CN110334460A - Roller gear mesh stiffness calculation method - Google Patents
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Abstract
The invention discloses roller gear mesh stiffness calculation methods, it is related to technical field of mechanical design, according to the theory of engagement, engagement face is unfolded and divides the position of contact point, then flank of tooth carrying contact equation is established, flank of tooth normal direction flexibility is calculated based on microtomy and energy method, flank of tooth carrying contact equation is calculated based on solution by iterative method, finally obtains the mesh stiffness for considering the roller gear of flank of tooth distribution error.The mesh stiffness for considering the roller gear of flank of tooth distribution error can be calculated using the present invention, so that the calculating of follow-up driving force is more accurate.Present invention also improves efficiency and precision that roller gear mesh stiffness calculates simultaneously.
Description
Technical field
The present invention relates to technical field of mechanical design, more particularly to roller gear mesh stiffness calculation method.
Background technique
Gear pair time-variant mesh stiffness and manufacture/rigging error are the two class main insides for influencing gear train dynamic property
Motivator.Domestic and foreign scholars have conducted extensive research the calculation method of Gear Meshing Stiffness, and the big spininess of the research of early stage
To ideal spur gear pair, and usually by gear it is loaded be approximately that two-dimensional plane problem is handled.For helical gear pair or herringbone
Gear pair, since contact line direction and Gear axis are not parallel, even if the Total contact ratio of gear pair is integer, each engagement position
The contact line total length set also will be different, and dynamic engagement process will also generate dynamic engagement excitation, engagement point
Analysis is complicated three-dimensional space contact problems.For ideal gear pair, the calculating of mesh stiffness is that gear teeth meshing elasticity becomes
The calculating of shape.However, engineering is in practice, the presence of manufacture/rigging error is inevitable, the distributed error meeting on the flank of tooth
The practical contact condition and desired contact state for making gear pair generate difference, under different loads operating condition, the practical contact of the flank of tooth
Region also will be different, so that the excitation of gear pair dynamic engagement be made to change.Marine Helical Gears higher for registration
Or double helical tooth wheel set, while meshed gears, to also more, influence of the manufacture/rigging error to gear teeth meshing is just more complicated.
Existing method when calculating mesh stiffness, solve the flank of tooth normal direction flexibility when be finite element subsctructure method, it is this
Method has great advantage when studying the influence of tooth surface error or correction of the flank shape, it is only necessary to construct a finite element model.However,
If being applied to the parameter designing and matching of ship gear train design initial stage, it is still necessary to construct finite element mould repeatedly
Type, design efficiency just seems low at this time.Therefore, easier flank of tooth method is proposed the present invention is based on energy method and microtomy
To flexibility calculation method, the computational efficiency of mesh stiffness is substantially increased.
Summary of the invention
The embodiment of the invention provides roller gear mesh stiffness calculation methods, can solve existing in the prior art ask
Topic.
The present invention provides roller gear mesh stiffness calculation methods, method includes the following steps:
According to theory of engagement Generating gear pair engagement face, which is marked off into continuous contact line, continuous
Contact line it is discrete be multiple contact points；
The flexible deformation of each contact point is decomposed into macroscopic deformation and juxtaposition metamorphose, is calculated using energy method and microtomy
Macroscopic deformation calculates juxtaposition metamorphose using juxtaposition metamorphose analytic formula, is built according to the macroscopic deformation and juxtaposition metamorphose that are calculated
The compatibility of deformation relationship that contact point is met after vertical load, while establishing what contact conditions and each contact point after load undertook
The relationship of the sum of load and gear pair normal direction full payload, the above-mentioned relationship of simultaneous and condition obtain flank of tooth carrying contact equation；
Contact equation is carried using the flank of tooth described in solution by iterative method, obtains contact force distribution and Static transmissions error；
Gap value is arranged according to flank of tooth actual error value between each contact point pair, according to the gap value, contact force
The mesh stiffness of roller gear is calculated in distribution and Static transmissions error.
