CN107491627A - Composite drilling process finite element Global sensitivity analysis method - Google Patents

Composite drilling process finite element Global sensitivity analysis method Download PDF

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Publication number
CN107491627A
CN107491627A CN201710961870.9A CN201710961870A CN107491627A CN 107491627 A CN107491627 A CN 107491627A CN 201710961870 A CN201710961870 A CN 201710961870A CN 107491627 A CN107491627 A CN 107491627A
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CN107491627B (en
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齐振超
尚逸鸣
杨晓伟
张若凡
杨家伟
李玖阳
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Jiangsu Hangpu Guochuang Composite Material Research Institute Co ltd
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Nanjing University of Aeronautics and Astronautics
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    • G06FELECTRIC DIGITAL DATA PROCESSING
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    • G06F30/23Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]

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Abstract

A kind of composite drilling process finite element Global sensitivity analysis method, it is characterized in that it comprises the following steps:First, multigroup random number is produced according to the distribution of the relevant parameter of composite to input as sample;Secondly, drilling process is emulated by finite element software and produces corresponding cutting force as sample output by the use of least squares method;3rd, according to " state-contingent parametric method "(States Dependent Parameter,SDP)Conditional expectation of the parameters for output is sought respectively;4th, according to Global sensitivity analysis method --- " sobol methods " analyzes level of sensitivity of the different parameters for multiple material drill thrust.The present invention gives composite drilling process finite element Global sensitivity analysis method, embodies composite each parameter in drilling and, for the influence degree of drill thrust, is advantageous to, to Simplified analysis process, save the time, improves efficiency.

