CN104484526A - Method for improving finite element analysis accuracy of transmission case - Google Patents
Method for improving finite element analysis accuracy of transmission case Download PDFInfo
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Abstract
The invention relates to a method for improving finite element analysis accuracy of a transmission case. The method comprises the steps of establishing a finite element model of an assembly consisting of major parts such as a clutch case, the transmission case, an upper cover and gears, applying gear engagement force to gear engagement nodes, fixing bolt holes of the clutch case connected with a flywheel case, applying rotation freedom degree constraints of gear shafts between all gears and corresponding supporting bearings on two sides and fully cutting off paths of transmission of torque from gear shafts to case bearing holes. The method for improving finite element analysis accuracy of the transmission case has the advantages that since the rotation freedom degree constraints of gear shafts are applied between all gears and corresponding supporting bearings on two sides, relative rotation or relative rotation trend between bearings and bearing holes is prevented, the problem that the stress of the bearing holes in the case is relatively large is solved, the finite element simulation of the transmission case is more compliant with the actual situation, the finite element analysis accuracy of the case is effectively improved, and further the goals of improving the product design accuracy, reducing the product test frequency and decreasing the product development cost are achieved.
Description
Technical field
The present invention relates to a kind of method improving auto parts and components finite element analysis precision, particularly a kind of method improving case of transmission finite element analysis precision.
Background technology
As important foundation part; case of transmission should have the effect of the load such as gear mesh force that the powerful torque of enough intensity opposing engine causes and the variator inertial force that uneven road surface causes; to reach support teeth wheel shaft, protection gear drive, meet the object of car load to the different torque of variator and rotation speed requirements needs.
At present, case of transmission strength check methods extensively adopts finite element method, first gear shaft torque conversion is gear mesh force (comprising radial force, axial force, the force of periphery) according to gear load computing formula by it, is then loaded on pitch point by gear mesh force; Simultaneously in order to prevent freely rotating and according to structure stress equivalence principle, also needing the rotary freedom retraining input shaft input end, output shaft output terminal of gear shaft.In theory, the support reaction on restrained gear shaft rotary freedom should equal the theoretical torque of gear shaft, but the torque of actual employing Finite element arithmetic is less than theoretical torque.Reason is, the curved surface finite element grid model of the cylindrical structural such as bearing, dead eye is made up of multiple less plane, if only retrain the rotary freedom of input shaft input end, output shaft output terminal, gear shaft torque is by until just can be terminated when being applied on restrained rotary freedom.In the process, because gear shaft belongs to elastic body, gear shaft will twist distortion, when its torsional deflection is by bearing, to relatively rotate between bearing finite element model and dead eye finite element model, or have the trend of relatively rotating, comparatively there is dislocation and extruding in multiple in the bearing so just making to contact with each other, dead eye finite element grid model, consumes partial torque thus between facet.The dislocation of bearing, dead eye finite element model will cause the expansion in radial directions of housing dead eye with extruding, thus causes dead eye distortion not conform to the actual conditions, and structural stress is bigger than normal, finally causes Shell Finite Element Method to analyze the problem of simulation accuracy decline.
Summary of the invention
For the problems referred to above, the object of this invention is to provide a kind of method of raising case of transmission finite element analysis precision newly.
