CN106802989B - Hypoid gear contact calculation method considering influence of dislocation quantity - Google Patents
Hypoid gear contact calculation method considering influence of dislocation quantity Download PDFInfo
- Publication number
- CN106802989B CN106802989B CN201710009493.9A CN201710009493A CN106802989B CN 106802989 B CN106802989 B CN 106802989B CN 201710009493 A CN201710009493 A CN 201710009493A CN 106802989 B CN106802989 B CN 106802989B
- Authority
- CN
- China
- Prior art keywords
- gear
- node
- finite element
- equivalent
- vector
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000004364 calculation method Methods 0.000 title claims abstract description 147
- 239000013598 vector Substances 0.000 claims abstract description 135
- 230000005540 biological transmission Effects 0.000 claims abstract description 84
- 238000006073 displacement reaction Methods 0.000 claims abstract description 59
- 230000003068 static effect Effects 0.000 claims abstract description 31
- 230000009471 action Effects 0.000 claims description 35
- 238000000034 method Methods 0.000 claims description 31
- 244000309464 bull Species 0.000 claims description 23
- 238000013519 translation Methods 0.000 claims description 23
- 238000010168 coupling process Methods 0.000 claims description 17
- 238000005859 coupling reaction Methods 0.000 claims description 17
- 230000008569 process Effects 0.000 claims description 15
- 230000008878 coupling Effects 0.000 claims description 14
- 230000009467 reduction Effects 0.000 claims description 8
- 239000011159 matrix material Substances 0.000 claims description 4
- 230000009466 transformation Effects 0.000 claims description 4
- 150000001875 compounds Chemical class 0.000 claims description 2
- 238000012360 testing method Methods 0.000 description 4
- 238000004458 analytical method Methods 0.000 description 3
- 238000005096 rolling process Methods 0.000 description 3
- 101150095130 URAD gene Proteins 0.000 description 2
- 238000005094 computer simulation Methods 0.000 description 2
- 238000013461 design Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000010205 computational analysis Methods 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 230000009347 mechanical transmission Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Geometry (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Computer Hardware Design (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Gears, Cams (AREA)
Abstract
The invention relates to a hypoid gear contact calculation method considering the influence of dislocation quantity, which comprises the following steps: establishing a hypoid gear finite element contact calculation model; carrying out finite element contact calculation on the gear without considering the influence of the dislocation quantity, and solving a unit vector of the acting direction of the equivalent meshing force and coordinates of an equivalent meshing node; establishing a finite element model of the gear transmission system; carrying out statics solution on a finite element model of the gear transmission system, and solving a gear center beam unit node displacement vector and a dislocation reference node displacement vector; changing the orientation of the finite element contact calculation model of the hypoid gear; carrying out finite element contact calculation of the gear considering the influence of the dislocation quantity; and carrying out iterative solution between the gear finite element contact calculation considering the influence of the dislocation quantity and the transmission system finite element model statics solution, solving the statics equilibrium state of the gear finite element contact calculation model and the transmission system finite element model, and calculating the hypoid gear contact calculation result accurately considering the influence of the dislocation quantity.
Description
Technical Field
The invention relates to a gear contact calculation method, in particular to a hypoid gear contact calculation method considering the influence of dislocation quantity.
Background
The hypoid gear is widely applied to mechanical transmission systems such as a drive axle and a gearbox, and the gear transmission systems deform under load, so that gear dislocation can be caused, and the meshing state of the gears is changed. In order to ensure that the hypoid gear design meets the performance requirement, it is usually necessary to perform load Contact Analysis (LTCA), and Contact calculation of the gear can be effectively realized by using commercial finite element Analysis software such as Abaqus. However, when a finite element contact calculation method is adopted to analyze a gear transmission system comprising a plurality of rolling bearings, considering that a contact relation exists between each roller and a raceway of the bearing and is limited by convergence and calculation scale, in the existing research, other transmission system components such as the rolling bearings and a shell are often ignored during modeling, only finite element contact calculation is carried out on a single pair of gear pairs, and the influence of gear dislocation caused by load deformation of the transmission system on the gear contact calculation is not considered. In order to realize numerical simulation of a gear transmission system comprising a plurality of rolling bearings, an analytic form of a nonlinear bearing unit and a hypoid gear equivalent meshing unit are applied to a gear transmission system model, but the equivalent meshing parameters of the hypoid gear are usually obtained according to a theoretical formula, the influence of tooth surface friction and a gear nonlinear contact state is not considered, and an effective means for accurately embodying the gear dislocation quantity obtained by the statics calculation of the transmission system in a gear finite element contact calculation model is lacked. Because there is coupling between the meshing state of the hypoid gear and the nonlinear stiffness of the bearing, a calculation method capable of accurately considering the coupling influence between the meshing state of the hypoid gear and a transmission system including a plurality of nonlinear bearing units is required to accurately realize the hypoid gear contact calculation considering the influence of the misalignment amount.
Disclosure of Invention
In view of the above problems, it is an object of the present invention to provide a method for calculating a hypoid gear contact in consideration of an influence of a misalignment amount, which can accurately calculate a hypoid gear contact in consideration of an influence of a coupling between a hypoid gear meshing state and a transmission system including a plurality of nonlinear bearing units.
In order to achieve the purpose, the invention adopts the following technical scheme: a hypoid gear contact calculation method taking into account the influence of the amount of misalignment, comprising the steps of:
1) establishing a hypoid gear finite element contact calculation model;
2) carrying out finite element contact calculation on the gear without considering the influence of the dislocation quantity, and solving a unit vector N of the action direction of the equivalent meshing force and an equivalent meshing node coordinate R;
3) establishing a finite element model of the gear transmission system according to the unit vector N of the acting direction of the equivalent meshing force and the coordinate R of the equivalent meshing node;
4) carrying out statics solution on a finite element model of the gear transmission system to obtain a gear central beam unit node displacement vector deltao1And deltao2And a misalignment reference node displacement vector deltap1And deltap2；
5) According to the gear central beam unit node displacement vector deltao1And deltao2And a misalignment reference node displacement vector deltap1And deltap2Changing the orientation of the finite element contact calculation model of the hypoid gear; carrying out finite element contact calculation of the gear considering the influence of the dislocation quantity, and solving an equivalent meshing force action direction unit vector N 'and an equivalent meshing node coordinate R' considering the influence of the dislocation quantity;
6) and carrying out iterative solution between the gear finite element contact calculation considering the influence of the dislocation quantity and the transmission system finite element model statics solution, solving the statics equilibrium state of the gear finite element contact calculation model and the transmission system finite element model, and calculating the hypoid gear contact calculation result accurately considering the influence of the dislocation quantity.
The step 1) of establishing the finite element contact calculation model of the hypoid gear comprises the following steps:
firstly, respectively establishing finite element models of a small wheel and a large wheel, enabling the axis of the small wheel to be parallel to the X axis of a global coordinate system, enabling the axis of the large wheel to be parallel to the Y axis of the global coordinate system, and enabling the small wheel to be offset along the Z axis of the global coordinate system; then, a center node o is established at the centroid positions of the small wheel and the large wheel, respectively1And o2Respectively coupling the central nodes of the small wheel and the large wheel with the body unit models of the small wheel and the large wheel by adopting a rigid connection unit; then, respectively establishing offset reference nodes of the small wheel and the large wheel at the intersection points of the common perpendicular lines of the axes of the small wheel and the large wheelp1And p2(ii) a Finally, a face-to-face contact pair is sequentially established between tooth surfaces that may be in contact during the calculation, and a tooth surface friction coefficient is defined.
