CN110378011A - A kind of metal bellows hydraulic bulging process robust design method - Google Patents
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Abstract
A kind of metal bellows hydraulic bulging process robust design method, the quality evaluation index for selecting bellows hydraulic bulging process to optimize is as optimization aim and optimization constraint condition；For material parameter as noise factor, technological parameter formulates factor level table as controllable factor；Virtual test is carried out using Taguchi robust design method, every kind of process conditions combination in test table is calculated, the result of mass property is obtained；According to the mass property of acquisition as a result, calculating the signal-to-noise ratio of mass property, Standardization Quality loss is converted by signal-to-noise ratio, and synthesize comprehensive quality loss；Selecting comprehensive quality loss is optimization aim, using homing method, constructs the response surface Robust model of comprehensive quality loss and design variable；Optimal value is solved with response surface Robust model of the genetic algorithm to constructed comprehensive quality loss and design variable.The method can solve the problem that quality control is inaccurate, product qualification rate is low, consistency is poor during conventional metals bellows hydraulic expanding-forming.
Description
Technical field
The present invention relates to metal bellows hydraulic expanding-forming technical field, in particular to a kind of metal bellows hydraulic expanding-forming work
Skill robust design method.
Background technique
Wavy metal tubing part is navigating due to having the multiple functions such as sealing, flexible compensation, energy storage as elastic element
The fields such as empty space flight, ship, petrochemical industry, electric power, building, nuclear energy are widely applied.Bellows forming mode multiplicity, with metal
Bellows high-performance, precise treatment degree require continuous improvement, hydraulic expanding-forming be increasingly becoming the accurate plasticity of metal bellows at
The major way of shape.However, metal bellows hydraulic expanding-forming is that material nonlinearity, geometrical non-linearity, boundary condition are nonlinear
Complicated physical process, forming parameters are numerous, it is difficult to which comprehensively control, layers of material flowing are easy to appear uncoordinated phenomenon, pole
Stress easily occurs to concentrate, the problems such as wall thickness excessive thinning, rupture, corrugation, insufficient fill occurs, leads to product shaping low precision,
Forming quality is difficult to ensure.The production of bellows relies primarily on experience and trial-and-error method at present, and the period is long, at high cost, and to list
The raising of a performance indicator frequently can lead to the reduction of other indexs, it is difficult to carry out comprehensive regulation to more forming indexs.And by
The influence of uncertain factor in the productions such as material mechanical performance fluctuation, the qualification rate of existing product is low, and homogeneity of product is poor.
Therefore obtaining reasonable combination of process parameters to the based Robust Design of metal bellows hydraulic expanding-forming process spread technique is to realize wave
The premise of line pipe forming quality accurately controlled.
Summary of the invention
In order to solve the above technical problems, the purpose of the present invention is to provide a kind of metal bellows hydraulic bulging process is steady
It is good for design method, quality control is inaccurate during solution conventional metals bellows hydraulic expanding-forming, product qualification rate is low, consistency is poor
The problem of.
To achieve the goals above, the technical solution adopted by the present invention is that:
A kind of metal bellows hydraulic bulging process robust design method, includes the following steps；
Step 1: the quality evaluation index for selecting bellows hydraulic bulging process to optimize is as optimization aim and optimization constraint
Condition.The weight influenced by factor on forming quality, experiment arrangement carry out factor Significance Analysis, select and eliminate and is inessential
Influence factor；
Step 2: in the obtained key factor of step 1, chosen material parameter is as noise factor, technological parameter
Controllable factor, and formulate factor level table；
Step 3: estimated under interior orthogonal arrage controlling elements horizontal combination using the variation of the outer orthogonal arrage analogue noise factor
Fluctuation orthogonal experiment is all made of to inside and outside orthogonal arrage and is assessed with interior orthogonal arrage come the level of preferred controllable factor, field
Mouth based Robust Design experimental program are as follows: using the direct product of inside and outside orthogonal arrage, the model under every kind of process combination in test table is carried out
It calculates, and obtains the result of mass property；
Step 4: the resulting associated analog of extraction step three as a result, calculate mass property signal-to-noise ratio, utilize standardization matter
Costing bio disturbance formula is measured, Standardization Quality loss is converted by signal-to-noise ratio, and synthesize comprehensive quality loss, is obtained using MINITAB
To design parameter and noise factor to the response table and main effect figure of mass property, analysis process parameter is to bellows forming quality
The influence sequence of index；
Step 5: selecting comprehensive quality loss is optimization aim, using homing method, the data obtained using step 4,
Construct the response surface Robust model of comprehensive quality loss and design variable；
Step 6: with genetic algorithm to the steady mould of response surface of the loss and design variable of comprehensive quality constructed by step 5
Type solves optimal value；
Step 7: correlation values simplation verification is carried out to the result that step 6 solves, completes optimization.
