WO2019140819A1 - Method for designing electrode diameter and furnace shell shape of two-phase direct-current (dc) fused magnesia furnace - Google Patents

Abstract

A method for designing an electrode diameter and a furnace shell shape of a two-phase DC fused magnesia furnace, comprising: designing the structure of the two-phase DC fused magnesia furnace system; calculating an arc power distribution on the surface of a fusing pool under joint effects of a cathode and an anode; determining physical parameters of the two-phase DC fused magnesia furnace system, comprising calculating the electrode diameter; and determining the furnace shell shape according to the arc power distribution on the surface of the fusing pool under the joint effects of the cathode and the anode and the calculated electrode diameter. Analyzing the operating state and electrical configuration of the two-phase DC fused magnesia furnace, enables effective calculation of an electrode diameter and a furnace shell shape that satisfy an optimal operating state of the two-phase DC fused magnesia furnace, thereby effectively reducing the consumption of materials and electrical energy in industrial production processes.

Description

Method for designing pole center distance and furnace shell shape for two-phase direct current magnesium melting furnace Technical field

The invention belongs to the technical field of industrial electrolytic molten magnesia extraction magnesia crystal, and particularly relates to a method for designing a pole center distance and a furnace shell shape for a two-phase direct current magnesium melting furnace.

technical background

The existing three-phase AC fused magnesium furnace in Liaoning Province generally has a capacity of about 10 tons. The furnace type has a slender cylindrical shape and the transformer capacity is generally above 1000kVA, with an annual output of no more than 2,000 tons. According to the melting mass accounting for 40% of the total material, the existing electric furnace transformer needs to work at full power for about 10 hours to complete the heating task. The electric furnace transformer often works in an overload state, and according to statistics, the average overload reaches 1.62 times. Long-term overload operation of the transformer shortens the service life of the transformer and reduces the electrical efficiency of the system. Due to the limitation of the output capacity of the transformer, the effective heating space of the arc is small, and it must be matched with an elongated cylindrical furnace body. The maximum heating temperature of the electric arc furnace of this structure is limited, and the purification process of the raw material cannot be sufficiently performed, and the purity and density of the product are low. Due to the long heating time, the carbon pollution caused by the arc is also serious.

It has been recognized that the provision of high capacity electric furnace transformers for systems is a prerequisite for increased throughput and quality. Increasing the unit power of the smelting system can significantly shorten the smelting time and greatly increase productivity. In addition, increasing the power density can also increase the melting temperature and energy efficiency of the arc.

The existing three-phase AC fused magnesium furnace expands the problem of the AC arc heating technology itself when the capacity is expanded. The main problems are as follows:

(1) The alternating current arc crosses zero to 100 times per second, the arc is extinguished near the zero point, and then the arc is re-arced in the second half, so the stability of the alternating current arc is poor.

(2) The AC system has low power factor and frequent fluctuations in reactive power, causing the grid voltage to flicker and requires expensive dynamic compensation devices.

(3) The arc length and power variation of the three-phase arc are inconsistent in time, the three-phase load is asymmetrical, the three arc powers are unbalanced, and the furnace wall hot spot is generated.

(4) Three-phase AC fused magnesium furnace is a typical multi-input and multi-output three-phase coupling system with nonlinear, time-varying and distributed parameters. It has the following characteristics: high order, which is described by a simplified mathematical model. At the end of the system, it can reach more than 20 orders; strong nonlinearity, AC arc resistance has strong nonlinearity; disturbance is complex, large-scale disturbance and randomness coexist, and this disturbance exists in the system, non-plus Sexual; strong coupling, the main circuit of the three-phase fused magnesium furnace has strong coupling, so that the change of the arc length of any phase can simultaneously cause the change of the effective value of the three-phase arc AC; the rapidity of the adjustment process, a certain When the phase electrode is short-circuited, the electrode regulator must adjust the electrode to the proper position in time, usually from a few seconds to a few seconds. For such complex systems, conventional control effects are less than ideal and new control strategies must be sought.