The step 2) of gear finite element contact calculation without considering the influence of the dislocation quantity comprises the following steps:
I. constraint small wheel center node o1X, Y, Z direction translation freedom degree and Y, Z direction rotation freedom degree, and restrains large wheel center node o2X, Y, Z translational degree of freedom and X, Z rotational degree of freedom, at o1Exerts a constant input torque T on the X-direction rotational degree of freedom1At o2Is subjected to a constant rotational speed omega in the rotational degree of freedom in the Y direction2Setting the total solving time of contact calculation as t, the solving step length as delta t and the corresponding axial rotation angle of the large wheel
II. Respectively calculating the equivalent contact force vector and the equivalent action point coordinate of each surface-surface contact pair at each solving moment;
wherein the equivalent contact force vector f of the ith surface-to-surface contact pair at the moment jijAnd coordinates r of equivalent point of actionijRespectively expressed as:
fij＝[fxij,fyij,fzij]T
rij＝[xij,yij,zij]T
in the formula (f)xij,fyij,fzijIs the force component of the equivalent contact force in the global coordinate system; x is the number ofij,yij,zijCoordinate components of the equivalent action points in the global coordinate system; i denotes the ith tooth face contact pair; j represents the jth touch computation time;
III, respectively calculating the total gear meshing force vector, the unit vector of the equivalent meshing force action direction of the gear and the coordinate position of the equivalent meshing node in the global coordinate system at each solving moment;
wherein the total gear mesh force at time jVector FjUnit vector N of direction of action of equivalent meshing force of gear at time jjCoordinate position R of equivalent meshing node in global coordinate system at moment jjRespectively expressed as:
Fj＝[Fxj,Fyj,Fzj]T
Nj＝[nxj,nyj,nzj]T
Rj＝[xj,yj,zj]T
the force equivalence and moment balance relationship are used to obtain:
zj＝(Myj+Fzjxj)/Fxj
yj＝(Mxj+Fyjzj)/Fzj
in the formula, xj,zj,yjCoordinate position R of equivalent meshing node in global coordinate system for moment jjA component in the direction X, Y, Z;
n is the surface-to-surface contact logarithm between the gear pairs; n isxj,nyj,nzjUnit vector N of direction of action of equivalent meshing force of gear at moment jjA component in the direction X, Y, Z; n isxj＝Fxj/|Fj|；nyj＝Fyj/|Fj|；nzj＝Fzj/|Fj|；MxjAnd MyjMoment of the gear meshing force at the moment j to the X axis and the Y axis of the global coordinate system respectively;
IV, taking an average value of the data of one meshing period, and calculating an equivalent meshing force action direction unit vector N and an equivalent meshing node coordinate R in the whole meshing process, wherein the unit vector N and the equivalent meshing node coordinate R are respectively expressed as:
N＝[nx,ny,nz]T
R＝[x,y,z]T
in the formula, nx、ny、nzA component of a unit vector N in the direction X, Y, Z representing the equivalent engagement force action direction of the entire engagement process;
x, y and z are components of an equivalent meshing node coordinate R of the whole meshing process in the direction X, Y, Z;
t1-t0m is the number of times that the time range encompasses, one meshing cycle of the hypoid gear.
The step 3) of establishing the finite element model of the gear transmission system specifically comprises the following steps:
firstly, a space beam unit is adopted to simulate a transmission shaft, and a beam unit node is established at the center of a bearing and the center of a gear, and a gear center node o1And o2Adopting coordinates consistent with those in the hypoid gear finite element contact calculation model; then, establishing a body unit finite element model of the shell, constraining the node freedom degree of an external supporting part, establishing a node in the center of the bearing, respectively coupling the rigid connection unit and the shell finite element model, carrying out dimension reduction transformation on a rigidity matrix of the axle shell model, and only keeping the node freedom degree of the bearing center; then, a nonlinear bearing unit is adopted to simulate a bearing, one end of the bearing unit is connected with a bearing central node corresponding to the transmission shaft beam unit, and the other end of the bearing unit is connected with a bearing central node corresponding to the shell dimension reduction model; then, an equivalent meshing model is adopted to simulate a hypoid gear, and equivalent meshing nodes m of a small wheel and a large wheel are respectively established1And m2，o1And m1、o2And m2Are all connected by rigid beams m1And m2Through equivalent meshing rigidity KmCoupling; finally, the common sag between the small wheel axis and the large wheel axisRespectively establishing dislocation reference nodes p of small wheel and large wheel at line intersection positions1And p2，o1And p1、o2And p2All connected by rigid beams.
The statics solving of the finite element model of the gear transmission system in the step 4) comprises the following steps:
firstly, an input torque T is applied to the axial rotation freedom degree of a node of the small wheel shaft input end beam unit1The axial rotation freedom degree of the beam unit node at the output end of the large wheel shaft is restrained; then, carrying out statics nonlinear iterative solution on a finite element model of the transmission system containing the nonlinear bearing unit to obtain a gear central beam unit node displacement vector delta under the corresponding load working conditiono1And deltao2And a misalignment reference node displacement vector deltap1And deltap2；
Wherein, the gear center beam unit node displacement vector deltao1And deltao2And a misalignment reference node displacement vector deltap1And deltap2Are respectively:
δo1＝[xo1，yo1，zo1，αo1，βo1，γo1]T
δo2＝[xo2,yo2,zo2,αo2,βo2，γo2]T
δp1＝[xp1，yp1，zp1，αp1，βp1，γp1]T
δp2＝[xp2，yp2，zp2，αp2，βp2，γp2]T
in the formula, xo1,yo1,zo1、xo2,yo2,zo2、xp1,yp1,zp1、xp2,yp2,zp2Respectively representing gear central beam unit node displacement vectors deltao1And deltao2And a misalignment reference node displacement vector deltap1And deltap2α translation displacement vectoro1,βo1,γo1、αo2,βo2,γo2、αp1,βp1,γp1、αp2,βp2,γp2Respectively representing gear central beam unit node displacement vectors deltao1And deltao2And a misalignment reference node displacement vector deltap1And deltap2The angular displacement vector of (a).
The step 5) specifically comprises the following steps:
a. with small wheel center node o1For reference, the small wheel finite element model is rotated β around the Y-axis and Z-axis respectivelyo1And gammao1An angle;
b. along vector [ xo1,yo1,zo1]TTranslating the finite element model of the small wheel;
c. with the centre node o of the bull wheel2For reference, the large wheel finite element model is rotated α around the X-axis and Z-axis respectivelyo2And gammao2An angle;
d. along vector [ xo2,yo2,zo2]TTranslating the finite element model of the bull wheel;
e. along vector [ xo1,yo1,zo1]TTranslational small wheel central node o1Obtaining a new small wheel center node o1', along a vector [ x ]o2,yo2,zo2]TTranslation bull wheel center node o2Obtaining a new center node o of the bull wheel2', along a vector [ x ]p1,yp1,zp1]TTranslation small wheel offset reference node p1Obtaining a new small round offset reference node p1', along a vector [ x ]p2,yp2,zp2]TTranslation large wheel dislocation reference node p2Obtaining a new large round of offset reference nodes p2′；
f. Establishing a local coordinate system to make the small wheel local coordinate system X1Shaft is composed of1' Direction p1', local coordinate system X of bull wheel2Shaft is composed of2' Direction p2', at o1' X of1Applying a constant input torque T to the degree of freedom of the direction rotation1At o2' X of2Applying a constant rotational speed omega to the degree of freedom of the direction rotation2And carrying out gear finite element contact calculation, and solving an equivalent meshing force action direction unit vector N 'and an equivalent meshing node coordinate R' which take the influence of the dislocation quantity into consideration.
