CN109815518A - Vehicle rudder design method based on rotary inertia constraint - Google Patents
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Abstract
The invention discloses a kind of vehicle rudder design methods based on rotary inertia constraint, for solving the big technical problem of the rotary inertia of the rudder face of existing vehicle rudder design method design around the shaft.Technical solution is that this method initially sets up rudder face structural finite element model, then load and boundary condition is arranged to rudder face structural finite element model, gives solid material Young's modulus E(0)With Poisson's ratio μ, finite element analysis is carried out to rudder face structural finite element model is established, calculates rudder face structure entirety compliance, given volume constrains upper limit VU, calculate the structural volume V of current iteration stepC, give rotary inertia upper limit IU, calculate the structure rotary inertia I of current iteration stepC, topological optimization model is defined, sensitivity analysis and Optimized Iterative are carried out.After tested, under the premise of not reducing other mechanical properties, the rotary inertia of designed rudder face is by 7445kg*mm2Drop to 6764kg*mm2, decrease by 10.1%.
Description
Technical field
The present invention relates to a kind of vehicle rudder design method, in particular to a kind of aircraft based on rotary inertia constraint
Rudder face design method.
Background technique
Rudder face is the important composition component of aircraft, is the control surface of aircraft, is had to the overall performance for guaranteeing aircraft
Great influence.As the performance indicator to aircraft is constantly promoted, rudder face performance requirement is also continuously improved.The rotation of rudder face is used
Measure closely related with the performance of aircraft: on the one hand, the rotary inertia of rudder face directly affects response speed when its rotation, rotates
Inertia is bigger, and response speed is slower；On the other hand, during motion of rudder, biggish rotary inertia can generate biggish
Acceleration can bring biggish impact force to itself, influence the service life of rudder face.Therefore, rudder face structure is reasonably carried out to set
Meter is reduced its rotary inertia while guaranteeing the mechanical property of traditional rudder face structure, the globality of aircraft is promoted with this
It can just seem and be even more important.
Document " performance evaluation of aircraft rudder surface hydraulic servo actuating system ", which establishes, considers that the rigidity of structure and rudder face rotate
The hydraulic servo actuating system mathematical model of axis rotary inertia, is emulated under MATLAB environment by taking certain type machine as an example, is ground
Aircraft rudder surface hydraulic servo actuating system performance is studied carefully and the rigidity of structure, rudder face rotates around the axis the structural parameters such as inertia to actuation
The influence of system performance.Conclusion in text points out to consider the step response of actuating system after rigidity and equivalent quality than when not considering
Rise time it is elongated, i.e., initial communication lags, so in airplane design, the rigidity of structure is big as far as possible, and rudder face
Rotary inertia around the shaft is small as far as possible.
Summary of the invention
In order to overcome the shortcomings of that the rotary inertia of the rudder face of existing vehicle rudder design method design around the shaft is big, this hair
It is bright that a kind of vehicle rudder design method based on rotary inertia constraint is provided.This method initially sets up rudder face structure finite element mould
Type, then load and boundary condition are arranged to rudder face structural finite element model, give solid material Young's modulus E(0)And Poisson's ratio
μ carries out finite element analysis to rudder face structural finite element model is established, and calculates rudder face structure entirety compliance, given volume constraint
Upper limit VU, calculate the structural volume V of current iteration stepC, give rotary inertia upper limit IU, calculate the structure rotation of current iteration step
Inertia IC, topological optimization model is defined, sensitivity analysis and Optimized Iterative are carried out.The present invention is minimum with rudder face entirety compliance
Optimization aim is constrained as optimization using rudder face structural volume and rotary inertia and carries out topology optimization design.After tested, it is not dropping
Under the premise of other low mechanical properties, the rotary inertia of rudder face is decreased obviously.
A kind of the technical solution adopted by the present invention to solve the technical problems: vehicle rudder based on rotary inertia constraint
Design method, its main feature is that the following steps are included:
Step 1: geometric manipulations are carried out in UG three-dimensional software to rudder face initial geometric model, then in finite element software
The pre-processing module HyperMesh of HyperWorks carries out FEM meshing, as rudder face structural finite element model, and another
Save as cdb format.In addition, topology design variable x is arranged in a programiInitial value, its value changes between 0-1 in optimization.I is
Positive integer indicates design domain element number, 1≤i≤ne, neIndicate structural unit sum in design domain.To avoid stiffness matrix odd
It is different, the lower limit x of topology design variable is setL, i.e.,
Step 2: according to simulate come aerodynamic loading, original strong plane of load of being pressurized is divided into several pieces of pressure values differences
Region load and boundary condition are arranged to rudder face structural finite element model by command stream APDL language.
