CN108681655A - A kind of finite element modeling method of the asymmetric cylindrical straight gear wheel set of Double pressure angles - Google Patents
A kind of finite element modeling method of the asymmetric cylindrical straight gear wheel set of Double pressure angles Download PDFInfo
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- CN108681655A CN108681655A CN201810706991.3A CN201810706991A CN108681655A CN 108681655 A CN108681655 A CN 108681655A CN 201810706991 A CN201810706991 A CN 201810706991A CN 108681655 A CN108681655 A CN 108681655A
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Abstract
The present invention relates to a kind of finite element modeling methods of the asymmetric cylindrical straight gear wheel set of Double pressure angles, the coordinate of equal portions key point in flank profil is calculated first with the tooth profile equation of unsymmetric gear, flank profil key point is created with ANSYS softwares, flank profil spline curve is generated by key point, then monodentate end face, whole increment face, asymmetric spur gear wheel physical model, asymmetric spur gear wheel transmission physical model are from bottom to top established, finally divide finite element grid, Dynamic Constraints and load are set, asymmetric spur gear wheel transmission finite element model is obtained.The entire modeling process of the present invention realizes parametrization, can greatly improve gear train assembly finite element modeling quality, improves analysis efficiency.
Description
The application be application No. is：201410568362.0 invention and created name is《A kind of asymmetric cylindrical straight gear wheel set
Modeling method》, the applying date is：The divisional application of the application for a patent for invention on October 22nd, 2014.
Technical field
The present invention relates to a kind of gear finite element modeling method based on Explicit Dynamics analysis, especially a kind of double pressure
The finite element modeling method of the asymmetric cylindrical straight gear wheel set in angle.
Background technology
In single-direction transmission, increase flank of tooth compression-side pressure angle, so that compression lateral tooth flank is formed with not subjected to pressure lateral tooth flank not right
Claim distribution, gear-driven registration can be significantly improved, reduces Gear Contact stress, Dedenda's bending stress, gear shaft constraint
Counter-force, to improve gear drive stability.Unsymmetric gear is a kind of effective to improve the new of gear teeth performance and bearing capacity
Type gear.The dynamic value simulation analysis of unsymmetric gear transmission is one of the effective ways for studying its transmission performance and mechanism.
Traditional gear modeling is to utilize 3D sculpting software (Pro/E, UG), by inputting the basic parameter of standard spur gear wheel,
The monodentate geometrical model for establishing symmetrical gear, is then transferred in finite element analysis software and establishes its finite element model, into traveling one
Step analysis.Traditional modeling method is difficult to realize the Geometric Modeling of unsymmetric gear, and geometrical model is transferred in finite element software very
It is easily lost partial geometry information, and modeling is only the certain types of gear of some single and establishes model every time, increases
The workload of analysis is studied gear and designed using finite element technique.Single gear tooth is realized in traditional finite element analysis mostly
Between or monodentate and rack between engage, when analysis, is typically based on the static analysis of more meshing states, belongs to pseudo- dynamic analysis, Bu Nengshi
Continuous dynamic simulation analysis in the complete swing circle of existing gear.
Invention content
The technical problem to be solved in the present invention is to provide a kind of asymmetric circles of Double pressure angles based on Explicit Dynamics analysis
The finite element Direct Modeling of column spur gear pair, can improve the modeling efficiency of asymmetric Series Gear, realize asymmetric
Gear dynamic mesh analysis parameterizes, is intelligent.
