CN109255182A - A kind of hard brittle material technology-parameter predictive model and its Multipurpose Optimal Method - Google Patents

A kind of hard brittle material technology-parameter predictive model and its Multipurpose Optimal Method Download PDF

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CN109255182A
CN109255182A CN201811047325.XA CN201811047325A CN109255182A CN 109255182 A CN109255182 A CN 109255182A CN 201811047325 A CN201811047325 A CN 201811047325A CN 109255182 A CN109255182 A CN 109255182A
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factor
parameter
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brittle material
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金明生
董晓星
王礼明
康杰
钱佳彬
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Zhejiang University of Technology ZJUT
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Abstract

The invention discloses a kind of hard brittle material technology-parameter predictive model and its Multipurpose Optimal Method, include the following steps: that 1) root is according to Preston equationIt is determining multifactor to be tested；2) single goal sensitivity is ranked up under single factor by Responds Surface Methodology and variance analysis, reasonable single-factor variable increment is individually determined by sensitivity and distributes；3) according to gray theory, based on degree of association convergence principle, number, grey derivative, grey differential equation are generated to model GM (0, N) and the multifactor single-goal function modeling of GM (1, N) model progress；4) 3 steps are repeated, establish other target function models, the present invention is in the case where the New Super-precision that the hard brittle material of gradient function abrasive disk uniformly removes processes background, provide a kind of hard brittle material technological parameter anticipation function model and its Multipurpose Optimal Method, more reasonable allocation factor sensitivity overcomes passing existing optimization method that can only optimize to existing result the influence degree of target.

Description

A kind of hard brittle material technology-parameter predictive model and its Multipurpose Optimal Method
Technical field
The present invention relates to Ultraprecision Machining fields, more specifically more particularly to a kind of hard brittle material technological parameter Prediction model and its Multipurpose Optimal Method.
Background technique
The hard brittle materials such as sapphire, YAG crystal, special cermacis, crystalline material have hardness height, fusing point high, thermostabilization Property the good characteristics such as good and chemical property stabilization, be used widely in national defence, aerospace, industry and sphere of life. And in the grinding and polishing process to hard brittle material, crackle, fracture belt, pit, convex often is left in wafer surface It rises and the surface defects such as field trash, surface defect can be divided by research by following several types:
1) concave defect, i.e., to the defects of, such as groove, road plan, crackle, crow pawl, edge chipping, notch, pit and striped Deng；
2) convex defect, i.e., outside defect, such as volcanic crater, field trash, overlap, attachment and hillock；
3) mix defect, i.e., part outward and part to the defects of, remnants and tangerine, scratch, are cut at foldings in such as annular hole Skin etc..
As a kind of substrate material, the processing of hard brittle material substrate, grinding and polishing are with occupying very important process Position should pay close attention to surface roughness, material removing rate, superficial lesions, residual stress, put down while focusing on processing efficiency The technical indicators such as smooth degree (surface precision).Currently, can be used when hard brittle material is as a kind of substrate material based on gradient function The New Super-precision processing technology that the hard brittle material of energy abrasive disk uniformly removes, the technology utilize radially elasticity modulus ladder The gradient function polishing disk workpieces processing for spending variation is broken through since the technology belongs to emerging technology having been achieved with the relevant technologies While, there is also some the problem of can not be ignored, for example are also easy to produce following problem in Sapphire Substrate processing:
1) generate unfilled corner, slight crack and chipping phenomenon account for sum ratio it is higher, about 5~8%；
2) unequal factor is removed with material because abrasive material is unevenly distributed, the substrate surface precision after making grinding is poor, increases The removal amount of subsequent handling, production take time and effort, and are difficult to control, and maintenance cost is higher；
3) later grinding and polishing process in the attainable processing efficiency of institute it is lower and many after processing For sapphire sheet since surface scratch is heavier, there is thick, deep scratch on about 20% sapphire substrate surface, need to re-grind polishing, from And cause to do over again；
4) partially the sapphire substrate through doing over again easily occur grinding and polishing excessively and cause sapphire thickness excessively thin, generation is scrapped, Improve the processing cost of hard brittle material substrate.