Summary of the invention

In view of the many shortcomings of the traditional three-phase alternating current fused magnesium furnace, and the existing two-phase direct current fused magnesium furnace, the problem of waste of electric energy and materials due to the unreasonable design of the center distance and the furnace type, the present invention provides a use The design method of the center distance and furnace shape of the two-phase direct current magnesium melting furnace.

The technical scheme of the present invention is as follows:

A method for designing a pole center distance and a furnace shell shape for a two-phase direct current magnesium melting furnace, comprising:

Designing the structure of a two-phase direct current fused magnesium furnace system;

Obtaining an arc power distribution under the influence of the cathode and the anode on the surface of the molten pool;

Determine the physical parameters of the two-phase DC fused magnesium furnace system, including:

Find the center of the heart;

The shape of the furnace shell is determined according to the arc power distribution under the influence of the cathode and the anode and the obtained pole center distance.

The specific method for determining the arc power distribution under the influence of the cathode and the anode on the surface of the molten pool includes:

Calculating the cathode cutoff voltage and the anode cutoff voltage according to the equivalent voltage drop of the electron energy in the cathode region and the equivalent electronic pressure drop of the anode region;

Find the arc power and the voltage across the arc;

The cathode arc length and the anode arc length are obtained according to the voltage across the arc, the cathode cutoff voltage, and the anode cutoff voltage;

Determine the arc power distribution on the surface of the molten pool under the influence of the cathode and the arc power distribution on the surface of the molten pool under the influence of the anode, and then determine the arc power distribution under the influence of the cathode and the anode on the surface of the molten pool.

The method of calculating the cathode cutoff voltage and the anode cutoff voltage is as follows:

Calculating the equivalent voltage drop of the electron energy in the cathode region and the equivalent pressure drop of the electron energy in the anode region according to the temperature at the heating spot of the electrode;

The cathode cut-off voltage and the anode cut-off voltage were calculated based on the equivalent voltage drop of the electron thermal energy in the cathode region and the equivalent electronic pressure drop of the anode region.

The method for solving the arc power is as follows:

Calculate the resistance of the two electrodes according to the electrode size and resistivity, and measure the resistance of the short grid, and calculate the sum R of the resistance of the two electrodes and the short grid resistance;

Estimate the weld pool resistance r ₃ according to the size of the weld pool and the resistivity of the weld pool;

Calculating a DC current I _d ' when the arc power P _{1 is} maximum when the rectifier output voltage U _d is known;

The arc power P ₁ =(U _d -RI _d '-r ₃ I _d '-U _jz1 -U _jz2 )I _d ' is obtained, and U _jz1 is the cathode cutoff voltage U _jz2 is the anode cutoff voltage.

The voltage across the arc is solved by the following formula:

U _c =0.5×(U _d -RI _d '-r ₃ I _d '-U _jx1 -U _jz2 )

Where U _d is the rectifier output voltage, I _d ' is the DC current when the arc power P _{1 is} maximum when the output voltage of the rectifier is known, R is the sum of the resistance of the two electrodes and the short grid resistance, and r ₃ is the bath resistance , U _jz1 is the cathode cut-off voltage, and U _jz2 is the anode cut-off voltage.

The calculation formulas of the cathode arc length and the anode arc length are as follows:

Wherein l ₁ is the length of the cathodic arc, l ₂ is the length of the anode arc, U _jz1 is the cathode cutoff voltage, U _jz2 is the anode cutoff voltage, U _c is the voltage across the arc, and b is the arc voltage coefficient.

The method for determining the arc power distribution of the surface of the molten pool under the influence of the cathode and the arc power distribution of the surface of the molten pool under the influence of the anode are as follows:

The heating heat flow distribution of the arc on the surface of the molten pool is regarded as a normal distribution, and the heating heat flow distribution is expressed as

Where q _max is the maximum heat flow at the center of the heated spot, r is the distance from any point on the surface of the molten pool to the center of the heated spot, and α is the coefficient of thermal energy concentration;

Find the maximum heat flow at the center of the heated spot

Where Q is the distribution of the actual unipolar arc power on the surface of the molten pool, and the heating heat flow distribution formula

Integrate on the heated spot area, P ₁ is the arc power; thermal energy concentration factor