Realize that the technical solution of the object of the invention is to provide a kind of having for asymmetric cylindrical straight gear wheel set of Double pressure angles
Meta Model method is limited, is included the following steps：
1. parametrization establishes asymmetric involute profile curve, detailed process is：
1.1) tooth curve of Unsymmetric involute gear is divided into：Compression-side tooth curve, compression-side tooth root are crossed and are write music
Line, not subjected to pressure side tooth curve, four part of not subjected to pressure side tooth root transition curve；With the number of teeth of gear, modulus, gear compression side pressure
Power angle, not subjected to pressure lateral pressure angle, addendum coefficient, tip clearance coefficient are input parameter, will be non-using the APDL programming languages of ANSYS
Symmetrical flank profil carries out parametric programming, calculates tooth curve, and every section of tooth curve is taken a little by equal portions are carried out；
Gear compression-side flank profil key point coordinates (xA, yA)：
In above formula：αAdThe pressure angle of compression-side curve point,
M- moduluses；The n- numbers of teeth；αdCompression-side pressure angle of graduated circle；Compression-side addendum coefficient；
Gear compression-side tooth root key point coordinates (xB, yB), by compression-side variable element, equal portions take based on a little within the scope of value value
It calculates：
In above formula：αBdVariable element, αd≤αBd≤90°；
R- knife tip circle angular radius,
αcNot subjected to pressure side pressure angle of graduated circle；Compression side gear radial clearance coefficient；
Q- cutter parameters,
Gear not subjected to pressure side flank profil key point coordinates (xC, yC)：
In above formula：αCcThe pressure angle of not subjected to pressure side point,
Gear not subjected to pressure side tooth root key point coordinates (xD, yD)：
In formula：αDcVariable element, αc≤αDc≤90°；
1.2) compression-side and not subjected to pressure side point are separately connected using spline curve, generate tooth curve；
2. parameterizing the modeling of monodentate end face, detailed process is：
2.1) two peak of tooth curve is crossed, using coordinate origin as the center of circle, made this 2 points of circular arc, and generated outside circle
Arc；
2.2) coordinate origin generate a key point, from coordinate origin to two tooth root transition curves at minimum point connection two
Root straight line；Pass through this two straight lines, compression-side tooth root transition curve, compression-side tooth curve, addendum circle arc, not subjected to pressure side flank profil
Curve, not subjected to pressure side tooth root transition curve generate monodentate end face；
3. parameterizing whole increment face modeling, detailed process is：
3.1) monodentate end face is copied to n monodentate of the number of teeth under polar coordinates, deviation angle is 360/n degree successively；
3.2) operation is overlapped to each monodentate end face and obtains face of gear；
3.3) using coordinate origin as the center of circle, justified with gear circular hole radius RK works, by Boolean subtraction calculation, obtain gear end
Face；
4. parameterizing gear solid modelling, detailed process is：
Under cartesian coordinate system, gear face is stretched to the length of facewidth B along end face vertical direction, obtains the three of gear
Tie up physical model；
5. parameterizing driven gear modeling, detailed process is：
5.1) under cartesian coordinate system, gear face is moved up to the distance of a gear pair central moment；
5.2) physical model of driven gear 1., 2., 3., is 4. established with step, if the driving gear number of teeth is even number,
Driven gear rotates counterclockwise half of driven gear monodentate angle around coordinate origin；
6. parameterizing gear finite element modeling, detailed process is：
6.1) gear material constant, cell type, cell parameters are defined；
6.2) flank of tooth unit size is set, using the division methods of sweeping grid, unsymmetric gear pair is divided into finite element
Two inner ring gears are divided into rigid element by grid；
7. unsymmetric gear contact, constraint definition, definition load based on the analysis of ANSYS Explicit Dynamics, detailed process
For：7.1) node group is created：Select driving and driven gear compression side gusset, and definition node group；
7.2) definition contact：Node group is contact assembly on driving gear, and node group is target element on driven gear, if
Set CONTACT WITH FRICTION parameter；
7.3) barycenter of driving gear and driven gear is defined, the displacement of driving gear and driven gear is constrained；
7.4) apply angular speed on driving gear inner ring, the locked-in torque on driven gear inner ring.
The present invention has the effect of positive：The present invention is by four sections of tooth profile curve equations of unsymmetric gear, with corresponding
Pressure angle and change ginseng ginseng measure point into change and obtain tooth curve using APDL Programming with Pascal Language, avoid four sections of curves and intersect
And overlapping.Unsymmetric gear physical model is generated by tooth curve, Explicit Dynamics parameter is defined, asymmetric tooth may be implemented
The dynamic engagement of wheel is analyzed.It can be by changing input parameter, different ginsengs of the structure including symmetrical gear in modeling process
The finite element model of number lower tooth wheel set.The present invention integrates tooth Profile Design, solid modelling, parameter definition, and it is non-right to may be implemented
Parametrization and the intelligence for claiming the analysis of gear drive dynamic engagement, can effectively put forward the quality and efficiency of finite element analysis.