This series of problems passes through Preston equationIt is found that point of substrate and polishing disk footprint pressure It is the important of substrate processing quality difference that material caused by cloth unevenness and the heterogeneity of relative velocity distribution, which removes non-homogeneous, Root.Therefore sapphire this kind hard brittle material is uniformly removed in the hard brittle material based on gradient function abrasive disk new Under type Ultraprecision Machining background, urgent need provides a kind of technology-parameter predictive model and its analyzes technological parameter, makes It can finally reach the method for process optimization.
Summary of the invention
It is an object of the invention to solve to add in the New Super-precision that the hard brittle material of gradient function abrasive disk uniformly removes Under work background, the problem of optimization to its working process parameter, a kind of hard brittle material technology-parameter predictive model and its more is provided Purpose optimal method, this method are suitable for sapphire one kind hard brittle material processing technology on gradient function polishing disk and optimize.
The present invention is through the following technical solutions to achieve the above objectives: a kind of hard brittle material technology-parameter predictive model, packet Include following steps:
Step 1: according to Preston equationΔ z in formula --- grinding removal amount, v --- abrasive grain phase To movement velocity, the relative pressure of p --- abrasive grain, kp includes some factors relevant to abrasive grain itself, to its factor kp, p, V is tested, and test table is established；
Step 2: mathematical method is applied into New Super-precision and processes lower technological parameter sensitivity sequence, passes through response surface Analytic approach and variance analysis are ranked up single goal sensitivity under single factor, and reasonable single factor test is individually determined by sensitivity and becomes Increment distribution is measured, Responds Surface Methodology and variance analysis are a kind of statistical mathematics methods, are expressed asY is receptance function in formula；β0For constant；βiβiiβijFor regression coefficient； ε is error term；
Step 3: according to gray theory, based on degree of association convergence principle, generate number, grey derivative, grey differential equation to mostly because Plain single goal model carries out GM (0, N) modeling and models with GM (1, N), and (the wherein number that N is factor) establishes more factor single goals Modeling, gray theory are the mathematical modeling thought proposed for rawness, the few certain problem of data, and GM (0, N) is to establish Static prediction model, GM (1, N) are to establish dynamic prediction model, and specific modeling method is as follows:
1, GM (0, N) model is established, the specific steps are as follows:
Step 1: carrying out x to the data that test obtainsi (0)Make 1-AGO sequence,
If x1 (0)=[x1 (0)(1),x1 (0)(2)...x1 (0)It (n)] is system features data sequence,
x2 (0)=[x2 (0)(1),x2 (0)(2)...x2 (0)(n)],
x3 (0)=[x3 (0)(1),x3 (0)(2)...x3 (0)(n)],
xN (0)=[xN (0)(1),xN (0)(2)...xN (0)(n)],
U=[a, b2...bN]；
Step 2: B and Y is calculated,
Step 3: calculating μ1=(BTB)-1BTY, wherein μ1The operation coefficient obtained for matrix operation.
Step 4: establishing multifactor GM (0, N) model:
x1 (1)(k)=a+b2x2 (1)(k)+b3x3 (1)(k)+....+bNxN (1)(k)；Wherein a is principal impact factor, b2b3bNFor Regression coefficient,
2, GM (1, N) model is established, the specific steps are as follows:
Step 1: carrying out xi (0) to the data that test obtains makees 1-AGO sequence,
If x1 (0)=[x1 (0)(1),x1 (0)(2)...x1 (0)It (n)] is system features data sequence,
x2 (0)=[x2 (0)(1),x2 (0)(2)...x2 (0)(n)]；
x3 (0)=[x3 (0)(1),x3 (0)(2)...x3 (0)(n)]；
xN (0)=[xN (0)(1),xN (0)(2)...xN (0)(n)]；
xi (1)For xi (0)1-AGO sequence, z1 (1)For x1 (1)Close to formation sequence, calculation formula isWherein-a is System Development coefficient, bixi (1)It (k) is driving item, biFor drive factor, u =[a, b2...bN] it is that parameter arranges；
Step 2: B, Y are calculated,
Step 3: calculating μ1=(BTB)-1BTY, wherein μ1The operation coefficient obtained for matrix operation.
Step 4: establishing multifactor GM (1, N) model:
3, by GM (0, N) model and GM (1, N) model and existing test data relative error, take precision the higher person as pre- Model is surveyed, determines multifactor single goal model prediction subsequent delta.
Step 4: repeat step 3 kind GM (0, N) model and GM (1, N) model and modeling pattern, carry out multiple monoculars The modeling of scalar functions.
A kind of Multipurpose Optimal Method of hard brittle material technology-parameter predictive model, includes the following steps:
Step 1: hard brittle material technology-parameter predictive model is established；
Step 2: carrying out supplement orthogonal test, and orthogonal test is to seek a kind of efficiency test mode of optimum combination, this hair There are 3 processing factors in bright, collection is combined into p={ p1,p2,p3, the horizontal L={ l of corresponding parameter 21,l2, orthogonal scheme 9 Kind, prediction factor is added and carries out orthogonal test, can also to established GM (0, N) model or GM (1, N) model prediction result into Row verifying；
Step 3: any combination prediction of result is carried out to having multifactor parameter by effect forecast, effect forecast is established On the basis of orthogonal test, the average level removal amount avr of factor is calculated, the horizontal l of each factor is utilizediIt is pre- that-avr carries out effect It surveys；
Step 4: seek multiple objective function optimal solution using apart from congestion PSO particle swarm optimization algorithm, algorithm becomes in decision Quantity space initializes a population, and the parameter of each particle is provided by effect forecast data, by multi-objective optimization question Multiple objective function completes flight of the particle in decision variable space jointly, makes to eventually fall into non-bad optimal objective domain, decision goes out Optimal solution writes program using MATLAB；Specific step is as follows:
Step 1: initialization population: population size N is given by effect forecast data, velocity location x is randomly generatedi, Speed vi；
Step 2: objective function f1(x),f2(x) fitness value of each particle is calculated separately:
For i=1to N
Fitness1 [i]=f1(X[i])；
Fitness1 [i]=f1(X[i])；
Next i；
Step 3: determining the local optimum and global optimum's degree of each particle:
For i=1to N
PBest [1, i]=f1(x)
PBest [1, i]=f1(x)
Next i；
GBest [1, i]=f1(x)
GBest [1, i]=f1(x)；
Step 4: speed and the position of renewal function, comparison function it is optimal optimal with itself；
Step 5: adjustment particle rapidity, judges the number of iterations, if meeting suspension condition, exits, otherwise return to step 4；
Step 6: obtaining output optimal result；
Step 5: the optimal solution obtained according to particle swarm algorithm carries out actual process examination to its optimal solution parameter kp, v, p Verifying, when the theoretical process results and actual tests result error that algorithm obtains are less than 10%, identification algorithm solution is effectively to solve, It and is the optimal procedure parameters of process optimization.
The beneficial effects of the present invention are: the present invention uniformly removed in the hard brittle material of gradient function abrasive disk it is novel super Under Precision Machining background, a kind of hard brittle material technological parameter anticipation function model and its Multipurpose Optimal Method are provided, more Reasonable allocation factor sensitivity overcomes passing existing optimization method can only be to existing result the influence degree of target It optimizes, the present invention predicts subsequent delta as a result, compared with existing effect forecast method, by 3 groups of experiments, can predict Subsequent multi-group data at least guarantees subsequent 2 groups of data precisions, by effect forecast method, at least obtains 243 groups of data；Reach It does a small amount of experiment and obtains the purpose of a large amount of target factor process results；By the calculating of particle swarm algorithm to the data of technological parameter Analysis obtains optimal optimum results；Full experiment method by establishing this set of standard technology optimization replaces artificial experience not It is disconnected fuzzy to attempt, it can also offer reference for the processing technology of other similar hard brittle material and prioritization scheme.
Detailed description of the invention
Fig. 1 is a kind of flow diagram of the Multipurpose Optimal Method of hard brittle material technology-parameter predictive model of the present invention.
Fig. 2 is that a kind of signal population of the Multipurpose Optimal Method of hard brittle material technology-parameter predictive model of the present invention is calculated Method is to process optimization schematic diagram.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings:
As depicted in figs. 1 and 2, a kind of hard brittle material technology-parameter predictive model, includes the following steps:
Step 1: according to Preston equationΔ z in formula --- grinding removal amount, v --- abrasive grain phase To movement velocity, the relative pressure of p --- abrasive grain, kp includes some factors relevant to abrasive grain itself, to its factor kp, p, V is tested, and test table is established；Experimental result material removes depth write-in test table one and roughness write-in experiment table two；
Test table one
Test table two
Step 2: mathematical method is applied into New Super-precision and processes lower technological parameter sensitivity sequence, passes through response surface Analytic approach and variance analysis are ranked up single goal sensitivity under single factor, and reasonable single factor test is individually determined by sensitivity and becomes Increment distribution is measured, Responds Surface Methodology and variance analysis are a kind of statistical mathematics methods, are expressed asY is receptance function in formula；β0For constant；βiβiiβijFor regression coefficient； ε is error term.
Calculated result indicates fitting material removal amount equation as follows:
Mr=0.912+2.72p-0.0113n+0.189d-2.6p2+
0.0012n2+0.0018d2+0.00129pn+0.053pd+0.1014nd；
It is fitted roughness equation:
Ra=1.028-11.55p-0.00065-0.1145d+63.41p2
+0.000012n2-0.0157d2+0.282pn+1.511pd+0.00087nd；
Single goal sensitivity is ranked up under single factor by Responds Surface Methodology and variance analysis, the result shows that p For principal element, reasonable single-factor variable increment, distribution pressure increment is individually determined by sensitivity secondly, be finally kp in v 0.05Mpa, incremental speed 250r/min, kp increment are 1；
Step 3: according to gray theory, and this experiment uses 3 factors, based on degree of association convergence principle, generates number, ash Derivative, grey differential equation model model GM (0,3) modeling with GM (1,3), establish more factor single goal modelings, specific modeling step It is rapid as follows
1: x is carried out to the data that orthogonal test obtainsi (0)Make 1-AGO.
2: calculating B, YN。
3: calculating (BTB)-1。
4: parameter being asked to arrange
5: multifactor GM (0,3) model and GM (1,3) model are established,
Material removal amount GM (0,3) model is x1 (1)K=0.1917+0.074x2 (1)k-0.0008x3 (1)k+1.1103x4 (1) K, material removal amount GM (1,3) model are x1 (1)k-0.0593z2 (1)K=0.0043x2 (1)k+0.0004x3 (1)k+0.0639x4 (1)k Roughness GM (0,3) model is x1 (1)K=0.6052+0.0187x2 (1)k-0.0003x3 (1)k+0.2809x4 (1)K, roughness GM (1,3) model is x1 (1)k-0.0866z2 (1)K=0.0072x2 (1)k+0.0011x3 (1)k+0.0529x4 (1)k
Prediction result filling test table one and test table two in, and with existing test data relative error, take precision higher Person is as prediction model, and it is prediction model that one material of table removal depth, which takes GM (0,3), and two roughness of table takes GM (1,3) for prediction Model.
A kind of Multipurpose Optimal Method of hard brittle material technology-parameter predictive model, includes the following steps:
Step 1: hard brittle material technology-parameter predictive model is established；
Step 2: carrying out supplement orthogonal test, and orthogonal test is to seek a kind of efficiency test mode of optimum combination, this hair There are 3 processing factors in bright, collection is combined into p={ p1,p2,p3, the horizontal L={ l of corresponding parameter 21,l2, orthogonal scheme 9 Kind, prediction factor is added and carries out orthogonal test, can also to established GM (0, N) model or GM (1, N) model prediction result into Row verifying；
Step 3: any combination prediction of result is carried out to having multifactor parameter by effect forecast, effect forecast is established On the basis of orthogonal test, the average level removal amount avr of factor is calculated, the horizontal l of each factor is utilizediIt is pre- that-avr carries out effect It surveys；Determine multifactor single goal model prediction subsequent delta result filling test table one and test table two, effect forecast filling examination Table three and test table four are tested, effect forecast result there are 243 groups of data, provides local data here.
Test table three
Test table four
Step 4: seek multiple objective function optimal solution using apart from congestion PSO particle swarm optimization algorithm, algorithm becomes in decision Quantity space initializes a population, and the parameter of each particle is provided by effect forecast data, by multi-objective optimization question Multiple objective function completes flight of the particle in decision variable space jointly, makes to eventually fall into non-bad optimal objective domain, decision goes out Optimal solution writes program using MATLAB；Specific step is as follows:
Step 1: initialization population: population size N is given by effect forecast data, velocity location x is randomly generatedi, Speed vi；
Step 2: objective function f1(x),f2(x) fitness value of each particle is calculated separately:
For i=1to N
Fitness1 [i]=f1(X[i])；
Fitness1 [i]=f1(X[i])；
Next i；
Step 3: determining the local optimum and global optimum's degree of each particle:
For i=1to N
PBest [1, i]=f1(x)
PBest [1, i]=f1(x)
Next i；
GBest [1, i]=f1(x)
GBest [1, i]=f1(x)；
Step 4: speed and the position of renewal function, comparison function it is optimal optimal with itself；
Step 5: adjustment particle rapidity, judges the number of iterations, if meeting suspension condition, exits, otherwise return to step 4；
Step 6: obtaining output optimal result；
Step 5: according to particle swarm algorithm obtain as a result, algorithm be finally given at pressure p be 0.15Mpa, velocity of rotation V is 1500 turns, in the case that kp factor is 2, has convergence property, the notional result that algorithm obtains to roughness and material removal amount Roughness is 0.2675Ra, and it is 0.4028mm that material, which removes depth,.Carry out technique actual tests, the results showed that be in pressure p 0.15Mpa, velocity of rotation v are 1500r/min, and in the case that kp factor is 2, roughness 0.2487Ra, material removes depth For 0.3755mm, roughness deviation 7.0%, material removes depth offset 6.7%, has to sapphire this kind hard brittle material Well processed effect.
The process optimization test data that this is determined is included in the expert system optimized specifically for skill with Optimal Parameters and is known Know in library, to provide more accurate model further directed to process optimization.
Above-described embodiment is presently preferred embodiments of the present invention, is not a limitation on the technical scheme of the present invention, as long as Without the technical solution that creative work can be realized on the basis of the above embodiments, it is regarded as falling into the invention patent Rights protection scope in.

Claims (2)

1. a kind of hard brittle material technology-parameter predictive model, which comprises the steps of: step 1: according to Preston EquationΔ z in formula --- grinding removal amount, v --- abrasive grain speed of related movement, p --- abrasive grain it is opposite Pressure, kp include some factors relevant to abrasive grain itself, are tested to its factor kp, p, v, and test table is established；
Step 2: mathematical method is applied into New Super-precision and processes lower technological parameter sensitivity sequence, passes through response surface analysis Method and variance analysis are ranked up single goal sensitivity under single factor, and reasonable single-factor variable is individually determined by sensitivity and increases Amount distribution, Responds Surface Methodology and variance analysis are a kind of statistical mathematics methods, are expressed asY is receptance function in formula；β0For constant；βiβiiβijFor regression coefficient； ε is error term；
Step 3: according to gray theory, based on degree of association convergence principle, number, grey derivative, grey differential equation are generated to multifactor list Object module carries out GM (0, N) modeling and models with GM (1, N), establishes more factor single goal modelings, gray theory is for no warp It tests, the mathematical modeling thought that the few certain problem of data proposes, GM (0, N) is to establish static prediction model, and GM (1, N) is to build Vertical dynamic prediction model, specific modeling method are as follows:
1, GM (0, N) model is established, the specific steps are as follows:
Step 1: carrying out x to the data that test obtainsi (0)Make 1-AGO sequence,
If x1 (0)=[x1 (0)(1),x1 (0)(2)...x1 (0)It (n)] is system features data sequence,
x2 (0)=[x2 (0)(1),x2 (0)(2)...x2 (0)(n)],
x3 (0)=[x3 (0)(1),x3 (0)(2)...x3 (0)(n)],
xN (0)=[xN (0)(1),xN (0)(2)...xN (0)(n)],
U=[a, b2...bN]；
Step 2: B and Y is calculated,
Step 3: calculating μ1=(BTB)-1BTY, wherein μ1The operation coefficient obtained for matrix operation.
Step 4: establishing multifactor GM (0, N) model:
x1 (1)(k)=a+b2x2 (1)(k)+b3x3 (1)(k)+....+bNxN (1)(k)；
2, GM (1, N) model is established, the specific steps are as follows:
Step 1: carrying out xi (0) to the data that test obtains makees 1-AGO sequence,
If x1 (0)=[x1 (0)(1),x1 (0)(2)...x1 (0)It (n)] is system features data sequence,
x2 (0)=[x2 (0)(1),x2 (0)(2)...x2 (0)(n)]；
x3 (0)=[x3 (0)(1),x3 (0)(2)...x3 (0)(n)]；
xN (0)=[xN (0)(1),xN (0)(2)...xN (0)(n)]；
xi (1)For xi (0)1-AGO sequence, z1 (1)For x1 (1)Close to formation sequence, calculation formula isIts In-a be System Development coefficient, bixi (1)It (k) is driving item, biFor drive factor, u=[a, b2...bN] it is that parameter arranges；
Step 2: calculating B, Y, wherein μ1The operation coefficient obtained for matrix operation.
Step 3: calculating μ1=(BTB)-1BTY,
Step 4: establishing multifactor GM (1, N) model:
3, by GM (0, N) model and GM (1, N) model and existing test data relative error, take precision the higher person as prediction mould Type determines multifactor single goal model prediction subsequent delta.
Step 4: repeat step 3 kind GM (0, N) model and GM (1, N) model and modeling pattern, carry out multiple monocular offers of tender Several modelings.
2. a kind of Multipurpose Optimal Method of hard brittle material technology-parameter predictive model, characterized by the following steps: step Rapid one: establishing hard brittle material technology-parameter predictive model；
Step 2: carrying out supplement orthogonal test, and orthogonal test is to seek a kind of efficiency test mode of optimum combination, in the present invention There are 3 processing factors, collection is combined into p={ p1,p2,p3, the horizontal L={ l of corresponding parameter 21,l2, orthogonal scheme is 9 kinds, Prediction factor is added and carries out orthogonal test, established GM (0, N) model or GM (1, N) model prediction result can also be tested Card；
Step 3: any combination prediction of result is carried out to having multifactor parameter by effect forecast, effect forecast is established just It hands in experimental basis, calculates the average level removal amount avr of factor, utilize the horizontal l of each factori- avr carries out effect forecast；
Step 4: seek multiple objective function optimal solution using apart from congestion PSO particle swarm optimization algorithm, algorithm is in decision variable sky Between initialize a population, the parameter of each particle provides by effect forecast data, passes through mesh more in multi-objective optimization question Scalar functions complete flight of the particle in decision variable space jointly, make to eventually fall into non-bad optimal objective domain, decision is optimal out Solution, writes program using MATLAB；Specific step is as follows:
Step 1: initialization population: population size N is given by effect forecast data, velocity location x is randomly generatedi, speed vi；
Step 2: objective function f1(x),f2(x) fitness value of each particle is calculated separately:
Step 3: determining the local optimum and global optimum's degree of each particle:
Step 4: speed and the position of renewal function, comparison function it is optimal optimal with itself；
Step 5: adjustment particle rapidity, judges the number of iterations, if meeting suspension condition, exits, otherwise return to step 4；
Step 6: obtaining output optimal result；
Step 5: the optimal solution obtained according to particle swarm algorithm carries out actual process to its optimal solution parameter kp, v, p and tests Card, when the theoretical process results and actual tests result error that algorithm obtains are less than 10%, identification algorithm solution is effectively to solve, and be The optimal procedure parameters of process optimization.
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CN113496324A (en) * 2020-03-20 2021-10-12 广东博智林机器人有限公司 Spray quality prediction method, spray quality prediction device, electronic equipment and storage medium
CN113919101A (en) * 2021-10-29 2022-01-11 哈尔滨工业大学 Ball head grinding wheel grinding process parameter optimization method based on response surface method and particle population optimization algorithm
CN116341151A (en) * 2023-05-18 2023-06-27 贵州大学 Surface shape error control method for central symmetrical concave surface shape of large-diameter sheet part

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