The principle of the present invention is that engagement face is unfolded to and is divided the position of contact point, is then built according to the theory of engagement
Vertical flank of tooth carrying contact equation, calculates flank of tooth normal direction flexibility based on microtomy and energy method, calculates the flank of tooth based on solution by iterative method
Carrying contact equation, finally obtains the mesh stiffness for considering the roller gear of flank of tooth distribution error.Compared with prior art
Beneficial effect is: firstly, the mesh stiffness for considering the roller gear of flank of tooth distribution error can be calculated using the present invention, so that
The calculating of follow-up driving force is more accurate.Secondly, the present invention improves the efficiency and precision of roller gear mesh stiffness calculating.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 be engagement face transform into and contact point arrangement schematic diagram；
Fig. 2 is that gear pair containing error loads front and back compatibility of deformation relation schematic diagram；
Fig. 3 is geometric parameter schematic diagram needed for Gear Contact deformation calculates；
Fig. 4 is gear slice and force analysis schematic diagram；
Fig. 5 load front and back contact point compatibility of deformation relation schematic diagram.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
The present invention provides roller gear mesh stiffness calculation methods, and the method steps are as follows:
Step 1, according to the theory of engagement, Generating gear pair engagement face, and the position of engagement and contact line are divided, it will be continuous
Contact line it is discrete be a series of contact points, to convert Point contact for the line contact problems of face.
Transforming into for contact pattern is based on the theory of engagement with the arrangement of contact point in the step, and detailed process is as follows:
The dynamic engagement process of helical gear pair is as shown in Figure 1.Rectangular area B1B2B3B4For gear pair engagement face.N1N2
And B1B2Respectively theoretical transverse path of contact and practical transverse path of contact.rbpAnd rbgThe respectively basic circle of driving wheel and driven wheel half
Diameter.OA-XAYAZAFor the coordinates computed system on engagement face.Op-XpYpZpFor the geometric coordinate system of driving wheel, Og-XgYgZgFor
The geometric coordinate system of driven wheel, wherein p indicates that driving wheel, g indicate driven wheel.
Fig. 1 is a certain instantaneous position of engagement for a pair of of helical gear pair that registration is 2~3.By every contact line uniformly from
It dissipates for a series of contact points, to convert Point contact for the line contact problems of gear pair.For a certain in contact line
The coordinate of contact point D, the subpoint D ' on transverse path of contact can be obtained by following formula:
In formula, rbp/gIndicate rbpOr rbg,
In formula, αmFor the gear pair angle of engagement, αagFor the outside circle pressure angle of driven wheel.
Step 2, gap value is arranged according to flank of tooth actual error value between each contact point pair, according to compatibility of deformation relationship
Establish flank of tooth carrying contact equation.
Gap value is arranged according to flank of tooth actual error value between each contact point pair in the step, is closed according to compatibility of deformation
The process that system establishes flank of tooth carrying contact equation is as follows:
The dynamic engagement process of gear pair can be considered the quasi-static carrying contact process of two elastomers.In external applied load FwWork
Under, two elastomers are close to each other and progress into contact condition.For considering the gear pair of flank of tooth complex distributions formula error,
The a certain position of engagement, the compatibility of deformation relationship of driving wheel and driven wheel mesh tooth face before and after carrying are as shown in Figure 2.
When continuous contact line by discrete for a series of deformation that after contact points, potential contact point i is met after load
Rapport are as follows:
δi (p)+δi (g)+εi-LSTE-di=0 (4)
In formula, δi (p)And δi (g)Respectively indicate the loaded deformation of potential contact point i on driving wheel and driven wheel；εiExpression can
The primary clearance of energy contact point i；LSTE indicates the rigid body approach amount of two elastomers, and for gear pair, LSTE indicates tooth
The Static transmissions error of wheel set；diThe residual gap of potential contact point i after indicating loaded.
