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CN100544874C - Electrochemical corrosion processing method with micro fine cylindrical group electrode - Google Patents

Electrochemical corrosion processing method with micro fine cylindrical group electrode Download PDF

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CN100544874C
CN100544874C CNB2006100968516A CN200610096851A CN100544874C CN 100544874 C CN100544874 C CN 100544874C CN B2006100968516 A CNB2006100968516 A CN B2006100968516A CN 200610096851 A CN200610096851 A CN 200610096851A CN 100544874 C CN100544874 C CN 100544874C
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electrode
group
processing
blank
electrochemical corrosion
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CN1943950A (en
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朱荻
王磊
曲宁松
王明环
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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Abstract

The present invention relates to a kind of electrochemical corrosion processing method with micro fine cylindrical group electrode, belong to the Electrolyzed Processing field.This method may further comprise the steps: (1) adopts Wire EDM or the making of little milling process to have a plurality of unipolar group's electrode blanks; (2) adopt FInite Element, design, making electrochemical corrosion tool cathode; (3) group's electrode blank immerses in the electrolyte as the electrochemical corrosion anode, makes that each single-column body is in below the liquid level fully on the blank; With the vertical in opposite directions parallel placement of electrochemical corrosion cathode and anode; (4) energising is carried out electrochemical corrosion processing to group's electrode blank, adopts constant voltage processing and charge method to control the shape and the processing dimension of group electrode respectively.Method of the present invention has process equipment and control mode is simple, working (machining) efficiency, crudy height, the characteristics of low cost of manufacture.

Description

Electrochemical corrosion processing method with micro fine cylindrical group electrode
Technical field
Electrochemical corrosion processing method with micro fine cylindrical group electrode of the present invention belongs to technical field of electrolysis processing.
Background technology
Fine array group hole has a wide range of applications in fields such as Aero-Space, precision instrument, chemical fibres as a kind of typical fine structure, as high-speed printer nozzle plate, the joints of optical fibre, chemical fibre spinneret, microfiltration net and electron microscope grating etc.For the processing of fine group's pore structure, fine electric machining has no mechanical cutting force effect with respect to conventional drilling processing, machining accuracy and working (machining) efficiency height, advantage such as can on low rigidity workpiece such as thin-walled, elastic component, process, so it is being with a wide range of applications aspect processing of fine group's pore structure.The processing of micro fine cylindrical group electrode is the key link that realizes the fine electric machining of group's pore structure.Micro fine cylindrical group electrode is meant by size combines formed overall electrode at a plurality of cylinder electrodes of micron to nano grade, can be used as the tool-electrode in fine electric spark, the micro-electrochemical machining processing; Simultaneously fine group's cylinder class part also is the important composition parts of micromachine and MEMS.
The processing method of common metal micro fine cylindrical group electrode comprises LIGA and accurate LIGA technology, anti-processing method, the porous alumina formwork method etc. copied of fine electric spark.Adopt the technological process of the fine group of LIGA fabrication techniques electrode mainly to comprise steps such as gluing-X ray degree of depth photoetching-development-little electrotyping forming-remove photoresist, fine group's electrode of making has advantages such as precision height, depth-to-width ratio are big, but because the LIGA technology adopts electroforming process, the electrode that can not prepare tungsten, Hardmetal materials, this Technology Need synchrotron radiation light source and special mask plate simultaneously, cost is high; Adopting the principle of the fine group of fine electric spark backcopy process processing electrode is at first to utilize line electrode electric spark grinding (WEDG) technology to process simple single cylindrical electrode; The movement locus of control electrode then, the target (sheet metal) of commute processing carries out fine electric spark perforation processing, in process, cylinder electrode is simultaneously rotated, one side feeding processing, use less discharge energy,, thereby on target, process the array microcellular structure so that can carry out stable discharge processing; Utilize target as tool-electrode at last, counter copying processes fine group electrode on cube electrode, but electric spark backcopy process equipment complexity, working (machining) efficiency are low, and there is the heat affected area in processing, and finished surface easily produces metamorphic layer and micro-crack; The alumina formwork method utilizes Woelm Alumina to be original mold, utilize dc electrodeposition metal preparation group electrode, the method relates generally to the processing of nano-scale group electrode, only be applicable to that the electrochemistry of solids kinetic parameter is measured and trace materials detects, be difficult to be applied in the microfabrication as tool-electrode.
Electrolyzed Processing is to utilize the electrochemistry anodic solution of metal in electrolyte to work the work piece into shape.In electrochemical machining process, the workpiece anode metal constantly loses electronics to be become ion and enters in the middle of the solution, the minimizing process of workpiece material is carried out with ionic species, because the size of metal ion is very small, so this micro dissolution removing method of Electrolyzed Processing is fit to the processing of fine structure very much.Simultaneously Electrolyzed Processing also has and not limited by material mechanical performance, process velocity is fast, can reach good surface roughness, there are not internal stress, distortion and burr, advantages such as cathode tool is lossless, it is significant to the high efficiency, the high-precision stable processing that realize fine group's pore structure therefore to utilize Electrolyzed Processing to prepare micro fine cylindrical group electrode.
Summary of the invention
The objective of the invention is at deficiencies such as the technological process complexity, manufacturing cost height, the crudy that exist in present fine group's method for making its electrode are low, a kind of high working (machining) efficiency, low manufacturing cost are provided, have processing method than the fine group of high-aspect-ratio electrode.
A kind of fine group's electrode electro Chemical corrosion processing method is characterized in that may further comprise the steps:
(1), according to required single micro fine cylindrical group electrode design group electrode blank dimensional parameters, the single electrode cross sectional shape is square on group's electrode blank, wherein single electrode blank length of side d 〉=2R or d 〉=3R, R is for processing single electrode diameter afterwards; Group's electrode blank length L, adjacent single electrode space D and single electrode height h 0Consistent with required single micro fine cylindrical group electrode dimensional parameters;
(2), by requirement of last step processing group electrode blank;
(3), make the electrochemistry tool cathode, wherein tool cathode is tabular, one side surface has the semicolumn boss, tool cathode major parameter cathode length S, first cylinder boss radius r of negative electrode, cathode and anode spacing f adopt the finite element method optimal design of electrochemical corrosion processing electric field to obtain, and guarantee that the current density on the electrochemical corrosion workpiece anode evenly distributes;
(4), with group's electrode blank as electrochemical corrosion workpiece anode, electrochemical corrosion adds man-hour, in electrolytic cell, tool cathode is fixed on the positioning fixture, by the position between numerical control table, NC table adjusting the two poles of the earth, make that the vertical in opposite directions parallel placement spacing of anode and cathode is f, by the feeding of machine tool chief axis, be h with the degree of depth in group's electrode blank immersion electrolyte 0, make that each single cylinder is in below the liquid level fully on the blank;
(5) energising, group's electrode blank is carried out electrochemical corrosion processing, adopt the shape of constant voltage machining control group electrode forming, and the size difference of group's electrode blank, making group electrode forming is that columniform machining voltage value also changes, for the group electrode blank of single electrode blank length of side d below 500 μ m, make it to be configured as columniform voltage usually in 2~8V scope, can determine this magnitude of voltage by the test of many times method: the less voltage of the initial employing of test, when voltage hour, electrode is thin coniform of root thick end, after boosted voltage value progressively, the tapering of electrode will reduce gradually, and during overtension, electrode is the thick spindle shape in the thin end of root, can finally determine the machining voltage of cylindrical electrode;
(6) adopt charge method control group electrode processing dimension, the required electric weight of micro fine cylindrical group electrode of processing certain diameter is Q 0 = 10 k ( d 2 - 1 4 π R 2 ) h 0 + 2 hL 3 ( d - R ) ,
In the formula: Q 0---processing electric weight (C);
K----volume electrochemical equivalent (cm 3/ (Ah));
h 0----group electrode blank immerses the degree of depth (cm) in the electrolyte;
H----electrolyte is along electrode blank surface lifting height (cm);
The d----single electrode blank length of side (cm);
R----processes back single electrode diameter (cm);
L----group's electrode length (cm);
In the process, gather processing electric current, by the electric weight that is passed through in the current value calculating processing process of gathering, promptly by data collecting card (8) Q = Σ i = 0 n I i Δt ,
In the formula: the actual processing of Q---electric weight;
I iThe current value of the collection in---each sampling time;
The Δ t---sampling time;
Work as Q=Q 0The time, the cutter lifting that cuts off the power supply machines.
Process principle
1. group's electrode shape control
Electrochemical corrosion processing is to utilize the electrochemistry anodic solution of metal in electrolyte to work the work piece into shape.With processing tungsten material group electrode is example explanation electrode moulding process, as shown in Figure 5.Connect dc source, beginning electrochemical corrosion processing anode metal becomes constantly that ion enters in the solution and dissolving gradually has gas to separate out on the negative electrode simultaneously, and its electro-chemical reaction equations is as follows:
Negative electrode 6H 2O+6e -→ 3H 2↑+6OH -
Anode W+8OH -→ WO 4 2-+ 4H 2O+6e -
The diffusion layer that anode surface forms in the original geometric form of anode and the reaction all can influence the shape of anode final molding, is referred to as geometric effect and diffusion layer effect respectively.In the anodic dissolution processes, geometric effect makes that the dissolving metal speed of anode curvature larger part is very fast, thereby causes the dissolution velocity of group electrode tip faster than root, therefore group electrode is had and is the thin cone shape trend of root thick end; The diffusion layer effect is to dissolve formed WO by anode metal 4 2-The migration and the diffusion motion of ion are caused, the WO of surface aggregation 4 2-Ion moves down along anode surface under the effect of gravity, thereby forms the diffusion layer of one deck upper-thin-lower-thick, the WO that the part of diffusion bed thickness produces 4 2-Ion is difficult to be diffused in the solution go more, causes this position electrochemical reaction rates slack-off, so the diffusion layer effect has and makes group electrode be the thick fusoid trend in the thin end of root.In group's electrode preparation, correctly control machined parameters, make the geometric effect of anodic solution with the mutual balance of the influence of diffusion layer effect, can prepare the uniform cylindrical group electrode of diameter.The shape of group's electrode can realize by the mode of control machining voltage and electric current.Along with the carrying out of electrochemical corrosion, anode metal constantly dissolves, and working (finishing) area reduces gradually, and the processing dimension in the process is measured very difficulty, therefore adopts the mode of keeping constant current density by direct control processing electric current to be difficult to realize; When adopting the constant voltage processing mode, the ever-reduced while of working (finishing) area, electric current between the cathode and anode is along with the carrying out of processing also constantly reduces, and machining voltage itself has just determined the formation of electrode reaction speed and diffusion layer, and certain machining voltage correspondence specific thickness of diffusion layer.Therefore, the mode of this method employing control machining voltage realizes the control to electrode shape.
2. group's electrode size control
The volume delta v of anode dissolved substances is directly proportional with the electric weight Q that passes through in the electrochemical corrosion course, by the electric weight that flows through between the control cathode and anode, just can control the ablation amount of anode metal in the electrochemical reaction, thereby realize control group's electrode processing dimension.Group's electrode volume ablation amount computation model as shown in Figure 6.The degree of depth h of the vertical immersed in liquid level of group's electrode blank 0Because surface tension effects, electrolyte can (record by test along electrode blank surface rising certain height h, when group's electrode blank immerses the electrolyte certain depth, the height that electrolyte rises along electrode blank surface is certain), this part will be corroded into parabolic type adding man-hour, and its volume ablation amount Δ v comprises the volume Δ v of liquid level with the bottom electrode dissolving 1With the volume Δ v of liquid level with the top electrode dissolving 2Two parts thus can be under the constant voltage processing conditions, and the micro fine cylindrical group electrode processing dimension with the pass of electric weight Q is: (formula is applicable to that all shapes are similar to group's electrode blank shown in Figure 3)
10 k ( d 2 - 1 4 π R 2 ) h 0 + 2 hl 3 ( d - R ) = Q 0
In the formula: k----volume electrochemical equivalent (cm 3/ (Ah));
h 0----group electrode immerses the electrolyte degree of depth (cm);
H----electrolyte is along electrode blank surface lifting height (cm);
The d----single electrode blank length of side (cm);
R----processes back single electrode diameter (cm);
L----group's electrode length (cm);
Q 0---processing electric weight (C).
Data collecting card 11 is constantly gathered the processing electric current value of process and is sent into computer 12, and computer program is according to the current value I of sampling time Δ t and the collection in each sampling time iCalculate the electric weight Q that is passed through in group's electrode processing process, promptly Q = Σ i = 0 n I i Δt , According to the size computation model, can calculate under certain processing dimension the electric weight Q that should pass through between the cathode and anode 0When the electric weight that passes through between the cathode and anode that computer obtains according to the current value of gathering reaches calculated value, i.e. Q=Q 0The time, the outage cutter lifting machines.
3. electrochemical corrosion tool cathode design
According to faraday's electrolysis processing law, the dissolution velocity of anode metal is directly proportional with current density on it.Thereby in the electrochemical corrosion process of group's cylinder, the current density Uniformity of Distribution has directly determined the uniformity of the single cylinder size in processing back on each cylinder of group's cylinder.For preparing group's cylinder of diameter unanimity, in process, the current density on each cylinder of group cylinder is evenly distributed.According to the electroform theory, the electric field problem that Electrolyzed Processing negative electrode designing institute relates to is to satisfy the steady electric field of Laplace equation, and the shaped design of negative electrode can be found the solution by the anti-border issue of Laplace equation in the electric field and obtain.In electrochemical corrosion processing, be full of electrolyte between the cathode and anode, the anode surface electrical conductivity of electrolyte everywhere is roughly the same, and like this, the electric field between electrochemical corrosion yin, yang the two poles of the earth just can be regarded the steady electric field in the conducting medium as.In group's electrode electro Chemical corrosion processing process, the shape of negative electrode and position have directly determined the anode surface electric current distribution, thereby have determined the uniformity of single cylinder dimensions on the group's electrode of processing back.Prove that according to a large amount of processing experiments if adopt the cylinder negative electrode, the rule strong in the middle of then the anode surface current density is, that both sides are weak distributes, the rule that single cylinder dimensions is thin by the centre, both sides are thick on the group's electrode that processes changes; And when negative electrode adopted plate electrode in the processing, the rule weak in the middle of the anode surface current density is, that both sides are strong distributed, and the rule that single cylinder dimensions is thick by the centre, both sides are thin on the group's electrode that processes changes.Therefore negative electrode is designed to shape shown in Figure 4, the anode surface current density is evenly distributed.The two-dimensional closed zone that will go out with the cathode and anode boundary formation is as finite element electrochemical corrosion analysis of electric field physical model, by the Electric Field Distribution in the finite element analysis computation group electrode electro Chemical corrosion processing process.After negative electrode is designed to as shown in Figure 4 shape, influence between the size r of cathode shape and S and the cathode and anode is the conforming decision influence factor of anode surface electric current distribution apart from f, therefore with parameter r, S and f design variable as cathode shape optimal design problem, the difference of maximum current density value and minimum electrical current density value as object function, is calculated the parameter that can obtain making anode surface electric current distribution unanimity by finite element optimization.
Method of the present invention has following characteristics: 1, copy for the process technology with respect to LIGA, fine electric spark are counter, the inventive method is owing to adopt the electrochemical corrosion processing technology, technological process is greatly simplified, and the working (machining) efficiency and the crudy of fine group's electrode have been improved, the inventive method combines the advantage of fine electric spark line cutting simultaneously, is easy to realize the processing of high depth-to-width ratio micro cylindrical group electrode; 2, in the electrochemical corrosion processing, the shape of negative electrode and position have directly determined the shape of anode moulding, the inventive method adopts the negative electrode through the FInite Element optimal design, has simplified the negative electrode design process greatly, processes the consistent micro fine cylindrical group electrode of diameter distribution; 3, the inventive method realizes that by accumulative total electric weight in control machining voltage and the process operation is simple to the control of the shape and size size of group's electrode; 4, owing to adopt the quiet liquid processing of electrochemical corrosion, need not the electrolyte circulation system in the conventional electrolysis processing, processing unit (plant) is simple; 5, the inventive method can be processed multiple metal material, and as carbide alloy, tungsten, stainless steel etc., the group's electrode blank material according to different adopts different electrolyte, and adaptability is extremely wide.
Description of drawings
Fig. 1 is fine group's electrode electro Chemical erosion machine overall structure schematic diagram.
Fig. 2 is a group electrode electro Chemical corrosion processing schematic diagram.
Fig. 3 is a group electrode blank schematic diagram.
Fig. 4 is an electrochemical corrosion negative electrode design diagram.
Fig. 5 is a group electrode process schematic diagram.
Fig. 6 is a group electrode volume ablation amount computation model.
Fig. 7 is an electrochemical corrosion processing back fine group electrode schematic diagram.
Fig. 8 is the software flow pattern of finite element method analysis method design negative electrode parameter.
Number in the figure title: 1, Z spindle motor, 2, machine body, 3, the Z axle, 4, anode sectional fixture, 5, electrolytic bath, 6, electrolyte, 7, negative electrode sectional fixture, 8, the workpiece anode, 9, tool cathode, 10, ammeter, 11, data collecting card, 12, computer, 13, numerical control table, NC table, 14, dc source, 15, diffusion layer, 16, metal cation.
The specific embodiment
As shown in Figure 1, micro fine cylindrical group electrode electrochemical corrosion processing comprise machine body 2, numerical control table, NC table 13, z axle 3 can realize carry out on the Digit Control Machine Tool that Three Degree Of Freedom moves; The electrochemical corrosion system of processing is by the electrolytic bath 5 that is installed on the numerical control table, NC table 13, be fixed on tool cathode 9 in the electrolytic bath by negative electrode sectional fixture 7, immerse workpiece anode 8 in the electrolyte by anode sectional fixture 4, and ammeter 10, data collecting card 11, computer 12, dc source 14 are formed.
By the mobile adjustment workpiece anode 8 of numerical control table, NC table 13 and the relative position between the tool cathode 9, make it reach the state of desired design, the degree of depth that workpiece anode 9 immerses electrolyte is controlled by moving up and down of Z axle 3, computer 12 is gathered the processing electric current value by data collecting card 11, by specific programme-control group electrode processing dimension size.As shown in Figure 2, in the electrochemical corrosion process, workpiece anode 8 and the parallel in opposite directions placement of tool cathode 9.
Group's electrode blank shown in Figure 3 is to adopt the Wire EDM processes to form, owing to adopt wire cutting technology, single electrode cross sectional shape is a square on it, and in electrochemical corrosion course, anode cusped edge sharp corner power line is concentrated, the current density height, and ablation is very fast, thereby group electrode blank finally can be corroded into cylindrical, as shown in Figure 7.The formed diffusion layer of cation has then influenced unipolar cylindricity on group's electrode in group's electrode process, as shown in Figure 5.
Below in conjunction with Fig. 1, Fig. 2, Fig. 3 and Fig. 4 method of the present invention is described, this example is processing tungsten material group electrode.Implementation process is passed through following step successively:
1. with reference to figure 3, adopt Wire EDM technology to make and have a plurality of unipolar group's electrode blanks.Blank has 10 single electrodes, and length L is 9.3mm, and the single electrode cross sectional shape on it is a square, and length of side d is 300 μ m.;
2. with reference to figure 4, adopt the tool cathode shape of FInite Element design electrochemical corrosion, influencing between the size r of cathode shape and S and the cathode and anode is the conforming decision influence factor of anode surface electric current distribution apart from f, therefore with parameter r, S and the f design variable as cathode shape optimal design problem.Investigate the uniformity that current density distributes at anode surface by the current density value that compares group's electrode blank single electrode cusped edge sharp corner node, with the difference of maximum current density value and minimum electrical current density value as object function, adopt the single order optimization method of ansys software, change the value of design variable in each iteration, along with reducing of target function value, the current density difference of then selected anode node is also just more little, and the distribution of current density at the selected node place is tending towards even more.Group's electrode blank corresponding shown in Figure 3, its optimal size parameter is:
Figure C20061009685100111
3. with reference to figure 1, the electrochemical corrosion processing cathode fixture of being made by epoxy resin 7 is placed in the electrolytic bath 5, and with the tool cathode cathode fixture of packing into, electrolytic bath 5 is fixed on the numerical control of machine tools workbench 3.With anode clamp 4 anode clusters electrode blank 8 is clamped, be fed down to suitable position by Z axle 3;
4. with reference to figure 1 and Fig. 2, X, the y-axis shift of adjusting numerical control table, NC table 3 are moving, make between the cathode and anode in accordance with regulations apart from parallel in opposite directions placement, spacing is 30.8mm, to be full of electrolyte in the electrolytic cell 5, regulate moving up and down of Z axle 3, make workpiece anode 8 immerse the following degree of depth of electrolysis liquid surface and reach h 0, when group's electrode blank immerses 2mol/LKOH electrolyte degree of depth h 0During for 1.5mm, it is 1.14mm along the surperficial height h that rises of electrode blank that test records electrolyte;
5. with reference to figure 1, Fig. 2,3 and Fig. 4, connect dc source, beginning electrochemical corrosion processing is for size group's electrode blank as shown in Figure 3, when machining voltage is lower than 5.7V, electrode is thin coniform of root thick end, and when machining voltage reached 5.7V, it is cylindric uniformly that electrode is diameter, when voltage surpassed 5.7V, electrode was the thick spindle shape in the thin end of root.
6. group's electrode blank shown in Figure 3 is processed into the micro fine cylindrical group electrode that single electrode is of a size of 40 μ m, according to group's electrode size computation model, to require the electric weight Q that passes through be 157.63C.When the electric weight that passes through between the cathode and anode that computer obtains according to the current value of gathering reaches 157.63C, the cutter lifting that cuts off the power supply, the actual processing dimension of group's last single electrode of electrode is:
7. with reference to figure 1, unclamp anode, take out workpiece, another group electrode blank is installed again, clamp in the back immersion electrolyte and process again.Like this, can realize efficient, the low-cost manufacturing of batch of group electrode.

Claims (1)

1, a kind of electrochemical corrosion processing method with micro fine cylindrical group electrode is characterized in that may further comprise the steps:
(1), according to required single micro fine cylindrical group electrode design group electrode blank dimensional parameters, the single electrode cross sectional shape is square on group's electrode blank, wherein single electrode blank length of side d 〉=2R or d 〉=3R, R is for processing single electrode diameter afterwards; Group's electrode blank length L, adjacent single electrode space D are consistent with required single micro fine cylindrical group electrode dimensional parameters with single electrode height h0;
(2), by requirement of last step processing group electrode blank;
(3), make the electrochemistry tool cathode, wherein tool cathode is tabular, one side surface has the semicolumn boss, tool cathode major parameter cathode length S, first cylinder boss radius r of negative electrode, cathode and anode spacing f adopt the finite element method optimal design of electrochemical corrosion processing electric field to obtain, and guarantee that the current density on the electrochemical corrosion workpiece anode evenly distributes;
(4), with group's electrode blank as electrochemical corrosion workpiece anode, electrochemical corrosion adds man-hour, in electrolytic cell, tool cathode is fixed on the positioning fixture, by the position between numerical control table, NC table adjusting the two poles of the earth, make that the vertical in opposite directions parallel placement spacing of anode and cathode is f, by the feeding of machine tool chief axis, be h with the degree of depth in group's electrode blank immersion electrolyte 0, make that each single cylinder is in below the liquid level fully on the blank;
(5) energising, group's electrode blank is carried out electrochemical corrosion processing, adopt the shape of constant voltage machining control group electrode forming, and the size difference of group's electrode blank, making group electrode forming is that columniform machining voltage value also changes, for the group electrode blank of single electrode blank length of side d below 500 μ m, make it to be configured as columniform voltage in 2~8V scope, can determine this magnitude of voltage by the test of many times method: the less voltage of the initial employing of test, when voltage hour, electrode is thin coniform of root thick end, after boosted voltage value progressively, the tapering of electrode will reduce gradually, and during overtension, electrode is the thick spindle shape in the thin end of root, can finally determine the machining voltage of cylindrical electrode;
(6) adopt charge method control group electrode processing dimension, the required electric weight of micro fine cylindrical group electrode of processing certain diameter is Q 0 = 10 k ( d 2 - 1 4 π R 2 ) h 0 + 2 hL 3 ( d - R ) ,
In the formula: Q 0---processing electric weight (C);
K----volume electrochemical equivalent (cm 3/ (Ah));
h 0----group electrode blank immerses the degree of depth (cm) in the electrolyte;
H----electrolyte is along electrode blank surface lifting height (cm);
The d----single electrode blank length of side (cm);
R----processes back single electrode diameter (cm);
L----group's electrode length (cm);
In the process, gather processing electric current, by the electric weight that is passed through in the current value calculating processing process of gathering, promptly by data collecting card (11) Q = Σ i = 0 n I i Δt ,
In the formula: the actual processing of Q---electric weight;
l iThe current value of the collection in---each sampling time;
The Δ t---sampling time;
Work as Q=Q 0The time, the cutter lifting that cuts off the power supply machines.
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