METHOD FOR CALCULATING THE LEVEL OF ENAMELLING AND TEMPERATURE CONDITIONS ON CURRENT CONDUCTORS AT DIFFERENT SPEEDS IN CABLE PRODUCTION PROCESSES

ABSTRACT

The article presents a methodology for calculating the level of enameling and temperature conditions on conductors at various speeds in the processes of cable production. The technique is intended for - solving the analytical problem of specific temperature heating of insulating varnish, which is the determination of the amount of application of protective coatings using heat treatment in the furnace enamel. The functionality of the technique makes it possible to calculate the technological process of the degree of enamel application on current-carrying parts to solve the problem of the degree of baking of wire enamel insulation, and as a result of which an insulating coating is formed for exploiting the insulating capacity of current-carrying parts of electrical installations. Allows you to increase the energy and resource saving of electrical installations, due to the smooth temperature control and increases the energy efficiency of this equipment.

АННОТАЦИЯ

В статьи приведено методика расчета уровня эмалирования и температурных режимов на токопроводах при различных скоростях в процессах кабельного производства. Методика предназначена для – решения аналитических задачи удельных температурных нагревов изоляционного лака, представляющей собой определение количества нанесения защитных покрытий при помощи теплового обработки в эмаль печи. Функциональные возможности методики позволяют осуществить расчет технологического процесса степени нанесения эмали на токоведущих частях для решения задачи по степени запечки изоляции эмаль проводов, и в результате которой образуется изоляционное покрытие для эксплуатации изоляционных способности токоведущих частей электроустановок. Позволяет повысить энерго- и ресурсосбережение электроустановок, за счет плавного регулирования температуры и повышает энергоэфективности данного оборудования.

Keywords: enameling, temperature regime, cable products, thermal energy, wire, enameling speed.

Ключевые слова: эмалирование, температурный режим, кабельная продукция, тепловая энергия, проволока, скорость эмалирования.

Wire enamelling is the application of liquid varnish to the surface of the wire, followed by heat treatment in an enamel oven, which results in the formation of an insulating coating. The quality of the resulting insulating coating depends on the physicochemical properties of the lacquer, on the quality of the surface of the enamelled wire, and on the correct modes of applying the lacquer to the wire, followed by heat treatment [1-3].

The productivity of the wire enameling process and the quality of the resulting wires are largely determined by the temperature conditions of the enamel furnace. Round enameled wires are usually made in the range of diameters from 0.05 to 2.5 mm, while the minimum insulation thickness (on one side) is on average, respectively, from 0.005 to 0.035 mm (PEV-2, PETV-2). The insulation is applied in 5-12 passes through the varnishing unit and the heat treatment oven.

When a wire with a layer of varnish applied to it is heated, the solvent is first removed, during which energy is spent on its evaporation. This energy should be taken into account when calculating the heating of the wire, especially if the wire diameter is less than 0.1 mm.

The heating of the wire occurs both due to the heat input during convective heat exchange with hot air q_к, and during heat exchange by radiation from the walls of the furnace chamber q_i. Convective heat transfer is the transfer of heat during the movement of a liquid or gas. Convective heat transfer is always accompanied by heat conduction, so one of the problems encountered in solving problems of convective heat transfer is the problem of assessing the influence of each of the two heat transfer mechanisms. Determination of the contribution of thermal conductivity and convection to the overall process of heat transfer greatly facilitates the construction of a mathematical model of the process under study [4-5].

Convective heat transfer - convective heat transfer between the surface of a solid body and a liquid. The calculation of the heat transfer process is based on the ratio of the Newton–Richmann law:

dQ_c=α(T_c – T_ж)dF (1)

according to which the heat flow dQ_c from the liquid to the body surface element dF is directly proportional to the area of the element dF and the temperature difference between the body surface T_c and the liquid temperature T_f. The temperature difference ∆T = T_c – T_f is called the temperature difference, and the surface of the body through which heat is transferred is the heat transfer surface or heat-releasing surface.