Step 3: given solid material Young's modulus E(0)With Poisson's ratio μ.After each iteration, according to current design variable
Value updates the respective material attribute in rudder face structural finite element model.Each is calculated separately using SIMP material interpolation model
Young's modulus E of the finite elements under current iteration stepi
Wherein, E(0)The Young's modulus of presentation-entity material.Penalty factor p value takes 3.
Step 4: the analysis model established to three above step carries out finite element analysis in finite element soft Ansys,
Obtain structural stiffness matrix, displacement structure vector information.
For linear static analysis, structure finite element equilibrium equation is written as
KU=F (3)
In formula, K is structure Bulk stiffness matrix, and U is modal displacement vector, and F is panel load vector.
Step 5: calculating rudder face structure entirety compliance
C=UTKU (4)
Rudder face structure entirety compliance C is calculated according to formula (3).By extracting i-th of unit in Finite element analysis results
Stiffness matrix kiWith motion vector ui, first calculate the compliance of each unitAgain the compliance of all units
It stacks up to obtain the whole compliance C of structure.
Step 6: given volume constrains upper limit VU, the structural volume V of current iteration step is calculated using formula (4)C。
Wherein, ViIndicate the volume of i-th of solid material unit.
Step 7: given rotary inertia upper limit IU, the structure rotary inertia I of current iteration step is calculated using formula (5)C。
Wherein, ρ indicates the density value of material, ViIndicate the volume of i-th of solid material unit, riIndicate i-th of entity material
Material unit is with a distance from rotary shaft.
Step 8: being constraint with structural volume, structure rotary inertia, establishing with the minimum target of structure entirety compliance
Topological optimization model.
In formula, x represents the set of design variable, xiFor the design variable value of i-th of finite elements, finite elements i is indicated
Density value, wherein 1≤i≤ne.Structural stiffness matrix is unusual when to avoid finite element analysis, introduces design variable lower limit xL,
neRepresent design domain unit sum.Optimization aim is that the whole compliance C of structure is minimum.It include volume constraint in constraint condition.VU
Represent design domain volume constraint VCThe upper limit, IURepresent design domain rotary inertia constraint ICThe upper limit, ViIt indicates i-th in design domain
The volume of a solid material unit, riDistance for i-th of units centre of mass apart from rotary shaft.
Step 9: acquiring sensitivity of the objective function about design variable.The GCMMA optimization algorithm based on gradient is chosen,
Iteration is optimized using self-editing topological optimization program, obtains taking rotary inertia as the Structural Topology Optimization Design knot for optimizing constraint
Fruit.
The beneficial effects of the present invention are: this method initially sets up rudder face structural finite element model, then to rudder face limited configurations
Load and boundary condition is arranged in meta-model, gives solid material Young's modulus E(0)With Poisson's ratio μ, have to rudder face structure is established
It limits meta-model and carries out finite element analysis, calculate rudder face structure entirety compliance, given volume constrains upper limit VU, calculate current iteration
The structural volume V of stepC, give rotary inertia upper limit IU, calculate the structure rotary inertia I of current iteration stepC, define topological optimization
Model carries out sensitivity analysis and Optimized Iterative.The present invention is with the minimum optimization aim of rudder face entirety compliance, with rudder face structure
Volume and rotary inertia are as optimization constraint progress topology optimization design.After tested, before not reducing other mechanical properties
It puts, the rotary inertia of rudder face is by 7445kg*mm2Drop to 6764kg*mm2, decrease by 10.1%.
It elaborates with reference to the accompanying drawings and detailed description to the present invention.
Detailed description of the invention
Fig. 1 is that the present invention is based on the flow charts of the vehicle rudder design method of rotary inertia constraint.
Fig. 2 is the initial geometric model schematic diagram in embodiment of the present invention method.
