CN110008594A - A kind of Gear Planet Transmission herringbone bear finite element grid automatic modeling and assembly method - Google Patents
A kind of Gear Planet Transmission herringbone bear finite element grid automatic modeling and assembly method Download PDFInfo
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Abstract
A kind of Gear Planet Transmission herringbone bear finite element grid automatic modeling of the present invention and assembly method, comprising: determine the node coordinate of single two lateral tooth flank of helical gear and the excessive profile of tooth root；The profile of intermediate wheel body is rotated into angle shared by a tooth around axis and obtains two sides tooth socket profile；On the basis of boundary profile, single helical gear entity is constructed using discrete point；Lead to mirror method for the other half helical gear node to determine；Determine tooth socket node；The herringbone bear of any tooth is generated from new progress unit and cell node number according to 8 node hexahedron linear unit node sequences；The theoretical corner that planetary gear corner determines sun gear, gear ring wheel is finally given, each pitch point is transformed by coordinate transform by the accurate assembly that unified reference frame completes gear pair finite element model according to the corner and installation relation.The grid data file that the method for the present invention generates can be introduced directly into Abaqus software and carry out loaded tooth contact analysis, significantly improve design of gears analysis precision and efficiency.
Description
Technical field
The invention belongs to aviations, navigation gear technique field, and in particular to a kind of star double helical tooth wheel set finite element grid
Automatically generate and Assembled modeling method.
Background technique
Herringbone planetary transmission system has many advantages, such as that smaller axial force, higher power density, transmission are more stable,
Straight-tooth is gradually replaced, helical teeth pair becomes the high speed such as aviation, navigation, the primary choosing of the gear train assembly of heavily loaded power dividing type
It selects, performance superiority and inferiority directly affects national defense safety.Gear modification technology has been found to be the effective way for improving meshing performance；
Obtaining the distribution of correction of the flank shape contact force, carrying driving error and meshing impact by gear LOADED TOOTH CONTACT ANALYSIS (LTCA) is to measure
The main path of flank engagement performance.However, business is limited due to the complexity of particularity and geometry in herringbone bear structure
Meta software is more and more to be applied to gear loaded tooth contact analysis.Although business finite element software is effectively analysis tool, so
And the correct assembly of finite element model mesh quality, flank of tooth node geometric accuracy, gear pair has become influence LTCA solving precision
Key factor.The parametric modeling in business finite element analysis software controls grid dividing using the program language of itself, but
It is difficult to model complicated tooth surface geometry model, especially the correction of the flank shape flank of tooth with this method, and very time-consuming, reduces analytical calculation
Efficiency and precision increase designer's workload.In addition, publication number CN104408421A, which proposes a kind of Helical Gears with Modification, to be had
The automatic generation method of first grid is limited, but is not suitable for complicated herringbone bear；Publication number CN10421286.5 proposes one kind
The automatic generation method of single external toothing herringbone bear finite element grid, the flank of tooth are transformed by rack cutter, are beyond expression multiple
The miscellaneous topological correction of the flank shape flank of tooth, and the density of transverse tooth thickness direction grid can not be carried out automatically controlling, it not can guarantee the peace of gear pair yet
Precision is filled, and the density degree and gear pair installation accuracy along the outermost layer flank of tooth grid in transverse tooth thickness direction are to analysis result and calculating
Efficiency has a significant impact, and is not suitable for the planet double helical tooth transmission system of complex topology correction of the flank shape.
Summary of the invention
It is limited it is an object of the invention in view of the above shortcomings of the prior art, provide a kind of Gear Planet Transmission herringbone bear
First grid automatic modeling and assembly method.
The present invention adopts the following technical scheme that realize:
A kind of Gear Planet Transmission herringbone bear finite element grid automatic modeling and assembly method, comprising: nibbled first according to gear
Closing principle indicates tool-tooth profile to obtain the standard involute flank of tooth in gear coordinate system, and the correction of the flank shape of inside and outside gear pair is placed on
On planetary gear, pass through the standard involute flank of tooth and the normal direction correction of the flank shape curved surface superimposed structure correction of the flank shape flank of tooth, it is determined that single helical gear two
The node coordinate of lateral tooth flank and the excessive profile of tooth root；Secondly, determining the wheel of intermediate wheel body according to the boundary point of the excessive profile of tooth root
The profile of intermediate wheel body is rotated angle shared by a tooth around axis and obtains two sides tooth socket profile by exterior feature；Then, in boundary profile
On the basis of, the entity part between profile is filled by Rotating Transition of Coordinate discrete point, is constructed using discrete point single oblique
The entity of gear；Lead to mirror method for the other half helical gear node to determine；It stretches one end helical gear inner face wheel body and determines tooth
Slot node；So far, monodentate node all determines, the node of other teeth is linear according to 8 node hexahedrons by being pivoted determination
Cell node sequence generates the herringbone bear of any tooth from new progress unit and cell node number；It is contacted in conjunction with planetary gear
TCA is analyzed, given planetary gear corner determines the theoretical corner of sun gear, gear ring wheel, according to the corner and installation relation by each tooth
Wheel node is transformed into the accurate assembly that unified reference frame completes gear pair finite element model by coordinate transform；Most
Afterwards, according to the redaction rule of Abaqus input inp file, by the node of above-mentioned finite element model, unit and required setting
Point set, boundary condition, contact setting etc., which are write, generates inp file, by programming input gear basic parameter, so that it may realize high-precision
Degree Gear Planet Transmission correction of the flank shape double helical tooth wheel set finite element grid automatically generate and the density of the flank of tooth outer layer grid control, assembly and it is preceding
Processing.