For achieving the above object, the method for raising case of transmission finite element analysis precision of the present invention comprises the steps:
One, set up case of transmission finite element model: carry out stress and strain model to each parts of clutch housing, variator respectively, then being contacted between parts by definition is assembled together them for contact relation;
Two, finite element model material is defined: according to elasticity modulus of materials E, Poisson ratio μ in the real material definition finite element model of each parts in clutch housing and variator;
Three, finite element model load is applied: assumed (specified) load comprises two classes, and one is gear mesh force, and it adopts gear load computing formula to calculate, and is then applied on the working pitch point of respective gears in variator; Two is bolt pretightenings, and it is obtained by the relational expression between bolt pretightening and bolt tightening moment, is then applied in the bolt shaft in variator;
Four, apply finite element model boundary condition: model boundary condition comprises two classes, one is the bolt hole fixing the clutch housing be connected with bell housing, with the supporting role of simulated engine to variator; Two is that the rotary freedom applying gear shaft by rigid unit between all gears of variator and gear two side bearing retrains, and is delivered to the path of case of transmission dead eye to interrupt torque each gear shaft from variator completely;
Five, carry out case of transmission finite element analysis: the stress and strain adopting newton-rapshon method iterative computation case of transmission, process is as follows:
Initial time t
0the displacement of=0
nodal force
Adopt following method iterative computation t
0the stress and strain of+Δ t case of transmission;
When
time termination of iterations, if total iterations is
after termination of iterations, the stress and strain of case of transmission adopts following formulae discovery:
I represents iterations, and it gets 1 successively, 2,3 ..., as i=1, in formula (1) ~ (2),
represent t
0the stiffness matrix of moment finite element model;
Δ { U}
(i)represent unbalanced load before the i-th step iteration
the displacement increment caused;
by t
0+ Δ t F
t, F
r, F
a, load level corresponding to F form, if the maximum moment is X, then t
0the load level of+Δ t is respectively
represent t
0+ Δ t is by the i-th-1 step iteration unit stress
the nodal force caused;
represent by t
0+ Δ t load
displacement after the iteration ends caused;
represent t
0the strain matrix in moment, it is determined by the cell node coordinate in finite element model;
[C] represents elastic matrix, and it is determined by elastic properties of materials model E and Poisson ratio μ;
Assuming that the solution of any time t is known, ask the solution of t+ Δ t by the following method;
t[K]Δ{U}
(i)＝
t+Δt{P}-
t+Δt{R}
(i-1)(5)
t+Δt{U}
(i)＝
t+Δt{U}
(i-1)+Δ{U}
(i)(6)
Formula (5) ~ (6) iteration initial value used is the solution of t, that is:
Formula (5) ~ (6) termination of iterations condition is:
t+Δt{P}-
t+Δt{R}
(i-1)≤{e} (7)
During formula (5) ~ (6) termination of iterations, i=n
t+ Δ t
After formula (5) ~ (6) termination of iterations, strain, stress adopt following formulae discovery:
In formula (5) ~ (9),
t[K] represents the stiffness matrix of t finite element model;
Δ { U}
(i)represent unbalanced load before the i-th step iteration
t+ Δ t{ P}-
t+ Δ t{ R}
(i-1)the displacement increment caused;
t+ Δ t{ P} is by t+ Δ t F
t, F
r, F
a, load level corresponding to F form, be X according to the maximum moment, then the load level of t+ Δ t is respectively
t+ Δ t{ R}
(i-1)represent that t+ Δ t is by the i-th-1 step element stress
t+ Δ t{ σ }
(i-1)the nodal force caused;
represent by t+ Δ t load
t+ Δ t{ the displacement that P} causes;
t[B] represents the strain matrix of t, and it is determined by the cell node coordinate in finite element model;
[C] represents elastic matrix, and it is determined by elastic properties of materials model E and Poisson ratio μ;
represent by t load
t{ the displacement after the iteration ends that P} causes;
N
t+ Δ trepresent t+ Δ t, equation obtains total iterations during convergence solution;
N
trepresent t, equation obtains total iterations during convergence solution;
{ e} represents calculating tolerance.
In described step one, the FEM meshing of parts contact site at least will ensure that two row's finite element grid unit are in contact condition; With case of transmission dead eye contact the bearing outer ring grid at position and case of transmission dead eye grid consistent; Case of transmission dead eye and the bearing outer ring position contacted with it are at least divided into 90 parts in a circumferential direction, are axially at least divided into 5 parts.
In described step 3, each gear mesh force comprises the force of periphery, radial force and axial force, it adopts formula (10) to calculate, when gear mesh force is applied in finite element model, by partial cylindrical coordinate system, the Z axis of coordinate system is along gear shaft axis direction, and R is along the radial direction of gear shaft, and t is determined according to right hand rule by Z, R; Bolt pretightening adopts formula (11) to calculate, and action direction is along the axis of bolt;
In formula (10), F
t, F
r, F
abe respectively the force of periphery of gear, radial force and axial force, M is the torque that gear transmits, and d is pitch circle diameter, a
nfor gear normal pressure angle, β is pitch circle place helix angle;
In formula (11), F is bolt pretightening, and T is bolt tightening moment, and k is Bolt Tightening Torque Coefficient, and D is the diameter of bolt.
In described step 4, the principal point of rigid unit is defined in the center of gear shaft, from the node of point selection between gear and bearing gear shaft finite element model.