D is the diameter of the electrode, l is the length of the arc, and refers to the length of the cathodic arc or the length of the anode arc;

Find the distribution of the arc power of the single electrode on the surface of the molten pool;

The straight line of the coordinate line of the center line of the two electrodes is the horizontal axis of the coordinate line, and the straight line of the center line of the two electrodes is the vertical axis of the coordinate axis, and the axis of the center of the anode is the positive direction of the horizontal axis, according to The distribution of the arc power of the single electrode on the surface of the molten pool indicates the arc power distribution of the surface of the molten pool under the influence of the cathode and the arc power distribution of the surface of the molten pool under the influence of the anode.

The arc power distribution of the surface of the molten pool under the influence of the cathode and the anode is the sum of the arc power distribution of the surface of the molten pool under the influence of the cathode and the arc power distribution of the surface of the molten pool under the influence of the anode.

The formula for calculating the pole center distance is as follows:

Where η ₁ is the heat dissipation efficiency, η ₂ is the proportion of heat preservation heat energy, q is the product energy consumption of magnesite as raw material, ρ is the density of fused magnesia, h is the crystal height, and P ₁ is the arc power. .

The method for determining the shape of the furnace shell includes:

According to the arc power distribution under the influence of the cathode and the anode and the obtained pole center distance, the equal power line on the surface of the molten pool is drawn; the shape of the shell is determined according to the equal power line around the surface of the bath.

Beneficial effects:

The invention analyzes the operating state and electrical composition of the two-phase direct current fused magnesium furnace, and can effectively calculate the pole center distance and the shape of the furnace shell satisfying the optimal operating state of the two-phase direct current magnesium melting furnace, and can be in the industrial production process. Effectively reduce the loss of materials and electrical energy.

DRAWINGS

1 is a schematic structural view of a two-phase direct current fused magnesium furnace system according to an embodiment of the present invention; wherein 1-transformer, 2-short mesh, 3-rectifier, 4-electrode, 5-furnace shell, 6-car, 7- Electrode holder, 8-arc, 9-melt pool;

Figure 2 shows the static volt-ampere characteristics of a DC arc. The abscissa is the current and the ordinate is the voltage. When the current is in the range 0-A, the voltage decreases with the increase of the current, which is the falling region. When the current is in A~ In the B interval, the voltage does not change with the increase of the current, and is a horizontal region. When the current is greater than B, the voltage increases with the increase of the current, and is a rising region;

3 is a schematic diagram of heat source distribution of arc electric heating on the surface of the molten pool, wherein the abscissa indicates the surface of the molten pool, and the ordinate indicates the electrode;

Figure 4 is an equivalent circuit diagram of a two-phase DC fused magnesium furnace, where U _d is the DC voltage output from the rectifier, R is the sum of the resistance of the two electrodes and the short grid resistance, U _jz1 , U _jz2 are the arc cathode and anode cutoff respectively The voltage, r ₁ , r ₂ are the cathode and anode arc resistance, respectively, and r ₃ is the bath resistance;

Figure 5 is a graph showing the relationship between arc power and rectifier output current;

Figure 6 is an approximate view of the surface of the molten pool;

Figure 7 is a graph showing the arc power distribution on the surface of the molten pool.

Detailed ways

The specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

A method for designing a pole center distance and a furnace shell shape for a two-phase direct current magnesium melting furnace, comprising:

Step 1. Design a structure of a two-phase direct current molten magnesium furnace system;

The structure of the two-phase direct current fused magnesium furnace system in the present embodiment is as shown in FIG. 1. The transformer 1, the short net 2, and the rectifier 3 are sequentially connected, the rectifier 3 is connected to the two electrodes 4, and the electrode 4 is sandwiched by the electrode holder 7. The two electrodes 4 are inserted into the molten pool 9 in the furnace shell 5 of the two-phase direct current fused magnesium furnace carried by the carriage 6, and an arc 8 is generated. The control system of the two-phase DC fused magnesium furnace system comprises: a power module, a voltage and current detecting device, a central controller, an amplifying actuator, and a pulse trigger. The power module mainly includes: a transformer 1, a rectifier 3, an isolating switch, and a circuit breaker.

