CN108959686A - A kind of correction method for finite element model based on sensitivity analysis - Google Patents
A kind of correction method for finite element model based on sensitivity analysis Download PDFInfo
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Abstract
The present invention relates to a kind of correction method for finite element model based on sensitivity analysis, solid modelling is carried out to assembly in three-dimensional software, modal test is carried out by modal test system to entire assembly model, assembly limit element artificial module is established using front and back processing software, and model analysis solution is carried out by finite element analysis software, pass through LMS.VirtualLab simulation analysis software, two modal testing results and Modal Analysis analysis result are subjected to correlation test, carry out Modal sensitivity analysis, it finds out to the more sensitive parametric variable of modal frequency, finite element model fundamental frequency and modal test fundamental frequency are matched by Optimized Iterative.Simulation analysis technology of the present invention has many benefits such as at low cost, the period is short compared to physical test, in the range of simulation result error allows, simulation analysis result can be used as the reference frame of Analysis of Vibration Characteristic, and this method has important reference value to dependence test work.
Description
Technical field
The present invention relates to the FEM updating fields of Complex Assembly body, specifically having based on sensitivity analysis
Limit meta-model modification method.
Background technique
In the fast development of field of industrial manufacturing CAE technology, by Finite Element Simulation Analysis, the vibration of research institution is special
Property, it is indicated that weak part in structure design avoids the generation of mechanism covibration at work it is proposed that prioritization scheme.Meanwhile
Finite element analysis has been extensively examined as the most widely used numerical analysis method of modern age engineering field, reliability.Pass through
Finite Element Simulation Analysis can reduce the number of physical test, to achieve the purpose that save the cost, assess the reasonability drop of configuration
Low-risk improves the quality of product, shortens the development cycle.
As Automatic manual transmission demand steps up, it is mechanical design and develop needs to faster, the direction of more secure and reliable sends out
Exhibition, the requirement to vibration characteristics are higher and higher.A kind of method of the model analysis as recent studies structural dynamic characteristic is extensive
Applied to Engineering Vibration field.Model analysis is used to determine the vibration characteristics of structure or machine part, has to Design of Mechanical Structure
It is significant, while the basis of model analysis or other dynamic analyses.
The development of computer visualization, virtual reality, Computerized intelligent technology in recent ten years, computer is in every field
Experiment is replaced to grow a lot, simulation analysis technology has many benefits such as at low cost, the period is short compared to test method.But
For complicated practical structures, the precision of finite element model is affected by many factors.The error of physical phantom includes
Simplify it is assumed that as in model analysis structural model belong to linear mathematical model, have ignored some non-thread present in practical structures
The influence discretization precision of sexual factor is related with sizing grid, and grid is more intensive, and freedom degree is more, and precision is higher.But grid is close
After collection, computational efficiency is just reduced, and needs to weigh the pros and cons between computational accuracy and computational efficiency in engineering.It is that modeling misses again
Difference, the physical parameter (density, elasticity modulus, Poisson's ratio) in finite element model can not coincide with actual conditions completely, this it
In must increase the error of modal analysis result Yu practical two modal testing results.
Summary of the invention
In view of the deficiencies of the prior art, the present invention provides a kind of correction method for finite element model based on sensitivity analysis,
Finite element model is modified with a small amount of structural test data obtained, obtains more accurately finite element model, solution
Finite element modeling of having determined emulates inaccurate problem.
Present invention technical solution used for the above purpose is:
A kind of correction method for finite element model based on sensitivity analysis, comprising the following steps:
Step 1: in three-dimensional software to assembly carry out solid modelling, to entire assembly model by modal test system into
Row modal test, obtains two modal testing results；
Step 2: use front and back processing software to establish assembly limit element artificial module, and by finite element analysis software into
Row model analysis solves, and obtains Modal Analysis analysis result；
Step 3: by LMS.VirtualLab simulation analysis software, two modal testing results and Modal Analysis being analyzed into result
Correlation test is carried out, if the error rate of same order frequency values and vibration shape MAC value are in claimed range, that currently establishes has
Limit meta-model is met the requirements, and does not need to correct；It is no to then follow the steps 4；
Step 4: carrying out Modal sensitivity analysis, find out to the more sensitive parametric variable of modal frequency, changed by optimization
In generation, matches finite element model fundamental frequency and modal test fundamental frequency.
