Abstract : Based on the short-wave infrared heating furnace used in galvanizing coating units, considering the influence of strip steel, coating, unit speed and other factors, the thermal balance of the infrared heating furnace was analyzed and the mathematical model for solving was established. After a series of theoretical deductions, the solution to the input voltage was finally established and the control of the infrared heating furnace was achieved.
l Introduction
In the production process of galvanized coated steel sheet, the drying of the coating is the key. In view of the good and quick drying effect of short-wave external heating furnaces, an electro-galvanizing coating unit of Baosteel adopts this equipment.
Infrared heating furnaces use infrared radiation principle to heat and dry materials. Compared with traditional heating and drying methods, infrared heating has high thermal conversion efficiency, fast response time, short time for heating and drying, compact footprint, stable and reliable operation, and convenient and safe maintenance [1]. Therefore, infrared heating technology has been gradually applied to more and more fields. However, the application of infrared heating furnace in dry electro-galvanizing is not very extensive, and the power analysis of infrared heating furnace is not yet mature. Analyze the strip steel through thermal equilibrium theory.
The influence of factors such as coating and unit speed on the power density of the system enables accurate control and easy operation of the infrared heating furnace.
2 Infrared heating furnace heat balance analysis
Using the heat balance method [1], according to the law of conservation of energy
Q'=Q1+Q2+Q3+Q4+Q5(1)
In the formula: Q'--the heat provided by the infrared heating furnace per unit of time;
Q1--heat required to heat the workpiece in unit time;
Q2 - the energy consumed to heat the workpiece substrate attachment in unit time;
Q3 - the amount of heat lost in the furnace in the unit;
Q4 - the amount of heat lost through the gap per unit of time;
Q5—The amount of heat taken away by the air per unit of time.
Taking into account other unknown heat losses, take the safety factor Kq, which ranges from 1.1 to 1.2. The actual infrared heating furnace power is:
Q=KqQ'(2)
Infrared heating furnace for continuous operation, that is, after setting the initial value, as long as the heating of the workpiece and the request does not change, the furnace will not change the working status, and the processed workpiece is to meet the requirements. This concludes that: In addition to the start-up phase, the infrared heating furnace is always in a stable state, ie the energy output and the energy input are in equilibrium. Therefore, the ratio of Q1 and Q2 as the effective energy consumption of the heating furnace remains basically unchanged. Then, the ratio between the two is the overall efficiency of the infrared heating furnace, which is denoted by η. It is generally 0.6 to 0.8. Then there are:
Q=(Q1+Q2)/η(3)
In order to simplify the calculation process, the right side of the equation is divided by the corresponding heated area and converted into a power density relationship. which is:
Qw=qcoil/εcoil+qcoating/εcoating+qvapor)/η(4)
Where: qw - the power density of the required infrared radiator;
Qcoil - the power density required to heat the workpiece;
Εcoil—absorption rate of the workpiece;
Qcoating--power density required for coating on the workpiece surface;
Εcoating - the absorptivity of the coating;
Qvapor - The power density at which the coating contains evaporated water.
The calculation method of each variable in equation (4) is introduced one by one below. First, calculate the required power density of the strip. This should take into account the thermal conductivity of the material and the effect of strip thickness.
Thermal conductivity, also known as thermal conductivity, is a measure of the material's thermal conductivity, expressed in λ, in W/m·K. According to heat transfer theory [2]
Q=λAΔT'/δ (5)
Where: Q - heat transfer, W / δ;
Thermal conductivity of λ--material, W/m·K;
A--heat transfer area, m2;
ΔT' - the temperature difference between the two sides of the thermal material, K;
Δ--thickness of material, m.
Let RK = δ/λA, call it thermal resistance, which can be understood by comparing the resistance.
Next introduce a term, thermal diffusion coefficient α [3], which is a measure of the speed of heat transfer, the unit is m2/s. The formula is:
α=λ/CPÏ(6)
Where: λ - the thermal conductivity of the material, W / m · K;
CP—specific heat capacity of the material, J/kg·K;
Ï - the density of the material, kg/m3.
The strip heating time td is:
Td=L/v(7)
Where: L - total heating length;
V - the speed of the strip.
According to the basic formula of heat transfer, the formula for calculating qcoil is:
Qcoil=Q/A=6λ0δΔT/(12αtd+δ2) (8)
Where: λ0 - overall thermal conductivity, W/m·K, usually taken as 1.0:
δ - strip thickness, m;
â–³T - temperature rise of strip, K;
α - thermal diffusion coefficient, m2/s;
Td - heating time, s.
