CN103793564B - A kind of system variant computational methods of gear - Google Patents
A kind of system variant computational methods of gear Download PDFInfo
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- CN103793564B CN103793564B CN201410035112.0A CN201410035112A CN103793564B CN 103793564 B CN103793564 B CN 103793564B CN 201410035112 A CN201410035112 A CN 201410035112A CN 103793564 B CN103793564 B CN 103793564B
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Abstract
The invention belongs to transmission and control technical field, tie up to deform under load effect for obtaining axle, improve computational efficiency, the present invention provides the system variant computational methods of a kind of gear, with axle system for basic calculating object, and on the basis of Shafting calculation, by the meshing relation between axle system and the coupled relation between housing and axle system, calculate the deformation of system.The gear magnitude of misalignment computational methods of the system stiffness impact that the present invention provides, with axle system as unit of account, on the basis of ensureing computational accuracy, improve computational efficiency, obtain the magnitude of misalignment of gear and bearing, and the minute design for axle system and transmission case provides design considerations.
Description
Technical field
The invention belongs to transmission and control technical field, be specifically related to the system of a kind of gear
Method for Calculating Deformation.
Background technology
Gear drive is to utilize the gear teeth of two gears to engage each other transmission power and the machinery of motion
Transmission, has the features such as compact conformation, efficiency height, life-span length.In all of machine driving,
Gear drive is most widely used, can be used to transmit the motion between two axles that relative position is not far and move
Power, lathe, aero-engine, agricultural machinery, building machinery, automobile and military vehicle etc.
Industry all have employed gear drive as power and motion transmission form.
Along with drive system lightweight requirements and the continuous lifting of power density, becoming more meticulous of product
It is the most imperative to design.During shafting structure Fatigue Design, due to axle and the support of bearing
Deformation, Gear Contact magnitude of misalignment has reached tens and has arrived hundreds of microns, with the play amount phase of bearing
When, the tired minute design of gear is produced important impact.Recent studies suggest that, axle and
Bearing rigidity size and deflection are interactional, it is impossible to by individually calculating parts stress
Obtain the accurate deformation of system.Therefore, axle system can only be carried out system analysis computation as entirety.
But, if directly using whole drive system as object of study, owing to parts are numerous, bearing
The non-linear behavior of rigidity, model is the hugest, and iteration is the most complicated, not only causes calculating tired
Difficulty, and as easy as rolling off a log make mistakes, unsuitable engineering popularization and application.
In view of the foregoing, how to develop a kind of axle system being basic calculating object with axle system to become
Shape computational methods, and on the basis of Shafting calculation, by the meshing relation between axle system and shell
Coupled relation between body and axle system, calculates the system variant of gear, to art technology
For personnel, it is very in the urgent need to the direction and goal striven for.
Summary of the invention
(1) to solve the technical problem that
The technical problem to be solved in the present invention is for obtaining gear system in load effect
Lower bearing, shaft distortion and the calculating of gear magnitude of misalignment, it is ensured that on the premise of computational accuracy, improve meter
Calculate efficiency.The present invention is with axle system for basic calculating object, it is provided that a kind of single shaft becomes bearing rigidity
Iterative calculation method, and on the basis of Shafting calculation, by the meshing relation between axle system
And the coupled relation between housing and axle system, calculate the system variant of gear.
(2) technical scheme
For solving above-mentioned technical problem, the present invention provides the system variant meter of a kind of gear
Calculation method, it is characterised in that: the iterative computation being become bearing rigidity by single shaft obtains axis rigidity
Matrix, is coupled as system stiffness matrix through housing stiffness matrix, gear teeth meshing stiffness matrix, meter
Calculating the system variant of gear, these computational methods specifically include following steps:
Step one, calculates axle stiffness matrix, applies boundary condition and load, sets up mechanical balance
Equation group, becomes the iterative computation of bearing rigidity by single shaft, solves and obtains single shafting deformation, and
Output single shafting stiffness matrix；
Step 2, on the basis of single shafting stiffness matrix, by housing rigidity and single shafting axle
Hold the coupling of rigidity and meshing gear between coupling, set up transmission case system stiffness matrix；
Step 3, applies boundary condition and load, sets up mechanical balance equation group, solve and obtain
Transmission case system variant.