The iterative solution in the step 6) comprises the following steps:
①, reestablishing a finite element model of the gear transmission system according to the unit vector N ' of the acting direction of the equivalent meshing force and the coordinate R ' of the equivalent meshing node, wherein the unit vector N ' of the acting direction of the equivalent meshing force is influenced by the dislocation quantity;
②, carrying out statics solution on a finite element model of the new gear transmission system, and solving a new gear center beam unit node displacement vector and a misalignment reference node displacement vector;
③, changing the orientation of the hypoid gear finite element contact calculation model according to the gear central beam unit node displacement vector and the dislocation reference node displacement vector, performing the gear finite element contact calculation considering the influence of the dislocation amount again, and solving a new unit vector N 'of the action direction of the equivalent meshing force and the coordinate R' of the equivalent meshing node considering the influence of the dislocation amount;
④, judging whether the equivalent gear meshing parameters obtained by two adjacent iterations meet the convergence criterion formula, if so, calculating convergence, finally obtaining the static equilibrium state of the gear contact calculation model and the transmission system model, and obtaining the hypoid gear contact calculation result accurately considering the influence of the dislocation quantity, otherwise, returning to step ①.
The convergence criterion formula is:
||Nk-Nk-1||+||Rk-Rk-1||＜g
in the formula, Nk-1And NkRespectively obtaining unit vectors of the action direction of the equivalent meshing force of the gear for the k-1 th iteration and the k-th iteration; rk-1And RkRespectively obtaining the coordinates of the equivalent meshing nodes of the gears for the k-1 th iteration and the k-th iteration; ε is the convergence tolerance.
The calculation result of the hypoid gear contact accurately considering the influence of the dislocation quantity in the step 6) comprises a loading contact print, a contact stress and a loading transmission error of the gear;
superposing instantaneous tooth surface contact stress at each moment to obtain tooth surface contact stress distribution within a complete time range, namely loading a meshing imprint on the hypoid gear;
the calculation formula of the hypoid gear transmission error e in the whole process is as follows:
in the formula, N1The number of teeth of the small gear is; n is a radical of2The number of teeth of the big gear;
the angle of the axial rotation of the small wheel is;
is the actual turning angle of the bull wheel.
Establishing a finite element model of the hypoid gear by adopting Abaqus software, wherein the unit type is a 6-surface unit; modeling only part of gear teeth participating in contact calculation, and establishing a finite element contact calculation model of the hypoid gear comprising a plurality of pairs of teeth; meanwhile, the size of the tooth surface grid is controlled within 1 mm.
Due to the adoption of the technical scheme, the invention has the following advantages: 1. according to the hypoid gear contact calculation method considering the influence of the dislocation quantity, the finite element contact calculation method can accurately realize the hypoid gear contact calculation, and the transmission system modeling method comprising the shell and the nonlinear bearing unit can accurately realize the modeling and calculation of the gear transmission system, so that the hypoid gear contact calculation method has a reliable theoretical basis. 2. According to the hypoid gear contact calculation method considering the influence of the dislocation quantity, the hypoid gear finite element contact calculation can be quickly and accurately realized by adopting commercial software such as Abaqus, the adopted transmission system modeling and calculation method are easy to realize in programming under various common programming language environments, and the calculation efficiency is high. 3. The invention discloses a hypoid gear contact calculation method considering the influence of dislocation quantity, and provides a method for applying gear contact parameters obtained by hypoid gear finite element contact calculation to a transmission system gear equivalent meshing model and accurately embodying the gear dislocation quantity obtained by transmission system statics calculation in the gear finite element contact calculation model. 4. According to the hypoid gear contact calculation method considering the influence of the dislocation amount, the hypoid gear contact calculation considering the influence of the dislocation amount is accurately realized through iterative solution between the gear contact calculation and the transmission system statics calculation, and the technical problem that the coupling influence between the hypoid gear meshing state and a transmission system comprising a plurality of nonlinear bearing units is difficult to accurately consider in the conventional method is solved.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic view of a hypoid gear finite element contact calculation model;
FIG. 3 is a plan view schematic of the transaxle final drive gear system;
FIG. 4 is a schematic view of a hypoid gear equivalent meshing unit;
FIG. 5 is a schematic view of a finite element contact calculation model of a hypoid gear comprising five pairs of teeth;
FIGS. 6(a), (b), and (c) are schematic diagrams showing the results of tests on the load mesh trace of the gear, the calculation result without considering the amount of misalignment, and the calculation result with considering the amount of misalignment, respectively;
FIG. 7 is a graph of transmission error curves without consideration of the amount of misalignment versus the amount of misalignment.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
As shown in fig. 1, the method for calculating hypoid gear contact considering the influence of the misalignment specifically includes the following steps:
1) and establishing a finite element contact calculation model of the hypoid gear.
As shown in FIG. 2, finite element models of a small wheel and a large wheel are respectively established, wherein the axis of the small wheel is parallel to the X axis of the global coordinate system, the axis of the large wheel is parallel to the Y axis of the global coordinate system, and the small wheel is offset along the Z axis of the global coordinate system. Establishing a central node o at the centroid positions of the small wheel and the large wheel respectively1And o2And coupling the central node with the body unit model by adopting a rigid connection unit. Establishing a displacement reference node p at the intersection point of the common perpendiculars of the axes of the small wheel and the large wheel1And p2. In turn, a face-to-face contact pair is established between the tooth flanks (small wheel concave and large wheel convex) that may be in contact during the calculation, and the tooth flank friction coefficient is defined.
2) Gear finite element contact calculations without consideration of the amount of misalignment.
The method comprises the following steps of calculating the finite element contact of the gear without considering the dislocation quantity, and solving the unit vector N of the acting direction of the equivalent meshing force and the coordinate R of the equivalent meshing node, wherein the method comprises the following steps:
constraint small wheel center node o1X, Y, Z direction translation freedom degree and Y, Z direction rotation freedom degree, and restrains large wheel center node o2X, Y, Z translational degree of freedom and X, Z rotational degree of freedom, at o1Exerts a constant input torque T on the X-direction rotational degree of freedom1At o2Is subjected to a constant rotational speed omega in the rotational degree of freedom in the Y direction2Setting the total solving time of contact calculation as t, the solving step length as delta t and the corresponding axial rotation angle of the large wheel
In order to obtain a complete gear mesh footprint, it is ensured that at least one pair of tooth flanks undergoes a complete meshing process.
The equivalent contact force vector f of the ith surface-surface contact pair at the moment j can be obtained by finite element contact calculation of the gearijAnd coordinates r of equivalent point of actionijRespectively expressed as:
fij＝[fxij，fyij，fzij]T
rij＝[xij，yij，zij]T
in the formula (f)xij，fyij，fzijIs the force component of the equivalent contact force in the global coordinate system; x is the number ofij，yij，zijCoordinate components of the equivalent action points in the global coordinate system; i denotes the ith tooth face contact pair; j denotes the jth touch computation time.
The total gear mesh force vector at time j is expressed as:
Fj＝[Fxj，Fyj，Fzj]
in the formula (I), the compound is shown in the specification,
n is the surface-to-surface contact logarithm between the gear pairs.
The unit vector of the equivalent meshing force action direction of the gear at the moment j is expressed as:
Nj＝[nxj，nyj，nzj]T
in the formula, nxj，nyj，nzjUnit vector N of direction of action of equivalent meshing force of gear at moment jjA component in the direction X, Y, Z; n isxj＝Fxj/|Fj|；nyj＝Fyj/|Fj|；nzj＝Fzj/|Fj|。
The coordinate position of the equivalent meshing node at the moment j in the global coordinate system is expressed as
Rj＝[xj，yj，zj]T
The force equivalence and moment balance relationship can be used to obtain:
zj＝(Myj+Fzjxj)/Fxj
yj＝(Mxj+Fyjzj)/Fzj
in the formula, xj，zj，yjCoordinate position R of equivalent meshing node in global coordinate system for moment jjA component in the direction X, Y, Z; mxjAnd MyjThe moment of the gear meshing force at the moment j to the X axis and the Y axis of the global coordinate system respectively.