For signal-to-noise ratio described in the step four according to the difference of mass property, signal-to-noise ratio, which is commonly divided into, hopes small, prestige
3 seed types such as big and prestige mesh need to be analyzed and be calculated according to the practical specific corresponding formula of selection of quality index；
The signal-to-noise ratio of Definite purpose: for the mass property of this type, output characteristics target value is determined, closer to target
It is better to be worth performance, calculation formula are as follows:
Hope the signal-to-noise ratio of small characteristic: the mass property of certain products is the smaller the better, best when taking zero, and properties of product with
Output characteristics value increases and is deteriorated, and mass loss increases, calculation formula are as follows:
The signal-to-noise ratio of Wogvily Mining Way: some products wish to take bigger qualitative character, and zero is worst, and properties of product are with output
Characteristic value increases and improves, and mass loss reduces, calculation formula are as follows:
In formula: n is test number (TN), yiValue for the mass property obtained in i-th test under identical test horizontal combination,
y0For the target value of product quality characteristics.
Standardization Quality described in the step (4) loses conversion formula are as follows:
In formula: 0≤μy(sn)≤1, μyIt (sn) is the satisfaction of some mass property y of signal-to-noise ratio SN；SN*And SN*Respectively
It is weight coefficient for the lower bound and the upper bound, α of the signal-to-noise ratio of measurement mass property satisfaction, it reflects each mass property pair
The percentage contribution that robustness requires, 0≤α≤1.
Comprehensive quality costing bio disturbance formula described in the step (4) are as follows:
In formula: yijFor standardized mass loss；For the biggest quality of i-th of mass property in its all test
Loss；Sn is signal-to-noise ratio；K is mass loss coefficient；αiFor weight coefficient, reflect that i-th of quality characteristic value wants robustness
Ask degree, 0≤αi≤1。
It is indicated in the step (5) with the response surface Robust model that comprehensive quality loss index is worth in response are as follows:
Li=bi0+bi1x1+bi2x2+…+bijxj+binxk (6)
In formula: L is that comprehensive quality loses index；X is design variable；N is the number of design variable；B is undetermined coefficient, by
Least square method is fitted to obtain.
Optimization aim described in the step one and optimization constraint condition refer respectively to the maximum wall after bellows forming
Thick reduction and wave height.
Noise factor is uncontrollable material parameter, including hardenability value, yield strength, thick anisotropy index；It is controllable because
Element is technological parameter, including matrix spacing, interior pressure, coefficient of friction.
The beneficial effects of the present invention are:
The method that this method is combined with steady optimisation technique based on numerical simulation is to metal bellows hydraulic expanding-forming process
It optimizes.Bellows hydraulic expanding-forming finite element model has been initially set up, then forming quality influence factor has been analyzed, has been sieved
Select design variable and noise factor；The value range of technological parameter is obtained by experience and theoretical formula method；By simple tension
Test obtains the basic value of material parameter, determines its fluctuation range；Inside and outside orthogonal arrage is arranged to carry out using Taguchi's method virtual
Orthogonal test establishes the mathematical model of objective function and design variable using comprehensive quality loss as objective function, calculates in conjunction with heredity
Method solves objective function, obtains the steady optimal forming parameter of control bellows quality.
Detailed description of the invention
Fig. 1 is bellows hydraulic bulging process parameter based Robust Design flow chart.