Step 2: obtaining an arc power distribution under the influence of the cathode and the anode on the surface of the molten pool;

The specific method for determining the arc power distribution under the influence of the cathode and the anode on the surface of the molten pool includes:

Step 2.1: calculating a cathode cutoff voltage and an anode cutoff voltage according to an equivalent voltage drop of the electron energy in the cathode region and an equivalent voltage drop of the electron energy in the anode region;

The method of calculating the cathode cutoff voltage and the anode cutoff voltage is as follows:

Step 2.1.1. Calculate the equivalent voltage drop of the electron energy in the cathode region and the equivalent pressure drop of the electron heat in the anode region according to the temperature at the heating spot of the electrode;

In this embodiment, the equivalent pressure drop of the electron thermal energy in the cathode region and the calculation formula of the equivalent thermal pressure drop of the electron thermal energy in the anode region are adopted.

Where UT is the equivalent voltage drop, e is the electron charge e=1.602*10^-19 coulomb; k is a constant, k=1.38*10^-23, T is the temperature at the heating spot, and the temperature of the cathode heating electrode spot is about At 4000K, the anode electrode heats the spot at a temperature of about 6000K. Therefore, the equivalent voltage drop U _T1 =0.52V of the electron thermal energy in the cathode region can be obtained, and the electron thermal equivalent voltage drop U _{T2 of the} anode region is 0.98V.

Step 2.1.2, calculate the cathode cut-off voltage and the anode cut-off voltage according to the equivalent voltage drop of the electron thermal energy in the cathode region and the equivalent electronic pressure drop of the anode region.

During the operation of the two-phase DC fused magnesium furnace system, the current is in the I _c >B segment shown in Figure 2, and the voltage corresponding to the point B is called the cut-off voltage. The cathode cut-off voltage U _jz1 = U ₁ - U _T1 , the anode cutoff voltage U _jz2 = U ₂ + U _T2 ; wherein U ₁ and U ₂ are the cathode region voltage drop and the anode region voltage drop, respectively, both being 10V. Therefore, U _jz1 = 9.48V and U _jz2 = 10.78V are obtained.

Step 2.2: Find the arc power and the voltage across the arc;

The method for solving the arc power is as follows:

(a) Calculate the resistance of the two electrodes according to the electrode size and the resistivity, and measure the resistance of the short grid, and calculate the sum R of the resistance of the two electrodes and the resistance of the short grid; in the present embodiment, both electrodes are 1 m long and have a diameter The 100mm cylindrical graphite electrode has a graphite resistivity of 1×10 ^-5 Ω·m, so the resistance of the single electrode is 1.27mΩ, and the measured short-net resistance is about 0.55mΩ. Therefore, the two electrodes are The sum of the resistance and the short-wire resistance is R=3.09mΩ.

(b) Estimating the weld pool resistance r ₃ according to the size of the molten pool and the resistivity of the molten pool;

Set the size of the weld pool to a cube with a length, width and height of 200 mm. The weld pool resistivity is about 1.2 × 10 ^-3 Ω·m, and the weld pool resistance is r ₃ = 6 mΩ.

(c) determining a direct current I _d ' when the arc power P _{1 is} maximized when the rectifier output voltage U _d is known;

According to the equivalent circuit of the two-phase DC fused magnesium furnace shown in Fig. 4, the expression of the arc power P ₁ is obtained: P ₁ =(U _d -RI _d -r ₃ I _d -U _jz1 -U _jz2 )I _d Where U _d is the rectifier output voltage and I _d is the circuit current.

According to the expression of the arc power P ₁ , the relationship between the arc power and the rectifier output current as shown in FIG. 5 is plotted in the case where the rectifier output voltage U _{d is} different (80 V, 100 V, 120 V, respectively), and the rectifier is known. When the output voltage U _d =120V, the DC current when the arc power P _{1 is} maximized is obtained.

It can be seen from Fig. 5 that the arc power P _{1 is the} largest when the two-phase DC fused magnesium furnace reaches this current I _d ' during constant current operation.