Description

Composite drilling process finite element Global sensitivity analysis method
Technical field
The present invention relates to a kind of composite technology, especially a kind of composite is subject to technology, specifically a kind of Composite drilling process finite element Global sensitivity analysis method, belong to the finite element Sensitivity Analysis Method of composite, The particularly composite Global sensitivity analysis method of material parameter to drill thrust in drilling process.
Background technology
Composite laminated structures have been obtained extensively with high specific strength, specific stiffness and low quality in aerospace field Application.The design of many empty day structures, using the special Buckling of composite and its stronger designability, with up to To the purpose for improving stability and reduction architecture quality.At present, Joining Technology main in composite assembling is that machinery connects Connect, this just needs the drilling processing that pre-manufactured hole is carried out to it.But because composite materials property has larger dispersiveness And randomness, it is therefore necessary to consider these uncertain influences to composite suffered drill thrust in drilling, i.e. composite wood Expect level of sensitivity of each parameter for drill thrust, and then Simplified analysis process, improve efficiency, shorten analysis time.
The sensitivity analysis of current research is only to export response directly to seek input variable local derviation, then tries to achieve and is inputting Derivative value at mean variable value point.The sensitivity analysis only considers that the uncertain of input variable responds not to output from part Deterministic influence, therefore referred to as Local sensitivity analysis, due to the dispersiveness and randomness of Compound Material Engineering characteristic, the method In analysis with certain limitation.Although having had some Global sensitivity analysis methods at present, such as Saltellid and The nonparametric technique of the propositions such as Hehon, the square independent analysis that Borgonovo is proposed, and Sobol propose based on variance Analysis method, but due to being started late to the research of composite drilling, composite is ground in drilling process sensitivity analysis Study carefully deficiency, Global sensitivity analysis method is when composite drilling is analyzed using seldom.
The content of the invention
The purpose of the present invention is to be directed to influence of the composite parameters to composite suffered drill thrust in drilling The needs of analysis, there is dispersed and randomness answer to overcome existing Local sensitivity analysis method not to be suitable for mechanical characteristic The deficiency of condensation material, existing Global sensitivity analysis method is used for reference, invent a kind of global spirit of composite drilling process finite element Basis of sensitivity analysis method, it considers composite each parameter in drilling and, for the influence degree of drill thrust, given based on side The composite drilling process finite element Global sensitivity analysis method of difference.
The technical scheme is that:
A kind of composite drilling process finite element Global sensitivity analysis method, its feature are as follows:
First, multigroup random number is produced according to the distribution of composite relevant parameter to input as sample;
Secondly, the three-dimensional Drilling model of composite is established using finite element software;
3rd, above-mentioned three-dimensional Drilling model is called, emulating drilling process by finite element software produces drill thrust-time Figure, obtain corresponding cutting force by the use of least squares method and exported as sample;
4th, each ginseng is asked according to " state-contingent parametric method " (States Dependent Parameter, SDP) respectively Conditional expectation of the number for output;
5th, according to the Global sensitivity analysis method based on variance --- " sobol methods " analyzes different parameters for multiple The size of the influence degree of material drill thrust.
The relevant parameter of described composite is all to obey the stochastic variable being just distributed very much, and the coefficient of variation is 0.06, And it is uncorrelated, the random sample X that sample size is N is produced according to the distributed constant of each variable using Matlab softwarest(x1,x2, x3…xi) (t=1,2,3 ... N) inputted as sample.
Described finite element software is ABAQUS/Explicit.
Three-dimensional Drilling model n times are called, corresponding cutting force Y is produced by Abaqus software emulations drilling processt(t= 1,2,3 ... N) exported as sample.
Parameters X is asked according to SDP methods respectively1, X2, X3,…XiFor sample output Y conditional expectation E (Y | X1), E (Y | X2) ... E (Y | Xi) step is as follows:
According to control theory, establishing state space SDP models is:
observation equation:Yt=Pi,t+ei,t