The unit vector N of the action direction of the equivalent meshing force and the coordinate R of the equivalent meshing node in the whole meshing process take the average value of data of one meshing period, and are respectively expressed as follows:
N＝[nx，ny，nz]T
R＝[x，y，z]T
in the formula, nx、ny、nzA component of a unit vector N in the direction X, Y, Z representing the equivalent engagement force action direction of the entire engagement process;
x, y and z are components of an equivalent meshing node coordinate R of the whole meshing process in the direction X, Y, Z;
t1-t0m is the number of times that the time range encompasses, one meshing cycle of the hypoid gear.
3) And establishing a finite element model of the gear transmission system according to the unit vector N of the acting direction of the equivalent meshing force and the coordinate R of the equivalent meshing node.
A finite element model of the transmission system including the transmission shaft, the housing, the bearings, and the gears is established as shown in fig. 3. The transmission shaft is simulated by adopting a space beam unit, a beam unit node is established at the center of the bearing and the center of the gear, and a gear center node o1And o2In accordance with the coordinates in the gear contact calculation model described above. Establishing a finite element model of the body unit of the shell, constraining the node freedom of the external supporting part, establishing a node in the center of the bearing, and respectively using a rigid connection sheetThe element is coupled with a shell finite element model, the dimension reduction transformation is carried out on the rigidity matrix of the axle housing model, and only the freedom degree of the bearing center node is reserved. The bearing is simulated by adopting a nonlinear bearing unit, one end of the bearing unit is connected with a bearing center node corresponding to the transmission shaft beam unit, and the other end of the bearing unit is connected with a bearing center node corresponding to the shell dimension reduction model. The hypoid gear is simulated by adopting an equivalent meshing model, and as shown in figure 4, equivalent meshing nodes m of a small wheel and a large wheel are respectively established1And m2The coordinate R is [ x, y, z ]]TCalculated from the gear contact, o1And m1、o2And m2Are all connected by rigid beams m1And m2Through equivalent meshing rigidity KmAnd (c) a coupling, in which,
in the formula, kmThe meshing stiffness coefficient can be determined according to the ISO standard.
Respectively establishing dislocation reference nodes p at the intersection points of the common perpendiculars of the axes of the small wheel and the large wheel1And p2，o1And p1、o2And p2All connected by rigid beams.
4) And (5) statically solving the transmission system model.
Carrying out statics solution on a finite element model of the gear transmission system to obtain a gear central beam unit node displacement vector deltao1And deltao2And a misalignment reference node displacement vector deltap1And deltap2The method comprises the following steps:
applying input torque T to the node axial rotation freedom of the small wheel shaft input end beam unit1Restraining the axial rotational freedom degree of the beam unit node at the output end of the large wheel shaft, and carrying out statics nonlinear iteration solution on a transmission system model containing a nonlinear bearing unit by adopting a Newton-Laverson method to obtain a gear center beam unit node displacement vector delta under the corresponding load working conditiono1And deltao2Offset reference node displacement vector deltap1And deltap2Expression is respectivelyComprises the following steps:
δo1＝[xo1，yo1，zo1，αo1，βo1，γo1]T
δo2＝[xo2,yo2,zo2,αo2,βo2，γo2]T
δp1＝[xp1，yp1，zp1，αp1，βp1，γp1]T
δp2＝[xp2，yp2，zp2，αp2，βp2，γp2]T
wherein [ x, y, z [ ]]TRepresenting translation displacement vectors [ α, gamma ]]TRepresenting an angular displacement vector.
5) Gear finite element contact calculations taking into account the amount of misalignment.
According to the gear central beam unit node displacement vector deltao1And deltao2And a misalignment reference node displacement vector deltap1And deltap2Changing the orientation of the hypoid gear finite element contact calculation model, thereby accurately embodying the gear dislocation amount obtained by the transmission system model in the gear finite element contact calculation model; and (3) carrying out finite element contact calculation of the gear considering the dislocation quantity, and solving an equivalent meshing force action direction unit vector N 'and an equivalent meshing node coordinate R' considering the influence of the dislocation quantity. The method specifically comprises the following steps:
a. with small wheel center node o1For reference, the small wheel finite element model is rotated β around the Y-axis and Z-axis respectivelyo1And gammao1An angle;
b. along vector [ xo1,yo1,zo1]TTranslating the finite element model of the small wheel;
c. with the centre node o of the bull wheel2For reference, the large wheel finite element model is rotated α around the X-axis and Z-axis respectivelyo2And gammao2An angle;
d. along vector [ xo2,yo2,zo2]TTranslation is bigA wheel finite element model;
e. along vector [ xo1,yo1,yo1]TTranslational small wheel central node o1Obtaining a new small wheel center node o1', along a vector [ x ]o2,yo2,zo2]TTranslation bull wheel center node o2Obtaining a new center node o of the bull wheel2', along a vector [ x ]p1,yp1,zp1]TTranslation small wheel offset reference node p1Obtaining a new small round offset reference node p1', along a vector [ x ]p2,yp2,zp2]TTranslation large wheel dislocation reference node p2Obtaining a new large round of offset reference nodes p2′；
f. Establishing a local coordinate system to make the small wheel local coordinate system X1Shaft is composed of1' Direction p1', local coordinate system X of bull wheel2Shaft is composed of2' Direction p2', at o1' X of1Applying a constant input torque T to the degree of freedom of the direction rotation1At o2' X of2Applying a constant rotational speed omega to the degree of freedom of the direction rotation2Carrying out gear finite element contact calculation to obtain an equivalent meshing force action direction unit vector N 'and an equivalent meshing node coordinate R' which are influenced by the dislocation quantity, and superposing instantaneous tooth surface contact stress at each moment to obtain tooth surface contact stress distribution in a complete time range, namely a hypoid gear loading meshing imprint;
g. calculating the hypoid gear transmission error e in the whole process, wherein the calculation formula is as follows:
in the formula, N1The number of teeth of the small gear is; n is a radical of2The number of teeth of the big gear;
the angle of axial rotation of the small wheel is
The theoretical turning angle of the big wheel is obtained according to the transmission ratio;
is the actual turning angle of the bull wheel.
6) And carrying out iterative solution between gear contact calculation and transmission system statics calculation, finally solving the statics balance states of the gear contact calculation model and the transmission system model, and obtaining a hypoid gear contact calculation result accurately considering the influence of the dislocation quantity, wherein the hypoid gear contact calculation result mainly comprises a loading contact print, a contact stress and a loading transmission error of the gear.
The following coupling relation exists between the gear contact calculation model and the transmission system model: gear orientation adjustment parameters (gear center node displacement and dislocation reference node displacement) in the gear contact calculation model are obtained through static calculation of the transmission system model; the gear equivalent meshing parameters (unit vectors of the acting direction of the equivalent meshing force and coordinates of equivalent meshing nodes) of the transmission system model are obtained by gear finite element contact calculation.