The flexible deformation of gear can be divided into two parts: the macroscopic deformation that is changed linearly with load and with load in non-linear
The localized contact of variation deforms.Then equation (4) can be rewritten as:
In formula,WithThe macroscopic deformation of driving wheel and driven wheel at potential contact point i is respectively indicated,
δContact_iIndicate the localized contact deformation of driving wheel and driven wheel at potential contact point i.
Since the macroscopic deformation of driving wheel and driven wheel is changed linearly with load, calculating formula is writeable are as follows:
In formula,WithIt respectively indicates driving wheel and driven wheel and investigates on the flank of tooth contact point j for contact point
The macroscopic deformation softness factor of i is defined as the macroscopic deformation amount when contact point j applies unit normal load at the i of contact point；Fj
For the load of contact point j；N is to investigate the number of potential contact point on the flank of tooth in the same position of engagement.
Then gear pair macroscopic deformation flexibility may be expressed as:
Geometric parameter needed for Gear Contact deformation calculates is as shown in Figure 3.It is non-linear with load to consider that localized contact is deformed
Formula (8) calculating can be used in coupled relation, the localized contact deformation at potential contact point i:
In formula, FiFor the load at potential contact point i；Dz is contact width；kpAnd kgRespectively on driving wheel and driven wheel
Contact point A is at a distance from the intersection points B of normal force direction and gear middle line；E and v is respectively the elasticity modulus and Poisson's ratio of material；a
For the contact half-band width in flank profil direction, calculating formula are as follows:
In formula, ρpAnd ρgThe respectively radius of curvature of driving wheel and driven wheel at contact point.
Formula (6) are substituted into formula (5), then the deformation compatibility condition at the i of contact point can be rewritten as:
It in the same position of engagement, has point of contact and is coupled by Static transmissions error, then n rank line can be obtained by formula (10)
Property equation group:
The matrix form of formula (11) is writeable are as follows:
[λ]Global{F}+{u}Local+ { ε }-LSTE- { d }=0 (12)
In formula, [λ]GlobalFor the macroscopic deformation flexibility matrix of contact point；{u}LocalIt is deformed for the localized contact of contact point；
{ ε } is the primary clearance of contact point；{ d } is the residual gap of contact point；LSTE is gear pair Static transmissions error.
After load, when the load of contact point i is greater than zero, illustrate that two mesh tooth faces are at this point in contact condition at this time,
Then the residual gap of contact point i is zero；When the load of contact point i is equal to zero, illustrate that two flank of tooth are not at this point at this time
Contact condition, then the residual gap of the contact point is greater than zero.Its expression formula are as follows:
The sum of load that all potential contact points undertake on the same position of engagement, each contact line should be total with gear pair normal direction
Load FzIt is equal, then have:
In formula, { I } is n rank unit matrix.
In conclusion joint type (12)~(14), can be obtained gear pair in the flank of tooth carrying contact of a certain position of engagement
The matrix form of equation.
Step 3, the flexible deformation of each contact point is decomposed into linear macroscopic deformation and nonlinear juxtaposition metamorphose, is adopted
Linear macroscopic deformation is calculated with potential energy method.
Linear macroscopic deformation is calculated based on energy method and microtomy in the step, and it is soft that macroscopic deformation is divided into bending
Degree shears flexibility, is compressed axially four part of part equivalent flexibility of flexibility and gear wheel body, calculates separately what summation obtained.
Easier flank of tooth normal direction flexibility calculation method is proposed the present invention is based on energy method and microtomy.
By gear along facewidth direction it is discrete for series of gears be sliced, gear hierarchical model and geometric parameter are as shown in Figure 4.
Gear pair normal direction engagement force effect under, gear slice deformation can be divided into bending deformation, shear-deformable, axial crushing deformation,
Wheel body deformation and Hertz contact deformation.