The present invention has the following advantages: the impact that 1, contemplated by the invention the force transferring parts such as gear shaft, bearing, bolt, the transmission assembly finite element model that to establish with case of transmission finite element model be research object, this makes case of transmission stressed more close to true.2, the present invention is by the finite element grid of refinement parts contact site, reaches the object improving gear mesh force, bolt pretightening transmitting accuracy between each parts; 3, present invention utilizes case of transmission stressed relevant with gear mesh force, and not relevant to gear shaft torque feature, fully between all gears and respective sides spring bearing, apply gear shaft rotary freedom to retrain, it has interrupted torque is delivered to housing dead eye path from gear shaft completely, avoid and to relatively rotate between bearing and dead eye or there is the trend of relatively rotating, it efficiently solves housing dead eye stress problem bigger than normal, improves Shell Finite Element Method analysis precision.Utilize the present invention to carry out case of transmission finite element analysis, more accurately can carry out case of transmission intensity evaluation, and then reach raising product design precision, reduce the product testing frequency, save the object of product development cost.
Accompanying drawing explanation
Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.
Case of transmission finite element model schematic diagram when Fig. 1 is one grade.
Fig. 2 is that strength of gear analyzes schematic diagram.
Fig. 3 is the schematic diagram setting up rigid unit rbe2 on input shaft.
Embodiment
As shown in Figure 1, Figure 2, Figure 3 shows, a kind of method improving case of transmission finite element analysis precision, it comprises the steps:
One, case of transmission finite element model is set up: carry out stress and strain model to clutch housing 1, case of transmission 2, upper cover 3, bolt 4, front bearing, input shaft 5, intermediate shaft front bearing 7, intermediate shaft rear bearing 14, front bearing, output shaft 10, rear bearing, output shaft 16, input shaft 6, intermediate shaft 11, output shaft 15, normal engagement follower gear 8, normal parts such as engagement driving gear 9, first speed driven gear 12, one grade of driving gear 13 etc. respectively, then being contacted with each other between parts by definition is assembled together them for contact relation.Have following rule to need to follow during grid division, namely the finite element grid of parts contact site will carefully divide, and it at least will ensure that two row's finite element grid unit are in contact condition; Want consistent with the contact bearing outer ring grid at position and case of transmission dead eye grid of case of transmission dead eye; Dead eye and the bearing outer ring position contacted with dead eye are at least divided into 90 parts in a circumferential direction, are axially at least divided into 5 parts.
Two, finite element model material is defined: clutch housing 1, case of transmission 2, upper cover 3 are aluminum alloy materials, its elastic modulus E=71000MPa, Poisson ratio μ=0.33; Other parts remaining are ferroalloy, its elastic modulus E=210000MPa, Poisson ratio μ=0.3
Three, finite element model load is applied: for gear arbitrary in variator, (comprise normal engagement follower gear 8, normal engagement driving gear 9, first speed driven gear 12, one grade of driving gear 13), the force of periphery F in gear mesh force
t, radial force F
rand axial force F
aadopt formula (1) to calculate, when they are applied on pitch point, need with reference to partial cylindrical coordinate system, as shown in Figure 2, the Z axis of cylindrical-coordinate system is along gear shaft axis direction, and R is along the radial direction of gear shaft, t is determined according to right hand rule by Z, R, force of periphery F
twith reference to t axle, radial force F
rwith reference to R axle, axial force F
awith reference to Z axis.The pretightning force F of bolt 4 adopts formula (2) to calculate, and action direction is along the axis of bolt 4.
In formula (1), F
t, F
r, F
abe respectively the force of periphery of gear, radial force and axial force, M is the torque that gear transmits, and d is pitch circle diameter, a
nfor gear normal pressure angle, β is pitch circle place helix angle.F
t, F
r, F
afor calculated amount, M, d, a
n, β is known quantity.
In formula (2), F is bolt pretightening, and T is bolt tightening moment, and k is Bolt Tightening Torque Coefficient, and D is the diameter of bolt.F is calculated amount, and T is known quantity, and k suggestion gets 0.2.
Four, the boundary condition of finite element model is applied: First Boundary Condition is the bolt hole of the fixing clutch housing front end be connected with bell housing, and with the supporting role of simulated engine to variator, namely 123 in Fig. 1 represent this type of boundary condition; Equations of The Second Kind border is that the rotary freedom applying gear shaft between all gears and gear two side bearing retrains, to interrupt torque to be delivered to housing dead eye path from gear shaft completely, as shown in Figure 3, this constraint can apply by rigid unit, now need to retrain the rotary freedom of rigid unit principal point along gear shaft axis direction, the principal point of rigid unit is defined in the center of gear shaft, from the node of point selection between gear and bearing gear shaft finite element model.As case, the rigid unit 21 in Fig. 3 and rigid unit 22 are set up for normal engagement driving gear 9, and the rotary freedom constraint of other gear shafts also needs to apply as stated above respectively.