Fig. 2 is design parameter to wave height signal-to-noise ratio effect response diagram.
Fig. 3 is design parameter to maximum reduction signal-to-noise ratio effect figure.
Fig. 4 is the numerical simulation forming results cloud atlas of steady optimum results.
Fig. 5 is the numerical simulation forming results waveform profiles figure of steady optimum results.
Fig. 6 is the numerical simulation forming results wall thickness reduction distribution map of steady optimum results.
Specific embodiment
Make narration in detail with reference to the accompanying drawing.
This example combines Fig. 1 bellows hydraulic bulging process parameter based Robust Design flow chart, using the wave of the double-deck U-shaped structure
Line pipe, inner layer material Inconel625, cladding material 316L, geometric dimension are as follows: outer diameter 88mm, internal diameter 65.5mm, wave
Away from 5.8mm, thickness of convolution 3.2mm, wave height 11.25mm, wave crest radius of corner 1.6mm, trough radius of corner 1.3mm, pipe single wall
Thick 0.2mm.
(1) select bellows hydraulic expanding-forming quality evaluation index --- wave height and thickest reduction --- as optimization
Target and optimization constraint condition.The weight influenced by factor on forming quality, experiment arrangement carry out factor Significance Analysis, choosing
Select and eliminate unessential influence factor.
(2) assume that outer layer 316L material mechanical parameters are stablized, it, will in the obtained key factor of (1) step
Hardenability value n, the yield strength σ of Inconel625 material0, thick tri- mechanics parameters of anisotropy index r be used as noise factor, general
Three matrix spacing, interior pressure, coefficient of friction technological parameters formulate factor level table as controllable factor, and specific data are such as
Shown in Tables 1 and 2, wherein 1 level of table, 2 respective value is material tensile test value.
(3) wave under interior orthogonal arrage controlling elements horizontal combination is estimated using the variation of the outer orthogonal arrage analogue noise factor
It is dynamic, with interior orthogonal arrage come the level of preferred controllable factor.L is all made of to inside and outside orthogonal arrage9(33) orthogonal experiment assessed.
Taguchi robust design experimental program are as follows: using the direct product of inside and outside orthogonal arrage, the combination of every kind of technique in test table is established limited
Meta-model is calculated, the result of available bellows wave height and thickest reduction.Inside and outside orthogonal arrage test number (TN) is each
It is 9 times, shares 81 kinds of combinations, wave height or thickest reduction result and specific combination is as shown in Table 3 and Table 4.
(4) extract the resulting wave height of (3) step and the simulation of thickest reduction as a result, calculating wave height, thickest
The signal-to-noise ratio of the mass propertys such as reduction converts Standardization Quality for signal-to-noise ratio using Standardization Quality costing bio disturbance formula
Loss, and synthesize comprehensive quality loss.Design parameter and noise factor is obtained using MINITAB wave height, thickest is thinned
The response table and main effect figure of rate, analysis process parameter is on forming wave height and thickest reduction influence sequence.If Fig. 2 is to set
Parameter is counted to wave height signal-to-noise ratio effect response diagram, Fig. 3 is design parameter to maximum reduction signal-to-noise ratio effect figure, passes through signal-to-noise ratio
For main effect figure it can be seen that each factor is to the effect tendency of result, corresponding when signal-to-noise ratio is maximized is optimal parameter
Value.
Since the index of bellows hydraulic expanding-forming forming quality examination is wave height and thickest reduction, wave height must meet
The requirement of detail of design, therefore wave height index is Definite purpose problem, and there is wall thickness during bellows hydraulic expanding-forming
Be thinned, wave crest be thinned maximum, trough be thinned it is smaller, the thinning pipe stress that will lead to of wall thickness sharply increases, under bellows stiffness
Therefore drop answers the reduction amount of its wall thickness of strict control, and it is desirable that thickest reduction is as small as possible, therefore thickest
Reduction index is the small characteristic issues of prestige,
Use formulaCalculate the signal-to-noise ratio of thickest reduction characteristic, calculated result such as table 3
It is shown.Utilize formulaThe signal-to-noise ratio of wave height characteristic is calculated, calculated result is as shown in table 4.It is public
N in formula is test number (TN), yiValue for the mass property obtained in i-th test under identical test horizontal combination, y0For product
The target value of mass property.