Potential energy of the gear tooth under load effect can be divided into bending deformation potential energy Ub, shear-deformable potential energy UsWith axial pressure
Contracting potential energy Ua, expression formula is respectively as follows:
In formula, E and G are respectively the elasticity modulus and modulus of shearing of material, AxAnd IxRespectively acted on apart from normal direction engagement force
Area of section and cross sectional moment of inertia at point x, FbFor the suffered end face tangential force of gear slice, FaFor the suffered end of gear slice
Face radial force, M are the torque for the integral infinitesimal that normal direction engagement force is dx relative to width, and calculating formula is respectively as follows:
Fb=Fcos αm (19)
Fa=Fsin αm (20)
M=Fbx-Fah (21)
In formula, hxThe half for indicating the corresponding transverse pitch of dx, brings formula (19)~(21) into (15)~(17), can be obtained
The bending flexibility of gear slice shears flexibility and is compressed axially flexibility and is respectively as follows:
Under engagement force F effect, the flexible deformation of gear wheel body portion are as follows:
In formula, ufAnd SfAs shown in figure 4, ufIndicate the vertical range of load(ing) point and Gear Root circle in end face, SfIndicate single
Root circle arc length of a tooth on gear face.Coefficient L*、M*、P*And Q*By polynomial approximation are as follows:
In formula, X*Represent L*、M*、P*And Q*,Ai、Bi、Ci、Di、EiAnd FiValue it is as shown in table 1.
Thus, the calculating formula of gear wheel body portion equivalent flexibility are as follows:
In conclusion macroscopic deformation can by the bending flexibility of driving wheel and driven wheel, shear flexibility, be compressed axially flexibility and
The equivalent flexibility of gear wheel body portion is superimposed to obtain, calculating formula are as follows:
In formula, p indicates that driving wheel, g indicate driven wheel.
1 coefficient value of table
Step 4, nonlinear juxtaposition metamorphose is calculated using juxtaposition metamorphose analytic formula.
Nonlinear juxtaposition metamorphose in the step is calculated using juxtaposition metamorphose analytic formulaIt obtains.
Step 5, it can solve to obtain the contact force distribution for considering flank of tooth complex distributions formula error and static state using iterative method
Transmission error.
The step can solve to obtain the contact force distribution for considering flank of tooth complex distributions formula error and static state using iterative method
Transmission error, specific iterative process are as follows:
(1) in a certain position of engagement, it is assumed that gear normal direction engagement force FnOn all potential contact points in each contact line
It is uniformly distributed, i.e. Fj(1)=P/n, (j=1,2 ..., n), obtain initial load distribution vector { F }.
(2) by known load distribution vector { F }, the juxtaposition metamorphose calculation formula provided in formula (8) can be used and calculate
To the juxtaposition metamorphose equivalent flexibility matrix of contact point:
λLocalj=uLocalj/Fj(k)(j=1,2 ..., n) (29)
[λLocal](k)=diag ([λLocal1,λLocal2,...,λLocaln]) (30)
(3) by contact point macroscopic deformation flexibility matrix [λGlobal] and contact point juxtaposition metamorphose equivalent flexibility matrix
[λLocal](k)Superposition, can be obtained contact point structural strain's flexibility matrix [λ](k):
[λ](k)=[λGlobal]+[λLocal](k) (31)
Formula (12) can be rewritten as formula (32):
[λ](k){ F }+{ ε }-LSTE- { d }=0 (32)
(4) as it is assumed that gear normal direction engagement force is uniformly distributed on all potential contact points in each contact line, therefore,
The residual gap of all potential contact points is zero.Introducing artificial variables F'} and LSTE', formula (32) can be rewritten as:
[λ](k){ F'}+{ ε }-LSTE'=0 (33)
Joint type (14) and formula (33), and the system of linear equations is solved using Gaussian reduction, can be obtained F'} and
LSTE'。
(5) from contact conditions formula (13) after loading: each contact point load is all larger than or is equal to zero, therefore, if it exists
Fj' < 0 then illustrates that mesh tooth face is in the contacting points position not in contact with state.Scratch [λ](k), { ε } and { corresponding to F'}
Row and column solves the system of linear equations that formula (14) and formula (33) form again, and judges artificial variables { each element in F'} again
It is positive and negative, so iteratively solve, up to artificial variables, { there is no minus elements in F'}, can jump out circulation.
