CN105912759A - Calculating method for determining percolation threshold of voltage-sensitive micro-balloons in nonlinear insulating material - Google Patents

Abstract

The invention relates to a calculating method for determining percolation thresholds of voltage-sensitive micro-balloons in a nonlinear insulating material. The calculating method includes the following steps: (1) generation of an insulating material integral calculation zone; (2) generation of micro-balloon distribution, wherein the micro-balloons are distributed in the generated calculation zone; (3) setting of material characteristics; (4) solution of compound voltage current characteristics; and (5) determination of compound percolation thresholds. The beneficial effects of the calculating method are that: simulation calculation is performed by matlab software to measure the percolation thresholds of the voltage-sensitive micro-balloons in a nonlinear compound; the percolation threshold of a ZnO/silicone rubber nonlinear compound with ZnO voltage-sensitive micro-balloons as a filling material is actually calculated; and for the problem that the percolation threshold of the nonlinear compound may change with a substrate or characters of the filling material of the voltage-sensitive micro-balloons, a method for speculating the percolation threshold of the compound through numerical calculation is provided, and then characteristic parameters are provided for preparation of the nonlinear compound and application design of the nonlinear compound on a high voltage insulation device.

Description

The computational methods of the percolation threshold of pressure-sensitive microsphere in determining non-linear dielectric materials

Technical field

The present invention relates to pharmaceutical analysis detection technique field, the computational methods of the percolation threshold of pressure-sensitive microsphere in specially determining non-linear dielectric materials.

Background technology

Insulator arrangement in alternating current-direct current power transmission and transformation system or parts, the Electric Field Distribution himself born is the most uneven, the insulated part of such as power cable termination, the high-pressure side part of various insulator, sleeve pipe etc., the electric field intensity born will be far beyond the meansigma methods of overall electric field intensity, even up to the several times of meansigma methods, thus bring the adverse effect of a series of design, manufacture view.Additionally, owing to insulator arrangement or parts self bear the inhomogeneities of Electric Field Distribution, electric field intensity is bigger, especially cause the dielectric substance that the position of the phenomenon such as corona, shelf depreciation occurs, its aging speed the most faster, degree even more serious, thus the long-term safety stable operation to system brings bigger threat.Therefore, rationally improve insulator arrangement or the uniformity coefficient of parts entirety Electric Field Distribution, relax high electric field intensity locally, the technical difficulty can reduce extra-high voltage equipment design, manufacturing, reduces power equipment cost, it is greatly saved power construction investment, and improves the security reliability of equipment longtime running.Compared with the traditional method using various the exterior measures, the performance parameter of insulative dielectric material self is regulated by various different materials, realize improving insulator arrangement or the effect of parts Electric Field Distribution uniformity coefficient, it it is the method widely used at present, effect is all pressed in reality, and reduce the aspects such as equipment design, manufacture difficulty, all there is obvious advantage.In all kinds of insulant, there is the effect that the insulant of high-level non-linear electric character can reach ideal in terms of the distortion of suppression internal field, uniform field strength distribution, have a wide range of applications.

According to correlational study, in the organic polymer insulant such as epoxy resin, silicone rubber, fill the new blend that a certain amount of miniature varistor granule generated can show the high-level non-linear electric character similar with based varistor, be applied to electric field in insulator arrangement be susceptible to distortion key position reflect following advantage: there is higher insulation resistance value, and under higher electric field intensity, carry out mild regulation, continuous print operation voltage can be born, under ac high voltage, still keep relatively low power consumption, have good thermal conduction characteristic；At transient characterisitics fast response time, regulatable non-linear domain two orders of magnitude higher than traditional gradient fields polymeric insulator thing, can be widely used in the electric field regulation and control in the insulation of electrical installation including cable, sleeve pipe etc..

Current miniature varistor granule in non-linear complex as filler is mainly spherical ZnO voltage-sensitive ceramic (the lower abbreviation pressure-sensitive microsphere of ZnO), and the actual selection applied for packing volume mark has the most harsh requirement.First, the volume fraction of filler has lower limit, because only that complex can show stable non-linear electric character when the volume fraction of ZnO pressure-sensitive microsphere filler exceedes the percolation threshold of such " filler/polymeric matrix " this dispersion.And more than percolation threshold, the volume fraction of filler is the lowest more good, because filler is preferably minimized for the impact of other physical characteristics of insulant such as thermal characteristics, mechanical property.Therefore, packing volume mark is to be advisable just above percolation threshold, it means that before preparation has the composite of non-linear electric character, need first to determine the percolation threshold of such complex.Despite the percolation threshold of the theoretical research report its theory of complex with spheroidal particle as filler as 16%vol about, but actually the percolation threshold of complex is affected very big by the microstructure of filler and polymeric matrix, the typical shape of influence factor's such as filler, particle diameter, or the elastic modelling quantity of matrix and pyrocondensation characteristic etc..Therefore, experiment the percolation threshold of each quasi-nonlinear complex recorded is between 15%vol to 40%vol, and most scholars think that ZnO complex to show its packing volume mark of stable non-linear electric character and need at more than 40%vol.Therefore, before every kind of non-linear complex with pressure-sensitive microsphere as filler puts into application, need first to measure the percolation threshold of this insulation system.

It is contemplated that the problem changed such as matrix or pressure-sensitive microsphere packing property for the percolation threshold of non-linear complex, propose a kind of method speculating complex percolation threshold by numerical computations, thus provide characteristic parameter for the preparation of non-linear complex and the Application Design on High-Voltage Insulation equipment thereof.

Summary of the invention

It is an object of the invention to provide the computational methods of the percolation threshold of pressure-sensitive microsphere in determining non-linear dielectric materials, with the problem solving to propose in above-mentioned background technology.

For achieving the above object, the present invention provides following technical scheme: the computational methods of the percolation threshold of pressure-sensitive microsphere in determining non-linear dielectric materials, comprises the following steps:

(1) generation in insulant overall calculation region

By matlab software for calculation, in given rectangular area, first carry out the generation of Voronoi grid.Voronoi grid is the continuous polygon being made up of the perpendicular bisector connecting two consecutive points straight lines in geometric graphics.For n point (referred to as Voronoi seed) in euclidean plane, plane is divided according to closest principle, each point is associated with its arest neighbors region, Voronoi polygon definition corresponding to each seed points be in this plane all with this seed points distance less than the set with the point of other seed points distance, Voronoi polygon corresponding to all seed points i.e. constitutes corresponding Voronoi grid, as shown in accompanying drawing 1 (a).

In the algorithm using auxiliary seed structure Voronoi seed position, it is critical only that the generation of Voronoi seed.Meeting under conditions of seed falls in given rectangular area, arranging seed according to the position of compact arranged several regular hexagon geometric centers, its basic parameter includes: Voronoi polygon average-size d, unit μm；Horizontal X direction of principal axis polygon average number NX, vertical Y direction polygon average number NY；Seed distribution degree of disorder s, s is the biggest, and the variance of each seed criterion distance position is the biggest, and polygon degree of irregularity is the highest.These parameters need according to depending on the microstructure of pressure-sensitive microsphere and the macro-size of the composite sample preparing gained.After Voronoi seed generates, existing Program Generating Voronoi polygon in available matlab, thus overall zoning is completed the work of subdivision, this region represents insulating material matrix in phantom.

(2) generation of microsphere distribution

In above-mentioned generated zoning, generate the circle of several random distributions according to a certain specific packing material size and volume fraction.These circles represent pressure-sensitive microsphere filler in phantom, it is wanted complete and falls within rectangular area, and the lap between circle not can exceed that 5% (if the most overlapping, then cannot simulate situation about contacting with each other between filler) of its diameter.Circular area summation and the ratio of zoning area are the volume fraction of filler.Therefore the Voronoi polygon in arbitrary circle that falls represents the crystal grain in pressure-sensitive microsphere filler, and the Voronoi polygon outside all circles that falls then represents a division unit of insulating material matrix.

(3) setting of material behavior

The Simulation Calculation that this patent is used, is converted into circuit model by electric field and solves.Polygonal for each Voronoi each limit is represented by it with a most perpendicular linear or nonlinear impedance, and each that the Voronoi seed at each Voronoi polygon center is in circuit calculates node, as shown in accompanying drawing 1 (b).So the emulation of material electrology characteristic can be changed into solving of impedance network response characteristic.It is thus desirable to each limit polygonal to each Voronoi judges, if it falls in a certain circular interior, then it has the attribute of pressure-sensitive microsphere filler；If it falls outside all circles, then it has the attribute of insulant.The characteristic of pressure-sensitive microsphere is mainly arranged according to the special volt-ampere of material or C-V characteristic；And its resistivity can be processed according to definite value by insulant with dielectric constant, but it is intended to consider its breakdown characteristics.And for the higher pressure-sensitive microsphere of filler such as ZnO, SiC of hardness, in addition it is also necessary to consider the contact resistance between granule.

(4) the solving of complex C-V characteristic

After all material featured configuration completes, on circuit network, resistive electricity component characteristic is the most all known quantity.Owing to grid is more, resistance quantity is the hugest, and therefore solving this circuit response characteristic under extrinsic motivated needs to use the nodal method in network graph theory to realize.The C-V characteristic of the most pressure-sensitive microsphere is generally nonlinear, its electrical parameter changes along with the change of applied voltage, therefore the method needing its C-V characteristic is carried out piece-wise linearization and small-signal analysis during calculating, voltage x current state with current circuit derives the electrical parameter of subsequent time nonlinear material, so can be greatly saved the calculating time.

When solving the C-V characteristic of material, the selection of extrinsic motivated is also a problem deserving of attention, is generally divided into the method that applied voltage asks response current and impressed current to seek response voltage.Owing to material has the most non-linear, its change that applied voltage is less when inelastic region can cause the change that response current is huge, thus is unfavorable for taking of data point.If extrinsic motivated is electric current, then can obtain more uniform voltage x current data point, therefore recommend this kind of excitation as circuit to be solved.

(5) determination of complex percolation threshold

The step for mainly by same zoning, generate same particle size scope but under different volumes mark pressure-sensitive microsphere distribution, and solve and obtain its C-V characteristic, measure its percolation threshold by the nonlinear wind vibration of complex along with the situation of change of pressure-sensitive microsphere packing volume mark.It is previously noted that the percolation threshold of complex is typically between volume fraction 15%vol-40%vol, therefore between 10%vol to 50%vol, one can be arranged every 2%vol and measure point, measure the C-V characteristic of complex under this packing volume mark.But under each volume fraction, need repeatedly to generate different random microsphere distributions, reason is: it is that inside compounds occurs a conductive channel carried throughout completely by microsphere that complex reaches the performance the most intuitively of percolation threshold, when packing volume mark is higher, such passage is easier to produce, and even can produce many；But when packing volume mark is near percolation threshold, in relatively limited computer capacity, the probability that such seepage channel occurs is slightly smaller, and owing to the arrangement of microsphere is randomly generated, has the biggest occasionality.The area of zoning can be expanded to reduce the impact of the occasionality of microsphere distribution in order to solve this problem, but so considerably increase amount of calculation.For non-linear complex, electric current always can select a seepage channel the shortest to flow through, and electric current on other passages is relatively small, this explanation is in some region of calculating, if if artificial for this region is divided into stem portion, if this stem portion can be considered as separate, because electric current is simply chosen a certain bar therein and passed through.Therefore new microsphere random distribution can repeatedly be generated for less zoning, and calculate its C-V characteristic, this is equivalent to that a sheet of zoning is divided into several less region and calculates, so can be greatly saved the calculating time, and from analysis above, calculate the biggest region and the effect repeatedly calculating smaller area should be close.Therefore when calculating non-linear complex C-V characteristic under a certain volume fraction, the random distribution of the different microsphere under 10～20 these volume fractions can be generated and calculate its C-V characteristic respectively, finally choosing one of pressure sensitive voltage in these C-V characteristics minimum (nonlinear characteristic occurs the most the earliest) as complex C-V characteristic under this volume fraction.It should be noted that in the generation of the microsphere random distribution of filler each time under each volume fraction, the scope of microspherulite diameter must be fixing, because complex percolation threshold also can be impacted by the scope of microspherulite diameter, need control variable herein.

Under obtaining each volume fraction after the C-V characteristic of non-linear complex, the percolation threshold of complex can be judged according to the feature of these VA characteristic curves.If under a certain volume fraction, have compared with its slightly lower complex of complex pressure sensitive voltage (breakdown voltage) and packing volume score ratio and reduce significantly, and can show typical nonlinear wind vibration than its higher complex of packing volume mark, then this volume fraction i.e. can be considered the percolation threshold of non-linear complex.Additionally can also be by being calculated the current density distributing figure in whole region, in this figure, a paths of highest current density is seepage flow (puncturing) path, if percolation path is substantially made up of pressure-sensitive microsphere under a certain volume fraction, then this volume fraction is the percolation threshold of complex.Two kinds of methods of summary are recommended jointly to determine the percolation threshold of non-linear complex.

Compared with prior art, the invention has the beneficial effects as follows: carry out the method for pressure-sensitive microsphere percolation threshold in simulation calculation measures non-linear complex by matlab software, the percolation threshold of the Practical Calculation non-linear complex of ZnO/ silicone rubber with the pressure-sensitive microsphere of ZnO as filler, the problem changed such as matrix or pressure-sensitive microsphere packing property for the percolation threshold of non-linear complex, a kind of method speculating complex percolation threshold by numerical computations is proposed, thus provide characteristic parameter for the preparation of non-linear complex and the Application Design on High-Voltage Insulation equipment thereof.

Accompanying drawing explanation

Fig. 1 is that Voronoi gridding method emulates non-linear complex volt-ampere spy's structure and Computing Principle schematic diagram；

Fig. 2 is Zinc-oxide piezoresistor crystal boundary area sub-model；

Fig. 3 is the equivalent circuit diagram of Zinc-oxide piezoresistor crystal boundary area sub-model；

Fig. 4 is the non-linear complex of ZnO/ silicone rubber simulation calculation and actual measurement nonlinear wind vibration comparison diagram under different volumes mark；

Fig. 5 is that the non-linear complex of ZnO/ silicone rubber pressure-sensitive (breakdown voltage) that obtains of simulation calculation is with packing volume mark variation diagram；

Fig. 6 is the ZnO/ silicone rubber non-linear complex current density distributing figure when total current reaches 0.1mA and corresponding flow event analysis chart under the different volumes mark that simulation calculation obtains.

Detailed description of the invention

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is clearly and completely described, it is clear that described embodiment is only a part of embodiment of the present invention rather than whole embodiments.Based on the embodiment in the present invention, the every other embodiment that those of ordinary skill in the art are obtained under not making creative work premise, broadly fall into the scope of protection of the invention.

The present invention provides a kind of technical scheme: the computational methods of the percolation threshold of pressure-sensitive microsphere in determining non-linear dielectric materials, comprises the following steps:

(1) generation in insulant overall calculation region

The pressure-sensitive microspherulite diameter of ZnO prepared by laboratory is distributed in 50-150 μm, and crystallite dimension is about 5-8 μm, with the pressure-sensitive microsphere of ZnO as filler, silicone rubber be composite sample thickness prepared by insulating material matrix be 0.5mm, radius 1cm.In order to have preferable contrast relationship with experiment, the generation in zoning matches with actual experiment with in terms of setting as far as possible.Several basic parameters of structure Voronoi grid: Voronoi polygon average-size d, can set according to the equal crystallite dimension of product of actual pressure-sensitive microsphere, i.e. d=7 μm；Vertically Y direction of principal axis Voronoi polygon average number NY, this parameter determines the width of zoning, this width should be close with the sample of the non-linear complex of preparation, thickness of sample is 0.5mm, and average grain size is 7 μm, therefore vertical direction Voronoi polygon number N Y=70；Horizontal X direction of principal axis polygon average number NX, this parameter determines the length of zoning, in theory should be equal with sample diameter, but such amount of calculation is the biggest, can suitably reduce zoning length and substitute with the method repeatedly calculated, therefore set horizontal direction polygon number N X=400.For unevenness s of seed distribution, in the seed obtained when test of many times arranges s=0.7 is distributed microsphere pressure-sensitive under Electronic Speculum, grain size distribution is the most similar, according to above-mentioned parameter, i.e. may make up the Voronoi grid in overall calculation region.

(2) generation of microsphere distribution

In above-mentioned generated zoning, a diameter of 60-80 μm of microsphere is set, and in the volume fraction range of 5%vol-50%vol, generates the filler distribution of the pressure-sensitive microsphere of ZnO every two volume fraction percentage points.

(3) setting of material behavior

First, the setting of microsphere packing property pressure-sensitive for ZnO: at present, the complete crystal boundary of ZnO varistor that scholars generally acknowledge with circuit model as shown in accompanying drawing 2 and Fig. 3, the impedance that during wherein RIL is crystal boundary subregion, the thick intergranular phase region of type-A is corresponding, RGA1, RGA2 is the resistance of left and right sides ZnO die portions corresponding to this region, RDB is the nonlinear resistance that double Schottky barrier districts of B type in crystal boundary subregion are corresponding, RGB1, RGB2 is the resistance of left and right sides ZnO die portions corresponding to this region, RGC1, RGC2 is the resistance of the left and right sides ZnO die portions that the direct contact area of C type crystal grain is corresponding.Owing to the electric capacity of double Schottky barrier parts occupies mastery reaction in ZnO varistor, the effect of other parts electric capacity is negligible in contrast, therefore only only accounts for the electric capacity CDB of double Schottky barrier part in above-mentioned model.

It can be seen that ZnO varistor is non-linear essentially from the grain boundary portion between crystal grain, and crystal grain itself can process according to fixed value resistance.Additionally, it is nonlinear pair of Schottky barrier district the most entirely between neighboring die, may also have direct contact area (can be considered shorting region) and Hou Jingjian district (can be considered high resistance area) of very small part, these two parts can be randomly distributed in crystal boundary according to a certain percentage in the calculation, it is also possible to ignores.When arranging the nonlinear characteristic of grain boundary portion, mainly fill, based on electric charge, the ZnO varistor crystal boundary electrical conduction model that surface state causes barrier height to reduce carry out zoning B crystal boundary C-V characteristic, as shown in formula (1) according to use that Blatter and Greuter propose.

$\{\begin{array}{c}{R}_{DB}=V/(J\×S)\\ J\left(V\right)=A^{*}{T}^2\exp \left(\frac{{\mathrm{e\Φ}}_B\left(V\right)+{\mathrm{\ϵ}}_{\mathrm{\ξ}}}{k_{B}T}\exp \right(-\frac{eV}{k_{B}T})-\frac{{\mathrm{e\Φ}}_B\left(V\right)+{\mathrm{\ϵ}}_{\mathrm{\ξ}}}{k_{B}T})\\ {\mathrm{\Φ}}_B=\frac{V_c}{4}{(1-\frac{V}{V_c})}^2\\ V_c=Q_i^2/\left(2{\mathrm{e\ϵ}}_0{\mathrm{\ϵN}}_i\right)\\ Q_i=e{\∫}_{{\mathrm{\ξ}}_i^n}^{\mathrm{\∞}}{N}_i\left(E\right)f_i\left(E\right)dE\\ f_i\left(E\right)=\frac{1}{1+\exp \left(\right(E-{\mathrm{\ξ}}_i)/k_{B}T)}\\ {\mathrm{\ξ}}_i=\mathrm{\ξ}-k_{B}T\ln \frac{2}{1+\exp (-eV/k_{B}T)}\end{array}---\left(1\right)$

Wherein, R_DBFor double Schottky barrier resistance；V is the applying voltage on double Schottky barrier；J is the electric current density flowing through double Schottky barriers that area is S；Φ_BIt it is barrier height under different applying voltage；Q_iIt is that crystal boundary intrinsic surface states fills charge density under difference applies voltage；V_cIt is an intermediate variable, there is no the meaning of reality；N_i(E) it is energy distribution function, have employed the function of impact distributional pattern: N the most in the calculation_i(E)=N_i*δ(E-E_i)；f_i(E) being Fermi distribution function, E is energy level；ξ is fermi level；ξ_iQuasi-Fermi level, its fermi level offset along with executing alive change after numerical value, ξ_inIt is neutral state lower surface state fermi level ε_ξIt is conduction level E_cEnergy level difference with fermi level ξ；A* is Jason Richardson (Richardson) constant；k_BIt it is baud the most graceful (Boltzman) constant；T is absolute temperature；E is electron charge；ε₀It it is permittivity of vacuum；ε is the relative dielectric constant of ZnO.

Being 3V by solve above formula i.e. can get pressure sensitive voltage, nonlinear factor, at the nonlinear wind vibration of crystal boundary of about 20, is dynamic electric resistor R_DBElement characteristic.And crystal boundary electric capacity C_DBProcess according to constant value.Now, in accompanying drawing 3, the element characteristic in circuit model obtains the most, and each red limit within the microsphere in accompanying drawing 1 (c) all represents such a circuit model.

And at the aspect that arranges of insulant, it can be arranged with dielectric constant according to silicone rubber electrical conductivity at normal temperatures, the two parameter is all constant.But at packing volume mark close in the non-linear complex of percolation threshold, insulant thin layer is had in the middle of adjacent two pressure-sensitive microspheres not being in close contact, as shown in accompanying drawing 1 (e), such thin layer is easy to breakdown, therefore also need to consider the breakdown characteristics of silicone rubber, as shown in formula (2), wherein E_brkBreakdown voltage for silicone rubber.Each white edge in accompanying drawing 1 (c) all represents such circuit characteristic.

$\{\begin{array}{cc}\mathrm{\&sigma;}={\mathrm{\&sigma;}}_1={10}^{12}\mathrm{\&Omega;}\&CenterDot;m& E<E_{brk}\\ \mathrm{\&sigma;}={\mathrm{\&sigma;}}_2=1\mathrm{\&Omega;}\&CenterDot;m& E\&GreaterEqual;E_{brk}\end{array}---\left(2\right)$

It addition, the contact resistance R that it is also contemplated that between the pressure-sensitive microsphere of ZnO of adjacent two contacts_c, it together can calculate with the volume resistance of microsphere, and the two addition is designated as apparent resistance ρ_a, shown in its computing formula such as formula (3).

$\frac{\mathrm{\&rho;}}{{\mathrm{\&rho;}}_a}=\frac{2}{\mathrm{\&pi;}{\left({\mathrm{\&pi;\&epsiv;}}_0{A}_{V}B\right)}^{1/5}{E_a}^{2/5}}---\left(3\right)$

Wherein E_aFor loading the average field-strength in composite sample；A_VFor constant, it is usual value 1.28 for the grit that contact angle is less；B is a physical quantity relevant with Poisson's coefficient υ to filler particles Young's modulus Y, B=3 (1-υ²)/4Y。

Contact resistance behavior shown in formula (3) is represent for the red limit of adjacent position in the microsphere of two close contacts in accompanying drawing 1 (c) (d).

(4) the solving of complex C-V characteristic

Voltage and current parameter and element characteristic being written as coefficient matrix form, is solved by nodal method, utilize piece-wise linearization to process the nonlinear problem in circuit with the method for small-signal analysis, concrete solution procedure is omitted.Extraneous power supply excitation uses current source, provides the current excitation of exponentially uniform increments from 1nA to 0.1mA.

(5) determination of complex percolation threshold

In 5%vol-50%vol scope, choose one every 2%vol measure point, calculate the nonlinear wind vibration of the ZnO non-linear complex of pressure-sensitive microsphere/silicone rubber, calculate 20 times under each volume fraction, take pressure sensitive voltage (breakdown voltage) minimum once as final result of calculation.For inspection result of calculation, test and prepare 47%vol, the composite sample of 43%vol, 39%vol, 35%vol, 30%vol, and measure its nonlinear wind vibration, compare with simulation result, as shown in Figure 3.The C-V characteristic testing the 35%-47%vol complex recorded as seen from the figure is the most identical with simulation result, and 30%vol complex does not embody nonlinear characteristic, and breakdown voltage is the highest, beyond the maximum output of experiment power supply, embody the most in the drawings.Being recorded 30%vol sample breakdown voltage by the special equipment measuring breakdown voltage afterwards is 5kV/mm, also close with simulation result, thus demonstrates the accuracy of Simulation Calculation.Being obtained pressure-sensitive (puncturing) voltage of non-linear complex along with the change of packing volume mark as shown in Figure 4 by simulation calculation, wherein red line is simulation result, and black line is experimental result.There is saltus step in complex pressure-sensitive (puncturing) voltage as seen from the figure at 33%vol, and packing volume mark can show typical nonlinear characteristic at more than 33%vol in being understood complex by accompanying drawing 3, such as the C-V characteristic of the complex of 35%vol-47%vol, therefore complex percolation threshold can be identified as 33%vol.

It addition, the computational methods proposed by this patent, it is also possible to obtain seepage flow (puncturing) path of non-linear complex, as shown in Figure 5, figure is to flow through the current density distributing figure when total current of complex reaches 0.1mA.In figure, the polygonal color of each Voronoi represents the electric current density size flowing through it, and color is the deepest then represents that electric current density is the highest.Introduction above is mentioned, complex forms seepage flow path after current and the shortest paths of selection can be concentrated to flow through, electric current elsewhere is the least, therefore packing volume mark CURRENT DISTRIBUTION in more than 33%vol complex only has a dark path running through head and the tail, it is the most all light grey, and this dark path is the conductive path of complex.Accompanying drawing 5 have chosen the more typical distribution situation of ratio in seepage flow (puncturing) path under each volume fraction, its can explain pressure-sensitive (puncturing) voltage of complex shown in accompanying drawing 4 along with the situation of change of packing volume mark: for when in complex, packing volume mark is relatively low, such as 5%vol complex, its breakdown path develops mainly along insulant, generation with electricity tree is quite similar with development, therefore its breakdown voltage is higher, and breakdown path is affected the least by pressure-sensitive microsphere filler.When composite body fraction is slightly higher such as the situation of 15%vol, the existence of microsphere filler enough produces certain impact to the breakdown path of complex, now these microsphere fillers can produce guiding function to breakdown path, this is owing to pressure-sensitive microsphere is less at inelastic region resistance, electric current can select to flow through these and nonlinear pressure-sensitive microsphere occurs, and therefore the breakdown voltage of complex also decreases.During packing volume mark raises from 15%vol to 30%vol, breakdown path distribution all along microsphere filler substantially develops downwards, and path ratio is more tortuous, also having more thicker silicone rubber gap between microsphere filler, therefore breakdown voltage is the biggest.But being as the increase of packing volume mark, the gap between microsphere filler slowly tails off thinning, and therefore breakdown voltage persistently reduces.After packing volume mark reaches 33%vol, substantially can form the seepage channel running through head and the tail formed by microsphere in complex, breakdown path now is the conductive path of complex.Even if some silicone rubber gap is the thinnest between microsphere, applied voltage these thin layers more slightly higher will puncture and complex entirety can show typical nonlinear characteristic, but it is not puncturing of minor insulation material thin-layer results in insulation breakdown herein and such recoverable when puncturing in the preferable insulating body of mobility is such as silicone rubber.Now, owing to conductive path is made up of pressure-sensitive microsphere substantially, the breakdown voltage of material is greatly reduced, and the change across the order of magnitude occurs.Hereafter, when in complex, packing volume mark is on 33%vol, complex can show the nonlinear characteristic of standard, or can have nonlinear characteristic after locally occurring lesser degree of insulation sub-layers to puncture.When packing volume mark reaches 38%vol, the silicone rubber thin layer in conductive path has been wholly absent, and now the breakdown voltage of complex can be described as pressure sensitive voltage.And conductive path slowly becomes more straight in the complex from 38%vol to 47%vol, therefore pressure sensitive voltage also gradually reduces, and arrive 47%vol time complex pressure sensitive voltage basicly stable.Obviously from the analysis to flow event, it is possible to obtain the conclusion that percolation threshold is 33%vol of complex more intuitively.

Although the present invention being described in detail with reference to previous embodiment; for a person skilled in the art; technical scheme described in foregoing embodiments still can be modified by it; or wherein portion of techniques feature is carried out equivalent; all within the spirit and principles in the present invention; the any modification, equivalent substitution and improvement etc. made, should be included within the scope of the present invention.

Claims (5)

1. the computational methods of the percolation threshold of pressure-sensitive microsphere in determining non-linear dielectric materials, it is characterised in that: Comprise the following steps:

(1), the generation in insulant overall calculation region: by matlab software for calculation, it is first determined meter Calculation region, and in zoning, carry out the generation of Voronoi grid, according to the microstructure of pressure-sensitive microsphere With the macro-size of the composite sample preparing gained, fall in given rectangular area meeting Voronoi seed Under conditions of Nei, arranging seed according to the position of compact arranged several regular hexagon geometric centers, it is basic Parameter includes: Voronoi polygon average-size d, unit μm；Horizontal X direction of principal axis polygon average Mesh NX, vertical Y direction polygon average number NY；Seed distribution degree of disorder s, at Voronoi seed After generation, with Program Generating Voronoi polygon existing in matlab, complete overall zoning Subdivision, this region represents insulating material matrix in phantom；

(2), the generation of microsphere distribution: in above-mentioned generated zoning, specifically fill out according to a certain Material particle diameter and volume fraction generate the circle of several random distributions, and described circle represents pressure in phantom Quick microsphere filler, it wants complete falling within rectangular area, and the lap between circle can not surpass Crossing the 5% of its diameter, circular area summation and the ratio of zoning area are the volume fraction of filler, The Voronoi polygon in arbitrary circle that falls represents the crystal grain in pressure-sensitive microsphere filler, and falls at all circles Voronoi polygon outside shape then represents a division unit of insulating material matrix；

(3), the setting of material behavior: by polygonal for each Voronoi each edge with geometrically Perpendicular linear or nonlinear impedance represents, and each Voronoi polygon center Voronoi seed be in circuit each calculate node, the emulation of material electrology characteristic will change into impedance Solving of network response characteristic, each limit polygonal to Voronoi each in zoning judges, If it falls in a certain circular interior, then it has the attribute of pressure-sensitive microsphere filler；If its fall all circles it Outward, then it has the attribute of insulant；

(4), the solving of complex C-V characteristic: write voltage x current and element characteristic as coefficient matrix and lead to Cross nodal method to solve this circuit, the method processing nonlinear circuit with small-signal analysis etc. with piece-wise linearization Realize quickly solving；

(5), the determination of complex percolation threshold: by same zoning, generate same particle size model Enclose but pressure-sensitive microsphere distribution under different volumes mark, and solve and obtain its C-V characteristic, by complex Nonlinear wind vibration measures its percolation threshold along with the situation of change of pressure-sensitive microsphere packing volume mark, with Time by being calculated the current density distributing figure in whole region, a paths of highest current density in this figure Be percolation path, if percolation path is substantially made up of pressure-sensitive microsphere under a certain volume fraction, then this Volume fraction is the percolation threshold of complex, and comprehensive the two method determines non-linear complex jointly Percolation threshold.

The most according to claim 1 determine non-linear dielectric materials in the meter of percolation threshold of pressure-sensitive microsphere Calculation method, it is characterised in that: in step (3), the characteristic of described pressure-sensitive microsphere is mainly special according to material Volt-ampere or C-V characteristic are arranged, for insulant, by its resistivity and dielectric constant according to definite value at Reason, considers its breakdown characteristics simultaneously, and for the higher filler of hardness, its resistivity is pressed with dielectric constant Process according to definite value, consider the contact resistance between granule simultaneously.

The most according to claim 2 determine non-linear dielectric materials in the meter of percolation threshold of pressure-sensitive microsphere Calculation method, it is characterised in that: the filler that described hardness is higher includes the pressure-sensitive microsphere of ZnO or the pressure-sensitive microsphere of SiC.

The most according to claim 1 determine non-linear dielectric materials in the meter of percolation threshold of pressure-sensitive microsphere Calculation method, it is characterised in that: in step (4), described solving circuit uses exponentially uniform increments Current source is as excitation.

The most according to claim 1 determine non-linear dielectric materials in the meter of percolation threshold of pressure-sensitive microsphere Calculation method, it is characterised in that: in step (5), arrange every 2%vol between 10%vol～50%vol Measure point for one, under each volume fraction, generate random distribution the difference of 10～20 different microspheres Calculate its C-V characteristic, finally choose one that in these C-V characteristics, pressure sensitive voltage is minimum and exist as complex C-V characteristic under this volume fraction.