The coefficient of proportionality α is called the heat transfer coefficient (measured in W/m².K). Transforming relation (1), we obtain:

α= dQ_{c c}/( T_c – T_f)dF= q_c/∆T    (2)

Relation (2) allows us to determine the heat transfer coefficient as the heat flux density q_c at the boundary of the liquid (gas) and the body being washed, referred to the temperature difference between the surface of this body and the environment. The calculation of convective heat transfer is associated with the determination of the heat transfer coefficient

If we take into account that the heat transfer from the heated gas to the wire in enamel furnaces occurs under conditions close to heat transfer with the free movement of the coolant, then using the criterion similarity equations, we can obtain an expression for the convective heat transfer coefficient:

α=1,18λ(gβ∆tPr)/d^0,625· v^0,625    (3)

where λ - the coefficient of thermal conductivity of the gas; g - the acceleration of the composite fall; β - the gas volume expansion coefficient; ∆t - the temperature difference between the wire and the gas; v - the coefficient of kinematic viscosity of the gas; Pr - the Prandtl criterion; d - the wire diameter.

The use of equation (3) for practical calculations is difficult, since most of the quantities included in it are variables that depend on the air temperature (λ, β, v, Pr) or on the temperature difference between the wire and air (∆Т).

При эмалировании проволоки в широких пределах изменяются как температура воздуха, так и температура проволоки; кроме того, при решении ряда практических задач заранее неизвестны температура газа по длине печи, а также температура проволоки, которую необходимо знать для определения ∆Т.

When enameling a wire, both the air temperature and the temperature of the wire change over a wide range; in addition, when solving a number of practical problems, the gas temperature along the length of the furnace, as well as the wire temperature, which must be known to determine ∆Т, are not known in advance.

The problem can be simplified by introducing a new notation into the equation

E=(gβ∆tPr)^0,125λ/v^0,625    (4)    then   α=(1,18/ d^0,625)E    (5)

The value of E is a function of the temperature of the gas and wire. Despite the change in air and wire temperature, within a wide range, the value of E along the height of the enamel oven does not change much and averages 0.39, and when enameled with polyester varnishes, E = 0.41. Similar calculations when using polyurethane varnishes give E = 0.38.

Thus, under different thermal conditions of enamelling, the value of E changes insignificantly. In this regard, for the conditions of wire enamelling, we can take the average value of Е_ср = 0.39. Taking into account Е_ср and equation (3), one can obtain a simple formula for α_ср

α=0,47/ d^0,625, kcal/m2•h•deg   (6)

Calculations by (6) give an error with respect to the values obtained by (3) within ±6%. It should be emphasized that according to (6) the average value of αav is determined in the process of heating the wire.

Comparison of the α_ср values obtained by (6) with the experimental data shows that the calculated and experimental results are quite close.

The heat input due to convection is determined by the formula

q_к=pα_к(T_в – T_н),    (7)

where p - the outer perimeter of the wire; Т_в - air temperature in the furnace chamber; α_k - the heat transfer coefficient.

Heat input due to thermal radiation

q_и=pα_и(T_с – T_н)=рφ_Пε_ПС₀θ(T_с⁴ – T_н⁴), (8)

where α_i = φ_Пε_ПС₀θ; Tc - the temperature of the furnace chamber walls; C₀=5,7.10^–8 J•m^–2·К^-4 – absolute black body radiation constant; ε_П = 0.05...0.1 is the emissivity of the surface of pure metals; ε_П = 0.8...0.9 - for polymer coatings; φ_П = 0.8...0.9 - angular coefficient of wire irradiance.

If d > 0.1 mm, then in furnaces without forced gas convection (old designs), the gas velocity is low, and formulas (7) are used to calculate the coefficient αk. With free convection

α_к=0,47d^-0,625                 (9)    

At an air velocity of more than 0.5 m / s in furnaces with forced circulation of gases, the formula is used

α_к=1,43v_в^0,41d^-0,59  (10)

v_в – air velocity, m/s. In the furnace chamber of enamel units, hot air moves at a significant speed (from 0.2 to 5 m/s), so the temperature difference between the air and the heated inner walls of the furnace can reach several tens of degrees. To measure the air temperature in the furnace, a thermocouple is pulled through and some effective temperature of the thermocouple sensor is determined, which differs from the air temperature in the furnace.

