application deemed withdrawn after publication |