A further improvement of the present invention lies in that specifically including following implemented step:
Step 1: input gear second parameter determines other parameters
Basic parameters of gear includes: that the number of teeth, modulus, pressure angle, helical angle, the unilateral facewidth, withdrawing be wide, height of teeth top, tooth root
High and cutter radius of corner, installation error, that is, crossed axis angle error and center are away from being reduced to sun gear, gear ring with respect to reference frame
Error, each planetary gear is without installation error；Profile modification and axial modification are all made of straight line+second-degree parabola modification curve, table
It is shown as rotation perspective plane parametric function；
Step 2: the expression of the standard involute flank of tooth
Tool-tooth profile is indicated based on Principles of Gear Connection to obtain the standard involute flank of tooth in gear coordinate system；Sun gear
It is transformed into planetary gear by rack cutter, gear ring is transformed by involute gear, and flank of tooth position vector, method arrow indicate are as follows:
In formula: Ri、NiRespectively flank of tooth position vector and per unit system arrow, i=s, p, g respectively indicates sun gear, star-wheel and gear ring；
Rci、NciRespectively cutter end face position vector and method arrow；uiAnd liIt is cutter parameters；Mi,ci(θi) it is from tool coordinate system SciTo gear
Coordinate system SiCoordinate conversion matrix, Li,ci(θi) it is its submatrix；θiFor the corner for being processed gear；
Step 3: the expression of the planetary gear correction of the flank shape flank of tooth
The two sides of planetary gear are engaged with gear ring and sun gear respectively, and for gear ring since size is larger, processing technology is complicated usually
Not correction of the flank shape is placed on planetary gear the correction of the flank shape of gear ring；The correction of the flank shape of sun gear is also placed on planetary gear, i.e. the two sides of herringbone bear
The flank of tooth all corrections of the flank shape；Symmetrical correction of the flank shape is usually taken in the left and right flank of tooth；Pass through the standard involute flank of tooth and normal direction correction of the flank shape curved surface superimposed structure
The correction of the flank shape flank of tooth of planetary gear, flank of tooth method arrow, position vector indicate are as follows:
In formula: Rpm、NpmFor planetary gear correction of the flank shape flank of tooth position vector；δ is normal direction profiling quantity, is the function of tooth surface parameters, usually
It is indicated with numerical value (x, y) on rotation perspective plane, uses modification curve along rack cutter parameter (u when solving correction of the flank shape flank of tooth method arrowp,
lp) direction cuts arrow, calculating process is as follows:
In formula: Rx,Ry,RzRespectively theoretical flank of tooth position vector coordinate components；
Step 4: single full teeth surface grids node calculates and the number of unit, cell node
Herringbone bear includes 3 each section of left side helical teeth, escape and the right helical teeth, along the left and right flank of tooth pair of axial double helical tooth
Claim, middle section is escape；One complete helical teeth divides are as follows: the flank of tooth, tooth root, wheel body, wheel body left side tooth socket, wheel body right side tooth
Slot；Firstly, each node location of profile is determined, in conjunction with these positions according to each section number of nodes radially, axially of single tooth
Point, the flank of tooth and tooth root profile discrete point coordinate values of left side helical teeth according to cutter tooth shape and correction of the flank shape according to front the step of it is true
It is fixed；Then, the profile coordinate that wheel body discrete point is determined according to the radial boundary of tooth root point and wheel body depth, by the left and right of wheel body
Angle shared by side profile rotation 1 tooth of rotation obtains the discrete dot profile coordinate of right, left tooth socket；In conjunction with these profiles, according to transverse tooth thickness
The number of nodes of direction each section by entity part of the Rotating Transition of Coordinate between discrete point " filling " profile, and then uses
Discrete point has constructed the entity of gear；Finally, according to single tooth radially, axially, transverse tooth thickness direction according to default rule, by institute
There is discrete point to carry out unit and cell node number according to 8 node hexahedron linear unit node sequences；
Step 5: the other half helical gear node of double helical tooth determines
Herringbone bear left and right tooth face is symmetrical, leads to " mirror image " method for the other half helical gear node and determines:
In formula: B is the helical gear facewidth；W is withdrawing groove width；Coordinate system is at left flank facewidth midpoint in text,
xli,j,k,yli,j,k, zli,j,kFor the single helical teeth mesh point coordinate in the right；
Step 6: double helical tooth escape node determines
After determining left and right flank of tooth wheel body coordinate, according to left helical gear wheel body inner face node along axial " stretching " escape
Width, then escape node are as follows:
In formula: subscript ic=1 ... Ic,jc=1 ... (2Jc+ J), kc=1 ... KcFor radial direction, transverse tooth thickness, axial node label, rise
Beginning position；KcFor axial grid number；
Step 7: the generation of arbitrarily a tooth flank of tooth node of double helical tooth and node serial number
By the single tooth whole node of above step it has been determined that rotating coordinate transformation can array generate whole teeth, and
The junction paid attention to the i.e. node of side does not repeat, and the node coordinate of i-th tooth indicates are as follows:
In formula: M is the rotational transformation matrix around gear axial direction, and Z is the number of teeth, and XI, YI, ZI is all node collection of i-th tooth
It closes, x, y, z is all node sets of single tooth；It is numbered while determination single helical gear node, it is symmetrical to determine
It when the other half helical gear and escape node, is added up on the basis of original number；According to the requirement of finite element adaptive grid generation,
Node is renumberd, by three layers of loop control, outer layer controls radial direction from tooth top to wheel body the last layer, secondary outer layer from
Side to the other side controls transverse tooth thickness direction, and innermost layer controls axial direction from an end face to another end face, successively by tooth from
New sort whole node, according still further to 8 node hexahedron linear unit node sequences from the new number for carrying out unit and cell node；
Step 8: planetary gear TCA analysis
TCA principle is continuous phase cut-grafting touching two flank of tooth any time in the same coordinate system to have public contact point and public law
Line is i.e.:
In formula:For the engagement corner of each gear；MfiTo convert square from gear movement coordinate system to installation reference frame
Battle array, LfiFor 3 × 3 submatrix thereon；Rfi、NfiPosition vector and per unit system for the flank of tooth in reference frame are sweared；Above formula is five available