Description of the drawings
Fig. 1 asymmetrical tooth space profile key point diagrams proposed by the present invention；
Fig. 2 asymmetrical tooth space profile curve graphs proposed by the present invention；
Fig. 3 asymmetric monodentate end view drawings proposed by the present invention；
Fig. 4 asymmetric whole tooth end view drawings proposed by the present invention；
Fig. 5 asymmetric straight driving gear sterograms of cylinder proposed by the present invention；
Fig. 6 asymmetric cylindrical straight gear wheel set sterograms proposed by the present invention；
Fig. 7 asymmetric cylindrical straight gear wheel set finite element model figures proposed by the present invention.
Specific implementation mode
(embodiment 1)
In the following with reference to the drawings and specific embodiments, the present invention is further explained, and a kind of Double pressure angles of the present embodiment are non-right
It includes the following steps to claim the finite element modeling method of cylindrical straight gear wheel set：
1. parametrization establishes asymmetric involute profile curve：
Table 1：Asymmetric spur gear wheel modeling parameters
| Driving gear number of teeth n1 | 45 | Driven gear number of teeth n2 | 22 |
| Modulus M | 3mm | Facewidth B | 22mm |
| Compression-side pressure angle AD | 28° | Not subjected to pressure lateral pressure angle AC | 20° |
| Addendum coefficient HA | 1 | Tip clearance coefficient CC | 0.25 |
1.1 are divided into the tooth curve of Unsymmetric involute gear：Compression-side tooth curve, compression-side tooth root are crossed and are write music
Line, not subjected to pressure side tooth curve, four part of not subjected to pressure side tooth root transition curve.By the number of teeth of 1 middle gear of table, modulus, gear by
It is input parameter to press lateral pressure angle, not subjected to pressure lateral pressure angle, addendum coefficient, tip clearance coefficient, utilizes the APDL programming languages of ANSYS
Asymmetrical tooth space profile equation is carried out parametric programming by speech, calculates tooth curve, and every section of tooth curve, which is carried out 6 equal portions, to be taken a little,
Number consecutively is 1~24.As shown in Figure 1.
(by compression-side pressure angle, 6 equal portions take a little gear compression-side flank profil key point coordinates (xA, yA) within the scope of value value
It calculates)：
In formula：αAdThe pressure angle (°) of compression-side curve point,
Mono- moduluses of m (mm)；The n- numbers of teeth；αdCompression-side pressure angle of graduated circle (°)；
Compression-side addendum coefficient.
(by compression-side variable element, 6 equal portions take a little gear compression-side tooth root key point coordinates (xB, yB) within the scope of value value
It calculates)：
In formula：αBdVariable element, αd≤αBd≤90°；
R- knife tip circle angular radius (mm),
αcNot subjected to pressure side pressure angle of graduated circle (o)；Compression side gear radial clearance coefficient；
Q- cutter parameters,
(by not subjected to pressure lateral pressure angle, 6 equal portions take a little not subjected to pressure side flank profil key point coordinates (xC, yC) within the scope of value value
It calculates)：
In formula：αCcThe pressure angle (o) of not subjected to pressure side point,
(by not subjected to pressure side variable element, 6 equal portions take a little not subjected to pressure side tooth root key point coordinates (xD, yD) within the scope of value value
It calculates)：
In formula：αDcVariable element, αc≤αDc≤90°。
1.2) compression-side and not subjected to pressure side point are sequentially connected using spline curve (BSPLIN) respectively, generate tooth curve
L1, L2, as shown in Figure 2.
2. parameterizing asymmetric monodentate end face modeling, including step has：
2.1) tooth curve two peak K12, K13 are crossed and made this 2 points of circular arc using coordinate origin as the center of circle, generated
Addendum circle arc L3.
2.2) coordinate origin generate a key point K25, from coordinate origin to two tooth root transition curves at minimum point K1,
K24 connections two straight lines L4, L5.Monodentate end face A1 shown in Fig. 3 is generated by L1, L2, L3, L4, L5.