SDP model:Pi,t=Pi,t-1+di,t-1
di,t=di,t-1i,t, ηi,t~N (0, σ2);
In formula:Pi,tFor with state variable Xi,tThe SDP state relevant parameters of change, it is basic variable Xi,tFunction, et (observation interference), ηi,t(system disturbance) be average be zero, variance σ2And ση 2White Gaussian noise input, its value can use Maximum likelihood optimization is estimated to obtain.
Then recursive Kalman filtering (kalam Filtreing, KF) is used in circulation backward fit procedure and is accordingly passed Smooth (Fixed Interval Smoothing, the FIS) rule of fixed interval is returned to estimate to obtain each state relevant parameter Pi,t
Finally according to formula:
E(Yt|Xi,t)=Yt-Pi,t
Calculate each parameter for output conditional expectation E (Y | Xi,t);
According to Global sensitivity analysis method --- " sobol methods " calculates each parameter XiGlobal sensitivity to exporting Y Process is as follows:
According to formula:
Calculate foregoing gained sample output YtVariance V (Y) and each parameter XiFor Y conditional expectation E (Y | Xi) variance V(E(Y|Xi));
The formula carried according to sobol methods:
Composite parameters are calculated in drilling process for the global sensitivity index S of cutting forcei
Beneficial effects of the present invention:
The Global sensitivity analysis method of the present invention can meet composite parameters to composite in drilling when institute By the demand of the impact analysis of drill thrust, existing Sensitivity Analysis Method is overcome not to be suitable for mechanical characteristic dispersiveness and random The deficiency of composite, when have studied the uncertainty of different input variables (Compound Material Engineering parameter) to composite drilling Export the influence size of response quautity (drill thrust).
The present invention is advantageous to, to Simplified analysis process, save the time, improves efficiency.
Brief description of the drawings:
Fig. 1 is the analysis calculation process of the present invention.
Fig. 2 is sample calculation analysis finite element simulation figure of the present invention.
Fig. 3 is the analysis of cases sensitivity results figure of the present invention.
Embodiment:
The present invention is further illustrated with reference to the accompanying drawings and detailed description.
As Figure 1-3.
A kind of composite drilling process finite element Global sensitivity analysis method, it comprises the following steps:
First, multigroup random number is produced according to the distribution of composite relevant parameter to input as sample;
Secondly, the three-dimensional Drilling model of composite is established using finite element software ABAQUS/Explicit;
3rd, the corresponding cutting force of drilling process generation is emulated by finite element software and is used as sample output;
4th, each ginseng is asked according to " state-contingent parametric method " (States Dependent Parameter, SDP) respectively Conditional expectation of the number for output;
5th, according to the Global sensitivity analysis method based on variance --- " sobol methods " analyzes different parameters for multiple The size of the influence degree of material drill thrust.
Comprise the following steps that:
First, it is assumed that each parameter of composite is all to obey equally distributed stochastic variable, and it is uncorrelated, utilize Matlab softwares produce the random sample X that sample size is N according to the distributed constant of each variablet(x1,x2,x3... xi) (t=1,2, 3 ... N) inputted as sample;
Secondly, the three-dimensional Drilling model of composite is established using finite element analysis software ABAQUS/Explicit;
3rd, call above-mentioned composite material model (i.e. the three-dimensional Drilling model of composite) n times, fortran language controls Abaqus software emulations drilling process processed obtains the curve Y of corresponding cutting force time changet- t schemes, using in least square Collimation method obtains the numerical value Y represented by the center line of curve in collimation method or arithmetic meant(t=1,2,3 ... N) exported as sample;
4th, parameters X is asked according to SDP methods respectively1, X2, X3,…XiFor sample output Y conditional expectation E (Y | X1), E (Y | X2) ... E (Y | Xi) step is as follows:
According to control theory related content, state space SDP models are:
observation equation:Yt=Pi,t+ei,t
SDP model:Pi,t=Pi,t-1+di,t-1
di,t=di,t-1i,ti,t~N (0, σ2);
In formula:Pi,tFor with state variable Xi,tThe SDP state relevant parameters of change, it is basic variable Xi,tFunction, et (observation interference), ηi,t(system disturbance) be average be zero, variance σ2And ση 2White Gaussian noise input, its value can use Maximum likelihood optimization is estimated to obtain.
Then recursive Kalman filtering (kalam Filtreing, KF) is used in circulation backward fit procedure and is accordingly passed Smooth (Fixed Interval Smoothing, the FIS) rule of fixed interval is returned to estimate to obtain each state relevant parameter Pi,t
Finally substitute into formula:
E(Yt|Xi,t)=Yt-Pi,t
Try to achieve each parameter for output conditional expectation E (Y | Xi,t);
5th:According to Global sensitivity analysis method --- " sobol methods " calculates each parameter XiTo the global sensitive of output Y Degree, its process are as follows:
Substitute into formula:
The gained sample of above-mentioned steps 2 output Y is tried to achieve respectivelytVariance V (Y), and each parameter X in step 3iFor Y condition It is expected E (Y | Xi) variance V (E (and Y | Xi))。
The formula carried according to sobol methods:
Composite parameters are calculated in drilling process for the global sensitivity index S of cutting forcei
With reference to T700 carbon fibre reinforced composites, details are as follows:
A kind of composite drilling process finite element Global sensitivity analysis method, its flow chart is as shown in figure 1, specific bag Include following steps:
First, multigroup random number is produced according to the distribution of the relevant parameter of composite to input as sample:With T700 carbon Exemplified by unidirectional (0 °) plate of fibre reinforced composites individual layer, such as Fig. 2.Its longitudinal stretching ultimate strength Y is obtained by testing1= 1900MPa, longitudinal ultimate compression strength Y2=1000MPa, cross directional stretch limiting chi1=84MPa, transverse compression limiting chi2= 250MPa, longitudinal Young's modulus E2=8.2GPa, horizontal Young's modulus E1=112GPa, Poisson's ratio ν=0.3, G=4500MPa. Using these parameters as input variable, remaining parameter keeps constant, it is assumed that and each parameter is all to obey equally distributed stochastic variable, And it is uncorrelated, produce the random sample X that sample size is 100 using uniform designt(t=1,2,3 ... 100) it is used as sample Input, partial data such as table 1;
Secondly, the three-dimensional Drilling model of composite is established using finite element analysis software ABAQUS/Explicit, is such as schemed Shown in 2, the cutter is that the cutter is 6 millimeters of drill bits, 118 ° of drift angle, 30 ° of helical angle.Kinematic constraint is in X and Y-direction, feeding speed Degree is 1.5mm/s, drilling speed 314rad/s.Carbon fibre composite is multidirectional laminate, is 12mm*12mm*5mm's by size 40 are formed according to 0 °/- 45 °/90 °/45 ° directions stackings, and the laminate border is fixed.
3rd, control Abaqus finite element analysis softwares to call above-mentioned composite material model (i.e. multiple using fortran language The three-dimensional Drilling model of condensation material) 100 times, pass through the song that software emulation drilling process produces corresponding cutting force time change Line Yt- t schemes, and the numerical value Y represented by the center line of curve is obtained using collimation method in least squares method or arithmetic meant(t=1, 2,3 ... 100) export as sample, partial results such as table 1;
The material parameter of table 1. exports with drill thrust
4th, according to SDP methods ask respectively parameters for sample export Y conditional expectation E (Y | Xt) step is as follows:
According to control theory related content, state space SDP models are:
observation equation:Yt=Pi,t+ei,t
SDP model:Pi,t=Pi,t-1+di,t-1
di,t=di,t-1i,t;ηi,t~N (0, σ2);
In formula:Pi,tFor with state variable Xi,tThe SDP state relevant parameters of change, it is basic variable Xi,tFunction, et (observation interference), ηi,t(system disturbance) be average be zero, variance σ2And ση 2White Gaussian noise input, its value can use Maximum likelihood optimization is estimated to obtain.
Then recursive Kalman filtering (kalam Filtreing, KF) is used in circulation backward fit procedure and is accordingly passed Smooth (Fixed Interval Smoothing, the FIS) rule of fixed interval is returned to estimate to obtain each state relevant parameter Pi,t
Finally substitute into formula:
E(Yt|Xi,t)=Yt-Pi,t
Try to achieve each parameter for output conditional expectation E (Y | Xi,t);
5th:According to Global sensitivity analysis method --- " sobol methods " calculates each parameter XiTo the global sensitive of output Y Degree, its process are as follows:
Substitute into formula:
The gained sample of above-mentioned steps 2 output Y is tried to achieve respectivelytVariance V (Y), and each parameter X in step 3iFor Y condition It is expected E (Y | Xi) variance V (E (and Y | Xi))。
The formula carried according to sobol methods:
Composite parameters are calculated in drilling process for the global sensitivity index S of cutting forcei.Result of calculation Such as table 2.
The Calculation of Sensitivity result of table 2.
For ease of analyzing to obtain block diagram, such as Fig. 3.Can with it is concluded that:The Young's modulus of material influences the most on drill thrust Significantly, Poisson's ratio has negatively influencing to drill thrust size, and the coefficient of rigidity on drill thrust almost without influence.
Part that the present invention does not relate to is same as the prior art or can be realized using prior art.