Independent scalar equation takes a series ofFor input quantity, solving remaining 5 unknown quantity can be obtained the institute of two flank engagement positions
It has point of contact and corner；
TCA analyzes to obtain planetary gear with respect to sun gear, gear ring with respect to planetary gear geometry driving error are as follows:
In formula:Respectively the initial corner of planetary gear, bull wheel, bull wheel include sun gear and gear ring；Z is the number of teeth；Certain
One position of engagement gives planetary gear cornerThe then accurate theoretical corner of sun gear or gear ringAre as follows:
Step 9: the first external, internal gear pair assembly node determination
Gear TCA analysis guarantees there is accurate position of engagement relationship in a certain position of engagement gear pair, and TCA analysis is gone
Sun gear, the gear ring of the star-wheel position of engagement examine the corner of coordinate system in engagement, according to installation relation, the accurate assembly of each gear
Node coordinate are as follows:
In formula: XAi、YAi、ZAiFor all node coordinate numerical value set of the full flank of tooth；XXi、YYi、ZZiFor unified reference coordinate
Complete all node coordinate numerical value set of the flank of tooth under system；
Step 10: the assembly node of other planetary gears determines
Other planetary gear nodes are assembled according to the gear corner that uniformly distributed established angle and TCA are emulated；Installation is missed
Difference is reduced to the installation error of sun gear and the relatively uniform referential of gear ring, and planetary gear and planet carrier are error free, therefore, direct handle
The node of the rapid accurate assembly model of step 9, node serial number write life according to the redaction rule of the input inp file of Abaqus
After importing Abaqus at inp file, then radial arrays planetary gear completes the assembly of multiple planetary gears；N-th of planetary gear is accurate
Assembly node coordinate are as follows:
In formula: XPn、YPn、ZPnFor all node coordinate numerical value set of the full flank of tooth of n-th of planetary gear, n=1 ... N, N are
Planetary gear number, XP、YP、ZPFor the 1st all node coordinate numerical value set of the full flank of tooth of planetary gear；
Step 11: the Abaqus pre-processing file of the different positions of engagement generates
The calculating of step 9~10 assembly nodes is sun gear, planetary gear, the gear ring of any full teeth based on preceding step
Calculating, then by planetary gear TCA calculate a tooth it is engaging-in to the corner for nibbling out process gear joint, to sun gear, tooth
Circle, each planetary gear finite element model assembled, according to Abqus input inp file redaction rule, by above-mentioned number with
And point set, boundary condition, contact setting for being arranged required for finite element etc. write and generate inp file, imported into Abaqus, i.e.,
Complete the high-precision modeling and pre-treatment setting of finite element model.
A further improvement of the present invention lies in that in step 4, specific point or less 3 steps:
The single helical gear flank of tooth of a and tooth root transition node calculate
According to the flank of tooth, radially, axially mesh parameter determines the profile discrete point coordinate of two lateral tooth flanks and tooth root transition,
Pass through entity part of the Rotating Transition of Coordinate between discrete point " filling " boundary point；The flank of tooth and the entire entity of tooth root transition
Node coordinate indicates are as follows:
In formula: Rx,Ry,RzIt include transition position vector coordinate components, r for the flank of toothi,k,ai,kFor according to flank of tooth grid data
Determining known radially, axially position point data；∠ q is the angle of corresponding flank of tooth node and transverse tooth thickness center line, according to node position
It sets and is determined by the cosine law；xli,j,k,yli,j,k, zli,j,kFor left side helical teeth mesh point coordinate, subscript i=1 ... I, j=
1 ... J, k=1 ... K are followed successively by radial direction, transverse tooth thickness, axial node label, and I, J, K is the flank of tooth and root portions all directions node total number；
The single helical gear wheel body node of b calculates
It is wheel body starting point by calculating the i.e. radial node of left and right flank of tooth easement curve and root circle intersection point, then takes turns body node
It calculates as follows:
In formula: is=1 ... IsFor wheel body radial direction vertex ticks, Is is wheel body radial direction number of nodes；S is wheel body radial direction step-length, tooth
Thick direction and axial direction number of nodes are unchanged；
C single helical gear wheel body two sides tooth socket node calculates
By the boundary node of wheel body left and right side to the right, left side rotate a tooth angle, θcObtain that right, left side tooth socket is corresponding
Node calculates as follows:
In formula: "+" indicates left side tooth socket node js=1, "-" indicates right side tooth socket node js=J；J=1 ... JcFor tooth socket
Transverse tooth thickness vertex ticks, JcFor transverse tooth thickness direction tooth socket number of nodes；Axial direction number of nodes is without constant.
The present invention has following beneficial technical effect:
A kind of Gear Planet Transmission herringbone bear finite element grid automatic modeling provided by the invention and assembly method, this method without
It need to be modeled by business finite element software, by programming input planet gear system basic parameter, installation error, the flank of tooth is repaired
Shape parameter, so that it may realize automatically generating and flank of tooth outer layer net for high-precision Gear Planet Transmission correction of the flank shape herringbone bear system finite element grid
Density control, assembly and the Preceding Dispose of FEA of lattice.The grid data file that the method for the present invention generates can be introduced directly into
Abaqus software carries out the analysis of planetary gear pair geometrical contact and LOADED TOOTH CONTACT ANALYSIS.
Detailed description of the invention
Fig. 1 is rack gear generated involute flank of tooth coordinate system of the present invention.
Fig. 2 is pinion cutter generated involute gear ring coordinate system of the present invention.
Fig. 3 is sun gear of the present invention, planetary gear, the single tooth flank of tooth of gear ring and root portions grid discrete point.
Fig. 4 is planetary gear topology modification curve of the present invention.
Fig. 5 is that the planetary gear theory flank of tooth of the present invention and the topological correction of the flank shape flank of tooth compare.
Fig. 6 is the position mark of herringbone increment of the present invention face each section.
Fig. 7 is that 8 node hexahedrons of the invention linearly reduce integral unit number order.
Fig. 8 is the non-homogeneous three gears finite element model of gear ring herringbone bear transverse tooth thickness grid of the present invention.
Fig. 9 is the uniform three gears finite element model of gear ring herringbone bear transverse tooth thickness grid of the present invention.
Figure 10 is the full flank of tooth finite element model of gear ring double helical tooth of the present invention.