The modal test system includes excitation system, pickup system and modal analysis system；Wherein excitation system master
It to include that modal forces are hammered into shape, pickup system mainly includes acceleration transducer and intelligent acquisition system, and modal analysis system is main to wrap
Include the included model analysis software of LMS.TestLab software mould measurement consultant and LMS.TestLab software.
The modal test is to test acceleration transducer and analyze by power hammer excitation, and LMS.TestLab software is adopted
With rank processing is determined after transmission function collection overall average, modal parameter is extracted after fitting, and pass through modal mass normalized, obtained
Modal frequency and Mode Shape feature.
Before and after the use processing software establish assembly limit element artificial module be each structural member is reduced to entity,
Shell and lumped mass are bolted using RBE2 unit simulation, are flexibly connected using Bush unit simulation.
The Modal Analysis analysis result includes each rank modal frequency and the vibration shape.
The correlation test is the difference for calculating Modal Analysis analysis frequency with experimental modal frequency on corresponding order,
Correlation between the two is determined by the error rate of same order frequency values.
The error rate of the same order frequency values are as follows:
Wherein: fAFor simulation analysis modal frequency；fTFor experimental modal frequency, ΔfFor the error rate of same order frequency values.
The vibration shape MAC value are as follows:
Wherein: VTest,VFERespectively indicate test and emulation Mode Shape vector, MACTest,FEFor vibration shape MAC value.
The Optimized Iterative is to the more sensitive parameter of modal frequency using sensitivity analysis gained as variable, with mode
The modal frequency of the corresponding order of test gained is as objective function, using Sequential Quadratic Programming method (SQP, Sequential
Quadratic Programming) it is iterated optimization calculating.
The Modal sensitivity analysis uses to analyze each rank modal frequency to the sensitivity of assembly system parameter
Sensitivity carries out Modal sensitivity analysis in LMS Virtual.Lab.
The invention has the following beneficial effects and advantage:
It present invention can be suitably applied to the FEM updating of various structural members and assembly, the simulation analysis after Modifying model
As a result it can be used as the reference frame of Analysis of Vibration Characteristic, this method has important reference value to dependence test work.
Detailed description of the invention
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is articulated mechanical arm structure chart；
Fig. 3 is MAC matrix diagram before optimizing；
Fig. 4 is preceding two ranks model analysis and test frequency vibration shape comparison diagram；
Fig. 5 is elasticity modulus of materials sensitivity matrix figure.
Specific embodiment
The present invention is described in further detail with reference to the accompanying drawings and embodiments.
It is as shown in Figure 1 flow chart of the method for the present invention.
The process of correction method for finite element model of the invention mainly divides following four step:
Step 1 is carried out solid modelling to assembly in three-dimensional software, is carried out about using mould measurement system to material object
The mould measurement of pencil state, and by LMS.TestLab software mould measurement consultant and its included model analysis software, it obtains
Each rank modal frequency of assembly and Mode Shape feature.
Step 2 carries out handling work before and after entire assembly model using HyperWorks software, and total is reduced to reality
Body, shell and concentration mass unit, are bolted to simulate using RBE2 rigid element, are flexibly connected using Bush unit simulation.
Solution calculating is carried out as solver by MSC.Nastran finite element analysis software.MSC.Nastran provides three classes mode
Characteristic value solution, respectively tracing, converter technique and Lan Suoshi (Lanczos) method, wherein Lan Suoshifa is very big for calculating
Sparse matrix eigenvalue problem it is most effective, the present invention use Lan Suoshi mode solving method, obtain each of finite element analysis model
Rank modal frequency and the vibration shape.
Step 3, by LMS.VirtualLab simulation analysis software, by step 1 two modal testing results and step 2 mould
State simulation analysis result carries out correlation test, compares each order frequency value and vibration shape MAC value.MAC value always between 0 and 1,
Usually simulation analysis mode and Modal Test are put into MAC (i, a j) matrix and observed.MAC if (i, j) matrix
Numerical value on middle diagonal line is greater than 0.8, then illustrates that simulation analysis mode and corresponding Modal Test correlation are relatively good, while square
The numerical value of remaining position is not more than 0.3 in battle array, illustrates that independence is good between mode corresponding to different rank, does not have from each other
By mutual influence.
Step 4 approaches in frequency for emulation mode and Modal Test, needs to optimize finite element model.
Firstly, carrying out mode sensitivity analysis to it, find out to the more sensitive parametric variable of modal frequency, with right obtained by modal test
Answer the modal frequency of order as objective function, using Sequential Quadratic Programming method Optimized Iterative by finite element model fundamental frequency and mode
Test fundamental frequency matches.