(d) to the arc power P ₁ expression, and direct current arc when the maximum power P ₁ I _d ', determined arc power _{P 1 = (U d -RI d} ' -r 3 I d '-U jz1 -U _jz2 )I _d '=355288W.

The voltage across the arc is solved by the following formula:

U _c =0.5×(U _d -RI _d '-r ₃ I _d '-U _jx1 -U _jz2 )≈24.9V

Where U _d is the rectifier output voltage, I _d ' is the DC current when the arc power P _{1 is} maximum when the output voltage of the rectifier is known, R is the sum of the resistance of the two electrodes and the short grid resistance, and r ₃ is the bath resistance , U _jz1 is the cathode cut-off voltage, and U _jz2 is the anode cut-off voltage.

Step 2.3, determining the cathode arc length and the anode arc length according to the voltage across the arc, the cathode cutoff voltage, and the anode cutoff voltage;

The arc length calculation formula is:

Where b is the arc pressure coefficient, the arc pressure coefficient is determined experimentally, and b=0.75V/mm is found in the literature, where U _jz is u _jz1 or U _jz2 , so the calculation formulas of the cathodic arc length and the anode arc length are respectively as follows:

Wherein l ₁ is the length of the cathodic arc, l ₂ is the length of the anode arc, U _c is the voltage across the arc, l ₁ = 20.56 mm, l ₂ = 18.83 mm.

Step 2.4: Determine the arc power distribution on the surface of the molten pool under the influence of the cathode and the arc power distribution on the surface of the molten pool under the influence of the anode, and then determine the arc power distribution under the influence of the cathode and the anode on the surface of the molten pool.

The method for determining the arc power distribution of the surface of the molten pool under the influence of the cathode and the arc power distribution of the surface of the molten pool under the influence of the anode are as follows:

The heating heat flow distribution of the arc on the surface of the molten pool is regarded as a normal distribution as shown in FIG. 3, and the heating heat flow distribution is expressed as

Where q _max is the maximum heat flow at the center of the heated spot, r is the distance from any point on the surface of the molten pool to the center of the heated spot, and α is the coefficient of thermal energy concentration.

Formula for heating heat flow distribution

Integrate on the heated spot area to find the distribution of the actual unipolar arc power on the surface of the molten pool

Due to power loss, empirically Q = (0.65 ~ 0.7) P ₁ ', this embodiment takes 0.68, P ₁ ' is the arc power of a single electrode, that is, P ₁ ' = 0.5P ₁ , and the maximum heat flow at the center of the heated spot is obtained.

Where Q is the distribution of the actual unipolar arc power on the surface of the molten pool, and the heating heat flow distribution formula

Integral on the heated spot area, P ₁ is the arc power; according to the heating spot boundary radius r _m =0.5D+2l, the boundary heat flow q(r _m )=0.05q _max , and the heating heat flow distribution expression q(r) Find the thermal energy concentration factor

D is the electrode diameter, l is the arc length, and refers to the cathodic arc length or the anode arc length.

Find the distribution of the arc power of the single electrode on the surface of the molten pool: according to the obtained maximum heat flow q _max of the heating spot center, the thermal energy concentration coefficient α and the heating heat flow distribution expression q(r), the arc power of the single electrode is obtained. The distribution expression of the surface of the molten pool:

Where r is the distance from a point on the surface of the bath to the center of the heated spot.

The straight line of the coordinate line of the center line of the two electrodes is the horizontal axis of the coordinate line, and the straight line of the center line of the two electrodes is the vertical axis of the coordinate axis, and the axis of the center of the anode is the positive direction of the horizontal axis, according to The distribution of the arc power of a single electrode on the surface of the bath, p(r), represents the arc power distribution p ₁ (x, y) of the surface of the bath under the influence of the cathode and the arc power distribution p _{2 of the} surface of the bath under the influence of the anode (x) , y).

For a two-phase direct current fused magnesium furnace, due to the mutual exclusion of the electromagnetic force between the two opposite arcs, the two arcs are respectively shifted away from each other, and the center of the spot moves to the outside of the electrode by about 20 to 30 mm. The value is 25mm. therefore:

Where (x, y) is the coordinate of a point on the surface of the molten pool, and d is the center distance.