Figure 11 is the full flank of tooth finite element model of sun gear double helical tooth of the present invention.
Figure 12 is the full flank of tooth finite element model of planetary gear double helical tooth of the present invention.
Figure 13 is planet herringbone bear system mounting coordinate of the present invention system.
Figure 14 is a certain external toothing pair mounting coordinate system of the present invention.
Figure 15 is helical gear TCA emulation on the left of correction of the flank shape planet herringbone bear of the present invention.
Figure 16 is internal messing profile modifying gear pair of the present invention in engaging-in accurate assembly enlarged drawing.
Figure 17 is external toothing profile modifying gear pair of the present invention in engaging-in accurate assembly enlarged drawing.
Figure 18 is correction of the flank shape planet herringbone bear system of the present invention at the engaging-in accurate installation diagram in position (1 planetary gear).
Figure 19 is correction of the flank shape planet herringbone bear system of the present invention at the engaging-in accurate installation diagram in position (4 planetary gears).
Figure 20 is design-calculated flow chart of the present invention.
Specific embodiment
The present invention is made further instructions with reference to the accompanying drawing.
A kind of Gear Planet Transmission herringbone bear finite element grid automatic modeling provided by the invention and assembly method, including it is following
Step:
(1) input gear second parameter determines other parameters.It includes: the number of teeth, modulus, pressure angle, spiral that basic parameter, which is shown in Table 1,
The parameters such as angle, the unilateral facewidth, withdrawing be wide, height of teeth top, height of teeth root, cutter radius of corner.The installation error of inside and outside engaging tooth wheel set
(crossed axis angle error, center away from) is reduced to sun gear, gear ring with respect to reference frame error, and each planetary gear is without installation error；Too
Sun is taken turns, the installation error of gear ring is Δ Es=Δ Er=0.01mm, γs=γr=1 '.
(2) the standard involute flank of tooth is expressed.Based on Principles of Gear Connection, sun gear, planetary gear are transformed by rack cutter
As shown in Figure 1, gear ring is transformed into as shown in Figure 2 by involute gear.θiFor the corner for being processed gear；riTo be processed gear
Pitch radius；isFor gear ring and pinion cutter gear ratio.Tool-tooth profile is indicated to obtain standard involute gear in gear coordinate system
Face:
In formula: Ri、Ni(i=s, p, g indicate star-wheel, sun gear and gear ring) is respectively flank of tooth position vector and per unit system arrow；Rci、
NciRespectively cutter position vector and method arrow；uiAnd liIt is cutter parameters；Mi,ci(θi) it is from tool coordinate system SciTo gear coordinate system Si
Coordinate conversion matrix, Li,ci(θi) it is its submatrix.
(3) the planetary gear correction of the flank shape flank of tooth is expressed.The two sides of planetary gear are engaged with gear ring and sun gear respectively, and gear ring is due to size
Larger, the complicated usually not correction of the flank shape of processing technology can be placed on planetary gear the correction of the flank shape of gear ring；The correction of the flank shape of sun gear can also be placed on
On planetary gear, i.e. two lateral tooth flanks all corrections of the flank shape of herringbone bear；Symmetrical correction of the flank shape is usually taken in the left and right flank of tooth.Pass through standard involute
The correction of the flank shape flank of tooth of the flank of tooth and normal direction correction of the flank shape curved surface superimposed structure planetary gear, flank of tooth method arrow, position vector indicate are as follows:
In formula: Rpm、NpmFor planetary gear correction of the flank shape flank of tooth position vector；δ is normal direction profiling quantity, is the function of tooth surface parameters, but logical
Numerical value (x, y) indicates on common rotation perspective plane, uses modification curve along rack cutter parameter when solving correction of the flank shape flank of tooth method arrow
(up,lp) direction cuts arrow, calculating process is as follows:
In formula: Rx,Ry,RzRespectively theoretical flank of tooth position vector coordinate components.It can be true according to radially, axially grid division number
The wide part of fixed tooth and tooth root transition flank of tooth mesh point coordinate as shown in figure 3, planetary gear modification curve as shown in figure 4,
The planetary gear correction of the flank shape flank of tooth and theoretical flank of tooth comparison are as shown in Figure 5.
(4) number of single full teeth surface grids node calculating and unit, cell node.Herringbone bear includes that the left side is oblique
Tooth, escape, 3 each section of the right helical teeth, symmetrical along the left and right flank of tooth of axial double helical tooth, middle section is escape.One complete
Helical teeth can divide are as follows: the flank of tooth, tooth root, wheel body, wheel body left side tooth socket, wheel body right side tooth socket are as shown in Figure 6.X, Y, Z-direction difference
For transverse tooth thickness, radially, axially, face portion abih, root portions bcji, tooth socket part is efdc on the left of wheel body, and wheel body is right
Side tooth socket part is jklm, and wheel body portion is cdkj.Firstly, being determined according to each section number of nodes radially, axially of single tooth
Each node location of profile, in conjunction with these location points, ab, ih sections of the face portion of left side helical teeth and bc, ji sections of tooth root of profile
Discrete point coordinate values are determined according to cutter tooth shape and correction of the flank shape according to the step of front；Then, according to the radial boundary of tooth root point
" c " and " i " and wheel body depth determine the profile coordinate of cd sections and jl sections discrete points of wheel body, and cd sections of jl sections of coordinates of wheel body are revolved respectively
Turn the discrete dot profile coordinate that angle shared by 1 tooth determines ef sections and lm sections of tooth socket section；There are these profiles, according to transverse tooth thickness direction
The number of nodes of each section, by entity part of the Rotating Transition of Coordinate between discrete point " filling " profile, thus with discrete
Point has constructed the entity of gear；Finally, according to each section unit number of the single tooth of 2 all directions of table according to certain rule, by institute
There is discrete point to write the number and component units of unit according to 8 node hexahedron linear unit node sequence shown in Fig. 7
Node serial number.Following 3 steps can specifically be divided:
The single helical gear flank of tooth and tooth root transition node calculate in a step 4.It is radial total i.e. along the axial region acih
8 units are counted, then i=1,2 ... 9；Transverse tooth thickness direction amounts to 4 units, then j=1, and 2 ... 5；14 units are axially amounted to, then k
=1,2 ... 15；448 units are amounted to, radially, axially mesh parameter determines two lateral tooth flanks and tooth root transition according to the flank of tooth
Profile discrete point coordinate, pass through entity part of the Rotating Transition of Coordinate between discrete point " filling " boundary point.The flank of tooth and tooth
The entire entity node coordinate representation of root transition are as follows:
The single helical gear wheel body node of b calculates.3 units are radially amounted to along the axial region cdki, then is=1,
2,…3；Transverse tooth thickness direction amounts to 4 units, then j=1, and 2 ... 5；14 units are axially amounted to, then k=1,2 ... 15；Amount to 168
A unit.It is radial by calculating position vector (I=9 herein) and wheel body thickness at left and right flank of tooth easement curve and root circle intersection point k, i
Step-length s=0.4 is determined, then it is as follows to take turns body node calculating:
Single helical gear wheel body two sides tooth socket node calculates in step c 4.It is radial total i.e. along the axial region efdc and jklm
Count 3 units；Transverse tooth thickness direction amounts to 1 unit, then j=1；14 units are axially amounted to, then k=1,2 ... 15；Two sides each 56
A unit amounts to 112 units.By node (I=9, i at efs=1,2 ... 4, js=1) θ is rotated to the rightc=360 °/Z (Z is tooth
Number) obtain node at the tooth socket of right side, node (I=9, i at same iks=1,2 ... 4, js=4) it rotates to the left to obtain left side tooth socket
Node calculates as follows:
(5) the other half helical gear node of double helical tooth determines.Herringbone bear left and right tooth face is symmetrical, for the other half helical gear section
Logical " mirror image " method of point determines:
In formula: B is the helical gear facewidth；W is withdrawing groove width；Coordinate system is at left flank facewidth midpoint in text,
xli,j,k,yli,j,k, zli,j,kFor the single helical teeth node coordinate in the right.
(6) double helical tooth escape node determines.After determining left and right flank of tooth wheel body coordinate, according to left helical gear wheel body inner end
The region nfmp along axial " stretching " withdrawing groove width；Radial 2 unit ic=1 ... 3, it is a from the 9th (I=9, Is=3, Ic=3)
Node location starts；6, transverse tooth thickness direction unit jc=1,2 ... 7；Axially it is evenly dividing as Kc=6 units of equal portions meter 6, then kc
=1,2 ... 6；Amount to 72 units, escape node are as follows:
(7) generation of arbitrarily a tooth flank of tooth node of double helical tooth and node serial number.Pass through the single tooth whole node of above step
It has determined.Rotating coordinate transformation can array generate whole teeth, it should be noted that the node of junction (side) can not
To repeat, the node coordinate of i-th tooth is indicated are as follows:
In formula: M is the rotational transformation matrix around gear axial direction, and Z is the number of teeth, and XI, YI, ZI is all node collection of i-th tooth
It closes, x, y, z is all node sets of single tooth.It is numbered while determination single helical gear node, it is symmetrical true
It when the other half fixed helical gear and escape node, is added up on the basis of original number.According to wanting for finite element adaptive grid generation
It asks, it is necessary to node is renumberd, by three layers of loop control, outer layer controls radial direction from tooth top to wheel body the last layer,
Secondary outer layer controls transverse tooth thickness direction from side to the other side, and innermost layer controls axial direction from an end face to another end face, according to
It is secondary by tooth from new sort whole node, carry out unit and unit section from new according still further to 8 node hexahedron linear unit node sequences
The number of point.By repetition test and verifying, above-mentioned node determines that method application is easy, and the cell configuration of formation is neat, operation
It is easy, computational accuracy is high.Fig. 8, Fig. 9 non-homogeneous, uniform three gears finite element model for gear ring herringbone bear transverse tooth thickness grid；Figure 10
~12 be gear ring, sun gear, the full flank of tooth finite element model of planetary gear herringbone bear.
(8) planetary gear TCA is analyzed.Planetary gear TCA is each inside and outside engaging tooth wheel set different from single pair gear TCA's
TCA equation needs to be transformed into unified fixed coordinate system and the driving error of each gear pair calculates, and needs using identical initial
Corner just can reflect the opposite primary clearance of contact Tooth of each profile modifying gear pair under installation error in this way.Such as Figure 13 institute
Show, Of-XfYfZfIt is the unified fixed coordinate system using planet carrier rotation center as origin, and YfAxis passes through the 1st planetary gear center,
Planetary gear reference frame Ofpi-XfpiYfpiZfpi(i=1,2...N, N are planetary gear number) is parallel with it, and planetary gear is uniformly distributed, the sun
Wheel, gear ring reference frame are Ofs-XfsYfsZfs、Ofr-XfrYfrZfr；Opi-XpiYpiZpi、Os-XsYsZs、Or-XrYrZrIt is planet
The moving coordinate system of wheel, sun gear and gear ring, origin are overlapped with respective reference frame and rotate around z-axis；Installation error simplifies
Are as follows: the installation error (crossed axis angle error, center away from) of inside and outside engaging tooth wheel set；It is expressed as each reference gear coordinate system phase
To Of-XfYfZfError, each planetary gear is without installation error.Figure 14, θ are shown in a certain external gear pump pair installationp1、θs, E be capable respectively
Star-wheel, sun gear corner and installation center are away from γs、ΔEsIt is crossed axis angle and center respectively away from installation error, internal messing refers to it
It establishes.TCA principle is that continuous phase cut-grafting touches two flank of tooth in the same coordinate system Of-XfYfZfThere is public contact point in middle any time
I.e. with common normal:
In formula: Ri、Ni(i=s, p, r indicate sun gear, planetary gear) is that flank of tooth position vector and per unit system are sweared；For each gear
Engagement corner.MfiFor from gear movement coordinate system to installation reference frame transformation matrix, LfiFor 3 × 3 submatrix thereon；
Rfi、NfiPosition vector and per unit system for the flank of tooth in reference frame are sweared；Five independent scalar equations can be obtained in above formula, take a system
ColumnFor input quantity, solve remaining 5 unknown quantity can be obtained two flank engagement positions have point of contact and corner.TCA points