The iterative solution comprises the following steps:
①, reestablishing a finite element model of the gear transmission system according to the unit vector N ' of the acting direction of the equivalent meshing force and the coordinate R ' of the equivalent meshing node, wherein the unit vector N ' of the acting direction of the equivalent meshing force is influenced by the dislocation quantity;
②, carrying out statics solution on a finite element model of the new transmission system, and solving a new gear central beam unit node displacement vector and a misalignment reference node displacement vector;
③, changing the orientation of the hypoid gear finite element contact calculation model according to the gear central beam unit node displacement vector and the dislocation reference node displacement vector, performing the gear finite element contact calculation considering the dislocation amount again, and solving a new unit vector N 'of the action direction of the equivalent meshing force and the coordinate R' of the equivalent meshing node, which are considered to be influenced by the dislocation amount;
④, judging whether the equivalent gear meshing parameters obtained by two adjacent iterations meet the convergence criterion formula, if so, calculating convergence, finally obtaining the static equilibrium state of the gear contact calculation model and the transmission system model, and obtaining the hypoid gear contact calculation result accurately considering the influence of the dislocation quantity, otherwise, returning to step ①.
Wherein the convergence criterion formula is as follows:
||Nk-Nk-1||+||Rk-Rk-1||＜g
in the formula, Nk-1And NkRespectively obtaining unit vectors of the action direction of the equivalent meshing force of the gear for the k-1 th iteration and the k-th iteration; rk-1And RkRespectively obtaining the coordinates of the equivalent meshing nodes of the gears for the k-1 th iteration and the k-th iteration; ε is the convergence tolerance, a small positive number, and is calculated to be 0.1.
In the above embodiment, an Abaqus software is used to build a finite element model of a hypoid gear, and the element type is a 6-face element. In the actual modeling calculation, the analysis requirement, the calculation precision and the calculation cost are comprehensively considered, only part of the gear teeth participating in the contact calculation can be modeled, and a finite element contact calculation model of the hypoid gear containing 5 pairs of teeth is established, as shown in fig. 5. The tooth surface mesh size is controlled within 1mm to ensure the contact calculation accuracy and convergence.
A method for calculating the contact of a hypoid gear in consideration of the influence of the shift amount according to the present invention will be further described with reference to a hypoid gear transmission system of a main reduction gear of a transaxle shown in fig. 3 as a specific embodiment, in which the parameters of the hypoid gear are shown in table 1.
TABLE 1 hypoid Gear parameters
| Parameter(s) | Small wheel | Big wheel |
| Number of teeth | 7 | 39 |
| Modulus/mm | 10.9 | 10.9 |
| Mean pressure angle/(°) | 22.5 | 22.5 |
| Helix angle/(°) | 43.85 | 35.84 |
| Tooth width/mm | 64.79 | 61 |
| Offset/mm | 26 | 0 |
| Direction of rotation | Left hand rotation | Right hand rotation |
The invention relates to a hypoid gear contact calculation method considering the influence of a dislocation quantity, which specifically comprises the following steps:
1) and establishing a finite element contact calculation model of the hypoid gear.
The center of the differential is defined as the origin O of a global coordinate system, the axis of the small wheel is parallel to the X axis of the global coordinate system, the axis of the large wheel is parallel to the Y axis of the global coordinate system, and the small wheel is offset along the Z axis of the global coordinate system. For creating hypoid gears using Abaqus softwareThe finite element model is a 6-surface unit, analysis requirements, calculation accuracy and calculation cost are comprehensively considered during actual modeling calculation, only part of gear teeth participating in contact calculation can be modeled, and a hypoid gear finite element contact calculation model containing 5 pairs of teeth is established, as shown in fig. 5. The tooth surface mesh size is controlled within 1mm to ensure the contact calculation accuracy and convergence. Respectively establishing finite element models of a small wheel and a large wheel, and respectively establishing a central node o at the centroid positions of the small wheel and the large wheel1(-181.025, -55,26) and o2(0, -18.145,0) coupling the central node with the body element model using rigid connection elements. Establishing a displacement reference node p at the intersection point of the common perpendiculars of the axes of the small wheel and the large wheel1(0, -55,26) and p2(0, -55,0). In the calculation process, a face-face contact pair is sequentially established between tooth surfaces (a small wheel concave surface and a large wheel convex surface) which are possibly contacted, and the friction coefficient of the tooth surfaces is 0.15.
2) And (4) carrying out finite element contact calculation on the gear without considering the dislocation quantity, and solving a unit vector N of the acting direction of the equivalent meshing force and an equivalent meshing node coordinate R.
Constraint small wheel center node o1X, Y, Z direction translation freedom degree and Y, Z direction rotation freedom degree, and restrains large wheel center node o2X, Y, Z translational degree of freedom and X, Z rotational degree of freedom, at o1Exerts a constant input torque T on the X-direction rotational degree of freedom11615.5n.m, at o2Is subjected to a constant rotational speed omega in the rotational degree of freedom in the Y direction2And (4) setting the total solving time t of contact calculation to be 1.0s and the solving step length to be delta t to be 0.005s at 0.5 rad/s. Determining the unit vector N [ -175.48, -15.11,31.35 ] of the effective direction of the equivalent engaging force]TAnd equivalent mesh node coordinates R [ -0.643, -0.184, -0.743]T。
3) And establishing a finite element model of the gear transmission system according to the unit vector N of the acting direction of the equivalent meshing force and the coordinate R of the equivalent meshing node.
The small wheel shaft, the large wheel shaft and the differential shaft are simulated by adopting a space beam unit, and beam unit nodes are established at the center of a bearing and the center of a gear, and the center node o of the gear1(-181.025, -55,26) and o2(0, -18.145,0) are consistent with the coordinates in the gear contact calculation model. Establishing a body unit finite element model of the shell, constraining the node degree of freedom of the position of the plate spring, establishing a node in the center of the bearing, respectively coupling the rigid connection unit and the shell finite element model, carrying out dimension reduction transformation on a rigidity matrix of the axle housing model, and only keeping the node degree of freedom of the center of the bearing. The transmission system comprises 1 cylindrical roller bearing and 4 tapered roller bearings, and is simulated by adopting a nonlinear bearing unit, one end of the bearing unit is connected with a bearing center node corresponding to the transmission shaft beam unit, and the other end of the bearing unit is connected with a bearing center node corresponding to the shell shrinkage dimension model. The hypoid gear is simulated by adopting an equivalent meshing model, and equivalent meshing nodes m of a small wheel and a large wheel are respectively established1And m2The coordinates R [ -0.643, -0.184, -0.743 [ ]]TCalculated from the gear contact, o1And m1、o2And m2Are all connected by rigid beams m1And m2Through equivalent meshing rigidity KmCoupling in which the unit vector N of the direction of action of the equivalent meshing force is [ -175.48, -15.11,31.35]TCoefficient of meshing stiffness km＝1.22×106N/mm. Respectively establishing dislocation reference nodes p at the intersection points of the common perpendiculars of the axes of the small wheel and the large wheel1(0, -55,26) and p2(0,-55,0)，o1And p1、o2And p2All connected by rigid beams.
4) Carrying out statics solution on a finite element model of the gear transmission system to obtain a gear central beam unit node displacement vector deltao1And deltao2And a misalignment reference node displacement vector deltap1And deltap2。
Applying input torque T to the node axial rotation freedom of the small wheel shaft input end beam unit1Constraining the axial rotation freedom degree of the beam unit node at the output end of the large wheel shaft as 1615.5N.m, and performing statics nonlinear iterative solution on a transmission system model containing a nonlinear bearing unit by adopting a Newton-Raffson method to obtain a gear center beam unit node displacement vector deltao1And deltao2Offset reference node displacement vector deltap1And deltap2The results are shown in Table 2 below.