(6) judge that contact force is distributed { F }(k+1){ F }(k)Relative error be less than convergence tolorence it is whether true.If not at
It is vertical, then go to (2) step；If so, iteration is then terminated, while exporting contact force distribution { F } and Static transmissions error LSTE.
It step 6, can be true according to the gap value between Static transmissions error, each contact point pair and the normal load undertaken
The mesh stiffness of fixed tooth wheel set.
The step can be true according to the gap value between Static transmissions error, each contact point pair and the normal load undertaken
The mesh stiffness of fixed tooth wheel set.The comprehensive mesh stiffness calculating formula of gear pair for considering error is writeable are as follows:
In short, the present invention is calculated for the roller gear mesh stiffness for considering flank of tooth distribution error, computational efficiency
Higher, computational accuracy is more accurate.
Although preferred embodiments of the present invention have been described, it is created once a person skilled in the art knows basic
Property concept, then additional changes and modifications may be made to these embodiments.So it includes excellent that the following claims are intended to be interpreted as
It selects embodiment and falls into all change and modification of the scope of the invention.
Obviously, various changes and modifications can be made to the invention without departing from essence of the invention by those skilled in the art
Mind and range.In this way, if these modifications and changes of the present invention belongs to the range of the claims in the present invention and its equivalent technologies
Within, then the present invention is also intended to include these modifications and variations.
Claims (7)
1. roller gear mesh stiffness calculation method, which is characterized in that method includes the following steps:
According to theory of engagement Generating gear pair engagement face, which is marked off into continuous contact line, continuously connecing
It is multiple contact points that it is discrete, which to touch line,；
The flexible deformation of each contact point is decomposed into macroscopic deformation and juxtaposition metamorphose, macroscopic view is calculated using energy method and microtomy
Deformation calculates juxtaposition metamorphose using juxtaposition metamorphose analytic formula, is established and added according to the macroscopic deformation and juxtaposition metamorphose being calculated
The compatibility of deformation relationship that contact point is met after load, while establishing the load that contact conditions and each contact point after load undertake
The sum of relationship with gear pair normal direction full payload, the above-mentioned relationship of simultaneous and condition obtain flank of tooth carrying contact equation；
Contact equation is carried using the flank of tooth described in solution by iterative method, obtains contact force distribution and Static transmissions error；
Gap value is arranged according to flank of tooth actual error value between each contact point pair, is distributed according to the gap value, contact force
The mesh stiffness of roller gear is calculated with Static transmissions error.
2. roller gear mesh stiffness calculation method as described in claim 1, which is characterized in that use energy method and microtomy
When calculating the macroscopic deformation, macroscopic deformation is divided into and is bent flexibility, shears flexibility, is compressed axially flexibility and the portion of gear wheel body
Divide four part of equivalent flexibility, the sum of this tetrameric flexibility is macroscopic deformation；
When calculating above-mentioned flexibility, gear is discrete for multiple gears slice along facewidth direction, and the macroscopic deformation that gear is sliced is divided into
It is bent flexibility δb, shearing flexibility δs, be compressed axially flexibility δa, wheel body portion equivalent flexibility；
Under engagement force F effect, the flexible deformation of gear wheel body portion are as follows:
In formula, ufIndicate the vertical range of load(ing) point and Gear Root circle in end face, SfIndicate tooth of the single tooth on gear face
Root circular arc is long, L*、M*、P*And Q*For coefficient, αmFor the gear pair angle of engagement, E is the elasticity modulus of material, and dz is contact width, by
This can be obtained, the calculating formula of gear wheel body portion equivalent flexibility are as follows:
Therefore the macroscopic deformation of gear pair is calculated by following formula:
In formula, p indicates that driving wheel, g indicate driven wheel.