Fig. 3 is that the initial geometric model load applying zone in embodiment of the present invention method divides and boundary condition application is shown
It is intended to.
Fig. 4 is rudder face design result figure in embodiment of the present invention method.
Specific embodiment
Referring to Fig.1-4.The present invention is based on the vehicle rudder design method of rotary inertia constraint, specific step is as follows:
(a) the rudder face construction geometry model for needing to optimize is established using 3D software UG, and model is carried out referring to engineering design
Tamping operations.Finite element grid is carried out to the geometrical model using the pre-processing module HyperMesh of HyperWorks software to draw
Point.First carry out GTD model, using based on hexahedron when grid dividing, covering is using being assigned to surface layer unit with a thickness of 1.5mm
Shell unit carry out equivalent substitution, structural unit sum is 49980, is finally designed the division in domain and non-design domain.
(b) load and boundary condition are set.For rudder face structure by aerodynamic loading during military service, there is pressure in upper and lower surface
It is strong poor, and the pressure difference of different zones is different, applies 95000Pa pressure in 1 region, applies 62000Pa pressure in 2 regions,
Apply 40000Pa pressure in 3 regions, apply 82000Pa pressure in 4 regions, applies 52000Pa pressure in 5 regions, in 6 regions
Apply 30000Pa pressure.Boundary condition is the end face of fixed rudderpost.
(c) solid material Young's modulus E is given(0)And Poisson's ratio.After each iteration, according to current design variate-value, update
Respective material attribute in structural finite element model.Each finite elements is calculated separately using SIMP material interpolation model working as
Young's modulus E under preceding iteration stepi
E(0)The Young's modulus of presentation-entity material, penalty factor p value take 3.
(d) for linear static analysis, structure finite element equilibrium equation can be written as
KU=F (3)
In formula, K is structure Bulk stiffness matrix, and U is modal displacement vector, and F is panel load vector.
(e) rudder face structure entirety compliance is calculated
C=UTKU (4)
Rudder face structure entirety compliance C is calculated according to formula (3).It is by extracting in Finite element analysis results when specific calculating
I-th of unit stiffness matrix kiWith motion vector ui, first calculate the compliance of each unitAgain all
The compliance of unit stacks up to obtain the whole compliance C of structure.
(f) the structural volume V of current iteration step is calculated using formula (4)C
Wherein ViIndicate the volume of i-th of solid material unit.
Given design domain volume upper limit V in the present embodimentU=0.4.
(g) the structure rotary inertia I of current iteration step is calculated using formula (5)C
Wherein ViIndicate the volume of i-th of solid material unit.
Given design domain volume upper limit I in the present embodimentU=8000kg*mm2。
(h) topological optimization model is defined
It is constraint, topological optimization with the volume in overall construction design domain with the minimum optimization aim of structure entirety compliance
It designs a model as follows
X represents the set of design variable, x in formulaiFor the design variable value of i-th of finite elements, indicate finite elements i's
Density value, being worth when being 1 indicates to be solid material at this, and being worth when being 0 indicates at this without material.All design variable initial values are all provided with
It is set to 0.35.Structural stiffness matrix is unusual when to avoid finite element analysis, introduces design variable lower limit xL=10-3, neIt represents
Design domain unit sum.Optimization aim is that the whole compliance C of structure is minimum.Constraint condition is design domain volume.VURepresentative is set
Count domain volume constraint VCThe upper limit, IURepresent design domain rotary inertia constraint ICThe upper limit, ViIndicate i-th of entity in design domain
The volume of material cell, riDistance for i-th of units centre of mass apart from rotary shaft.
(i) in each Optimized Iterative, model is subjected to a finite element analysis first；Choose the GCMMA based on gradient
Optimization algorithm optimizes iteration using self-editing topological optimization program.It illustrates, other optimization algorithms based on gradient are such as
ConLin, GCM, MDPA, SLP, QP etc. are able to achieve Optimized Iterative.In addition, some other optimization methods such as Method of Optimality Criteria,
Mathematical programming approach, Evolutionary structural optimization etc. also can be carried out the optimization design of the method for the present invention.