Wherein, described axle system refers under the support of housing, with the axle that the external world exists meshing relation
The assembly of all structural members with on axle.
Wherein, the type of described stiffness matrix includes axle unit stiffness matrix, bearing unit rigidity
Matrix, housing stiffness matrix, single shafting stiffness matrix and drive system stiffness matrix.
Wherein, the beam list of two nodes it is reduced to after described axle unit stiffness matrix spindle partitioning site
Unit, each node has six-freedom degree；The letter of described bearing unit stiffness matrix spindle bearing unit
Turning to the variable rate spring unit of two nodes, each node has six-freedom degree, calculates with load
Lotus change presents the stiffness matrix of the bearing of non-linear behavior；Housing stiffness matrix refers to housing axle
The bearing inner ring degree of freedom on a node basis is coupling on inner ring Centroid, extracts coupling by finite element software
Close the stiffness matrix at node；Single shafting stiffness matrix spindle and have the bearing of connection relation with axle
The stiffness matrix that stiffness coupling is formed；Drive system stiffness matrix refers to by gear teeth meshing rigidity coupling
That the stiffness coupling between meshing relation each axle system, between axle system and housing formed is firm for having of closing
Degree matrix.
Wherein, described coupled relation include axle and bearing coupling, axle and gear coupling, housing with
Couple between the coupling of axle system and axle system.
Wherein, described axle and bearing couple spindle system inner couplings, by node on axle and bearing
The compatibility of deformation coupling of inner ring；Axle and gear coupling spindle system inner couplings, by axle
Node and the compatibility of deformation coupling of gear teeth base；Housing couples spindle system with outside with axle system
Coupling, by bearing outer ring and housing bearing block compatibility of deformation coupling；Between axle system, coupling refers to
Coupled relation between axle system is mainly coupled by housing and gearing relationships, passes through bearing
Outer ring and housing bearing block, the compatibility of deformation coupling of the contact point of meshing gear.
Wherein, the beam element composition after the spindle partitioning site of single shaft stiffness matrix described in step one
Stiffness matrix, single shafting stiffness matrix be through become Rigidity Matrix of Bearings iteration finally firm by bearing
Degree matrix and the coupling of single shaft stiffness matrix form stiffness matrix.
Wherein, mechanical balance equation group described in step one refers to rigidity displacement equation, i.e. formula
(1):
δS=KS -1×F (1)
δ in formula (1)SFor axle system modal displacement, KSFor single shafting stiffness matrix.
Wherein, mechanical balance equation group described in step 3 refers to rigidity displacement equation, i.e. formula
(2):
δsys=Ksys -1×Fsys (2)
δ in formula (2)sysFor system node displacement, KsysFor axle system and housing rigidity, the gear teeth
The system stiffness matrix that mesh stiffness coupling is formed.
Wherein, the iterative computation of described single shaft change bearing rigidity comprises the steps:
Step S1, power shaft external form and material information, external applied load information, position of bearings and base
This parameter information；
Step S2, partitioning site, calculate beam element stiffness matrix KBEAM；
Step S3, generates load column F；
Step S4, bearing initial stiffness assignment KB0；
Step S5, coupling generates single shafting stiffness matrix KS；
Step S6, to KSPretreatment is carried out with F；
Step S7, solves single shafting deformation δS；
Step S8, it may be judged whether meet the condition of convergence；
Step S9, if being unsatisfactory for the condition of convergence, deforms δ by single shaftingSCompatibility of deformation obtains
Bearing deformation；
Step S10, calculation bearing stiffness matrix KB；
Step S11, output single shafting deformation δS, bearing rigidity KB, bearings counter-force FB,
Single shafting stiffness matrix KS。
Wherein, axle external form information described in step S1 include the external diameter by the length records axle of axle and
Internal diameter size, the material information of axle includes the elastic modelling quantity of axle, modulus of shearing and Poisson's ratio；Outward
Load information comprises by the length records load position of action point of axle, load type, magnitude of load,
Position of bearings information includes the length records bearings position of action point by axle and bearing type,
Bearing basic parameter information includes the type of bearing and the different parameters information of dissimilar bearing.
Wherein, partitioning site described in step S2 refer to an axle as segmentation beam, outside having on axle
Footpath or internal diameter change, load applies, emphasis is asked for coordinating place's conduct at displacement and with other parts
Cell node is countershaft carries out dividing elements.