Resulting signal-to-noise ratio data will be calculated, the numerical value being converted between reflection designer's satisfaction standardized 0~1,
I.e. Standardization Quality loses, and conversion formula is as follows:
In formula, 0≤μy(sn)≤1, μyIt (sn) is the satisfaction of some mass property y of signal-to-noise ratio SN；SN*And SN*Respectively
It is weight coefficient for the lower bound and the upper bound, α of the signal-to-noise ratio of measurement mass property satisfaction, it reflects each mass property pair
The percentage contribution that robustness requires, 0≤α≤1, calculated result are as shown in table 5.
Comprehensive quality is lost, its calculation formula is:
In formula, yijFor standardized mass loss；For the biggest quality of i-th of mass property in its all test
Loss；Sn is signal-to-noise ratio；K is mass loss coefficient；αiFor weight coefficient, reflect that i-th of quality characteristic value wants robustness
Ask degree, 0≤αi≤1.Carrying out selected weight coefficient when comprehensive quality costing bio disturbance is α1=1, α2=0.8, calculated result
It is shown in Table 5.
(5) selecting comprehensive quality loss is optimization aim, using homing method, the data for utilizing (4) step to obtain, and building
The response surface Robust model of comprehensive quality loss and design variable.Robust error estimator mathematical model indicates are as follows:
In formula: L is comprehensive quality loss, x1For matrix spacing, x2For interior pressure, x3For coefficient of friction.Wherein
24.5≤x1≤27.1
5.5≤x2≤18
0.1≤x3≤0.5
(6) with genetic algorithm to the response surface Robust model of the loss and design variable of comprehensive quality constructed by (5) step
Optimal value is solved, the most optimized parameter combination: matrix spacing 24.5mm, pressure 14.02MPa in bulging, coefficient of friction 0.23 are obtained.
(7) the most optimized parameter combination solved using (6) step carries out correlation values simulation, to based Robust Design and non-robust
The numerical simulation result of design compares verifying, and as shown in figures 4-6, Fig. 4 is the Numerical-Mode of steady optimum results to analog result
Quasi- forming results cloud atlas, Fig. 5 are the numerical simulation forming results waveform profiles figure of steady optimum results, and Fig. 6 is steady optimization knot
The numerical simulation forming results wall thickness reduction distribution map of fruit finds that the bellows stress distribution after based Robust Design is uniform,
Wave height and wall thickness meet tolerance.As shown in Table 8, the wave height of based Robust Design is 11.19mm, and thickest reduction is
19.3%, wave height is met the requirements, and comprehensive quality loss decline, product quality is met the requirements, and completes optimization.1 Inconel625 of table
Material parameter fluctuation range and level
2 controllable factor of table and level
3 field of table mouthful orthogonal design table maximum reduction
4 field of table mouthful orthogonal design table wave height result
The noise of each mass property of table 5 when standardized value
6 design parameter of table responds table to wave height signal-to-noise ratio
7 design parameter of table is to maximum reduction signal-to-noise ratio effect figure
The comparison of 8 optimum results of table
Claims (7)
1. a kind of metal bellows hydraulic bulging process robust design method, which is characterized in that include the following steps；
Step 1: the quality evaluation index for selecting bellows hydraulic bulging process to optimize is as optimization aim and optimization constraint item
Part.The weight influenced by factor on forming quality, experiment arrangement carry out factor Significance Analysis, select and eliminate and is unessential
Influence factor；
Step 2: in the obtained key factor of step 1, for chosen material parameter as noise factor, technological parameter is controllable
Factor, and formulate factor level table；
Step 3: the wave under interior orthogonal arrage controlling elements horizontal combination is estimated using the variation of the outer orthogonal arrage analogue noise factor
It is dynamic, with interior orthogonal arrage come the level of preferred controllable factor, orthogonal experiment is all made of to inside and outside orthogonal arrage and is assessed, field mouthful is steady
Strong contrived experiment scheme are as follows: using the direct product of inside and outside orthogonal arrage, the model under every kind of process combination in test table is counted
It calculates, and obtains the result of mass property；
Step 4: the resulting associated analog of extraction step three as a result, calculate mass property signal-to-noise ratio, damaged using Standardization Quality
Calculation formula is lost, Standardization Quality loss is converted by signal-to-noise ratio, and synthesize comprehensive quality loss, is set using MINITAB
Parameter and noise factor are counted to the response table and main effect figure of mass property, analysis process parameter is to bellows forming quality index
Influence sequence；
Step 5: selecting comprehensive quality loss is optimization aim, using homing method, the data obtained using step 4, and building
The response surface Robust model of comprehensive quality loss and design variable；
Step 6: comprehensive quality constructed by step 5 is lost with genetic algorithm and is asked with the response surface Robust model of design variable
Solve optimal value；
Step 7: correlation values simplation verification is carried out to the result that step 6 solves, completes optimization.