It is that TCA analyzes to obtain planetary gear with respect to the sun with respect to planetary gear geometry driving error that analysis, which obtains planetary gear with respect to sun gear, gear ring,
Wheel, gear ring are with respect to planetary gear geometry driving error are as follows:
In formula:Respectively planetary gear, bull wheel (sun gear, gear ring) initial corner；Z is the number of teeth.Figure 15 is correction of the flank shape
Helical gear TCA emulation on the left of planet herringbone bear, right flank engagement mark and transmission are accidentally symmetrical with left side.The a certain position of engagement is given
Determine planetary gear cornerThe then accurate theoretical corner of sun gear or gear ringAre as follows:
(9) first external, internal gear pair assembly node determinations.In order to guarantee that planetary system has accurate assembly,
Firstly the need of the accurate assembly for guaranteeing single gear pair, secondly guarantees that each planetary gear node meets and uniformly divide along reference frame
Cloth requirement.Gear TCA analysis can guarantee there is accurate position of engagement relationship in a certain position of engagement gear pair, and TCA analysis obtains
The sun gear of the planetary gear position of engagement, gear ring examine the corner of coordinate system in engagement, according to installation relation, each gear it is accurate
Assembly node coordinate are as follows:
In formula: XAi、YAi、ZAi(i=s, p, r indicate sun gear, planetary gear and gear ring) is that all nodes of the full flank of tooth are sat
Mark numerical value set；XXi、YYi、ZZiFor all node coordinate numerical value set of the full flank of tooth under unified reference frame.Figure 18 is correction of the flank shape
Planet herringbone bear system accurately installs (1 planet herringbone bear) engaging-in position；Figure 16 is internal messing profile modifying gear pair
In engaging-in accurate assembly enlarged drawing；Figure 17 is external toothing profile modifying gear pair in engaging-in accurate assembly enlarged drawing.
(10) determination of the assembly node of other planetary gears.Other planetary gear nodes are emulated according to uniformly distributed established angle and TCA
Obtained gear corner is assembled.The accurate assembly node coordinate of n-th of planetary gear are as follows:
In formula: XPn、YPn、ZPnFor n-th (n=1 ... N, N are planetary gear number) all node coordinates of a full flank of tooth of planetary gear
Numerical value set, XP、YP、ZPFor the 1st all node coordinate numerical value set of the full flank of tooth of planetary gear.Installation error letter in the present invention
The installation error of sun gear and the relatively uniform referential of gear ring is turned to, planetary gear and planet carrier are error free, therefore, can also direct handle
The node of the rapid accurate assembly model of step 9, node serial number write life according to the redaction rule of the input inp file of Abaqus
After importing Abaqus at inp file, then radial arrays planetary gear completes the assembly of multiple planetary gears.Figure 19 is to have 4 planets
The correction of the flank shape herringbone bear system of wheel is accurately installed engaging-in position.
(11) the Abaqus pre-processing file of the different positions of engagement generates.The calculating of step 9~10 assembly nodes is to be based on
The calculating of the sun gear, planetary gear, gear ring of any full teeth of preceding step, is only that node coordinate is changed, therefore not
It needs that node is numbered again.It is engaging-in to the corner for nibbling out process gear joint by planetary gear TCA one tooth of calculating, it is right
Sun gear, gear ring, each planetary gear finite element model are assembled, will according to the redaction rule of the input inp file of Abqus
Point set, boundary condition, contact setting for being arranged required for above-mentioned number and finite element etc., which are write, generates inp file, imported into
In Abaqus, that is, complete the high-precision modeling and pre-treatment setting of finite element model.Figure 20 is calculation flow chart stream of the present invention
Cheng Tu.
Table 1 is Gear Planet Transmission double helical tooth spoke basic parameter of the present invention；
Table 2 is single tooth complete in the present invention along X, Y, Z-direction each section grid dividing unit number；
Claims (3)
1. a kind of Gear Planet Transmission herringbone bear finite element grid automatic modeling and assembly method characterized by comprising root first
Tool-tooth profile is indicated according to Principles of Gear Connection to obtain the standard involute flank of tooth in gear coordinate system, inside and outside gear pair is repaired
Shape is placed on planetary gear, passes through the standard involute flank of tooth and the normal direction correction of the flank shape curved surface superimposed structure correction of the flank shape flank of tooth, it is determined that single
The node coordinate of two lateral tooth flank of helical gear and the excessive profile of tooth root；Secondly, being determined according to the boundary point of the excessive profile of tooth root intermediate
The profile of intermediate wheel body is rotated angle shared by a tooth around axis and obtains two sides tooth socket profile by the profile of wheel body；Then, on side
On the basis of boundary's profile, the entity part between profile is filled by Rotating Transition of Coordinate discrete point, is constructed using discrete point
Single helical gear entity out；Lead to mirror method for the other half helical gear node to determine；Stretch one end helical gear inner face wheel
Body determines tooth socket node；So far, monodentate node all determines that the node of other teeth is by being pivoted determination, according to 8 nodes six
Face body linear unit node sequence generates the herringbone bear of any tooth from new progress unit and cell node number；In conjunction with planet
Gear Contact analyzes TCA, and given planetary gear corner determines the theoretical corner of sun gear, gear ring wheel, is closed according to the corner and installation
Each pitch point is transformed into unified reference frame by coordinate transform and completes the accurate of gear pair finite element model by system
Assembly；Finally, according to the redaction rule of Abaqus input inp file, by the node of above-mentioned finite element model, unit and required
Point set, boundary condition, contact setting of setting etc., which are write, generates inp file, by programming input gear basic parameter, so that it may real
Now high-precision Gear Planet Transmission correction of the flank shape double helical tooth wheel set finite element grid automatically generate and the density of the flank of tooth outer layer grid control, dress
Match and pre-treatment.