The power density qcoating absorbed on each side of the strip coating is:
Qcoating=Q2'/tdA=CcoatingÏcoatingAΔT/tdA=CcoatingÏcoatingΔT/td(9)
Where: Ccoating - specific heat capacity of the coating, J / kg · K;
Ρcoating - coating thickness, kg/m2;
â–³T - temperature rise of the coating, K;
Td - heating time, s.
The power density, qvapor, required to volatilize the moisture contained in the coating on each side of the strip is:
Qvapor=Q2'/tdA=βÏcoatingALs/tdA=βÏcoatingLs/td(10)
Where: β - the humidity of the coating;
Ρcoating - coating thickness, kg/m2;
Ls - the heat of evaporation of water, usually 2272 × 103J/kg;
Td - heating time, s.
Substituting equations (7), (8), and (9) (10) into (4) gives the actual required power density calculation formula. Notice the few unknowns inside: coating thickness Ïcoating, humidity β, strip speed ν, and strip thickness δ.
Set a coating, then determine the coating thickness and humidity. When the strip speed is fixed, the relationship between power density and strip thickness is plotted using Matlab software as shown in Figure 1.
As can be seen from the figure, as the strip thickness increases, the absorbed power density also increases, but the trend gradually slows down. This is mainly due to the effect of thermal diffusivity, and the heat transferred during a limited period of time does not increase with thickness. When the strip thickness reaches 2mm, the absorbed power density is basically no longer much changed.
3 infrared heating furnace control strategy
To improve the efficiency of the infrared heating furnace, the key is to achieve the best matching absorption, which is the control of the infrared heater temperature. The main factor affecting the heater surface temperature is the voltage [1]. Therefore, the control of the voltage is the key. From the power formula:
P=U2/R(11)
Then there are:
P/P0=(U2/R)/(U02/R0)=(U/U0)2R0/R(12)
In the formula: P0, U0 - infrared lamp rated power and voltage;
P, U - infrared lamp actual power and voltage;
R0——Resistance of infrared lamp at rated voltage;
R—IR lamp resistance at actual voltage.
Since U0>U, the heat of the infrared lamp at a rated voltage per unit time is greater than that under actual conditions, and the temperature of the infrared lamp is higher than that under actual conditions. It is also known that the resistance and temperature of a tungsten wire approximately satisfy the following formula:
R2=Rl(1+0.0045T)(13)
l Introduction
In the production process of galvanized coated steel sheet, the drying of the coating is the key. In view of the good and quick drying effect of short-wave external heating furnaces, an electro-galvanizing coating unit of Baosteel adopts this equipment.
Infrared heating furnaces use infrared radiation principle to heat and dry materials. Compared with traditional heating and drying methods, infrared heating has high thermal conversion efficiency, fast response time, short time for heating and drying, compact footprint, stable and reliable operation, and convenient and safe maintenance [1]. Therefore, infrared heating technology has been gradually applied to more and more fields. However, the application of infrared heating furnace in dry electro-galvanizing is not very extensive, and the power analysis of infrared heating furnace is not yet mature. Analyze the strip steel through thermal equilibrium theory.
The influence of factors such as coating and unit speed on the power density of the system enables accurate control and easy operation of the infrared heating furnace.
2 Infrared heating furnace heat balance analysis
Using the heat balance method [1], according to the law of conservation of energy
Q'=Q1+Q2+Q3+Q4+Q5(1)
In the formula: Q'--the heat provided by the infrared heating furnace per unit of time;
Q1--heat required to heat the workpiece in unit time;
Q2 - the energy consumed to heat the workpiece substrate attachment in unit time;
Q3 - the amount of heat lost in the furnace in the unit;
Q4 - the amount of heat lost through the gap per unit of time;
Q5—The amount of heat taken away by the air per unit of time.
Taking into account other unknown heat losses, take the safety factor Kq, which ranges from 1.1 to 1.2. The actual infrared heating furnace power is:
Q=KqQ'(2)
Infrared heating furnace for continuous operation, that is, after setting the initial value, as long as the heating of the workpiece and the request does not change, the furnace will not change the working status, and the processed workpiece is to meet the requirements. This concludes that: In addition to the start-up phase, the infrared heating furnace is always in a stable state, ie the energy output and the energy input are in equilibrium. Therefore, the ratio of Q1 and Q2 as the effective energy consumption of the heating furnace remains basically unchanged. Then, the ratio between the two is the overall efficiency of the infrared heating furnace, which is denoted by η. It is generally 0.6 to 0.8. Then there are:
Q=(Q1+Q2)/η(3)
In order to simplify the calculation process, the right side of the equation is divided by the corresponding heated area and converted into a power density relationship. which is:
Qw=qcoil/εcoil+qcoating/εcoating+qvapor)/η(4)
Where: qw - the power density of the required infrared radiator;
Qcoil - the power density required to heat the workpiece;
Εcoil—absorption rate of the workpiece;
Qcoating--power density required for coating on the workpiece surface;
Εcoating - the absorptivity of the coating;
Qvapor - The power density at which the coating contains evaporated water.