Embodiment:
The present invention carries out the FEM updating based on sensitivity analysis for five articulated mechanical arm structures.
Firstly, carrying out solid modelling to mechanical arm in three-dimensional software, mechanical arm is to realize end by cradle head
Spatial position change, mechanical arm tool there are five cradle head, i.e. five freedom degrees, including orientation joint, one return
Turn joint and three pitching joints.Solid modelling, structure are carried out in three-dimensional software Solidworks to the articulated mechanical arm
It is detailed in Fig. 2.The mould measurement of restrained condition, specific implementation method are carried out to mechanical arm material object by LMS.TestLab software
Are as follows: it is evenly distributed with acceleration transducer in mechanical arm, exciting is hammered into shape by modal forces, observes the coherence of each measuring point signal, it is only relevant
The signal of 0.8 or more coefficient is just effective, carries out transmission function processing to satisfactory signal, completes mode and determines rank and fitting work
Make.Modal parameter is extracted after fitting, and passes through modal mass normalized.
Then, handle before and after manipulator model using HyperWorks software, using MSC.Nastran finite element fraction
Software is analysed as solver and carries out solution calculating.Entire mechanical arm mechanism is reduced to entity, shell and lumped mass, with RBE2 unit
It is bolted to simulate.The rigidity of each joint speed reducer of mechanical arm is very big on overall stiffness influence, to each joint of mechanical arm
Retarder carries out statics Analysis, obtains the rigidity data of retarder by Rigidity Calculation theory.In the foundation of finite element model
In the process, using the intra-articular retarder torsion stiffness of three-dimensional spring-damper CBUSH unit simulation.And it is solved by Nastran
Device carries out model analysis to mechanical arm finite element model using Lanczos method.
It is by LMS.VirtualLab simulation analysis software, step 1 mechanical arm two modal testing results and step 2 are mechanical
Arm Modal Analysis analyzes result and carries out correlation test, compares each order frequency value and vibration shape MAC value.Correlation analysis is to calculate mould
Difference of the state simulation analysis frequency with experimental modal frequency on corresponding order, correlation between the two is determined by error rate
Property.
In formula: fAFor mechanical arm simulation analysis modal frequency；fTFor mechanical arm experimental modal frequency.
Vibration shape MAC value is a kind of mode decision criteria, is that correlation is answered between evaluation test mode and simulation analysis mode
With more extensive means, the correctness of mode is assessed by comparing the vibration shape.Mode decision criteria is defined as follows:
In formula: VTest,VFERespectively indicate test and emulation Mode Shape vector.
MAC value always between 0 and 1, usually by simulation analysis mode and Modal Test be put into a matrix into
Row observation.If the numerical value in MAC (i, j) matrix on diagonal line is greater than 0.8, illustrate simulation analysis mode and corresponding test
Modal Correlation is relatively good, at the same in matrix remaining position numerical value be not more than 0.3, illustrate mode corresponding to different rank it
Between independence it is good, from each other not by mutual influence.
After the Modal Test of mechanical arm and emulation modal analysis result are carried out vibration shape similarity calculation, MAC value before optimizing
Matrix is as shown in Figure 3, and two rank Mode Shapes and frequency comparison are as shown in Figure 4 before mechanical arm.Pass through emulation mode and Modal Test
Correlation analysis, preceding two ranks MAC value is bigger, reaches 0.8 or more, it is believed that the vibration shape and FEM calculation mould of Modal Test
The vibration shape of state is similar.First step mode frequency phase-difference 3.19Hz, second-order modal frequency differ 5.54Hz, it is therefore desirable to right
Finite element model optimizes, and approaches to emulate mode and Modal Test in frequency.
By analysis, the possible coupling stiffness of the connection carried out in finite element model with RBE2 unit is on the weak side, can increase material
The elasticity modulus of material, to compensate coupling stiffness on the weak side.Since there are many mechanical arm part, needing to select influences modal frequency
The elasticity modulus of bigger part can be found out by mode sensitivity analysis to the more sensitive springform of modal frequency
Amount.By sensitivity analysis, as shown in figure 5, obtaining the elasticity modulus of each part to the sensitivity of the modal frequency of preceding two rank.
Bigger component elasticity modulus (E) 14, (E) 12, (E) 40, (E) 43, (E) 20 and (E) 22 will be influenced on modal frequency, use
Sequential Quadratic Programming method is iterated optimization and calculates.After optimization calculates, the vibration shape similarity of mode and Modal Test is emulated
MAC value increases, and reduces the frequency of emulation mode and the frequency of Modal Test, and frequency error drops to 1% or less.