TABLE 2 hypoid gear equivalent mesh model nodal displacement
| Node point | X translation/mm | Y translation/mm | Z translation/mm | X rotation/(°) | Y rotation/(°) | Z rotation/(°) |
| Small wheel center node | -0.0752 | -0.0056 | -0.1367 | 0.5034 | -0.0215 | 0.0166 |
| Small wheel offset reference node | -0.0752 | 0.0467 | -0.0688 | 0.5034 | -0.0215 | 0.0166 |
| Centre node of bull wheel | 0.0162 | 0.0297 | 0.0348 | 0.0039 | 0.0007 | -0.0071 |
| Large wheel offset reference node | 0.0116 | 0.0297 | 0.0323 | 0.0039 | 0.0007 | -0.0071 |
5) Gear finite element contact calculation taking the amount of misalignment into account:
based on the calculation results of table 2, the orientation of the finite element contact calculation model for hypoid gears was adjusted as follows:
a. with small wheel center node o1For reference, the small wheel finite element model is rotated β around the Y-axis and Z-axis respectivelyo1-0.0215 ° and γo1＝0.0166°；
b. Along vector [ -0.0752, -0.0056, -0.1367]TTranslating the finite element model of the small wheel;
c. with the centre node o of the bull wheel2For reference, the large wheel finite element model is rotated α around the X-axis and Z-axis respectivelyo20.0039 ° and γo2＝-0.0071°；
d. Along the vector [0.0162,0.0297,0.0348]TTranslating the finite element model of the bull wheel;
e. along vector [ -0.0752, -0.0056, -0.1367]TTranslational small wheel central node o1Obtaining a new small wheel center node o1', along a vector [0.0162,0.0297,0.0348]TTranslation bull wheel center node o2Obtaining a new center node o of the bull wheel2', along the vector [ -0.0752,0.0467, -0.0688]TTranslation small wheel offset reference node p1Obtaining a new small round offset reference node p1', along a vector [0.0116,0.0297,0.0323]TTranslation large wheel dislocation reference node p2Obtaining a new large round of offset reference nodes p2′；
f. Establishing a local coordinate system to make the small wheel local coordinate system X1Shaft is composed of1' Direction p1', local coordinate system X of bull wheel2Shaft is composed of2' Direction p2', at o1' X of1Applying a constant input torque T to the degree of freedom of the direction rotation11615.5n.m, at o2' X of2Applying a constant rotational speed omega to the degree of freedom of the direction rotation2The gear finite element contact calculation is carried out under-0.5 rad/s, and a new unit vector N' of the equivalent meshing force action direction is obtained under-177.15, -14.91 and 31.05]TAnd equivalent mesh node coordinates R [ -0.645, -0.184, -0.742]T。
6) Performing iterative solution between gear contact calculation and transmission system statics calculation:
and (3) taking the equivalent meshing parameter obtained by gear contact calculation without considering the dislocation amount as an initial value, carrying out iterative solution between the gear contact calculation and the transmission system statics calculation, and iterating for 2 times to calculate convergence, wherein the gear equivalent meshing parameter obtained by each iteration is shown in tables 3 and 4.
TABLE 3 hypoid gear equivalent meshing node coordinates
| Number of iterations | X coordinate/mm | Y coordinate/mm | Z coordinate/mm |
| 0 | -175.48 | -15.11 | 31.35 |
| 1 | -177.15 | -14.91 | 31.05 |
| 2 | -177.08 | -14.93 | 31.04 |
TABLE 4 hypoid gear equivalent meshing force action direction unit vector
| Number of iterations | Component X | Component Y | Component Z |
| 0 | -0.6433 | -0.1845 | -0.7431 |
| 1 | -0.6451 | -0.1842 | -0.7416 |
| 2 | -0.6448 | -0.1845 | -0.7417 |
Under the working condition, the comparison between the large wheel output torque obtained by the two models and the test result is shown in the table 5, and the effectiveness of the method is illustrated.
TABLE 5 big wheel output Torque
| Type of result | Torque value/N.m | Relative error/%) |
| Test of | 8437 | - |
| Gear contact calculation | 8445 | 0.09 |
| Driveline calculations | 8492 | 0.65 |
Comparing the load meshing trace of the tooth surface of the large wheel, as shown in fig. 6(a), (b), and (c), if the influence of the misalignment amount is not considered, the obtained meshing trace is biased to the small end of the tooth, and after the misalignment amount of the gear is considered, the obtained meshing trace is more consistent with the test result.
Comparing hypoid gear transmission errors, as shown in fig. 7, when the dislocation amount is not considered, the average value of absolute values of the transmission errors is 454.1urad, and the peak-to-peak value is 23.3 urad; taking the amount of misalignment into account, the absolute values of the transmission errors were averaged to 427.3urad, with a peak-to-peak value of 24.9 urad. Under the working condition, if the influence of the dislocation quantity is not considered, the obtained transmission error peak-to-peak value is smaller.
In summary, the hypoid gear contact calculation method considering the influence of the dislocation amount provided by the invention can accurately realize the hypoid gear contact calculation considering the influence of the dislocation amount, and overcomes the technical problem that the existing method is difficult to accurately reflect the coupling influence between the gear nonlinear contact state and the loaded deformation of a transmission system comprising a plurality of nonlinear bearing units. The method can be widely applied to design modeling and computational analysis of hypoid gear transmission systems and similar gear transmission systems.
The above embodiments are only used for illustrating the present invention, and the structure, the arrangement position, the connection mode, and the like of each component can be changed, and all equivalent changes and improvements based on the technical scheme of the present invention should not be excluded from the protection scope of the present invention.
Claims (9)
1. A hypoid gear contact calculation method taking into account the influence of the amount of misalignment, comprising the steps of:
1) establishing a hypoid gear finite element contact calculation model;
2) carrying out finite element contact calculation on the gear without considering the influence of the dislocation quantity, and solving a unit vector N of the action direction of the equivalent meshing force and an equivalent meshing node coordinate R;
3) establishing a finite element model of the gear transmission system according to the unit vector N of the acting direction of the equivalent meshing force and the coordinate R of the equivalent meshing node;
4) carrying out statics solution on a finite element model of the gear transmission system to obtain a gear central beam unit node displacement vector deltao1And deltao2And a misalignment reference node displacement vector deltap1And deltap2；
5) According to the gear central beam unit node displacement vector deltao1And deltao2And a misalignment reference node displacement vector deltap1And deltap2Changing the orientation of the finite element contact calculation model of the hypoid gear; carrying out finite element contact calculation of the gear considering the influence of the dislocation quantity, and solving an equivalent meshing force action direction unit vector N 'and an equivalent meshing node coordinate R' considering the influence of the dislocation quantity;
6) carrying out iterative solution between gear finite element contact calculation considering the influence of the dislocation quantity and transmission system finite element model statics solution, solving the statics equilibrium state of the gear finite element contact calculation model and the transmission system finite element model, and calculating the hypoid gear contact calculation result accurately considering the influence of the dislocation quantity; wherein, the iterative solution comprises the following steps:
①, reestablishing a finite element model of the gear transmission system according to the unit vector N ' of the acting direction of the equivalent meshing force and the coordinate R ' of the equivalent meshing node, wherein the unit vector N ' of the acting direction of the equivalent meshing force is influenced by the dislocation quantity;
②, carrying out statics solution on a finite element model of the new gear transmission system, and solving a new gear center beam unit node displacement vector and a misalignment reference node displacement vector;
③, changing the orientation of the hypoid gear finite element contact calculation model according to the gear central beam unit node displacement vector and the dislocation reference node displacement vector, performing the gear finite element contact calculation considering the influence of the dislocation amount again, and solving a new unit vector N 'of the action direction of the equivalent meshing force and the coordinate R' of the equivalent meshing node considering the influence of the dislocation amount;
④, judging whether the equivalent gear meshing parameters obtained by two adjacent iterations meet the convergence criterion formula, if so, calculating convergence, finally obtaining the static equilibrium state of the gear contact calculation model and the transmission system model, and obtaining the hypoid gear contact calculation result accurately considering the influence of the dislocation quantity, otherwise, returning to step ①.