If a stationary thermocouple is placed in the furnace chamber, then

α_к= (T_в - Т_т)+α_и(T_с - Т_т)=0,              (11)

where Т_т - the thermocouple temperature; α_к and α_и - heat transfer coefficients by convection and radiation for a thermocouple

In accordance with equation (11), the temperature of the thermocouple Т_т is in the interval between the air temperature Tb and the wall temperature Tc. The radiative heat transfer coefficient α_и can also be calculated using equation (11) with the remaining parameters α_к, T_c, T_т, T_в. known.

To increase the speed of enamelling, the intensity of heating the wire is increased. To do this, they strive to maintain the maximum temperature throughout the furnace chamber and increase the heat transfer coefficient α by increasing the circulation rate of hot gases in the furnace chamber. However, at very high temperatures it is possible to ignite solvent and varnish vapors on the wire, especially at the time of a wire break and other shutdowns. In addition, at high temperatures, the strength of the metal decreases and the wire breakage increases. Typically, the temperature in the chamber does not exceed 500...550 °C, and the gas velocity is within 2...8 m/s.

The heat balance for a wire can be written as an equation:

q_м+q_э+q_p= q_м+q_к, (12)

where q_м, q_э, q_p - the consumption of thermal energy for heating the metal of the wire, the enamel layer and removing the solvent.

The energy consumption for heating the wire metal and enamel per unit length of the wire is:

q_э+ q_м=( С_э+ С_м)dT_п/dt=k_эC_мdT_п/dt,  (13)

energy consumption for solvent removal:

q_р= – r_мdG_p/dt= –r_иρ_эS_эdW/dt, (14)

where T_п - the temperature of the wire.

The consumption of thermal energy for heating the enamel film to the boiling point of the solvent Т_к and its evaporation per unit length of the wire is:

q_э = m_эc_эT_к+m_рr_и=m_э(с_эТ_к+xr_и).         (15)

Let us determine the consumption of thermal energy for heating the metal of the wire and the enamel film per unit of its length:

q_м = m_мc_э∆Т_м =π/4d²_мρ_мc_м∆Т_м, (16)

q_э = m_эc_эS_э  (17)

where S_м and S_э  are the cross section of metal and enamel; с_м and с_э - their specific heat capacities; W, x - respectively, the mass of the solvent and its proportion contained in the enamel; Se is the section of the enamel layer applied in one pass; ρ_э – enamel density; r_и - the specific heat of evaporation of the solvent from the lacquer.

If the temperature in the leak were maintained constant and greatest along the entire length of the heating zone, then Т_т in equation (11) would not depend on the length of the furnace. Under these conditions, this equation takes the form

T_н = T_т – (T_т – T_и)e^-μt,     (18)

where Т_н is the initial temperature of the wire when it enters the furnace; t - the time spent by the wire at a constant temperature Т_п; 1/μ = τ – wire heating time constant.

For rectangular wire

µ= αP/kc_мS_мρ_м,     (19)

For round wire

µ= 4α/kc_мdρ_м,       (20)

where α=α_к+α_и;k=1 dimensionless coefficient.

As the wire is heated, its temperature will reach the base temperature Tb, at X=L₁ in the range of x from 0 to L₁, the solvent is removed. With further heating of the wire in the area from x = L₁ to x = L (L is the total length of the furnace), the process of film formation occurs. At the end of heating, at x = L, the temperature of the wire is maximum, Т_п = T_м.

Since the air temperature along the length of the furnace is in practice unevenly distributed, therefore, equation (15) makes it possible to calculate only an approximate value of the wire temperature in each section of the furnace. The greatest difference between the temperature of the wire and its calculated value will take place in the initial heating section.

In the literature, there is a method for calculating the temperature of the wire and the average rate of its heating based on the degree of completion of the baking process. With a linear law of temperature change in the areas of solvent evaporation and film formation, the total residence time of the wire in the furnace t = L/ν and the enameling rate ν are determined

v = Lμ/((T_т – T_н)/(T_т – T_м)).               (21)

The above equation gives an underestimated enamelling rate, which is mainly due to an underestimated value of T_b.