Wherein, load column described in step S3 is by each panel load
Fi=[Fxi,Fyi,Fzi,Mxi,Myi,Mzi]TThe column vector of composition.
Wherein, for ball bearing in bearing initial stiffness described in step S4, initial stiffness sets
For diagonal matrix diag (105,105,105,0,108,108)；Holding for axis of a cylinder, initial stiffness sets
It is set to diagonal matrix diag (106,106,106,0,109,109)。
Wherein, described in step S5, coupling generates single shafting stiffness matrix KSIt is that single shafting is simplified
For truss structure, using bearing as spring supporting unit, by Rigidity Matrix of Bearings and axle rigidity
Matrix coupling generates.
Wherein, to K described in step S6SCarry out pretreatment with F to refer to K%S=DKS, F%=DF；
Wherein D is diagonal matrix, its diagonal element diMeet formula (3)
K in formula (3)SijFor single shafting stiffness matrix KSIn element.
Wherein, the condition of convergence described in step S8 is to deform δ according to single shaftingSChange, root
Change according to Rigidity Matrix of Bearings, the change according to bearings counter-force and the change of other parameters
Change.
Wherein, the bearing rigidity solution procedure described in step S10 is the deformation by bearing
δB=[δx,δy,δz,θy,θz] load F of calculation bearingB=[Fx,Fy,Fz,My,Mz], and then obtain axle
The stiffness matrix held.
(3) beneficial effect
Compared with prior art, the present invention possesses following beneficial effect:
The system variant computational methods of the gear that the present invention provides, single with axle system for calculating
Position, on the basis of ensureing computational accuracy, improves computational efficiency, obtains the mistake of gear and bearing
Position amount, the minute design for axle system and transmission case provides design considerations.
Accompanying drawing explanation
Single shaft tying in the computational methods of the gear system variant that Fig. 1 provides for the present invention
Structure is reduced to the model simplification figure of truss structure；
The transmission case system structure schematic diagram that Fig. 2 provides for the present invention；
Fig. 3 becomes the iterative calculation method flow chart of bearing rigidity for the single shaft that the present invention provides；
Fig. 4 is the simplified model figure of Traditional calculating methods；
The computational methods middle (center) bearing rigidity of the gear system variant that Fig. 5 provides for the present invention
Iterative process figure；
The line position of the computational methods axis of the gear system variant that Fig. 6 provides for the present invention
Move result figure；
Fig. 7 is to run business software to obtain the displacement of the lines result figure of axle；
The position, angle of the computational methods axis of the gear system variant that Fig. 8 provides for the present invention
Move Comparative result figure；
Fig. 9 is to run business software to obtain the angular displacement result figure of axle.
Detailed description of the invention
For making the purpose of the present invention, content and advantage clearer, below in conjunction with the accompanying drawings and implement
Example, is described in further detail the detailed description of the invention of the present invention.
The system variant computational methods of the gear that the present invention provides, these computational methods are concrete
Comprise the steps:
Step one, calculates axle stiffness matrix, applies boundary condition and load, sets up mechanical balance
Equation group, becomes the iterative computation of bearing rigidity by single shaft, solves and obtains single shafting deformation, and
Output single shafting stiffness matrix；
Step 2, on the basis of single shafting stiffness matrix, by housing rigidity and single shafting axle
Hold the coupling of rigidity and meshing gear between coupling, set up transmission case system stiffness matrix；
Step 3, applies boundary condition and load, sets up mechanical balance equation group, solve and obtain
Transmission case system variant.
Wherein, described axle system refers under the support of housing, with the axle that the external world exists meshing relation
The assembly of all structural members with on axle, structure as shown in Figure 1 is typical shafting structure.
Wherein, described transmission case system is to be joined through gear engagement and housing by multiple shafting structures
The system structure with certain function of knot composition, is by two shafting structure warps as shown in Figure 2
Gear engagement and the transmission case system schematic of housing connection composition.
Wherein, the type of described stiffness matrix includes axle unit stiffness matrix, bearing unit rigidity
Matrix, housing stiffness matrix, single shafting stiffness matrix and drive system stiffness matrix.