2. The method for calculating the contact of the hypoid gear considering the influence of the dislocation quantity according to claim 1, wherein the step 1) of establishing the finite element contact calculation model of the hypoid gear comprises the steps of:
firstly, respectively establishing finite element models of a small wheel and a large wheel, enabling the axis of the small wheel to be parallel to the X axis of a global coordinate system, enabling the axis of the large wheel to be parallel to the Y axis of the global coordinate system, and enabling the small wheel to be offset along the Z axis of the global coordinate system; then, a center node o is established at the centroid positions of the small wheel and the large wheel, respectively1And o2Respectively coupling the central nodes of the small wheel and the large wheel with the body unit models of the small wheel and the large wheel by adopting a rigid connection unit; then, respectively establishing a misalignment reference node p of the small wheel and the large wheel at the intersection point position of the common perpendicular lines of the axes of the small wheel and the large wheel1And p2(ii) a Finally, a face-to-face contact pair is sequentially established between tooth surfaces that may be in contact during the calculation, and a tooth surface friction coefficient is defined.
3. The hypoid gear contact calculation method taking into account the influence of the misalignment amount according to claim 1, wherein the step 2) of finite element contact calculation of the gear without taking into account the influence of the misalignment amount comprises the steps of:
I. constraint small wheel center node o1X, Y, Z direction translation freedom degree and Y, Z direction rotation freedom degree, and restrains large wheel center node o2X, Y, Z translational degree of freedom and X, Z rotational degree of freedom, at o1Exerts a constant input torque T on the X-direction rotational degree of freedom1At o2Is subjected to a constant rotational speed omega in the rotational degree of freedom in the Y direction2Setting the total solving time of contact calculation as t, the solving step length as delta t and the corresponding axial rotation angle of the large wheel
II. Respectively calculating the equivalent contact force vector and the equivalent action point coordinate of each surface-surface contact pair at each solving moment;
wherein the equivalent contact force vector f of the ith surface-to-surface contact pair at the moment jijAnd coordinates r of equivalent point of actionijRespectively expressed as:
fij＝[fxij，fyij，fzij]T
rij＝[xij，yij，zij]T
in the formula (f)xij，fyij，fzijIs the force component of the equivalent contact force in the global coordinate system; x is the number ofij，yij，zijCoordinate components of the equivalent action points in the global coordinate system; i denotes the ith tooth face contact pair; j represents the jth touch computation time;
III, respectively calculating the total gear meshing force vector, the unit vector of the equivalent meshing force action direction of the gear and the coordinate position of the equivalent meshing node in the global coordinate system at each solving moment;
wherein, the total gear engagement force vector F at the moment jjUnit vector N of direction of action of equivalent meshing force of gear at time jjCoordinate position R of equivalent meshing node in global coordinate system at moment jjRespectively expressed as:
Fj＝[Fxj，Fyj，Fzj]T
Nj＝[nxj，nyj，nzj]T
Rj＝[xj，yj，zj]T
the force equivalence and moment balance relationship are used to obtain:
zj＝(Myj+Fzjxj)/Fxj
yj＝(Mxj+Fyjzj)/Fzj
in the formula, xj，zj，yjCoordinate position R of equivalent meshing node in global coordinate system for moment jjA component in the direction X, Y, Z;
n is the surface-to-surface contact logarithm between the gear pairs; n isxj，nyj，nzjUnit vector N of direction of action of equivalent meshing force of gear at moment jjA component in the direction X, Y, Z; n isxj＝Fxj/|Fj|；nyj＝Fyj/|Fj|；nzj＝Fzj/|Fj|；MxjAnd MyjMoment of the gear meshing force at the moment j to the X axis and the Y axis of the global coordinate system respectively;
IV, taking an average value of the data of one meshing period, and calculating an equivalent meshing force action direction unit vector N and an equivalent meshing node coordinate R in the whole meshing process, wherein the unit vector N and the equivalent meshing node coordinate R are respectively expressed as:
N＝[nx，ny，nz]T
R＝[x，y，z]T
in the formula, nx、ny、nzA component of a unit vector N in the direction X, Y, Z representing the equivalent engagement force action direction of the entire engagement process;
x, y and z are components of an equivalent meshing node coordinate R of the whole meshing process in the direction X, Y, Z;
t1-t0is quasi-dualAnd m is the number of moments included in the time range.
4. The hypoid gear contact calculation method considering the influence of the misalignment amount according to claim 1, wherein the step 3) of establishing a finite element model of the gear transmission system comprises the following steps:
firstly, a space beam unit is adopted to simulate a transmission shaft, and a beam unit node is established at the center of a bearing and the center of a gear, and a gear center node o1And o2Adopting coordinates consistent with those in the hypoid gear finite element contact calculation model; then, establishing a body unit finite element model of the shell, constraining the node freedom degree of an external supporting part, establishing a node in the center of the bearing, respectively coupling the rigid connection unit and the shell finite element model, carrying out dimension reduction transformation on a rigidity matrix of the axle shell model, and only keeping the node freedom degree of the bearing center; then, a nonlinear bearing unit is adopted to simulate a bearing, one end of the bearing unit is connected with a bearing central node corresponding to the transmission shaft beam unit, and the other end of the bearing unit is connected with a bearing central node corresponding to the shell dimension reduction model; then, an equivalent meshing model is adopted to simulate a hypoid gear, and equivalent meshing nodes m of a small wheel and a large wheel are respectively established1And m2，o1And m1、o2And m2Are all connected by rigid beams m1And m2Through equivalent meshing rigidity KmCoupling; finally, respectively establishing a misalignment reference node p of the small wheel and the large wheel at the intersection point position of the common perpendicular lines of the axes of the small wheel and the large wheel1And p2，o1And p1、o2And p2All connected by rigid beams.
5. The hypoid gear contact calculation method considering the influence of the misalignment amount according to claim 1, wherein the gear transmission system finite element model statics solution in the step 4) comprises the steps of:
firstly, an input torque T is applied to the axial rotation freedom degree of a node of the small wheel shaft input end beam unit1The axial rotation freedom degree of the beam unit node at the output end of the large wheel shaft is restrained; then, carrying out statics nonlinear iterative solution on a finite element model of the transmission system containing the nonlinear bearing unit to obtain a gear central beam unit node displacement vector delta under the corresponding load working conditiono1And deltao2And a misalignment reference node displacement vector deltap1And deltap2；
Wherein, the gear center beam unit node displacement vector deltao1And deltao2And a misalignment reference node displacement vector deltap1And deltap2Are respectively:
δo1＝[xo1，yo1，zo1，αo1，βo1，γo1]T
δo2＝[xo2，yo2，zo2，αo2，βo2，γo2]T
δp1＝[xp1，yp1，zp1，αp1，βp1，γp1]T
δp2＝[xp2，yp2，zp2，αp2，βp2，γp2]T
in the formula, xo1，yo1，zo1、xo2，yo2，zo2、xp1，yp1，zp1、xp2，yp2，zp2Respectively representing gear central beam unit node displacement vectors deltao1And deltao2And a misalignment reference node displacement vector deltap1And deltap2α translation displacement vectoro1，βo1，γo1、αo2，βo2，γo2、αp1，βp1，γp1、αp2，βp2，γp2Respectively representing gear central beam unit node displacement vectors deltao1And deltao2And a misalignment reference node displacement vector deltap1And deltap2Vector of angular displacementAmount of the compound (A).