Determination of thermal parameters of enameling wires PET 155 with a diameter of 1.25 mm

We determine the coefficient of convective heat transfer by the formula (10):

α_к=1,43v_в^0,41d^-0,59

where v_в=1 m/s is the air velocity in the furnace; d = 1.25 – enameled wire diameter, mm; then

α_к=1,43·1^0,41(1,25·10^-3)^-0,59=73,8 Вт/м²·°C

We determine the radiation coefficient based on formula (11) for the stationary mode:

α_к= (T_в - Т_т)+α_и(T_с - Т_т)=0,

α_из= α_из(T_в - Т_т)+α_и(T_с - Т_т)=73,8·(500-525)/(550-525) = 73,8 Вт/м²·°C,

We find the constant of the heating rate of the wire µ according to the equation (20):

μ¹=4(α_к/α_из)kc_мd=4·(73,8+73,8)/1·385·1,25·10^-3 = 1227,1 kg/s·м³

где c_м = 385 Дж/кг·К– удельная теплоемкость меди; k = 1 – безразмерный коэффициент; d = 1,25 мм – диаметр провода.

where c_м = 385 J/kg•K is the specific heat capacity of copper; k = 1 is the dimensionless coefficient; d = 1.25 mm - wire diameter.

μ=μ¹/ ρ_м=1227,1/8900=0,138 с^-1

where  = 8900 kg/m³ – copper density

The time constant for heating a wire with a diameter of 1.25 mm is:

τ=1/ μ=1/0,138=7,25 с

Let's determine the amount of heat to heat 1 m of copper wire to a temperature Т_mах = 525

q_м = c_мm_м(T_мах – T_н) = c_мρ_мπR²l(T_мах – T_н) =

= 385·8900·3,14·(0,625·10^-3)²·1·(525 – 25) = 2101 J

where m_м – the mass of 1 m of wire, kg

Let's determine the amount of heat to heat 1 m of the enamel film to a temperature of T_max = 525 °C:

q_э = c_эm_э(T_мах – T_н) = с_эρ_э2πRl∆ =

1300·1200·2·3,14·0,625·10^-3·1·1·10^-5·(525-25) = 30,6 J

where m_e - the mass of enamel on a wire length of 1 m, kg; ρ_э,с_э – density specific heat of enamel; ∆ is one-sided enamel thickness.

Let us determine the amount of heat for the evaporation of the solvent over a wire length of 1 m:

q¹_р = m_рq_исп = ρ_рSlq_исп = q_рπd∆lq_исп = 1030·3,14·1,25·10^-3·1·10^-5·1·420 = 16,98 J,

where m - the mass of the solvent per 1 meter of wire, kg; ρ_р- the density of the solvent (Tricresol technical coal); q_исп –the specific heat of evaporation of the solvent. However, in real conditions, the enamel film contains from 60 to 65% of the solvent, then

q_р = 60...65 %; q_р'= 0,6·16,98 = 10,19 J.

In table. 1 shows the calculated data on thermophysical properties for a wire diameter of 1.25 mm.

Table 1.

Thermophysical properties of the enameled wire

Calculation of the temperature of a wire with a diameter of 1.25 mm along the length of the furnace in a vertical line type "YL 7100" for various enameling speeds

The calculation of the temperature distribution of the wire with a diameter of 1.25 mm along the length of the furnace passage is carried out according to the formula (18). We divide the air temperature distribution curve in the furnace into time intervals (Fig. 1) and calculate the wire temperature in sections for an enameling speed of 25 m/min. Formula (1) is valid for a stationary mode, that is, when the air temperature in the furnace has a constant value and does not change along the entire length. However, in real conditions, the air temperature in the furnace is not constant and has a non-linear distribution (Fig. 1). In contrast to the Kholodny method, in order to increase the accuracy when calculating the wire temperature, we divide the air temperature distribution curve into sections with a duration of 0.6 s. That is, we replace the curve with a stepped distribution (Fig. 1), and in each section we find the average value of the air temperature T_т. Then the initial temperature of the wire at the entrance to the next section T_н will be equal to the temperature of the wire at the end of the previous section. At an enameling speed of 25 m/min, an elementary section of wire passes through the furnace in 14.4 s. We divide the curve into sections with a duration of 0.6 s (Fig. 1) and for each section we calculate the temperature of the wire at the exit from this section according to expression (1).