Wherein, the beam list of two nodes it is reduced to after described axle unit stiffness matrix spindle partitioning site
Unit, each node has six-freedom degree；The letter of described bearing unit stiffness matrix spindle bearing unit
Turning to the variable rate spring unit of two nodes, each node has six-freedom degree, according to
《ISO/TS16281Rolling bearings-Methods for calculating the modified
Reference rating life for universally loaded bearings " the rigidity square of calculation bearing
Battle array (presenting non-linear behavior with load change)；Housing stiffness matrix refers in housing bearing block
The circle degree of freedom on a node basis is coupling on inner ring Centroid, extracts switching node by finite element software
The stiffness matrix at place；Single shafting stiffness matrix spindle and have the bearing rigidity coupling of connection relation with axle
Close；Drive system stiffness matrix refers to have each axle of meshing relation by gear teeth meshing stiffness coupling
Stiffness coupling between system, between axle system and housing.
Wherein, described coupled relation include axle and bearing coupling, axle and gear coupling, housing with
Couple between the coupling of axle system and axle system.
Wherein, described axle and bearing couple spindle system inner couplings, by node on axle and bearing
The compatibility of deformation coupling of inner ring；Axle and gear coupling spindle system inner couplings, by axle
Node and the compatibility of deformation coupling of gear teeth base；Housing couples spindle system with outside with axle system
Coupling, by bearing outer ring and housing bearing block compatibility of deformation coupling；Between axle system, coupling refers to
Coupled relation between axle system is mainly coupled by housing and gearing relationships, passes through bearing
Outer ring and housing bearing block, the compatibility of deformation coupling of the contact point of meshing gear.
Wherein, the beam element composition after the spindle partitioning site of single shaft stiffness matrix described in step one
Stiffness matrix, single shafting stiffness matrix is finally by bearing rigidity through Rigidity Matrix of Bearings iteration
Matrix and the coupling of single shaft stiffness matrix form stiffness matrix.
Wherein, mechanical balance equation group described in step one refers to rigidity displacement equation, i.e. formula
(1):
δS=KS -1×F (1)
δ in formula (1)SFor axle system modal displacement, KSFor single shafting stiffness matrix.
Wherein, mechanical balance equation group described in step 3 refers to rigidity displacement equation, i.e. formula
(2):
δsys=Ksys -1×Fsys (2)
δ in formula (2)sysFor system node displacement, KsysFor axle system and housing rigidity, the gear teeth
The system stiffness matrix that mesh stiffness coupling is formed, its middle shell rigidity and gear teeth meshing rigidity are
Constant value.
As it is shown on figure 3, the iterative calculation method that the single shaft that the present invention provides becomes bearing rigidity passes through
Calculate the deformation of axle system, coordinate to obtain bearing deformation through displacement deformation, and then carry through solving bearing
Lotus obtains Rigidity Matrix of Bearings.The method avoids and use Newton-Raphson traditionally
Method passes through power and the moment Nonlinear System of Equations multidimensional rooting to displacement and corner, not only improves
Arithmetic speed, also improves computing stability.
Wherein, described single shaft becomes the iterative computation of bearing rigidity and comprises the steps:
Step S1, power shaft external form and material information, external applied load information, position of bearings and base
This parameter information；
Step S2, partitioning site, calculate beam element stiffness matrix KBEAM；
Step S3, generates load column F；
Step S4, bearing initial stiffness assignment KB0；
Step S5, coupling generates single shafting stiffness matrix KS；
Step S6, to KSPretreatment is carried out with F；
Step S7, solves single shafting deformation δS；
Step S8, it may be judged whether meet the condition of convergence；
Step S9, if being unsatisfactory for the condition of convergence, deforms δ by single shaftingSCompatibility of deformation obtains
Bearing deformation；
Step S10, calculation bearing stiffness matrix KB；
Step S11, output single shafting deformation δS, bearing rigidity KB, bearings counter-force FB,
Single shafting stiffness matrix KS。
Wherein, axle external form information described in step S1 include the external diameter by the length records axle of axle and
Internal diameter size, the material information of axle includes the elastic modelling quantity of axle, modulus of shearing and Poisson's ratio.Outward
Load information comprises by the length records load position of action point of axle, load type, magnitude of load,
Position of bearings information includes the length records bearings position of action point by axle and bearing type,
Bearing basic parameter information includes the type of bearing and the different parameters information of dissimilar bearing,
Such as: deep groove ball bearing essential information includes ball diameters, outer fissure Curvature Radius Coefficient, septal fossula
Curvature Radius Coefficient, pitch diameter, play, spin number, fit tolerance；Cylinder roller bearing
Essential information includes roller length, roller diameter, play, roller number, fit tolerance；Circle
Taper roller bearing essential information include roller length, roller diameter, pitch diameter, contact angle,
Play, roller number, fit tolerance；Four-point contact ball essential information include ball diameters,
Outer fissure Curvature Radius Coefficient, septal fossula Curvature Radius Coefficient, pitch diameter, contact angle, play,
Spin number and fit tolerance.