The calculation method of each variable in equation (4) is introduced one by one below. First, calculate the required power density of the strip. This should take into account the thermal conductivity of the material and the effect of strip thickness.
Thermal conductivity, also known as thermal conductivity, is a measure of the material's thermal conductivity, expressed in λ, in W/m·K. According to heat transfer theory [2]
Q=λAΔT'/δ (5)
Where: Q - heat transfer, W / δ;
Thermal conductivity of λ--material, W/m·K;
A--heat transfer area, m2;
ΔT' - the temperature difference between the two sides of the thermal material, K;
Δ--thickness of material, m.
Let RK = δ/λA, call it thermal resistance, which can be understood by comparing the resistance.
Next introduce a term, thermal diffusion coefficient α [3], which is a measure of the speed of heat transfer, the unit is m2/s. The formula is:
α=λ/CPÏ(6)
Where: λ - the thermal conductivity of the material, W / m · K;
CP—specific heat capacity of the material, J/kg·K;
Ï - the density of the material, kg/m3.
The strip heating time td is:
Td=L/v(7)
Where: L - total heating length;
V - the speed of the strip.
According to the basic formula of heat transfer, the formula for calculating qcoil is:
Qcoil=Q/A=6λ0δΔT/(12αtd+δ2) (8)
Where: λ0 - overall thermal conductivity, W/m·K, usually taken as 1.0:
δ - strip thickness, m;
â–³T - temperature rise of strip, K;
α - thermal diffusion coefficient, m2/s;
Td - heating time, s.
The power density qcoating absorbed on each side of the strip coating is:
Qcoating=Q2'/tdA=CcoatingÏcoatingAΔT/tdA=CcoatingÏcoatingΔT/td(9)
Where: Ccoating - specific heat capacity of the coating, J / kg · K;
Ρcoating - coating thickness, kg/m2;
â–³T - temperature rise of the coating, K;
Td - heating time, s.
The power density, qvapor, required to volatilize the moisture contained in the coating on each side of the strip is:
Qvapor=Q2'/tdA=βÏcoatingALs/tdA=βÏcoatingLs/td(10)
Where: β - the humidity of the coating;
Ρcoating - coating thickness, kg/m2;
Ls - the heat of evaporation of water, usually 2272 × 103J/kg;
Td - heating time, s.
Substituting equations (7), (8), and (9) (10) into (4) gives the actual required power density calculation formula. Notice the few unknowns inside: coating thickness Ïcoating, humidity β, strip speed ν, and strip thickness δ.
Set a coating, then determine the coating thickness and humidity. When the strip speed is fixed, the relationship between power density and strip thickness is plotted using Matlab software as shown in Figure 1.
As can be seen from the figure, as the strip thickness increases, the absorbed power density also increases, but the trend gradually slows down. This is mainly due to the effect of thermal diffusivity, and the heat transferred during a limited period of time does not increase with thickness. When the strip thickness reaches 2mm, the absorbed power density is basically no longer much changed.
3 infrared heating furnace control strategy
To improve the efficiency of the infrared heating furnace, the key is to achieve the best matching absorption, which is the control of the infrared heater temperature. The main factor affecting the heater surface temperature is the voltage [1]. Therefore, the control of the voltage is the key. From the power formula:
P=U2/R(11)
Then there are:
P/P0=(U2/R)/(U02/R0)=(U/U0)2R0/R(12)
In the formula: P0, U0 - infrared lamp rated power and voltage;
P, U - infrared lamp actual power and voltage;
R0——Resistance of infrared lamp at rated voltage;
R—IR lamp resistance at actual voltage.
Since U0>U, the heat of the infrared lamp at a rated voltage per unit time is greater than that under actual conditions, and the temperature of the infrared lamp is higher than that under actual conditions. It is also known that the resistance and temperature of a tungsten wire approximately satisfy the following formula:
R2=Rl(1+0.0045T)(13)
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