The arc power distribution under the influence of the cathode and the anode on the surface of the molten pool is the sum of the arc power distribution on the surface of the molten pool under the influence of the cathode and the arc power distribution on the surface of the molten pool under the influence of the anode, that is, p(x, y)=p ₁ (x, y) + p ₂ (x, y).

Step 3: Determine physical parameters of the two-phase DC fused magnesium furnace system, including:

(1) Find the center distance;

According to the law of conservation of energy, the expression of the surface area of the molten pool is determined: during the operation of the two-phase direct current molten magnesium furnace, the arc power P ₁ mainly acts as a molten material, and the resistance of the molten pool is mainly used for heat preservation. The portion of the thermal energy used to melt the material in the arc heat is referred to as the effective arc heat W. During the smelting process, the uppermost layer of the material in contact with the air radiates heat outward, and the heat dissipation efficiency is η ₁ . A small part of the arc heat is also used to heat the molten pool. This part of the heat is called thermal insulation, and its proportion is η ₂ . The surface area of the weld pool is determined by the law of conservation of energy:

Where q is the unit energy consumption of the magnesite as a raw material, ρ is the density of the fused magnesia, and h is the crystallization height. From the literature, it can be found that q = 2611 kWh / t, ρ = 3580 kg / m ³ , η ₁ = 0.03, η ₂ = 0.16, and the crystal height h is 0.2 m.

According to the shape of the surface of the molten pool, the expression of the surface area of the molten pool is determined: in the smelting process, if the pole center distance is too large, the maximum temperature between the two electrodes is low, resulting in an unmelted dead zone in the middle; Small, the maximum temperature between the two electrodes is too high, the temperature gradient is large, and the molten pool area is small. It can be seen that the smelting effect is best when the pole center length is exactly the melting radius of the electrode. At this time, the surface of the molten pool is approximated as shown in Fig. 6, and the expression of the surface area of the molten pool is obtained:

The two molten pool surface area expressions are combined to obtain the formula for calculating the pole center distance as follows:

Substituting the value is d≈0.175m.

(2) Determine the shape of the furnace shell according to the arc power distribution under the influence of the cathode and the anode and the obtained pole center distance.

The method for determining the shape of the furnace shell includes:

According to the arc power distribution p(x, y) and the obtained pole center distance d under the influence of the cathode and the anode on the surface of the molten pool, draw the equal power line on the surface of the molten pool, as shown in Fig. 7; according to the surface of the molten pool The outer power line determines the shape of the furnace shell as "peanut" type.

Claims (10)

1. A method for designing a pole center distance and a furnace shell shape for a two-phase direct current magnesium melting furnace, characterized in that it comprises:

   Designing the structure of a two-phase direct current fused magnesium furnace system;

   Obtaining an arc power distribution under the influence of the cathode and the anode on the surface of the molten pool;

   Determine the physical parameters of the two-phase DC fused magnesium furnace system, including:

   Find the center of the heart;

   The shape of the furnace shell is determined according to the arc power distribution under the influence of the cathode and the anode and the obtained pole center distance.
2. The method according to claim 1, wherein the specific method for determining the arc power distribution under the influence of the cathode and the anode on the surface of the molten pool comprises:

   Calculating the cathode cutoff voltage and the anode cutoff voltage according to the equivalent voltage drop of the electron energy in the cathode region and the equivalent electronic pressure drop of the anode region;

   Find the arc power and the voltage across the arc;

   The cathode arc length and the anode arc length are obtained according to the voltage across the arc, the cathode cutoff voltage, and the anode cutoff voltage;

   Determine the arc power distribution on the surface of the molten pool under the influence of the cathode and the arc power distribution on the surface of the molten pool under the influence of the anode, and then determine the arc power distribution under the influence of the cathode and the anode on the surface of the molten pool.
3. The method according to claim 2, wherein said method of calculating a cathode cutoff voltage and an anode cutoff voltage is as follows:

   Calculating the equivalent voltage drop of the electron energy in the cathode region and the equivalent pressure drop of the electron energy in the anode region according to the temperature at the heating spot of the electrode;