Claims (6)

1. a kind of composite drilling process finite element Global sensitivity analysis method, its feature are as follows:
First, multigroup random number is produced according to the distribution of composite relevant parameter to input as sample;
Secondly, the three-dimensional Drilling model of composite is established using finite element software;
3rd, above-mentioned three-dimensional Drilling model is called, emulating drilling process by finite element software produces drill thrust-time diagram, profit Corresponding cutting force is obtained by the use of least squares method to export as sample;
4th, parameters pair are asked according to " state-contingent parametric method " (States Dependent Parameter, SDP) respectively In the conditional expectation of output;
5th, according to the Global sensitivity analysis method based on variance --- " sobol methods " analysis different parameters bore for multiple material Cut the size of the influence degree of power.
2. according to the method for claim 1, it is characterized in that the relevant parameter of described composite is all to obey just to divide very much The stochastic variable of cloth, the coefficient of variation are 0.06, and uncorrelated, are produced using Matlab softwares according to the distributed constant of each variable The random sample X that raw sample size is Nt(x1,x2,x3…xi) (t=1,2,3 ... N) inputted as sample.
3. according to the method for claim 1, it is characterized in that described finite element software is ABAQUS/Explicit.
4. according to the method for claim 1, it is characterized in that calling three-dimensional Drilling model n times, pass through Abaqus software emulations Drilling process produces corresponding cutting force Yt(t=1,2,3 ... N) exported as sample.
5. according to the method for claim 1, it is characterized in that seeking parameters X respectively according to SDP methods1, X2, X3,…XiFor Sample output Y conditional expectation E (Y | X1), E (Y | X2) ... E (Y | Xi) step is as follows:
According to control theory, establishing state space SDP models is:
observation equation:Yt=Pi,t+ei,t
SDP model:Pi,t=Pi,t-1+di,t-1
di,t=di,t-1i,t, ηi,t~N (0, σ2);
In formula:Pi,tFor with state variable Xi,tThe SDP state relevant parameters of change, it is basic variable Xi,tFunction, et(observation is dry Disturb), ηi,t(system disturbance) be average be zero, variance σ2And ση 2White Gaussian noise input, its value can use maximum likelihood Optimal estimating obtains.
Then consolidated in circulation backward fit procedure with recursive Kalman filtering (kalam Filtreing, KF) and corresponding recurrence Determine smooth (Fixed Interval Smoothing, the FIS) rule in section to estimate to obtain each state relevant parameter Pi,t
Finally according to formula:
E(Yt|Xi,t)=Yt-Pi,t
Calculate each parameter for output conditional expectation E (Y | Xi,t);
6. according to the method for claim 1, it is characterized in that according to Global sensitivity analysis method --- " sobol methods " calculates Each parameter XiThe process of global sensitivity to exporting Y is as follows:
According to formula:
<mrow> <mi>V</mi> <mrow> <mo>(</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>Y</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>E</mi> <mo>(</mo> <msub> <mi>Y</mi> <mi>t</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>;</mo> </mrow>
<mrow> <mi>V</mi> <mrow> <mo>(</mo> <mi>E</mi> <mo>(</mo> <mrow> <mi>Y</mi> <mo>|</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mo>&amp;lsqb;</mo> <msup> <mrow> <mo>(</mo> <mi>E</mi> <mo>(</mo> <mi>Y</mi> <mo>|</mo> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <mo>)</mo> <mo>-</mo> <mi>E</mi> <mo>(</mo> <mi>E</mi> <mo>(</mo> <mrow> <mi>Y</mi> <mo>|</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>;</mo> </mrow>
Calculate foregoing gained sample output YtVariance V (Y) and each parameter XiFor Y conditional expectation E (Y | Xi) variance V (E (Y|Xi));
The formula carried according to sobol methods:
<mrow> <msub> <mi>S</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mi>V</mi> <mrow> <mo>(</mo> <mi>E</mi> <mo>(</mo> <mrow> <mi>Y</mi> <mo>|</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> <mrow> <mi>V</mi> <mrow> <mo>(</mo> <mi>Y</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>;</mo> </mrow>
Composite parameters are calculated in drilling process for the global sensitivity index S of cutting forcei
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CN110232255A (en) * 2019-06-24 2019-09-13 南京航空航天大学 A kind of method of carbon fibre reinforced composite drilling axial force prediction
CN113111539A (en) * 2021-05-03 2021-07-13 西北工业大学 Fuzzy variable-based global sensitivity analysis method for series thermoelectric generator
CN114741792A (en) * 2022-04-20 2022-07-12 合肥工业大学 Method for calculating material parameter sensitivity of solid rocket engine nozzle

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Publication number Priority date Publication date Assignee Title
CN110232255A (en) * 2019-06-24 2019-09-13 南京航空航天大学 A kind of method of carbon fibre reinforced composite drilling axial force prediction
CN113111539A (en) * 2021-05-03 2021-07-13 西北工业大学 Fuzzy variable-based global sensitivity analysis method for series thermoelectric generator
CN114741792A (en) * 2022-04-20 2022-07-12 合肥工业大学 Method for calculating material parameter sensitivity of solid rocket engine nozzle
CN114741792B (en) * 2022-04-20 2024-02-13 合肥工业大学 Method for calculating sensitivity of nozzle material parameters of solid rocket engine

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