2. a kind of Gear Planet Transmission herringbone bear finite element grid automatic modeling according to claim 1 and assembly method,
It is characterized in that, specifically includes following implemented step:
Step 1: input gear second parameter determines other parameters
Basic parameters of gear include: the wide number of teeth, modulus, pressure angle, helical angle, the unilateral facewidth, withdrawing, height of teeth top, height of teeth root and
Cutter radius of corner, installation error, that is, crossed axis angle error and center away from being reduced to sun gear, gear ring with respect to reference frame error,
Each planetary gear is without installation error；Profile modification and axial modification are all made of straight line+second-degree parabola modification curve, are expressed as revolving
Turn perspective plane parametric function；
Step 2: the expression of the standard involute flank of tooth
Tool-tooth profile is indicated based on Principles of Gear Connection to obtain the standard involute flank of tooth in gear coordinate system；Sun gear and row
Star-wheel is transformed by rack cutter, and gear ring is transformed by involute gear, and flank of tooth position vector, method arrow indicate are as follows:
In formula: Ri、NiRespectively flank of tooth position vector and per unit system arrow, i=s, p, g respectively indicates sun gear, star-wheel and gear ring；Rci、
NciRespectively cutter end face position vector and method arrow；uiAnd liIt is cutter parameters；Mi,ci(θi) it is from tool coordinate system SciTo gear coordinate
It is SiCoordinate conversion matrix, Li,ci(θi) it is its submatrix；θiFor the corner for being processed gear；
Step 3: the expression of the planetary gear correction of the flank shape flank of tooth
The two sides of planetary gear are engaged with gear ring and sun gear respectively, and gear ring since size is larger, do not repair usually by processing technology complexity
Shape is placed on planetary gear the correction of the flank shape of gear ring；The correction of the flank shape of sun gear is also placed on planetary gear, i.e. two lateral tooth flanks of herringbone bear
All corrections of the flank shape；Symmetrical correction of the flank shape is usually taken in the left and right flank of tooth；Pass through the standard involute flank of tooth and normal direction correction of the flank shape curved surface superimposed structure planet
The correction of the flank shape flank of tooth of wheel, flank of tooth method arrow, position vector indicate are as follows:
In formula: Rpm、NpmFor planetary gear correction of the flank shape flank of tooth position vector；δ is normal direction profiling quantity, is the function of tooth surface parameters, usually with rotation
Turning numerical value (x, y) on perspective plane indicates, uses modification curve along rack cutter parameter (u when solving correction of the flank shape flank of tooth method arrowp,lp) side
To arrow is cut, calculating process is as follows:
In formula: Rx,Ry,RzRespectively theoretical flank of tooth position vector coordinate components；
Step 4: single full teeth surface grids node calculates and the number of unit, cell node
Herringbone bear includes 3 each section of left side helical teeth, escape and the right helical teeth, symmetrical along the left and right flank of tooth of axial double helical tooth, in
Between partially be escape；One complete helical teeth divides are as follows: the flank of tooth, tooth root, wheel body, wheel body left side tooth socket, wheel body right side tooth socket；It is first
First, according to each section number of nodes radially, axially of single tooth, each node location of profile is determined, it is left in conjunction with these location points
The flank of tooth and tooth root profile discrete point coordinate values of side helical teeth are determined according to cutter tooth shape and correction of the flank shape according to the step of front；So
Afterwards, the profile coordinate that wheel body discrete point is determined according to the radial boundary of tooth root point and wheel body depth, by the left and right side profile of wheel body
Angle shared by rotation 1 tooth of rotation obtains the discrete dot profile coordinate of right, left tooth socket；It is each according to transverse tooth thickness direction in conjunction with these profiles
Partial number of nodes by entity part of the Rotating Transition of Coordinate between discrete point " filling " profile, and then uses discrete point
The entity of gear is constructed；Finally, according to single tooth radially, axially, transverse tooth thickness direction according to default rule, will be all discrete
O'clock carrying out unit and cell node according to 8 node hexahedron linear unit node sequences numbers；
Step 5: the other half helical gear node of double helical tooth determines
Herringbone bear left and right tooth face is symmetrical, leads to " mirror image " method for the other half helical gear node and determines:
In formula: B is the helical gear facewidth；W is withdrawing groove width；Coordinate system is in left flank facewidth midpoint, xl in texti,j,k,
yli,j,k, zli,j,kFor the single helical teeth mesh point coordinate in the right；
Step 6: double helical tooth escape node determines
After determining left and right flank of tooth wheel body coordinate, according to left helical gear wheel body inner face node along axial " stretching " withdrawing groove width, then
Escape node are as follows:
In formula: subscript ic=1 ... Ic,jc=1 ... (2Jc+ J), kc=1 ... KcFor radial direction, transverse tooth thickness, axial node label, start bit
It sets；KcFor axial grid number；
Step 7: the generation of arbitrarily a tooth flank of tooth node of double helical tooth and node serial number
By the single tooth whole node of above step it has been determined that rotating coordinate transformation can array generate whole teeth, and pay attention to
Junction, that is, side node do not repeat, the node coordinate of i-th tooth indicates are as follows:
In formula: M is the rotational transformation matrix around gear axial direction, and Z is the number of teeth, XI, YI, and ZI is all node sets of i-th tooth, x,
Y, z are all node sets of single tooth；It is numbered while determination single helical gear node, symmetrically determines the other half
It when helical gear and escape node, is added up on the basis of original number；According to the requirement of finite element adaptive grid generation, to node
Renumber, by three layers of loop control, outer layer controls radial direction from tooth top to wheel body the last layer, secondary outer layer from side to
The other side controls transverse tooth thickness direction, and innermost layer controls axial direction from an end face to another end face, successively by tooth from new sort
Whole nodes, according still further to 8 node hexahedron linear unit node sequences from the new number for carrying out unit and cell node；