Five, case of transmission finite element analysis is carried out: the stress and strain adopting newton-rapshon method iterative computation case of transmission, basic thought is, assuming that the solution of t is known, and asks the solution of t+ Δ t.Then the strength character that shell stress evaluates case of transmission is applied.Detailed process is as follows:
Initial time t
0the displacement of=0
nodal force
Adopt following method iterative computation t
0the stress and strain of+Δ t case of transmission;
......
The iteration initial value of formula (1), formula (2) is:
When
time termination of iterations, if iterations is
after termination of iterations, the stress and strain of case of transmission adopts following formulae discovery:
I represents iterations, and it gets 1 successively, 2,3
represent t
0the stiffness matrix of moment finite element model;
Δ { U}
(i)represent unbalanced load before the i-th step iteration
the displacement increment caused;
by t
0+ Δ t F
t, F
r, F
a, load level corresponding to F form, if the maximum moment is X (X is a setting value), then t
0the load level of+Δ t is respectively
represent t
0+ Δ t is by the i-th-1 step iteration unit stress
the nodal force caused;
represent by t
0+ Δ t load
displacement after the iteration ends caused;
represent t
0the strain matrix in moment, it is determined by the cell node coordinate in finite element model;
[C] represents elastic matrix, and it is determined by elastic properties of materials model E and Poisson ratio μ;
Assuming that the solution of any time t is known, ask the solution of t+ Δ t by the following method;
t[K]Δ{U}
(i)＝
t+Δt{P}-
t+Δt{R}
(i-1)(11)
t+Δt{U}
(i)＝
t+Δt{U}
(i-1)+Δ{U}
(i)(12)
Formula (11) ~ (12) iteration initial value used is the solution of t, that is:
Formula (11) ~ (12) termination of iterations condition is:
t+Δt{P}-
t+Δt{R}
(i-1)≤{e} (13)
During formula (11) ~ (12) termination of iterations, i=n
t+ Δ t
After formula (11) ~ (12) termination of iterations terminates, strain, stress adopt following formulae discovery:
In formula (11) ~ (15),
I represents iterations, and it gets 1 successively, 2,3
t[K] represents the stiffness matrix of t finite element model;
Δ { U}
(i)represent unbalanced load before the i-th step iteration
t+ Δ t{ P}-
t+ Δ t{ R}
(i-1)the displacement increment caused;
t+ Δ t{ P} is by t+ Δ t F
t, F
r, F
a, load level corresponding to F form, be X according to the maximum moment, then the load level of t+ Δ t is respectively
t+ Δ t{ R}
(i-1)represent that t+ Δ t is by the i-th-1 step element stress
t+ Δ t{ σ }
(i-1)the nodal force caused;
represent by t+ Δ t load
t+ Δ t{ the displacement that P} causes;
t[B] represents the strain matrix of t, and it is determined by the cell node coordinate in finite element model;
[C] represents elastic matrix, and it is determined by elastic properties of materials model E and Poisson ratio μ;
represent by t load
t{ the displacement after the iteration ends that P} causes;
represent that t is by n-th
t-1 step iteration unit stress
t{ σ }
(n-1)the nodal force caused;
{ e} represents calculating tolerance, and be a dimensionless, it is desirable
N
t+ Δ trepresent t+ Δ t, equation obtains total iterations during convergence solution;
N
trepresent t, equation obtains total iterations during convergence solution.
If calculate
t+ Δ t{ σ }
(i)in each cell node stress value be all less than the strength degree 240MPa of material, then illustrate that the structural strength of housing meets the demands.
Described method not only increases case of transmission dead eye place stress precision, and also improves the stress precision of other positions of case of transmission, and it is significant for correctly, reasonably evaluating whole case of transmission intensity.