3. parameterizing asymmetric whole increment face modeling, including step has：
3.1) monodentate end face is copied to 1 monodentate of tooth number Z under polar coordinates, and deviation angle is 360/Z1 degree successively.
3.2) operation is overlapped to each monodentate end face and obtains face of gear A2.
3.3) using coordinate origin as the center of circle, circle A4 is made with gear circular hole radius RK=40m, face of gear carries out gear sky
Subtract operation, obtains gear face A5 shown in Fig. 4.
4. parameterizing asymmetric spur gear wheel solid modelling：Under cartesian coordinate system, gear face is hung down along end face
Histogram obtains gear three-dimensional entity model V1 shown in fig. 5 to the length for stretching facewidth B=22mm.
5. parameterizing asymmetric cylinder driven gear modeling, including step has：
5.1) under cartesian coordinate system, gear face is moved up into gear pair central moment DY=M* (Z1+Z2)/2
Distance.
5.2) the physical model V2 that driven gear is established in same steps 1 and 2,3,4, by driven gear model V2 around coordinate origin
Half of driven gear monodentate angle 180/Z2 is rotated counterclockwise, asymmetric cylindrical straight gear wheel set entity shown in fig. 6 can be obtained
Model.
6. parameterizing asymmetric cylindrical straight gear wheel set finite element modeling, including step has：
6.1) gear material constant, cell type shown in table 2 are defined.
Table 2：Gear material parameter, cell type
6.2) setting flank of tooth unit size is 2m, using the division methods of sweeping grid, by asymmetric cylindrical straight gear wheel set
Finite element grid SOLID164 is divided, two inner ring gears are divided into rigid element SHELL163.
7. unsymmetric gear contact, constraint definition, definition load based on the analysis of ANSYS Explicit Dynamics, including step
Have：
7.1) select driving gear compression side gusset, and definition node be node group ZHUJIECHU, select driven gear by
Side gusset is pressed, and definition node is node group CONGJIECHU.
7.2) definition contact：Using node group ZHUJIECHU on driving gear as contact assembly, node group is on driven gear
CONGJIECHU target elements, setting friction coefficient F=0.1.
7.3) barycenter of driving gear and driven gear is defined on its gear circle centre position, constrains driving gear and driven tooth
Take turns all displacements other than the rotation displacement ROTZ around Z.
7.4) add angular speed RBRZ=150.8rad/s, the locked-in torque on driven gear inner ring on driving gear inner ring
RBMZ=230Nm.
Obtained asymmetric cylindrical straight gear wheel set finite element model is as shown in Figure 7.
Claims (3)
1. a kind of finite element modeling method of the asymmetric cylindrical straight gear wheel set of Double pressure angles, it is characterised in that include the following steps：
1. parametrization establishes asymmetric involute profile curve, detailed process is：
1.1) tooth curve of Unsymmetric involute gear is divided into：It is compression-side tooth curve, compression-side tooth root transition curve, non-
Compression-side tooth curve, four part of not subjected to pressure side tooth root transition curve；With the number of teeth of gear, modulus, gear compression-side pressure angle,
Not subjected to pressure lateral pressure angle, addendum coefficient, tip clearance coefficient are input parameter, will be asymmetric using the APDL programming languages of ANSYS
Flank profil carries out parametric programming, calculates tooth curve, and every section of tooth curve is taken a little by equal portions are carried out；
Gear compression-side flank profil key point coordinates (xA, yA)：
In above formula：αAdThe pressure angle of compression-side curve point,
M- moduluses；The n- numbers of teeth；αdCompression-side pressure angle of graduated circle；Compression-side addendum coefficient；
Gear compression-side tooth root key point coordinates (xB, yB), by compression-side variable element, equal portions take calculating within the scope of value value：
In above formula：αBdVariable element, αd≤αBd≤90°；
R- knife tip circle angular radius,
αcNot subjected to pressure side pressure angle of graduated circle；Compression side gear radial clearance coefficient；
Q- cutter parameters,
Gear not subjected to pressure side flank profil key point coordinates (xC, yC)：
In above formula：αCcThe pressure angle of not subjected to pressure side point,
Gear not subjected to pressure side tooth root key point coordinates (xD, yD)：