2. a kind of metal bellows hydraulic bulging process robust design method according to claim 1, which is characterized in that institute
For signal-to-noise ratio described in the step of stating four according to the difference of mass property, signal-to-noise ratio, which is commonly divided into, hopes small, prestige greatly and hopes mesh etc. 3
Seed type need to be analyzed and be calculated according to the practical specific corresponding formula of selection of quality index；
The signal-to-noise ratio of Definite purpose: for the mass property of this type, output characteristics target value is determined, closer to target value
Can be better, calculation formula are as follows:
Hope the signal-to-noise ratio of small characteristic: the mass property of certain products is the smaller the better, best when taking zero, and properties of product are with output
Characteristic value increases and is deteriorated, and mass loss increases, calculation formula are as follows:
The signal-to-noise ratio of Wogvily Mining Way: some products wish to take bigger qualitative character, and zero is worst, and properties of product are with output characteristics
Value increases and improves, and mass loss reduces, calculation formula are as follows:
In formula: n is test number (TN), yiValue for the mass property obtained in i-th test under identical test horizontal combination, y0For
The target value of product quality characteristics.
3. a kind of metal bellows hydraulic bulging process robust design method according to claim 1, which is characterized in that institute
Standardization Quality described in the step of stating (4) loses conversion formula are as follows:
In formula: 0≤μy(sn)≤1, μyIt (sn) is the satisfaction of some mass property y of signal-to-noise ratio SN；SN*And SN*Respectively weigh
The lower bound and the upper bound, α for measuring the signal-to-noise ratio of mass property satisfaction are weight coefficient, it reflects each mass property to steady
Property require percentage contribution, 0≤α≤1.
4. a kind of metal bellows hydraulic bulging process robust design method according to claim 1, which is characterized in that institute
Comprehensive quality costing bio disturbance formula described in the step of stating (4) are as follows:
In formula: yijFor standardized mass loss；The biggest quality for being i-th of mass property in its all test loss；
Sn is signal-to-noise ratio；K is mass loss coefficient；αiFor weight coefficient, reflect requirement journey of i-th of quality characteristic value to robustness
Degree, 0≤αi≤1。
5. a kind of metal bellows hydraulic bulging process robust design method according to claim 1, which is characterized in that institute
It is indicated in the step of stating (5) with the response surface Robust model that comprehensive quality loss index is worth in response are as follows:
Li=bi0+bi1x1+bi2x2+…+bijxj+binxk (6)
In formula: L is that comprehensive quality loses index；X is design variable；N is the number of design variable；B is undetermined coefficient, by minimum
Square law is fitted to obtain.
6. a kind of metal bellows hydraulic bulging process robust design method according to claim 1, which is characterized in that institute
Optimization aim described in the step of stating one and optimization constraint condition refer respectively to bellows forming after thickest reduction and
Wave height.
7. a kind of metal bellows hydraulic bulging process robust design method according to claim 1, which is characterized in that make an uproar
Sound factor is uncontrollable material parameter, including hardenability value, yield strength, thick anisotropy index；Controllable factor is technique ginseng
Number, including matrix spacing, interior pressure, coefficient of friction.
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