The rotary inertia upper limit of the method for the present invention given design domain volume and whole rudder face, by being obtained after 264 step iteration
Optimum Design Results.Obtained structural configuration clear and rational is designed by the design result of Fig. 4 is visible.Background technique method designs rudder
The rotary inertia of face structure is 7445kg*mm2, the rudder face structure rotary inertia of the method for the present invention Configuration design is 6764kg*mm2,
Under the premise of not reducing other mechanical properties, 10.1% is decreased by.This example demonstrates that be based on rotation used for the method for the present invention
Measure the validity of the vehicle rudder Topology Optimization Method of constraint.Illustrate that the optimum results that this method obtains are guaranteeing not reduce it
The rotary inertia for reducing rudder face in the case where his mechanical property simultaneously effectively improves response speed when rudder face work, from
And achieve the effect that the overall performance for promoting aircraft.
Claims (1)
1. a kind of vehicle rudder design method based on rotary inertia constraint, it is characterised in that the following steps are included:
Step 1: geometric manipulations are carried out in UG three-dimensional software to rudder face initial geometric model, then in finite element software
The pre-processing module HyperMesh of HyperWorks carries out FEM meshing, as rudder face structural finite element model, and another
Save as cdb format；In addition, topology design variable x is arranged in a programiInitial value, its value changes between 0-1 in optimization；I is
Positive integer indicates design domain element number, 1≤i≤ne, neIndicate structural unit sum in design domain；To avoid stiffness matrix odd
It is different, the lower limit x of topology design variable is setL, i.e.,
Step 2: according to simulate come aerodynamic loading, original strong plane of load of being pressurized is divided into several pieces of different areas of pressure values
Load and boundary condition is arranged to rudder face structural finite element model by command stream APDL language in domain；
Step 3: given solid material Young's modulus E(0)With Poisson's ratio μ；After each iteration, according to current design variate-value, more
Respective material attribute in new rudder face structural finite element model；Each limited list is calculated separately using SIMP material interpolation model
Young's modulus E of the member under current iteration stepi
Wherein, E(0)The Young's modulus of presentation-entity material；Penalty factor p value takes 3；
Step 4: the analysis model established to three above step carries out finite element analysis in finite element soft Ansys, obtain
Structural stiffness matrix, displacement structure vector information；
For linear static analysis, structure finite element equilibrium equation is written as
KU=F (3)
In formula, K is structure Bulk stiffness matrix, and U is modal displacement vector, and F is panel load vector；
Step 5: calculating rudder face structure entirety compliance
C=UTKU (4)
Rudder face structure entirety compliance C is calculated according to formula (3)；By extracting the rigid of i-th of unit in Finite element analysis results
Spend matrix kiWith motion vector ui, first calculate the compliance of each unitThe compliance of all units is superimposed again
Get up to obtain the whole compliance C of structure；
Step 6: given volume constrains upper limit VU, the structural volume V of current iteration step is calculated using formula (4)C；
Wherein, ViIndicate the volume of i-th of solid material unit；
Step 7: given rotary inertia upper limit IU, the structure rotary inertia I of current iteration step is calculated using formula (5)C；
Wherein, ρ indicates the density value of material, ViIndicate the volume of i-th of solid material unit, riIndicate i-th of solid material list
Member is with a distance from rotary shaft；
Step 8: being constraint with structural volume, structure rotary inertia, establishing topology with the minimum target of structure entirety compliance
Optimized model；
In formula, x represents the set of design variable, xiFor the design variable value of i-th of finite elements, the density of finite elements i is indicated
Value, wherein 1≤i≤ne；Structural stiffness matrix is unusual when to avoid finite element analysis, introduces design variable lower limit xL, neIt represents
Design domain unit sum；Optimization aim is that the whole compliance C of structure is minimum；It include volume constraint in constraint condition；VUIt represents
Design domain volume constraint VCThe upper limit, IURepresent design domain rotary inertia constraint ICThe upper limit, ViIndicate i-th of reality in design domain
The volume of body material cell, riDistance for i-th of units centre of mass apart from rotary shaft；
Step 9: acquiring sensitivity of the objective function about design variable；The GCMMA optimization algorithm based on gradient is chosen, is used
Self-editing topological optimization program optimizes iteration, obtains taking rotary inertia as the Structural Topology Optimization Design result for optimizing constraint.
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Application publication date: 20190528 |