3. roller gear mesh stiffness calculation method as described in claim 1, which is characterized in that nonlinear juxtaposition metamorphose is adopted
It is calculated with juxtaposition metamorphose analytic formulaIt obtains, in formula, FiIt is possible
Load at the i of contact point；Dz is contact width；kpAnd kgRespectively on driving wheel and driven wheel contact point A and normal force direction and
The distance of the intersection points B of gear middle line；E and v is respectively the elasticity modulus and Poisson's ratio of material；A is half band of contact in flank profil direction
Width, calculating formula are as follows:
In formula, F is engagement force, ρpAnd ρgThe respectively radius of curvature of driving wheel and driven wheel at contact point.
4. roller gear mesh stiffness calculation method as claimed in claim 3, which is characterized in that when continuous contact line by from
It dissipates for a series of compatibility of deformation relationship that after contact points, potential contact point i is met after load are as follows:
In formula,WithRespectively indicate the loaded deformation of potential contact point i on driving wheel and driven wheel；εiExpression may contact
The primary clearance of point i；LSTE indicates the rigid body approach amount of two elastomers, and for gear pair, LSTE is to indicate gear pair
Static transmissions error；diThe residual gap of potential contact point i after indicating loaded；
Then equation (5) is rewritten are as follows:
In formula,WithThe macroscopic deformation of driving wheel and driven wheel at potential contact point i is respectively indicated,
δContact_iIndicate the localized contact deformation of driving wheel and driven wheel at potential contact point i；
Since the macroscopic deformation of driving wheel and driven wheel is changed linearly with load, macroscopic deformation calculating formula is written as:
In formula,WithIt respectively indicates driving wheel and driven wheel and investigates on the flank of tooth contact point j for contact point i's
Macroscopic deformation softness factor is defined as the macroscopic deformation amount when contact point j applies unit normal load at the i of contact point；FjFor
The load of contact point j；N is to investigate the number of potential contact point on the flank of tooth in the same position of engagement；
Gear pair macroscopic deformation flexibility indicates are as follows:
Consider the nonlinear coupling relationship of localized contact deformation and load, the localized contact deformation at potential contact point i uses formula
(9) it calculates:
Formula (7) are substituted into formula (6), then the compatibility of deformation relationship at potential contact point i is rewritten are as follows:
It in the same position of engagement, has point of contact and is coupled by Static transmissions error, then n rank linear equation is obtained by formula (10)
Group:
The matrix form of formula (11) is written as:
[λ]Global{F}+{u}Local+ { ε }-LSTE- { d }=0 (12)
In formula, [λ]GlobalFor the macroscopic deformation flexibility matrix of contact point；{u}LocalIt is deformed for the localized contact of contact point；{ ε } is
The primary clearance of contact point；{ d } is the residual gap of contact point；LSTE is gear pair Static transmissions error.
5. roller gear mesh stiffness calculation method as claimed in claim 4, which is characterized in that after load, when contact point i's
When load is greater than zero, two mesh tooth faces are at this point in contact condition, then the residual gap of contact point i is zero；As contact point i
Load when being equal to zero, two flank of tooth are at this point in not in contact with state, then the residual gap of the contact point is greater than zero, expression formula
Are as follows:
The sum of the load undertaken that has point of contact on the same position of engagement, each contact line should be with gear pair normal direction full payload FzPhase
Deng then having:
In formula, { I } is n rank unit matrix；
In conclusion joint type (12)~(14), obtain gear pair in the square of the flank of tooth carrying contact equation of a certain position of engagement
Formation formula.