   The cathode cut-off voltage and the anode cut-off voltage were calculated based on the equivalent voltage drop of the electron thermal energy in the cathode region and the equivalent electronic pressure drop of the anode region.
4. The method of claim 2 wherein the method of solving the arc power is as follows:

   Calculate the resistance of the two electrodes according to the electrode size and resistivity, and measure the resistance of the short grid, and calculate the sum R of the resistance of the two electrodes and the short grid resistance;

   Estimate the weld pool resistance r ₃ according to the size of the weld pool and the resistivity of the weld pool;

   Calculating a DC current I _d ' when the arc power P _{1 is} maximum when the rectifier output voltage U _d is known;

   The arc power P ₁ =(U _d -RI _d '-r ₃ I _d '-U _jz1 -U _jz2 )I _d ' is obtained, and U _jz1 is the cathode cutoff voltage U _jz2 is the anode cutoff voltage.
5. The method according to claim 2, wherein the voltage across the arc is solved by the following formula:

   U _c =0.5×(U _d -RI _d '-r ₃ I _d '-U _jx1 -U _jz2 )

   Where U _d is the rectifier output voltage, I _d ' is the DC current when the arc power P _{1 is} maximum when the output voltage of the rectifier is known, R is the sum of the resistance of the two electrodes and the short grid resistance, and r ₃ is the bath resistance , U _jz1 is the cathode cut-off voltage, and U _jz2 is the anode cut-off voltage.
6. The method of claim 2 wherein said cathode arc length and anode arc length are calculated as follows:

   

   

   Wherein l ₁ is the length of the cathodic arc, l ₂ is the length of the anode arc, U _jz1 is the cathode cutoff voltage, U _jz2 is the anode cutoff voltage, U _c is the voltage across the arc, and b is the arc voltage coefficient.
7. The method according to claim 2, wherein the method for determining the arc power distribution of the surface of the molten pool under the influence of the cathode and the arc power distribution of the surface of the molten pool under the influence of the anode are as follows:

   The heating heat flow distribution of the arc on the surface of the molten pool is regarded as a normal distribution, and the heating heat flow distribution is expressed as

   

   Where q _max is the maximum heat flow at the center of the heated spot, r is the distance from any point on the surface of the molten pool to the center of the heated spot, and α is the coefficient of thermal energy concentration;

   Find the maximum heat flow at the center of the heated spot

   

   Where Q is the distribution of the actual unipolar arc power on the surface of the molten pool, and the heating heat flow distribution formula

   

   Integrate on the heated spot area, P ₁ is the arc power; thermal energy concentration factor

   

   D is the diameter of the electrode, l is the length of the arc, and refers to the length of the cathodic arc or the length of the anode arc;

   Find the distribution of the arc power of the single electrode on the surface of the molten pool;

   The straight line of the coordinate line of the center line of the two electrodes is the horizontal axis of the coordinate line, and the straight line of the center line of the two electrodes is the vertical axis of the coordinate axis, and the axis of the center of the anode is the positive direction of the horizontal axis, according to The distribution of the arc power of the single electrode on the surface of the molten pool indicates the arc power distribution of the surface of the molten pool under the influence of the cathode and the arc power distribution of the surface of the molten pool under the influence of the anode.
8. The method according to claim 2, wherein the arc power distribution of the surface of the molten pool under the influence of the cathode and the anode is an arc power distribution of the surface of the molten pool under the influence of the cathode and an arc power of the surface of the molten pool under the influence of the anode The sum of the distribution.
9. The method of claim 1 wherein said polar distance is calculated as follows:

   

   Where η ₁ is the heat dissipation efficiency, η ₂ is the proportion of heat preservation heat energy, q is the product energy consumption of magnesite as raw material, ρ is the density of fused magnesia, h is the crystal height, and P ₁ is the arc power. .
10. The method of claim 1 wherein the method of determining the shape of the furnace shell comprises:

    According to the arc power distribution under the influence of the cathode and the anode and the obtained pole center distance, the equal power line on the surface of the molten pool is drawn; the shape of the shell is determined according to the equal power line around the surface of the bath.

Images