Step 8: planetary gear TCA analysis
TCA principle is continuous phase cut-grafting touching two flank of tooth any time in the same coordinate system to have public contact point and common normal
That is:
In formula:For the engagement corner of each gear；MfiFor from gear movement coordinate system to installation reference frame transformation matrix, Lfi
For 3 × 3 submatrix thereon；Rfi、NfiPosition vector and per unit system for the flank of tooth in reference frame are sweared；Five independences can be obtained in above formula
Scalar equation, take a series ofFor input quantity, solves available two all of flank engagement position of remaining 5 unknown quantity and connect
Contact and corner；
TCA analyzes to obtain planetary gear with respect to sun gear, gear ring with respect to planetary gear geometry driving error are as follows:
In formula:Respectively the initial corner of planetary gear, bull wheel, bull wheel include sun gear and gear ring；Z is the number of teeth；It is a certain to nibble
Coincidence sets given planetary gear cornerThe then accurate theoretical corner of sun gear or gear ringAre as follows:
Step 9: the first external, internal gear pair assembly node determination
Gear TCA analysis guarantees there is accurate position of engagement relationship in a certain position of engagement gear pair, and TCA analysis obtains planetary gear
Sun gear, the gear ring of certain position of engagement examine the corner of coordinate system in engagement, according to installation relation, the accurate assembly node of each gear
Coordinate are as follows:
In formula: XAi、YAi、ZAiFor all node coordinate numerical value set of the full flank of tooth；XXi、YYi、ZZiFor under unified reference frame
All node coordinate numerical value set of the full flank of tooth；
Step 10: the assembly node of other planetary gears determines
Other planetary gear nodes are assembled according to the gear corner that uniformly distributed established angle and TCA are emulated；By installation error letter
The installation error of sun gear and the relatively uniform referential of gear ring is turned to, planetary gear and planet carrier are error free, therefore, directly the 9th
The node of the accurate assembly model of step, node serial number write generation according to the redaction rule of the input inp file of Abaqus
After inp file imports Abaqus, then radial arrays planetary gear completes the assembly of multiple planetary gears；N-th of planetary gear accurately fills
With node coordinate are as follows:
In formula: XPn、YPn、ZPnFor all node coordinate numerical value set of the full flank of tooth of n-th of planetary gear, n=1 ... N, N are planet
Take turns number, XP、YP、ZPFor the 1st all node coordinate numerical value set of the full flank of tooth of planetary gear；
Step 11: the Abaqus pre-processing file of the different positions of engagement generates
The calculating of step 9~10 assembly nodes is based on the sun gear, planetary gear, gear ring of any full teeth by preceding step
It calculates, it is engaging-in to the corner for nibbling out process gear joint then to calculate a tooth by planetary gear TCA, to sun gear, gear ring, each
A planetary gear finite element model is assembled, and according to the redaction rule of the input inp file of Abqus, by above-mentioned number and is had
Point set, boundary condition, contact setting for being arranged required for limit member etc., which are write, generates inp file, imported into Abaqus, that is, completes
The high-precision modeling and pre-treatment setting of finite element model.
3. a kind of Gear Planet Transmission herringbone bear finite element grid automatic modeling according to claim 2 and assembly method,
It is characterized in that, in step 4, specific point or less 3 steps:
The single helical gear flank of tooth of a and tooth root transition node calculate
According to the flank of tooth, radially, axially mesh parameter determines the profile discrete point coordinate of two lateral tooth flanks and tooth root transition, passes through
Entity part of the Rotating Transition of Coordinate between discrete point " filling " boundary point；The flank of tooth and the entire entity node of tooth root transition
Coordinate representation are as follows:
In formula: Rx,Ry,RzIt include transition position vector coordinate components, r for the flank of toothi,k,ai,kTo be determined according to flank of tooth grid data
Known radially, axially position point data；∠ q is the angle of corresponding flank of tooth node and transverse tooth thickness center line, logical according to node location
The cosine law is crossed to determine；xli,j,k,yli,j,k, zli,j,kFor left side helical teeth mesh point coordinate, subscript i=1 ... I, j=1 ... J, k
=1 ... K is followed successively by radial direction, transverse tooth thickness, axial node label, and I, J, K is the flank of tooth and root portions all directions node total number；
The single helical gear wheel body node of b calculates
It is wheel body starting point by calculating the i.e. radial node of left and right flank of tooth easement curve and root circle intersection point, then takes turns body node calculating
It is as follows:
In formula: is=1 ... IsFor wheel body radial direction vertex ticks, Is is wheel body radial direction number of nodes；S is wheel body radial direction step-length, transverse tooth thickness side
To unchanged with axial direction number of nodes；
C single helical gear wheel body two sides tooth socket node calculates
By the boundary node of wheel body left and right side to the right, left side rotate a tooth angle, θcObtain right, left side tooth socket respective nodes
It calculates as follows:
In formula: "+" indicates left side tooth socket node js=1, "-" indicates right side tooth socket node js=J；J=1 ... JcFor tooth socket transverse tooth thickness
Vertex ticks, JcFor transverse tooth thickness direction tooth socket number of nodes；Axial direction number of nodes is without constant.
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| CN113742859A (en) * | 2021-08-13 | 2021-12-03 | 湖南磐钴传动科技有限公司 | Composite stress field construction method based on tooth surface residual stress and contact stress |
| CN113742859B (en) * | 2021-08-13 | 2024-03-08 | 湖南磐钴传动科技有限公司 | Composite stress field construction method based on tooth surface residual stress and contact stress |
| CN113742976A (en) * | 2021-09-15 | 2021-12-03 | 重庆理工大学 | High-speed gear finite element analysis tooth profile mesh discretization method based on sliding energy loss |
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| CN114818181A (en) * | 2022-04-21 | 2022-07-29 | 哈尔滨工程大学 | Tooth profile based straight toothed spur gear finite element mesh automatic generation method and computer equipment |
| CN114818181B (en) * | 2022-04-21 | 2023-08-25 | 哈尔滨工程大学 | Method and equipment for automatically generating finite element grid based on tooth profile straight-tooth cylindrical gear |
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