6. The hypoid gear contact calculation method taking into account the influence of the misalignment amount according to claim 5, wherein the step 5) specifically includes the steps of:
a. with small wheel center node o1For reference, the small wheel finite element model is rotated β around the Y-axis and Z-axis respectivelyo1And gammao1An angle;
b. along vector [ xo1，yo1，zo1]TTranslating the finite element model of the small wheel;
c. with the centre node o of the bull wheel2For reference, the large wheel finite element model is rotated α around the X-axis and Z-axis respectivelyo2And gammao2An angle;
d. along vector [ xo2，yo2，zo2]TTranslating the finite element model of the bull wheel;
e. along vector [ xo1，yo1，zo1]TTranslational small wheel central node o1Obtaining a new small wheel center node o1', along a vector [ x ]o2，yo2，zo2]TTranslation bull wheel center node o2Obtaining a new center node o of the bull wheel2', along a vector [ x ]p1，yp1，zp1]TTranslation small wheel offset reference node p1Obtaining a new small round offset reference node p1', along a vector [ x ]p2，yp2，zp2]TTranslation large wheel dislocation reference node p2Obtaining a new large round of offset reference nodes p2′；
f. Establishing a local coordinate system to make the small wheel local coordinate system X1Shaft is composed of1' Direction p1', local coordinate system X of bull wheel2Shaft is composed of2' Direction p2', at o1' X of1Applying a constant input torque T to the degree of freedom of the direction rotation1At o2' X of2Applying a constant rotational speed omega to the degree of freedom of the direction rotation2Calculating the finite element contact of the gear to obtain the testAnd (3) considering the unit vector N 'of the acting direction of the equivalent meshing force and the coordinates R' of the equivalent meshing node, which are influenced by the displacement.
7. The hypoid gear contact calculation method taking into account the influence of the amount of misalignment as set forth in claim 1, wherein the convergence criterion is formulated as:
||Nk-Nk-1||+||Rk-Rk-1||＜ε
in the formula, Nk-1And NkRespectively obtaining unit vectors of the action direction of the equivalent meshing force of the gear for the k-1 th iteration and the k-th iteration; rk-1And RkRespectively obtaining the coordinates of the equivalent meshing nodes of the gears for the k-1 th iteration and the k-th iteration; ε is the convergence tolerance.
8. The hypoid gear contact calculation method considering the influence of the misalignment amount according to claim 1 or 7, wherein the hypoid gear contact calculation result accurately considering the influence of the misalignment amount in step 6) includes a loaded contact footprint, a contact stress and a loaded transmission error of the gear;
superposing instantaneous tooth surface contact stress at each moment to obtain tooth surface contact stress distribution within a complete time range, namely loading a meshing imprint on the hypoid gear;
the calculation formula of the hypoid gear transmission error e in the whole process is as follows:
in the formula, N1The number of teeth of the small gear is; n is a radical of2The number of teeth of the big gear;
the angle of the axial rotation of the small wheel is;
is the actual turning angle of the bull wheel.
9. The method for calculating contact of hypoid gear considering influence of dislocation amount according to claim 1, wherein a finite element model of hypoid gear is established using Abaqus software, and the element type is 6-face element; modeling only part of gear teeth participating in contact calculation, and establishing a finite element contact calculation model of the hypoid gear comprising a plurality of pairs of teeth; meanwhile, the size of the tooth surface grid is controlled within 1 mm.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710009493.9A CN106802989B (en) | 2017-01-06 | 2017-01-06 | Hypoid gear contact calculation method considering influence of dislocation quantity |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710009493.9A CN106802989B (en) | 2017-01-06 | 2017-01-06 | Hypoid gear contact calculation method considering influence of dislocation quantity |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106802989A CN106802989A (en) | 2017-06-06 |
| CN106802989B true CN106802989B (en) | 2020-04-07 |
Family
ID=58985490
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710009493.9A Active CN106802989B (en) | 2017-01-06 | 2017-01-06 | Hypoid gear contact calculation method considering influence of dislocation quantity |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106802989B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107944174B (en) * | 2017-12-06 | 2020-07-07 | 清华大学 | Method for obtaining tooth direction load distribution coefficient of cylindrical gear |
| CN112747102B (en) * | 2020-12-31 | 2022-05-20 | 安徽江淮汽车集团股份有限公司 | Simulation calculation method, computer, and storage medium |
| CN114297801A (en) * | 2021-12-31 | 2022-04-08 | 重庆大学 | Method for testing internal dynamic engagement force and dynamic friction force of planetary gear train |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103927428B (en) * | 2014-05-09 | 2017-04-19 | 清华大学 | Bevel gear dislocation quantity finite element computing method with multi-factor influences taken into account |
-
2017
- 2017-01-06 CN CN201710009493.9A patent/CN106802989B/en active Active
Non-Patent Citations (1)
| Title |
|---|
| 准双曲面齿轮动态啮合性能的有限元分析研究;唐进元 等;《振动与冲击》;20111231;101-106 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106802989A (en) | 2017-06-06 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106960093B (en) | Transmission system numerical simulation method considering nonlinear coupling of gear and bearing | |
| CN107944174B (en) | Method for obtaining tooth direction load distribution coefficient of cylindrical gear | |
| Li | Design and strength analysis methods of the trochoidal gear reducers | |
| CN106802989B (en) | Hypoid gear contact calculation method considering influence of dislocation quantity | |
| US10423730B2 (en) | Contact modeling between objects | |
| Ding et al. | A data-driven programming of the human-computer interactions for modeling a collaborative manufacturing system of hypoid gears by considering both geometric and physical performances | |
| Hou et al. | Static contact analysis of spiral bevel gear based on modified VFIFE (vector form intrinsic finite element) method | |
| CN103927428B (en) | Bevel gear dislocation quantity finite element computing method with multi-factor influences taken into account | |
| Huang et al. | Positioning accuracy reliability analysis of industrial robots based on differential kinematics and saddlepoint approximation | |
| CN106354975B (en) | A kind of finite element method obtaining planetary gear magnitude of misalignment | |
| CN108416120B (en) | Method for determining load distribution rate of double-tooth meshing area of straight-toothed spur gear | |
| CN104772773A (en) | Mechanical arm kinematics formal analysis method | |
| Mavriplis et al. | Time spectral method for periodic and quasi-periodic unsteady computations on unstructured meshes | |
| CN113779735B (en) | Planetary gear box three-dimensional tolerance analysis method based on jacobian rotation model | |
| Lu et al. | A novel two-variable optimization algorithm of TCA for the design of face gear drives | |
| Xiong et al. | Dynamic surface control-backstepping based impedance control for 5-DOF flexible joint robots | |
| Zhang et al. | Dynamics analysis of spatial parallel robot with rigid and flexible links | |
| Raviola et al. | Multibody representation on the coupling between wave generator and flexspline in strain wave gears | |
| CN113010978A (en) | Aviation straight gear shaping method based on dynamic simulation | |
| Li et al. | Load sharing characteristics of multi-stage planetary gear train using analytical and finite element model | |
| Vivet et al. | A new gear contact method for the tooth contact analysis of spiral bevel gear drives in multibody simulations | |
| Inci et al. | Adaptive co-simulation framework exploiting system physics of mechatronic systems | |
| Croes et al. | A combined 1D-3D simulation approach for the energy analysis of a high speed weaving machine | |
| Tian et al. | A multi-fidelity integration method for reliability analysis of industrial robots | |
| Kostić et al. | Analysis of the influence of internal radial clearance on the load distribution of the rolling ball bearing |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |