RU2055708C1 - Electrochemical dimensional treatment method - Google Patents

Abstract

FIELD: electrochemical treatment of parts. SUBSTANCE: method involves imparting oscillatory motion to one of electrodes; supplying actuating pulses from power source with steep voltage-current characteristic, with initiation of pulse supplying being synchronized with electrodes approach phase; controlling voltage current value in pulse and regulating voltage value by changing treatment mode; establishing equilibrium electrode spacing and dividing each pulse under control with predetermined discreteness and measuring current and voltage values in obtained like points of adjacent pulses; calculating and comparing resistances; regulating in succession electrode feed speed and/or electrolyte pressure value at electrode spacing input , and/or current pulse supply moment, with conditions specified by a row of mathematic dependences being observed. EFFECT: increased efficiency and high dimensional precision of treatment. 7 dwg

Description

 The invention relates to precision electrochemical processing of metals and alloys, and in particular to methods of electrochemical dimensional processing.

 A known method of electrochemical processing in a flowing electrolyte under periodic oscillations of the electrode-tool, synchronized with pulses of the technological current, when the regulation of the electrode gap is carried out according to the values of the electrical parameters caused by cavitation of the electrolyte during the oscillation of the electrodes, in particular the value of the second derivative of the electrical resistance of the interelectrode gap during the tap tool electrode [1] However, this method is limited by controlling only electrode gap (MEZ).

 The method does not indicate how to deal with the parameters affecting the process in various situations. Therefore, it does not allow optimally regulating the values of factors influencing the process and thus does not make it possible to increase productivity, improve processing accuracy and improve surface quality.

 There is also known a method of electrochemical dimensional processing using a pulsed power supply with a falling current-voltage characteristic, in which the processing is performed when one of the electrodes is vibrated and voltage pulses are applied in the phase of the electrode approach, controlling the current value of the pulse voltage, highlighting voltage surges on the leading edge by the convergence section and the trailing edge of the pulse in the dilution section of the electrodes and regulate the moment of the pulse relative to the moment of maximum sat electrode leaks, while observing the equality of emissions along the leading and trailing edges, and they delay the supply of the pulse when the prevailing voltage surges in the convergence section and apply the pulse voltage ahead of time when the prevailing voltage surge in the breeding section (2).

 However, when implementing the existing ECHO methods, the control of the values of the influencing factors is carried out manually, observing the change in the shape of the pulse by an oscilloscope. And in order to determine what factor influences the shape of the voltage pulse under various conditions, it is necessary to perform complex theoretical calculations or obtain data based on a huge amount of scientific and experimental research. In practice, the correctness of the decisions made in various situations based on the shape of the voltage waveform depends on the qualifications of the technologist and operator, i.e. depends on subjective factors.

The closest analogue is the method of electrochemical dimensional processing, in which when using a pulsed power supply with a steeply damping current-voltage characteristic, the processing is performed by vibration of one of the electrodes and the supply of voltage pulses in the phase approach of the electrodes, in which the current value of the voltage pulses is controlled, highlighting voltage pulses in the areas of approach and dilution of the electrodes and adjusting their values, changing the electrolyte pressure at the entrance to the interelectrode gap [3]
The disadvantage of this method is, firstly, that it does not allow to obtain complete information about the dangerous value of the minimum interelectrode gap (MEZ) from the point of view of a short circuit, which does not allow the process to be carried out at the lowest values of the MEZ and, therefore, to achieve maximum performance , accuracy and quality of processing. Secondly, in various situations, the range of changes in the electrolyte pressure at the entrance to the MEZ may be insufficient to optimize the process. Moreover, there are no recommendations on determining the order and range of regulation under the simultaneous action (for example, electrolyte pressure, the moment of applying the voltage pulse relative to the moment of reaching the maximum approximation of the electrodes, the feed rate) of several parameters.

 In addition, the parameters are currently controlled manually, for example, the electrolyte pressure is changed by adjusting the capacity of the electrolyte supply pump or the moment of pulse supply, or the feed rate, visually observing the shape of the voltage pulse by an oscilloscope. This is done by a technologist or an experienced operator at his discretion, i.e. there is always a subjective factor, there is no criterion for an objective assessment of the existing situation in the MEP.

 Thus, the known methods of electrochemical dimensional processing in the application of oscillatory motion of the electrode, synchronized with the supply of voltage pulses, do not in all cases achieve maximum performance, accuracy and quality of processing when shaping complex shapes and piercing cavities of constant cross-section in a batch of parts, since achieving the maximum values of the output technological indicators depends on the qualification of the technologist or operator, i.e. from subjective factors.

 The basis of the invention is a method of electrochemical dimensional processing with forced oscillation of one of the electrodes, synchronized with the supply of voltage pulses to them, which makes it possible to automate the regulation of optimal parameter values and to choose such a combination and ranges of their regulation (for example, the electrolyte pressure at the entrance to the MEP, moment of pulse supply relative to the moment of maximum approximation of the electrodes, feed rate) according to reliable criteria, which will automatically and without the intervention of an experienced specialist, high technological output process indicators. Moreover, the automation of the process will accelerate and increase the reliability of the introduction of electrochemical machines in production.

≥

≥

a

(ΔR $\genfrac{}{}{0ex}{}{\text{j,j+1}}{\text{i}}$ )²-

(ΔR $\genfrac{}{}{0ex}{}{\text{j,j+1}}{\text{k}}$ )²

(U $\genfrac{}{}{0ex}{}{\text{j+1}}{\text{i}}$ -U $\genfrac{}{}{0ex}{}{\text{j}}{\text{i}}$ )²;

(U $\genfrac{}{}{0ex}{}{\text{j+1}}{\text{k}}$ -U $\genfrac{}{}{0ex}{}{\text{j}}{\text{k}}$ )² принимали минимальные значения, близкие к нулю, где
U $\genfrac{}{}{0ex}{}{\text{j}}{\text{i}}$ ; R $\genfrac{}{}{0ex}{}{\text{j}}{\text{i}}$ ; R $\genfrac{}{}{0ex}{}{\text{j+1}}{\text{i}}$ ;U $\genfrac{}{}{0ex}{}{\text{j+1}}{\text{i}}$ значения напряжений и сопротивлений (j+1) и j-того импульсов в i-й точке, выбранной в зоне сближения электродов;
U $\genfrac{}{}{0ex}{}{\text{j}}{\text{k}}$ ; R $\genfrac{}{}{0ex}{}{\text{j}}{\text{k}}$ ; U $\genfrac{}{}{0ex}{}{\text{j+1}}{\text{k}}$ ; R^j+1 значения напряжений и сопротивлений (j+1) и j-того импульсов в k-той точке, выбранной в зоне удаления электродов;
R

значение сопротивления межэлектродного промежутка в момент максимального сближения электродов при подаче (j+1) и j-того импульсов.The problem is solved by the fact that during electrochemical dimensional processing one of the electrodes is set to oscillate, feed working pulses from a power source with a steeply damping current-voltage characteristic, synchronizing the start of the supply of pulses with the phase approach of the electrodes, control the current voltage value in the pulse and adjust the voltage value by change processing modes, wherein upon installation of the equilibrium MEZ each divided pulse controlled at a predetermined increments Δ t at intervals of N ₁ the time of closest approach of the electrode to the start of the pulse and N ₂ intervals from the moment of closest approach of the electrode to the end pulse in the obtained corresponding points of adjacent pulses measured values of the process current and voltage is calculated and compared to the resistance and successively regulate the feed rate of the electrode and / or electrolyte pressure value at the entrance to the interelectrode gap, and / or the moment of supply of the current pulse from the condition of the following relations:
Δ R $\genfrac{}{}{0ex}{}{\text{j, j + 1}}{\text{i}}$ R $\genfrac{}{}{0ex}{}{\text{j + 1}}{\text{i}}$ R $\genfrac{}{}{0ex}{}{\text{j}}{\text{i}}$ ≅ 0;
Δ R $\genfrac{}{}{0ex}{}{\text{j, j + 1}}{\text{k}}$ R $\genfrac{}{}{0ex}{}{\text{j + 1}}{\text{k}}$ R $\genfrac{}{}{0ex}{}{\text{j}}{\text{k}}$ ≅ 0

≥

≥

a

(ΔR $\genfrac{}{}{0ex}{}{\text{j, j + 1}}{\text{i}}$ ) ² -

(ΔR $\genfrac{}{}{0ex}{}{\text{j, j + 1}}{\text{k}}$ ) ²

(U $\genfrac{}{}{0ex}{}{\text{j + 1}}{\text{i}}$ -U $\genfrac{}{}{0ex}{}{\text{j}}{\text{i}}$ ) ² ;

(U $\genfrac{}{}{0ex}{}{\text{j + 1}}{\text{k}}$ -U $\genfrac{}{}{0ex}{}{\text{j}}{\text{k}}$ ) ² took the minimum values close to zero, where
U $\genfrac{}{}{0ex}{}{\text{j}}{\text{i}}$ ; R $\genfrac{}{}{0ex}{}{\text{j}}{\text{i}}$ ; R $\genfrac{}{}{0ex}{}{\text{j + 1}}{\text{i}}$ ; U $\genfrac{}{}{0ex}{}{\text{j + 1}}{\text{i}}$ values of voltages and resistances (j + 1) and j-th impulses at the i-th point selected in the zone of proximity of the electrodes;
U $\genfrac{}{}{0ex}{}{\text{j}}{\text{k}}$ ; R $\genfrac{}{}{0ex}{}{\text{j}}{\text{k}}$ ; U $\genfrac{}{}{0ex}{}{\text{j + 1}}{\text{k}}$ ; R ^{j + 1} values of voltages and resistances (j + 1) and j-th impulses at the k-th point selected in the zone of removal of electrodes;
R

the value of the resistance of the interelectrode gap at the time of maximum approximation of the electrodes when applying (j + 1) and j-th impulses.

 The proposed method of electrochemical processing allows you to perform various copy-flashing operations and operations using a non-profiled electrode-tool (EI) in workpieces from hard-to-process materials with high productivity, accuracy and quality of processing both in the manufacture of batches of complex shapes and in the piercing of cavities of constant cross-section.

 In FIG. 1 shows a diagram of an implementation of the proposed method of electrochemical processing; in FIG. 2 is a time chart of the variation of the process parameters (voltage, resistance, current) during the oscillatory movement of EI relative to the surface of the workpiece; figure 3 the nature of the change in the interelectrode medium in the process of oscillation of the electrode; figure 4 the shape of the voltage and current pulses supplied at the time of maximum approximation of the electrodes at the beginning of processing; figure 5 time diagrams in the presence of a surge of voltage on the trailing edge of the pulse, corresponding to the removal of electrodes from each other; Fig.6 timing diagrams in the presence of a voltage surge on the leading edge of the pulse corresponding to the approximation of the electrodes; in FIG. 7 is a timing diagram of changes in the trajectory of the EI, voltage pulse and electrolyte pressure at small gaps.

The proposed method is as follows. From the power source 1 (FIG. 1), current pulses are supplied to the electrode, which is the tool 2, and to the electrode, which is the workpiece 3 being processed. The oscillations of the tool 2 in the directions indicated by the arrows are synchronized so that a current pulse is supplied in the phase of approach of the electrodes and at the time when the tool 2 and the workpiece 3 are located at a minimum distance S _min (Fig. 2a).

When electrochemical processing in a flowing electrolyte with a pressure of P ₁ (Fig. 1) at the inlet of the interelectrode gap S, the tool 2 approaches the workpiece 3 with a high speed of oscillatory motion created by the engine 4. The workpiece 3 is mounted on a table 5, moving in the direction to the tool 2 with a speed V. As a result of the rapid approach of the tool 2 to the workpiece 3 in the interelectrode gap S, the hydrodynamic pressure P _s (Fig. 3) of the electrolyte begins to increase, New bubbles 6 contained in the electrolyte and released during the electrochemical process are compressed and dissolved in the electrolyte. This leads to the fact that under these conditions, the process of anodic dissolution of the surface of the workpiece proceeds under conditions of a significant decrease in the probability of breakdown of the interelectrode gap S due to the absence of vapor-gas bubbles 6. This can significantly improve the accuracy, productivity and quality of processing due to the possibility of working with extremely small interelectrode S. gaps

With a quick removal of the tool from the workpiece 3, the pressure P _s drops sharply. In the interelectrode gap S, the intensive growth of vapor-gas bubbles 6 dissolved in the electrolyte begins, i.e. cavitation begins due to a drop in electrolyte pressure in the interelectrode gap S. This causes a sharp increase in the resistance of the interelectrode gap S and, consequently, the voltage U ₁ (Fig. 2c).

During electrochemical processing, the intensity of formation of gas-vapor bubbles 6 (Fig. 3) caused by cavitation during the supply and removal of the tool relative to the surface of the workpiece depends on the synchronization of the moment of supply of the current pulse relative to the moment of maximum approximation S _min (Fig. 2a) of the electrodes, and on the magnitude of the electrolyte pressure at the entrance of the interelectrode gap P ₁ (figure 1). Therefore, in the process of electrochemical processing with the oscillatory movement of the tool 2 synchronized with the supply of current pulses, surges U ₂ (R ₂ ) (Fig. 2c) and U ₁ (R ₁ ) (Fig. 2c) of voltage (resistance) may appear as along the front and on the trailing edges. Moreover, the amplitude of the emissions of U ₂ (R ₂ ) and U ₁ (R ₁ ) voltages (resistances) also depends on the advance or delay of the moment of supply of the current pulse relative to the moment of maximum approximation of the electrodes. These emissions U ₁ (R ₁ ), U ₂ (R ₂ ) of stresses (resistances) are associated not only with a change in the interelectrode gap S, but also with a change in the hydrodynamic conditions in it. Therefore, the synchronization of the moment of supply of current pulses with the moment of creation of optimal hydrodynamic conditions in the interelectrode gap S is very important.

In FIG. Figure 2c shows the case when the pressure of the electrolyte at the input of the interelectrode gap is more than optimal, i.e. P ₁ > P _opt. In this case, when the electrodes approach each other, when the interelectrode gap is still sufficiently large (S> S _min ) in the electrolyte flowing at a high speed, as a result of a sharp change in the direction of its flow ≈ 90 ^о , a turbulent flow is formed at the entrance to the end interelectrode gap with the occurrence of cavitation phenomena .

As a result of the formation of a vapor-gas mixture, the resistance R _{2 of the} interelectrode medium sharply increases and the process current I ₂ drops in the interelectrode gap. In this case, the voltage is redistributed between the internal resistance of the power source and the resistance of the interelectrode medium. This is manifested in the form of distortion of the waveforms of the voltage pulses U ₂ and the technological current I _{2 the} interelectrode gap. In this case, only the middle and second half of the voltage pulse are effectively used, therefore the technological characteristics of the process (productivity, accuracy and quality of processing) are low.

In FIG. Figure 2c shows the case when the electrolyte pressure at the input of the interelectrode gap is less than optimal, i.e. P ₁ <P _opt.
In this case, due to insufficient electrolyte consumption through the interelectrode gap, it is blocked by electrode reaction products (sludge, vapor-gas-liquid mixture) when a second half of the pulse is applied. In this case, the resistance R _{1 of the} interelectrode gap sharply increases, therefore, the voltage U ₁ and the density of the technological current I ₁ decrease, macroscopic breakdowns of the interelectrode gap occur, which subsequently lead to a short circuit. There is a deterioration in quality and a reduction in processing productivity.

 Thus, in this case, the technological parameters of the process are also low. Therefore, to optimize the process in order to improve the technological characteristics of electrochemical processing, it is necessary to actively influence the processing process by improving the hydrodynamic conditions in the interelectrode gap. This is achieved by increasing or decreasing the pressure of the electrolyte at the entrance of the interelectrode gap during the process. Due to the improvement of the hydrodynamic conditions in the interelectrode gap, practically all of the amount of electricity applied by the pulse current is effectively used.

The most productive, providing high accuracy and quality of processing is the case when P ₁ P _opt . In this case, the process of electrochemical dissolution takes place under optimal hydrodynamic conditions and the technological characteristics of the process are much higher than in the cases considered above.

 This corresponds to the situation when the outbursts of the electric parameter impulse (voltage, resistance) along the leading and trailing edges have approximately the same value.

In the process of electrochemical processing with the oscillatory movement of the electrode 2 (Fig. 1), synchronized with the supply of pulses, emissions of U ₁ (R ₁ ) (Fig. 5) and U ₂ (R ₂ ) (Fig. 6) voltage (resistance) may occur both on the trailing and trailing edges when applying pulses with delay or leading relative to the moment of reaching the minimum gap between the electrodes. Moreover, the amplitude of the emissions of U ₁ (R ₁ ) and U ₂ (R ₂ ) voltages (resistances) depends both on the hydrodynamic conditions and on the lead time or delay of the pulse supply relative to the moment of maximum approximation of the electrodes.

Studies have shown that with approximate equality of the amplitudes of the emissions U ₁ (R ₁ ), U ₂ (R ₂ ) of the voltage (resistance) on the trailing and leading edges, the productivity, accuracy and quality of processing are higher than when the amplitude of one of the surges U _{2 is} significantly exceeded (R ₂ ), U ₁ (R ₁ ) voltage (resistance) on the leading and trailing edges.

Therefore, if, when the electrodes are removed from each other, a significant surge of voltage (resistance) U ₁ (R ₁ ) is recorded at the trailing edge of the pulse, this means that poor hydrodynamic conditions are created in the interelectrode gap S or the process occurs with increased values of the interelectrode gap S, which manifests itself in a sharp decrease in current I ₁ , and optimal processing conditions are created when the electrodes approach each other. Therefore, in this case, a current pulse is supplied somewhat earlier than the moment of maximum approximation of the S _min electrodes. In this case, the moment of creation of optimal processing conditions is determined by the magnitude of the voltage (resistance) surges that appeared before and after the maximum approximation of S _{min of} electrodes. The amplitudes of these emissions should be approximately equal in magnitude, but less than the specified value. If when selecting the electrolyte pressure at the MEP input and synchronizing the moment of supply of the voltage pulse with the moment of approach of the electrodes, the moment of creation of optimal processing conditions passes, then the surge of U ₂ (R ₂ ) (Fig. 6) voltage (resistance) appears along the leading edge of the pulse. The mechanism of occurrence of this outlier, associated with hydrodynamic phenomena in the interelectrode gap, was considered above.

In order to reduce the amplitude of the emission U ₂ (R ₂ ) of the voltage (resistance) along the leading edge and, therefore, to create optimal processing conditions, the current pulse is applied with some delay relative to the moment of maximum approximation of S _{min of the} electrodes or the pressure is reduced, so that the amplitude of the emission U ₂ (R ₂ ) voltage (resistance) on the leading edge, corresponding to the approach of the electrodes, and the release of U ₁ (R ₁ ) (figure 5) voltage (resistance) on the falling edge, corresponding to the distance from each other of the electrodes, become approximately equal.

However, when processing at small interelectrode gaps, emergency situations can occur in the interelectrode gap, especially when processing surfaces with an area of 15 cm ² or more with the appearance of a pulse pressure of up to 20-30 kg / cm ² . This pulsed force applied to the EI and the workpiece being processed is capable of changing the natural law of the mutual movement of the moving masses of the mechanical system of the machine. Accordingly, there is a distortion of the harmonic vibration of the EI and a change in the minimum value of the interelectrode gap S _min (Fig. 7). So at the time point (or close to it), at which the pressure pulse amplitude P _s 'is maximum, the electrode gap S' increases for some time, and when the pressure P _s drops (Fig. 3) due to removal of the tool electrode 2 from the surface of the workpiece 3, the gap S _i '(Fig. 7) decreases (due to the action of mechanical elastic forces), and then continues to change in accordance with the kinematic system of the machine.

 Studies have shown that when the process is conducted at extremely small (0.01 mm or less) interelectrode gap values or when it sharply decreases due to the action of elastic forces, a moment occurs when a third surge U 'is formed in the middle part of the voltage (resistance) pulse (R '). Moreover, if the amplitude of the ejection of an electrical parameter (voltage, resistance) exceeds a predetermined value, then there is a danger of a short circuit between the electrodes.

 Therefore, when implementing the method of electrochemical processing, the electrode feed rate and / or the electrolyte pressure value at the inlet of the interelectrode gap are sequentially controlled and / or the moment of supply of the current pulse as a result of analysis of the above ratios.

PRI me R. The electrochemical treatment of a workpiece made of alloyed tool steel in an 8% aqueous solution of sodium nitrate to a depth of 10 mm with an area of 2500 mm ^{2 was performed} .

Before starting the processing, the oscillating electrode-tool 2 (Fig. 1) and the workpiece 3 are brought together until they touch each other when there is no voltage on them and they are retracted to the specified value of the minimum interelectrode gap S _min (Fig. 2a).

Then set the following processing mode:
frequency of voltage pulses and EI oscillations, (Hz) 30;
the duration of the voltage pulse, (ms) 8;
amplitude (A) fluctuations of EI, (mm) 0,2;
the amplitude of the voltage pulse at the time of the smallest distance between the electrodes, (V) 10;
electrolyte pressure at the entrance of the interelectrode gap, (mRa) 0.05;
electrolyte temperature, ( ^о С) 18.

At the beginning of processing, after establishing the equilibrium gap, the moment at which the voltage value is maximum was synchronized with the moment of maximum rapprochement S _{min of the} electrodes (Fig. 4). Then, with the further deepening of the electrode-tool 2 into the workpiece 3 and the formation of emissions of U ₂ (R ₂ ) (fg. 2c, 6) and U ₁ (R ₁ ) (Figs, 5) of the voltage pulse during periods of approach and removal of the electrodes and U '(Fig. 7) at the time of their maximum approximation, the electrolyte pressure at the MEP input gradually increased and the value of the process current and voltage were measured in each pulse with a resolution of 0.01 ms. The values of voltages and resistances of two next impulses at the corresponding measurement points were calculated and compared. Measurements were made over the entire length of the pulse. At the same time, the process parameters were regulated (feed rate, electrolyte pressure at the MEP input, moment of pulse supply relative to the moment of maximum approximation of the electrodes in such a way that the difference between the voltage sums at the same points of two next next pulses corresponding to both removal and approximation of the electrodes relative to the moment of maximum approximation electrodes (that is, along the entire length of the pulse), tended to zero, and the difference in resistance at the corresponding points of each two pulses along the entire length of the pulse would always while the difference between the total values of the resistances during the approach and removal of the electrodes was maintained greater than zero, while the ratios of the resistances at given points to the resistances at the point of maximum proximity of the electrodes of the subsequent pulse were always greater than or equal to the ratios of the corresponding resistances of the previous pulse as in the approximation , and when removing the electrodes.

 Implementation of the proposed method of electrochemical processing by automatic control of the above parameters ensures maximum productivity, accuracy of copying tool 2 (figure 1) in the workpiece 3 and the quality of the processed surface. The proposed method of electrochemical processing ensures the accuracy of copying complex elements of the electrode-tool 2 on the surface of the workpiece 3 to 0.01 mm when performing various copy-stitching operations and operations using non-profiled EI in difficult to conductive materials. In this case, the surface roughness reaches values up to 0.1 μm and the feed rate up to 1 mm / min.

 The high accuracy of the shaping of the machined surfaces virtually eliminates the problem of calculating and correcting EI. Having made EI once, it is possible to process with its use a large batch of parts that differ from each other by no more than 0.015 mm.

The optimal combination of hydrodynamic conditions, parameters of current pulses and oscillatory motion of EI and automatic process control (controlling the values of influencing factors) by limiting the emission of an electrical parameter according to the invention ensures a process with a minimum clearance S _min within 0.01-0.03 mm without damage electrode surfaces, and the proposed method of electrochemical dimensional processing is easily carried out using well-known in modern technology controllers constructions.

Claims (1)

METHOD OF ELECTROCHEMICAL DIMENSIONAL PROCESSING, in which the oscillatory movement of one of the electrodes is set, operating pulses are supplied from a power source with a steeply falling current-voltage characteristic, synchronizing the beginning of the supply of pulses with the phase approach of the electrodes, controlling the current voltage value in the pulse and adjusting the voltage value by changing processing modes, which differs the fact that after setting the equilibrium inter-electrode gap, each controlled pulse is divided with a given discreteness Δt by N ₁ about sections from the moment of maximum approximation of the electrodes to the beginning of the pulse and N ₂ segments from the moment of maximum approximation of the electrodes to the end of the pulse, the values of the technological current and voltage are measured at the same points of adjacent pulses, the resistance is calculated and compared, and the electrode feed rate is sequentially adjusted and / or the pressure of the electrolyte at the entrance to the interelectrode gap, and / or the moment of supply of the current pulse from the condition of the following relations:
ΔR $\genfrac{}{}{0ex}{}{\text{j, j + 1}}{\text{i}}$ = R $\genfrac{}{}{0ex}{}{\text{j + 1}}{\text{i}}$ -R $\genfrac{}{}{0ex}{}{\text{j}}{\text{i}}$ ≅ 0;
ΔR $\genfrac{}{}{0ex}{}{\text{j, j + 1}}{\text{k}}$ = R $\genfrac{}{}{0ex}{}{\text{j + 1}}{\text{k}}$ -R $\genfrac{}{}{0ex}{}{\text{j}}{\text{k}}$ ≅ 0;

took minimal values close to zero,
where u $\genfrac{}{}{0ex}{}{\text{j}}{\text{i}}$ , R $\genfrac{}{}{0ex}{}{\text{j}}{\text{i}}$ , R $\genfrac{}{}{0ex}{}{\text{j + 1}}{\text{i}}$ , U $\genfrac{}{}{0ex}{}{\text{j + 1}}{\text{i}}$ - the values of the resistance voltages of the (j + 1) th and jth pulses at the i-th point selected in the zone of proximity of the electrodes;
U $\genfrac{}{}{0ex}{}{\text{j}}{\text{k}}$ , R $\genfrac{}{}{0ex}{}{\text{j}}{\text{k}}$ , U $\genfrac{}{}{0ex}{}{\text{j + 1}}{\text{k}}$ , R $\genfrac{}{}{0ex}{}{\text{j + 1}}{\text{k}}$ - the values of voltages and resistances of the (j + 1) th and jth pulses at the kth point selected in the electrode removal zone;

- the value of the resistance of the interelectrode gap at the moment of maximum approximation of the electrodes when the (j + 1) th and jth pulses are applied.

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