Wherein, partitioning site described in step S2 refer to an axle as segmentation beam, outside having on axle
Footpath or internal diameter change, load applies, emphasis is asked for coordinating place's conduct at displacement and with other parts
Cell node is countershaft carries out dividing elements, and Fig. 1 illustrates axle node division situation.
Wherein, load column described in step S3 is by each panel load
Fi=[Fxi,Fyi,Fzi,Mxi,Myi,Mzi]TThe column vector of composition.
Wherein, bearing initial stiffness described in step S4 is very big, suitably on iterative step impact
Bearing initial stiffness arranges and largely adds rapid convergence.For ball bearing, initial stiffness sets
For diag (105,105,105,0,108,108), axis of a cylinder is held, initial stiffness is set as
diag(106,106,106,0,109,109)。
Wherein, described in step S5, coupling generates single shafting stiffness matrix KS, it is by single shafting letter
Turn to truss structure, using bearing as spring supporting unit, firm by Rigidity Matrix of Bearings and axle
Degree Matrix coupling generates.
Wherein, to K described in step S6SCarry out pretreatment with F to refer to: due to KSFor sparse
Matrix, therefore to KSIt is balanced pretreatment, by K% with FS=DKS, F%=DF.Wherein D
For diagonal matrix, its diagonal element diMeet formula (3)
K in formula (3)SijFor single shafting stiffness matrix KSIn element.
Wherein, the condition of convergence described in step S8 has multiple basis for estimation, as according to single shafting
Deformation δSChange, according to the change of Rigidity Matrix of Bearings, according to the change of bearings counter-force
Deng.
Wherein, the bearing rigidity solution procedure described in step S10 is according to " ISO16281 "
The method provided, by the deformation δ of bearingB=[δx,δy,δz,θy,θz] load of calculation bearing
FB=[Fx,Fy,Fz,My,Mz], and then obtain the stiffness matrix of bearing.
Wherein, single shafting stiffness matrix K described in step S11SIt is through iteration Rigidity Matrix of Bearings
The axis rigidity matrix of final convergence.
Respectively axle system each in transmission case system is carried out single shaft and becomes the iterative computation of bearing rigidity, defeated
The axis rigidity matrix gone out forms transmission case system stiffness through gear engagement and housing stiffness coupling
Matrix.
Embodiment
1. embodiment
Transmission case system structure shown in Fig. 2 is decomposed, can be analyzed to two single shaft tyings
Structure, two shafting structures connect through a pair gear engagement and housing.Wherein, the structure of axle system 1
As shown in Figure 1.
Structure shown in Fig. 1 is become the iterative computation example of bearing rigidity, with employing as single shaft
The calculated result of traditional method is analyzed.The material of axle is steel alloy, and material is joined
Number is as follows: elastic modulus E=206000MPa, shear modulus G=79380MPa, Poisson's ratio
λ=0.3.Axial end input torque 1000000Nmm, gear F loadedy=-2426.5N、
Fz=-6666.7N、Mx=-1000000Nmm, the physical dimension of axle and the essential information of bearing
As shown in Table 1 and Table 2.