6. roller gear mesh stiffness calculation method as claimed in claim 5, which is characterized in that obtained using solution by iterative method
Contact force distribution and Static transmissions error, specific iterative process are as follows:
(1) in a certain position of engagement, it is assumed that gear normal direction engagement force FnUniformly divide on all potential contact points in each contact line
Cloth, i.e. Fj(1)=P/n, j=1,2 ..., n obtains initial load distribution vector { F }；
(2) by known load distribution vector { F }, contact is calculated using the juxtaposition metamorphose calculation formula provided in formula (9)
The juxtaposition metamorphose equivalent flexibility matrix of point:
λLocalj=uLocalj/Fj(k) (15)
[λLocal](k)=diag ([λLocal1,λLocal2,...,λLocaln]) (16)
(3) by contact point macroscopic deformation flexibility matrix [λGlobal] and contact point juxtaposition metamorphose equivalent flexibility matrix [λLocal](k)It is folded
Add, contact point structural strain's flexibility matrix [λ] can be obtained(k):
[λ](k)=[λGlobal]+[λLocal](k) (17)
Formula (12) is rewritten as formula (18):
[λ](k){ F }+{ ε }-LSTE- { d }=0 (18)
(4) assume that gear normal direction engagement force is uniformly distributed on all potential contact points in each contact line, be likely to contact
The residual gap of point is zero, introducing artificial variables F'} and LSTE', formula (18) are rewritten are as follows:
[λ](k){ F'}+{ ε }-LSTE'=0 (19)
Joint type (14) and formula (19), and the system of linear equations is solved using Gaussian reduction, { F'} and LSTE' can be obtained；
(5) F if it existsj[λ] is scratched in ' < 0(k), { ε } and row and column corresponding to F'}, and again solve formula (14) and formula (19) group
At system of linear equations, and judge artificial variables again { each element be positive and negative in F'}, so iteratively solves, until artificial variables
{ element in F'} is all larger than or is equal to zero, jumps out circulation；
(6) judge that contact force is distributed { F }(k+1){ F }(k)Relative error be less than convergence tolorence it is whether true, if not,
Then go to (2) step；If so, iteration is then terminated, while exporting contact force distribution { F } and Static transmissions error LSTE.
7. roller gear mesh stiffness calculation method as claimed in claim 6, which is characterized in that the mesh stiffness meter of gear pair
Formula is written as:
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| CN117094200A (en) * | 2023-10-17 | 2023-11-21 | 安徽大学 | Gear time-varying meshing stiffness calculation method considering misalignment error |
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| CN113158479A (en) * | 2021-04-29 | 2021-07-23 | 清华大学 | Method for calculating transmission efficiency of cylindrical gear, computer device and readable storage medium |
| CN113158479B (en) * | 2021-04-29 | 2024-03-01 | 清华大学 | Cylindrical gear transmission efficiency calculation method, computer device and readable storage medium |
| CN113404842A (en) * | 2021-05-11 | 2021-09-17 | 重庆大学 | High-order tuning method capable of achieving near-zero fluctuation of gear time-varying meshing stiffness |
| CN113408082A (en) * | 2021-08-20 | 2021-09-17 | 宁波东力传动设备有限公司 | Method for calculating dynamic meshing force of external-meshing straight-tooth cylindrical gear pair |
| CN113987716A (en) * | 2021-11-11 | 2022-01-28 | 中国船舶重工集团公司第七0三研究所 | Dynamic three-dimensional contact stress calculation method for tooth surface of multistage gear pair |
| CN117094200A (en) * | 2023-10-17 | 2023-11-21 | 安徽大学 | Gear time-varying meshing stiffness calculation method considering misalignment error |
| CN117094200B (en) * | 2023-10-17 | 2024-01-16 | 安徽大学 | Gear time-varying meshing stiffness calculation method considering misalignment error |
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