Invention describes a kind of finite element model bearing calibrations based on Modal sensitivity analysis, by Modal Analysis point
Analysis and modal test correlation test and MAC decision criteria are analyzed, and the finite element finally obtained close to true mechanical arm material object is imitated
True mode.Simulation analysis technology has many benefits such as at low cost, the period is short compared to physical test, permits in simulation result error
Perhaps in the range of, simulation analysis result can be used as the reference frame of Analysis of Vibration Characteristic, and this method, which works to dependence test, to be had
There is important reference value.
Claims (10)
1. a kind of correction method for finite element model based on sensitivity analysis, it is characterised in that: the following steps are included:
Step 1: solid modelling being carried out to assembly in three-dimensional software, mould is carried out by modal test system to entire assembly model
State test, obtains two modal testing results；
Step 2: using front and back processing software to establish assembly limit element artificial module, and mould is carried out by finite element analysis software
State analysis and solution obtains Modal Analysis analysis result；
Step 3: by LMS.VirtualLab simulation analysis software, two modal testing results and Modal Analysis analysis result being carried out
Correlation test, if the finite element that the error rate of same order frequency values and vibration shape MAC value in claimed range, are currently established
Model is met the requirements, and does not need to correct；It is no to then follow the steps 4；
Step 4: Modal sensitivity analysis is carried out, is found out to the more sensitive parametric variable of modal frequency, it will by Optimized Iterative
Finite element model fundamental frequency matches with modal test fundamental frequency.
2. the correction method for finite element model according to claim 1 based on sensitivity analysis, it is characterised in that: the mould
State pilot system includes excitation system, pickup system and modal analysis system；Wherein excitation system mainly includes modal forces hammer,
Pickup system mainly includes acceleration transducer and intelligent acquisition system, and modal analysis system mainly includes LMS.TestLab soft
The model analysis software that part mould measurement consultant and LMS.TestLab software carry.
3. the correction method for finite element model according to claim 1 based on sensitivity analysis, it is characterised in that: the mould
To test acceleration transducer and analyzing by power hammer excitation, LMS.TestLab software uses transmission function lump for state test
Rank processing is determined after average, modal parameter is extracted after fitting, and pass through modal mass normalized, is obtained modal frequency and mode
Vibration shape feature.
4. the correction method for finite element model according to claim 1 based on sensitivity analysis, it is characterised in that: described to adopt
Establishing assembly limit element artificial module with front and back processing software is that each structural member is reduced to entity, shell and lumped mass,
It is bolted using RBE2 unit simulation, is flexibly connected using Bush unit simulation.
5. the correction method for finite element model according to claim 1 based on sensitivity analysis, it is characterised in that: the mould
State simulation analysis result includes each rank modal frequency and the vibration shape.
6. the correction method for finite element model according to claim 1 based on sensitivity analysis, it is characterised in that: the phase
It is the difference for calculating Modal Analysis analysis frequency with experimental modal frequency on corresponding order that closing property, which is examined, passes through same order frequency values
Error rate determine correlation between the two.
7. the correction method for finite element model according to claim 1 or 6 based on sensitivity analysis, it is characterised in that: institute
State the error rate of same order frequency values are as follows:
Wherein: fAFor simulation analysis modal frequency；fTFor experimental modal frequency, ΔfFor the error rate of same order frequency values.
8. the correction method for finite element model according to claim 1 based on sensitivity analysis, it is characterised in that: the vibration
Type MAC value are as follows:
Wherein: VTest,VFERespectively indicate test and emulation Mode Shape vector, MACTest,FEFor vibration shape MAC value.
9. the correction method for finite element model according to claim 1 based on sensitivity analysis, it is characterised in that: described excellent
Changing iteration is to the more sensitive parameter of modal frequency using sensitivity analysis gained as variable, with corresponding rank obtained by modal test
Secondary modal frequency is as objective function, using Sequential Quadratic Programming method (SQP, Sequential Quadratic
Programming optimization) is iterated to calculate.
10. the correction method for finite element model according to claim 1 based on sensitivity analysis, it is characterised in that: described
Modal sensitivity analysis is each rank modal frequency of analysis to the sensitivity of assembly system parameter, using LMS
Sensitivity carries out Modal sensitivity analysis in Virtual.Lab.
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