Figure 1. Stepwise distribution of air temperature along the length and time spent in the furnace of the enamel unit "YL 7100" (enamelling speed 25 m/min)

For the initial heating section of the wire (t₀) over a length of 0...25 cm, the initial data are:

t₀ = 0...0,6 с, Т_т  = 40 °C, T_н  = 22 °C,  µ = 0,138 с^-1, then

T_п = T_т – (T_т – T_н)·e^-µt = 40 – (40 – 22)·e^-0.138·0.6 = 23 °C

For the first (t₁) section:

t₁ = 0,6...1,2 с, Т_т  = 80 °C, T_н  = 23 °C,  µ = 0,138 с^-1, then

T_п = T_т – (T_т – T_н)·e^-µt = 80 – (80 – 23)·e^-0.138·0.6 = 28 °C

For the second (t₂) section:

t₂ = 1,2...1,8 с, Т_т  = 175 °C, T_н  = 28 °C,  µ = 0,138 c^-1, then

T_п = T_т – (T_т – T_н)·e^-µt = 80 – (80 – 28)·e^-0.138·0.6 = 40 °C

For the third (t₃) section

t₃ =1,8...2,4 с, Т_т  = 227,5 °C, T_н  = 40 °C,  µ = 0,138 c^-1, then

T_п = T_т – (T_т – T_н)·e^-µt = 227,5 – (227,5 – 40)·e^-0.138·0.6 = 55 °C

The results of Т_пр  calculations for enameling speeds of 25 and 20 m/min are presented for all subsequent sections in table. 2. Similarly, we divide the air temperature distribution curve in the oven into time intervals and perform the calculations indicated above for any enamelling speeds. On fig. 2 shows temperature dependences of PET 155 wire with a diameter of 1.25 mm along the length of the furnace of the YL 7100 enamel unit for various enamelling speeds.

Based on the calculated data, the dependences of the maximum wire temperature on the enameling rate for a wire with a diameter of 1.25 mm are plotted.

The results of Tpr calculations for enameling speeds of 25 and 20 m/min are presented for all subsequent sections in Table. 2. Similarly, we divide the air temperature distribution curve in the oven into time intervals and perform the calculations indicated above for any enamelling speeds. On Fig. 2 shows temperature dependences of PET 155 wire with a diameter of 1.25 mm along the length of the furnace of the YL 7100 enamel unit for various enamelling speeds.

Based on the calculated data, the dependences of the maximum wire temperature on the enameling rate for a wire with a diameter of 1.25 mm are plotted.

Figure 2. Temperature distribution of a wire with a diameter of 1.25 mm along the length of the furnace "YL 7100" at various enameling speeds, m/min: 1 – 25; 2 – 20; 3 – 15; 4 –10;

From fig. 2 it follows that with an increase in the enamelling rate, the wire heats up more slowly and its maximum temperature decreases. This is due to the fact that the higher the enameling speed, the shorter the time it is in the oven, being subjected to less temperature stress.

If the enamelling rate is slow, the wire will stay in the oven for too long and its insulation will age quickly due to the high temperatures in the oven. However, if the enameling speed is too high, the wire will not have time to heat up enough, the rate of the chemical reaction will slow down and, consequently, the degree of completion of the process of structuring the enamel coating will decrease. In both cases, the wire will not meet the necessary requirements. It is necessary to choose an enameling speed at which the wire would withstand all the foreseen tests on the product and ensure the rational use of materials and electricity. From the foregoing, the most energy-intensive system is temperature control, since the installation does not provide for smooth temperature control and the task is to increase both the reliability and energy efficiency of this equipment.

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