Claims (4)
1. improve a method for case of transmission finite element analysis precision, it is characterized in that comprising the steps:
One, set up case of transmission finite element model: carry out stress and strain model to each parts of clutch housing, variator respectively, then being contacted between parts by definition is assembled together them for contact relation;
Two, finite element model material is defined: according to elasticity modulus of materials E, Poisson ratio μ in the real material definition finite element model of each parts in clutch housing and variator;
Three, finite element model load is applied: assumed (specified) load comprises two classes, and one is gear mesh force, and it adopts gear load computing formula to calculate, and is then applied on the working pitch point of respective gears in variator; Two is bolt pretightenings, and it is obtained by the relational expression between bolt pretightening and bolt tightening moment, is then applied in the bolt shaft in variator;
Four, apply finite element model boundary condition: model boundary condition comprises two classes, one is the bolt hole fixing the clutch housing be connected with bell housing, with the supporting role of simulated engine to variator; Two is that the rotary freedom applying gear shaft by rigid unit between all gears of variator and gear two side bearing retrains, and is delivered to the path of case of transmission dead eye to interrupt torque each gear shaft from variator completely;
Five, carry out case of transmission finite element analysis: the stress and strain adopting newton-rapshon method iterative computation case of transmission, process is as follows:
Initial time t
0the displacement of=0
nodal force
Adopt following method iterative computation t
0the stress and strain of+Δ t case of transmission;
When
time termination of iterations, if total iterations is
after termination of iterations, the stress and strain of case of transmission adopts following formulae discovery:
I represents iterations, and it gets 1 successively, 2,3 ..., as i=1, in formula (1) ~ (2),
represent t
0the stiffness matrix of moment finite element model;
Δ { U}
(i)represent unbalanced load before the i-th step iteration
the displacement increment caused;
by t
0+ Δ t F
t, F
r, F
a, load level corresponding to F form, if the maximum moment is X, then t
0the load level of+Δ t is respectively
represent t
0+ Δ t is by the i-th-1 step iteration unit stress
the nodal force caused;
represent by t
0+ Δ t load
displacement after the iteration ends caused;
represent t
0the strain matrix in moment, it is determined by the cell node coordinate in finite element model;
[C] represents elastic matrix, and it is determined by elastic properties of materials model E and Poisson ratio μ;
Assuming that the solution of any time t is known, ask the solution of t+ Δ t by the following method;
t+Δt{U}
(i)＝
t+Δt{U}
(i-1)+Δ{U}
(i)(6)
Formula (5) ~ (6) iteration initial value used is the solution of t, that is:
Formula (5) ~ (6) termination of iterations condition is:
During formula (5) ~ (6) termination of iterations, i=n
t+ Δ t
After formula (5) ~ (6) termination of iterations, strain, stress adopt following formulae discovery:
In formula (5) ~ (9),
t[K] represents the stiffness matrix of t finite element model;
Δ { U}
(i)represent unbalanced load before the i-th step iteration
t+ Δ t{ P}-
t+ Δ t{ R}
(i-1)the displacement increment caused;
t+ Δ t{ P} is by t+ Δ t F
t, F
r, F
a, load level corresponding to F form, be X according to the maximum moment, then the load level of t+ Δ t is respectively
t+ Δ t{ R}
(i-1)represent that t+ Δ t is by the i-th-1 step element stress
t+ Δ t{ σ }
(i-1)the nodal force caused;
represent by t+ Δ t load
t+ Δ t{ the displacement that P} causes;
t[B] represents the strain matrix of t, and it is determined by the cell node coordinate in finite element model;
[C] represents elastic matrix, and it is determined by elastic properties of materials model E and Poisson ratio μ;
represent by t load
t{ the displacement after the iteration ends that P} causes;
N
t+ Δ trepresent the t+ Δ moment, equation obtains total iterations during convergence solution;
N
trepresent t, equation obtains total iterations during convergence solution;
{ e} represents calculating tolerance.
2. the method for raising case of transmission finite element analysis precision according to claim 1, is characterized in that in described step one, and the FEM meshing of parts contact site at least will ensure that two row's finite element grid unit are in contact condition; With case of transmission dead eye contact the bearing outer ring grid at position and case of transmission dead eye grid consistent; Case of transmission dead eye and the bearing outer ring position contacted with it are at least divided into 90 parts in a circumferential direction, are axially at least divided into 5 parts.
3. the method for raising case of transmission finite element analysis precision according to claim 1, it is characterized in that in described step 3, each gear mesh force comprises the force of periphery, radial force and axial force, it adopts formula (10) to calculate, when gear mesh force being applied in finite element model, by partial cylindrical coordinate system, the Z axis of coordinate system is along gear shaft axis direction, R is along the radial direction of gear shaft, and t is determined according to right hand rule by Z, R; Bolt pretightening adopts formula (11) to calculate, and action direction is along the axis of bolt;
In formula (10), F
t, F
r, F
abe respectively the force of periphery of gear, radial force and axial force, M is the torque that gear transmits, and d is pitch circle diameter, a
nfor gear normal pressure angle, β is pitch circle place helix angle;
In formula (11), F is bolt pretightening, and T is bolt tightening moment, and k is Bolt Tightening Torque Coefficient, and D is the diameter of bolt.
4. the method for raising case of transmission finite element analysis precision according to claim 1, it is characterized in that in described step 4, the principal point of rigid unit is defined in the center of gear shaft, from the node of point selection between gear and bearing gear shaft finite element model.
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