The dimensional parameters of table 1 axle
| Shaft part code name | External diameter (mm) | Internal diameter (mm) | Length (mm) |
| 1 | 60 | 0 | 100 |
| 2 | 120 | 0 | 200 |
| 3 | 180 | 0 | 130.415 |
| 4 | 300 | 0 | 80 |
| 5 | 180 | 0 | 89.585 |
| 6 | 120 | 0 | 200 |
The dimensional parameters of table 2 bearing
2. Traditional calculating methods
Fig. 4 is the statically indeterminate beam during coupled relation not considering bearing and axle.Wherein, bearing regards
For rigid support point.Use matrix displacement method to calculate the support reaction of this structure, obtain bearing 1
Counter-force Fy1=-250.4N、Fz1=-688.0N, counter-force F of bearing 2y2=1688.9N、Fz2=
4640.1N, counter-force F of bearing 3y3=988.0N、Fz3=2714.5N。
3. the computational methods that the present invention proposes
The single shaft provided according to the present invention becomes the iterative calculation method of bearing rigidity, to shown in Fig. 1
Shafting structure carry out deformation calculate, the iterative process of Y-direction bearing Main rigidity is plotted as figure
Table, as shown in Figure 5.As shown in Figure 5, iteration 25 step i.e. reaches the mechanical balance of axle system.Now,
Main rigidity in each bearing Y-direction is respectively as follows: the K of bearing 1yy1=0.7612×105N/mm、
The K of bearing 2yy2=0.4617×105N/mm, the K of bearing 3yy3=1.1041×105N/mm.Axle
Hold the reaction of bearing F of 1y1=605.5N、Fz1=1299.2N, the reaction of bearing F of bearing 2y2=
470.8N、Fz2=1808.7N, the reaction of bearing F of bearing 3y3=1351.7N、Fz3=
3558.8N.Output single shafting stiffness matrix is to comprise node on axle, bearing node and gear joint
The single shafting stiffness matrix K of pointS1。
4. result of calculation analysis
The result of calculation that contrast above two method obtains understands, if consider the elastic change of bearing
Shape, the distribution on bearing can great changes will take place for external applied load, also can in even shaft strength direction
Change.Therefore, the deformation of axle system calculates the Coupling Deformation pass that must take between all parts
System.
For verifying that the single shaft that the present invention provides becomes the accuracy of the iterative calculation method of bearing rigidity,
By displacement of the lines and angular displacement result of calculation and equal load and identical business software under the conditions of other
Result of calculation contrast.The gear dislocation of the system stiffness impact that Fig. 6 provides for the present invention
The displacement of the lines result figure of amount computational methods axis；Fig. 7 is the displacement of the lines result figure of business software axle；
The position, angle of the gear magnitude of misalignment computational methods axis of the system stiffness impact that Fig. 8 provides for the present invention
Move Comparative result figure；Fig. 9 is the angular displacement result figure of business software axle.
Comparing result understand, the present invention provide single shaft become bearing rigidity iterative calculation method with
The result of calculation goodness of fit of business software is the highest, and accuracy is verified.
5. with other axle systems and housing stiffness coupling
The single shaft using the present invention to provide becomes the iterative calculation method of bearing rigidity and can shaft 2 enter
Row deformation calculates, the single shafting stiffness matrix K of output shaft system 2S2。
The firm of bearing outer ring and housing junction housing switching node is extracted by finite element software
Degree matrix KBOX, according to correlation technique (such as gear teeth segmentally numerical calculation method or " ISO6336
Calculation of load capacity of spur and helical gears " the simplification algorithm that provides)
It is calculated gear teeth meshing stiffness matrix Kmesh。
According to the connection relation between axle system and axle system and the connection relation of housing, to single shafting rigidity
Matrix KS, the stiffness matrix K of housing switching nodeBOXWith gear teeth meshing stiffness matrix KmeshCarry out
Stiffness coupling, forms system stiffness matrix Ksys。
6. system variant calculates
Apply the moment shown in Fig. 2, set up mechanics of system equilibrium equation group, i.e. formula (2),
Solve and obtain transmission case system variant δsys。
It is constant value from formula (2), housing rigidity and gear teeth meshing rigidity, shown in Fig. 2
The accuracy of the result of calculation of two axle system deformation is the result of calculation standard affecting system variant amount
The really key factor of degree, the computational methods provided by the present invention obtain the calculating of axle system deformation
The accuracy of result is the most clearly verified by above-mentioned result of calculation analysis.
The above is only the preferred embodiment of the present invention, it is noted that lead for this technology
For the those of ordinary skill in territory, on the premise of without departing from the technology of the present invention principle, it is also possible to
Making some improvement and deformation, these improve and deformation also should be regarded as protection scope of the present invention.