In formula：αDcVariable element, αc≤αdc≤90°；
1.2) compression-side and not subjected to pressure side point are separately connected using spline curve, generate tooth curve；
2. parameterizing the modeling of monodentate end face, detailed process is：
2.1) two peak of tooth curve is crossed, using coordinate origin as the center of circle, made this 2 points of circular arc, and generated addendum circle arc；
2.2) generate a key point in coordinate origin, from coordinate origin to two tooth root transition curves at minimum point connect two it is straight
Line；It is bent by this two straight lines, compression-side tooth root transition curve, compression-side tooth curve, addendum circle arc, not subjected to pressure side flank profil
Line, not subjected to pressure side tooth root transition curve generate monodentate end face；
3. parameterizing whole increment face modeling, detailed process is：
3.1) monodentate end face is copied to n monodentate of the number of teeth under polar coordinates, deviation angle is 360/n degree successively；
3.2) operation is overlapped to each monodentate end face and obtains face of gear；
3.3) using coordinate origin as the center of circle, justified with gear circular hole radius RK works, by Boolean subtraction calculation, obtain gear face；
4. parameterizing gear solid modelling, detailed process is：
Under cartesian coordinate system, gear face is stretched to the length of facewidth B along end face vertical direction, the three-dimensional for obtaining gear is real
Body Model；
5. parameterizing driven gear modeling, detailed process is：
5.1) under cartesian coordinate system, gear face is moved up to the distance of a gear pair central moment；
5.2) physical model of driven gear 1., 2., 3., is 4. established with step, it is driven if the driving gear number of teeth is even number
Gear rotates counterclockwise half of driven gear monodentate angle around coordinate origin；
6. parameterizing gear finite element modeling, detailed process is：
6.1) gear material constant, cell type, cell parameters are defined；
6.2) flank of tooth unit size is set, using the division methods of sweeping grid, unsymmetric gear pair is divided into finite element grid,
Two inner ring gears are divided into rigid element.
2. a kind of finite element modeling method of the asymmetric cylindrical straight gear wheel set of Double pressure angles according to claim 1, special
Sign is：Step 1. 1.1) in, by every section of tooth curve by carry out 6 equal portions take a little, number consecutively be 1~24.
3. a kind of finite element modeling method of the asymmetric cylindrical straight gear wheel set of Double pressure angles according to claim 1, special
Sign is：Further include step 7.：7. unsymmetric gear contact, constraint definition, definition based on the analysis of ANSYS Explicit Dynamics carry
Lotus, detailed process are：
7.1) driving gear compression side gusset is selected, and definition node is node group ZHUJIECHU, selects driven gear compression-side
Node, and definition node is node group CONGJIECHU.
7.2) definition contact：Using node group ZHUJIECHU on driving gear as contact assembly, node group is on driven gear
CONGJIECHU target elements, setting friction coefficient F=0.1.
7.3) barycenter of driving gear and driven gear is defined on its gear circle centre position, constrains driving gear and driven gear removes
All displacements outside the rotation displacement ROTZ of Z.
7.4) add angular speed RBRZ, the locked-in torque RBMZ on driven gear inner ring on driving gear inner ring.
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| WO2021255059A1 (en) * | 2020-06-17 | 2021-12-23 | Sms Group Gmbh | Gear mechanism for a rolling mill drive, rolling mill drive with a gear mechanism, and the use of the gear mechanism as a rolling mill gear mechanism |
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| US10311182B2 (en) * | 2015-12-16 | 2019-06-04 | Dassault Systemes | Topological change in a constrained asymmetrical subdivision mesh |
| CN105587842B (en) * | 2016-03-24 | 2017-10-20 | 江苏理工学院 | High intensity low vibration low noise Spur Gear Driving mechanism |
| CN106227940B (en) * | 2016-07-25 | 2020-04-24 | 厦门理工学院 | Modeling method of cycloid gear |
| CN110195775B (en) * | 2019-05-05 | 2021-03-09 | 三峡大学 | Construction method of conical helical gear with point contact of convex-concave circular cross section |
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| CN104318017B (en) | 2018-07-20 |
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