Claims (18)
1. the system variant computational methods of a gear, it is characterised in that: by list
Axle becomes the iterative computation of bearing rigidity and obtains axis rigidity matrix, through housing stiffness matrix, the gear teeth
Mesh stiffness Matrix coupling is system stiffness matrix, calculates the system variant of gear, should
Computational methods specifically include following steps:
Step one, calculates axle stiffness matrix, applies boundary condition and load, sets up mechanical balance
Equation group, becomes the iterative computation of bearing rigidity by single shaft, solves and obtains single shafting deformation, and
Output single shafting stiffness matrix；
Step 2, on the basis of single shafting stiffness matrix, by housing rigidity and single shafting axle
Hold the coupling of rigidity and meshing gear between coupling, set up transmission case system stiffness matrix；
Step 3, applies boundary condition and load, sets up mechanical balance equation group, solve and obtain
Transmission case system variant.
The system variant computational methods of gear the most according to claim 1, its
It is characterised by: described axle system refers under the support of housing, with the axle that the external world exists meshing relation
The assembly of all structural members with on axle.
The system variant computational methods of gear the most according to claim 1, its
It is characterised by: the type of described stiffness matrix includes axle unit stiffness matrix, bearing unit rigidity
Matrix, housing stiffness matrix, single shafting stiffness matrix and drive system stiffness matrix.
The system variant computational methods of gear the most according to claim 3, its
It is characterised by: after described axle unit stiffness matrix spindle partitioning site, be reduced to the beam list of two nodes
Unit, each node has six-freedom degree；The letter of described bearing unit stiffness matrix spindle bearing unit
Turning to the variable rate spring unit of two nodes, each node has six-freedom degree, calculates with load
Lotus change presents the stiffness matrix of the bearing of non-linear behavior；Housing stiffness matrix refers to housing axle
The bearing inner ring degree of freedom on a node basis is coupling on inner ring Centroid, extracts coupling by finite element software
Close the stiffness matrix at node；Single shafting stiffness matrix spindle and have the bearing of connection relation with axle
The stiffness matrix that stiffness coupling is formed；Drive system stiffness matrix refers to by gear teeth meshing rigidity coupling
That the stiffness coupling between meshing relation each axle system, between axle system and housing formed is firm for having of closing
Degree matrix.
The system variant computational methods of gear the most according to claim 1, its
Be characterised by: described coupled relation include axle and bearing coupling, axle and gear coupling, housing with
Couple between the coupling of axle system and axle system.
The system variant computational methods of gear the most according to claim 5, its
It is characterised by: described axle and bearing couple spindle system inner couplings, by node on axle and bearing
The compatibility of deformation coupling of inner ring；Axle and gear coupling spindle system inner couplings, by axle
Node and the compatibility of deformation coupling of gear teeth base；Housing couples spindle system with outside with axle system
Coupling, by bearing outer ring and housing bearing block compatibility of deformation coupling；Between axle system, coupling refers to
Coupled relation between axle system is mainly coupled by housing and gearing relationships, passes through bearing
Outer ring and housing bearing block, the compatibility of deformation coupling of the contact point of meshing gear.
The system variant computational methods of gear the most according to claim 1, its
It is characterised by: the beam element composition after the spindle partitioning site of axle stiffness matrix described in step one
Stiffness matrix, single shafting stiffness matrix is through becoming Rigidity Matrix of Bearings iteration finally by bearing rigidity
Matrix and the coupling of single shaft stiffness matrix form stiffness matrix.
The system variant computational methods of gear the most according to claim 1, its
It is characterised by: mechanical balance equation group described in step one refers to rigidity displacement equation, i.e. formula
(1):
δS=KS -1×F (1)
δ in formula (1)SFor axle system modal displacement, KSFor single shafting stiffness matrix, F is single
Axle system load column.
The system variant computational methods of gear the most according to claim 1, its
It is characterised by: mechanical balance equation group described in step 3 refers to rigidity displacement equation, i.e. formula
(2):
δsys=Ksys -1×Fsys (2)
δ in formula (2)sysFor system node displacement, KsysFor axle system and housing rigidity, the gear teeth
The system stiffness matrix that mesh stiffness coupling is formed, FsysFor system load array.
The system variant computational methods of gear the most according to claim 1, its
It is characterised by: described single shaft becomes the iterative computation of bearing rigidity and comprises the steps:
Step S1, power shaft external form and material information, external applied load information, position of bearings and base
This parameter information；
Step S2, partitioning site, calculate beam element stiffness matrix KBEAM；
Step S3, generates load column F；
Step S4, bearing initial stiffness assignment KB0；
Step S5, coupling generates single shafting stiffness matrix KS；
Step S6, to KSPretreatment is carried out with F；
Step S7, solves single shafting deformation δS；
Step S8, it may be judged whether meet the condition of convergence；
Step S9, if being unsatisfactory for the condition of convergence, deforms δ by single shaftingSCompatibility of deformation obtains
Bearing deformation；
Step S10, calculation bearing stiffness matrix KB；
Step S11, output single shafting deformation δS, bearing rigidity KB, bearings counter-force FB,
Single shafting stiffness matrix KS。
The system variant computational methods of 11. gears according to claim 10,
It is characterized in that: described in step S1, axle external form information includes the external diameter by the length records axle of axle
And internal diameter size, the material information of axle includes the elastic modelling quantity of axle, modulus of shearing and Poisson's ratio；
External applied load information comprises by the length records load position of action point of axle, load type, load big
Little, position of bearings information includes the length records bearings position of action point by axle and bearing class
Type, bearing basic parameter information includes the type of bearing and the different parameters letter of dissimilar bearing
Breath.
The system variant computational methods of 12. gears according to claim 10,
It is characterized in that: partitioning site described in step S2 refer to an axle as segmentation beam, to have on axle
External diameter or internal diameter change, load applies, emphasis is asked for making at displacement and with other part places of cooperation
Dividing elements is carried out for cell node is countershaft.
The system variant computational methods of 13. gears according to claim 10,
It is characterized in that: load column described in step S3 is for by each panel load
Fi=[Fxi,Fyi,Fzi,Mxi,Myi,Mzi]TThe column vector of composition.
The system variant computational methods of 14. gears according to claim 10,
It is characterized in that: for ball bearing in bearing initial stiffness described in step S4, initial stiffness sets
It is set to diagonal matrix diag (105,105,105,0,108,108)；Axis of a cylinder is held, initial stiffness
It is set as diagonal matrix diag (106,106,106,0,109,109)。
The system variant computational methods of 15. gears according to claim 10,
It is characterized in that: coupling described in step S5 generates single shafting stiffness matrix KSIt is by single shafting letter
Turn to truss structure, using bearing as spring supporting unit, firm by Rigidity Matrix of Bearings and axle
Degree Matrix coupling generates.
The system variant computational methods of 16. gears according to claim 10,
It is characterized in that: to K described in step S6SWith F carry out pretreatment refer to by Wherein D is diagonal matrix, its diagonal element diMeet formula (3)
K in formula (3)SijFor single shafting stiffness matrix KSIn element.
The system variant computational methods of 17. gears according to claim 10,
It is characterized in that: the condition of convergence described in step S8 is for deforming δ according to single shaftingSChange,
Change according to Rigidity Matrix of Bearings, according to the change of bearings counter-force and the change of other parameters
Change.
The system variant computational methods of 18. gears according to claim 10,
It is characterized in that: the bearing rigidity solution procedure described in step S10 is the deformation by bearing
δB=[δx,δy,δz,θy,θz] load F of calculation bearingB=[Fx,Fy,Fz,My,Mz], and then obtain axle
The stiffness matrix held.
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| JP2013008259A (en) * | 2011-06-27 | 2013-01-10 | Keio Gijuku | Load transmission analysis device for nonlinear structure |
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| CN103530468A (en) * | 2013-10-23 | 2014-01-22 | 清华大学 | Multi-support shafting finite element method with bearing stiffness coupling nonlinearity considered |
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| JP2013008259A (en) * | 2011-06-27 | 2013-01-10 | Keio Gijuku | Load transmission analysis device for nonlinear structure |
| CN102982206A (en) * | 2012-11-27 | 2013-03-20 | 中国能源建设集团广东省电力设计研究院 | Equipment and method for evaluating static displacement and deformation of vibration insulating foundation of steam-turbine generator |
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