A method for predicting the surface temperature uniformity of casting roll

Abstract

The invention discloses a method for predicting the surface temperature uniformity of a casting roller, and the prediction method comprises the following steps: obtaining the geometric dimensions of the casting roller; calculating the pitch of the spiral flow channel of the casting roller, the total length of the spiral line, the flow channel width, the hydraulic diameter and the water flow rate in the spiral flow channel; calculating the Reynolds number (Re number) of the water flow; calculating the Darcy resistance coefficient of the turbulent flow in the spiral flow channel, the inlet effect correction coefficient and the Nusselt number (Nu number) of the heat exchange process between the solid and the water side inside the casting roller; calculating the total heat transfer coefficient of the casting roller; calculating the temperature slope of the casting roller shell to reflect the temperature uniformity of the casting roller. Compared with the finite element analysis method, the prediction method of the invention has a faster analysis speed and more flexible and universal applicability. The method is highly consistent with the three-dimensional simulation calculation results and has good accuracy. Therefore, it can save calculation time, facilitate the subsequent casting roller flow channel design and structural optimization, and save the manufacturing cost of the casting roller.

Description

Technical Field

[0001] The invention belongs to the field of film manufacturing, and in particular relates to a method for predicting the surface temperature uniformity of a casting roller. Background Art

[0002] In the process of film manufacturing by cast film method, the surface temperature uniformity of the casting roller directly affects the quality of the film. If the temperature difference on the roller surface is too large, the film may have poor crystallization and other problems. At present, the detection of temperature uniformity is often carried out by measuring the surface temperature of the roller using infrared imaging after the finished product is processed. Once the surface temperature uniformity of the casting roller does not meet the relevant requirements, it will cause huge economic losses. Therefore, it is necessary to predict the temperature uniformity through numerical simulation methods. The heat exchange process on the outer surface of the casting roller involves three forms: conduction, convection and radiation, and its temperature uniformity is difficult to control. As the size of the casting roller becomes larger and larger, the internal flow channel design is complex, and there are many factors affecting the temperature uniformity, it is becoming increasingly difficult to control the temperature range within a certain threshold.

[0003] By observing the temperature distribution of the casting roller shell, it was found that the shell surface temperature distribution is linear as a whole. Therefore, when the length of the casting roller remains unchanged, the shell surface temperature difference can be predicted based on the temperature slope value on the casting roller shell temperature distribution diagram. Summary of the invention

[0004] The purpose of the present invention is to overcome the above problems existing in the prior art and provide a method for predicting the surface temperature uniformity of a casting roller. The method can quickly predict the surface temperature uniformity of a casting roller with different parameter combinations and study the influence of different parameters on the temperature uniformity, which is convenient for subsequent optimization, reduces the cost and time of three-dimensional simulation calculations, and has more flexible and universal applicability.

[0005] In order to achieve the above technical objectives and the above technical effects, the present invention is implemented through the following technical solutions:

[0006] A method for predicting the surface temperature uniformity of a casting roll, the method comprising the following steps:

[0007] Step 1: Obtain the geometric dimensions of the casting roll as the data basis for subsequent calculations;

[0008] Step 2: extract the rise angle, diameter and number of the casting roll to calculate the pitch, total length of the spiral line, width of the spiral channel, hydraulic diameter and water flow rate in the spiral channel of the casting roll;

[0009] Step 3: extract the water flow rate, kinematic viscosity and hydraulic diameter in the spiral flow channel of the casting roller to calculate the Reynolds number of water;

[0010] Step 4: Extract the Reynolds number of water flow, the hydraulic diameter of the spiral flow channel, and the inner end diameter of the casting roller, and calculate the Darcy drag coefficient of the turbulent flow in the spiral flow channel, the inlet effect correction coefficient, and the Nu number of the heat exchange process between the solid and water sides inside the casting roller;

[0011] Step 5: Obtain the heat transfer resistance of each part to calculate the total heat transfer coefficient of the casting roller;

[0012] Step 6: Calculate the water temperature in the flow channel according to the general control equation of convection heat transfer, calculate the shell surface temperature difference according to the energy conservation equation, extract the shell surface temperature difference and the length of the casting roller, and calculate the casting roller shell temperature slope to reflect the temperature uniformity of the casting roller.

[0013] Furthermore, the geometric dimensions of the casting roll include the thickness, diameter, rise angle, length, number of heads, water flow parameters and thermal conductivity of the metal. The water flow parameters include density, kinematic viscosity, specific heat capacity, thermal conductivity and Planck number.

[0014] Furthermore, the pitch calculation formula in step 2 is: S G =πDtanα;

[0015] The total length of the spiral is calculated as:

[0016] The flow channel width calculation formula is:

[0017] The hydraulic diameter calculation formula is: The calculation formula of water flow velocity in the spiral flow channel is: Furthermore, the Reynolds number calculation formula of water in step 3 is: Furthermore, the calculation formula of Nu number in step 4 is:

[0018]

[0019] The calculation formula of Darcy's drag coefficient is: f = (1.82lgRe-1.64) -2 ;

[0020] The calculation formula of the inlet effect correction factor is: Furthermore, the heat exchange resistances of each part in step 5 include R1, R2, and R3, wherein:

[0021]

[0022]

[0023]

[0024] Furthermore, the total heat transfer coefficient calculation formula in step 5 is:

[0025]

[0026] Furthermore, the energy conservation equation in step 6 is calculated as:

[0027]

[0028] Furthermore, the temperature slope calculation formula in step 6 is:

[0029]

[0030] The beneficial effects of the present invention are:

[0031] Compared with the finite element analysis method, the prediction method of the present invention has a faster analysis speed and more flexible and universal applicability. There are many factors that affect the temperature uniformity of the casting roller. Through this method, the slope value of the shell temperature directly calculated by the formula can directly reflect the temperature uniformity of the casting roller. The method is highly consistent with the three-dimensional simulation calculation results and has good accuracy. Therefore, it can save calculation time, facilitate the subsequent casting roller flow channel design and structural optimization, and save the manufacturing cost of the casting roller. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0033] Figure 1 is a flow chart of the prediction method of the present invention;

[0034] Figure 2 Schematic diagram of the temperature distribution of the shell of the casting roller of the present invention;

[0035] Figure 3 Schematic diagram of the spiral flow channel of the present invention;

[0036] Figure 4 Schematic diagram of heat exchange resistance of various parts of the casting roller of the present invention;

[0037] Figure 5 It is a comparison between the prediction method of the present invention and the slope calculation results of three-dimensional simulation. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] like Figure 1 A method for predicting the surface temperature uniformity of a casting roll is shown, and the prediction method comprises the following steps:

[0040] Step 1: Obtain the geometric dimensions of the casting roller as the data basis for subsequent calculations; the geometric dimensions of the casting roller include the thickness, diameter, rise angle, length, number of heads, water flow parameters and thermal conductivity of the metal. The water flow parameters include density, kinematic viscosity, specific heat capacity, thermal conductivity and Planck number.

[0041] Step 2: Extract the rise angle, diameter and number of heads of the casting roller to calculate the pitch of the spiral flow channel of the casting roller, the total length of the spiral line, the flow channel width, the hydraulic diameter and the water flow rate in the spiral flow channel.

[0042] Step 3: Extract the water flow rate, kinematic viscosity and hydraulic diameter in the spiral flow channel of the casting roller to calculate the Reynolds number of water.

[0043] Step 4: Extract the Reynolds number of water flow, the hydraulic diameter of the spiral flow channel, and the inner end diameter of the casting roller, and calculate the Darcy resistance coefficient of the turbulent flow in the spiral flow channel, the inlet effect correction coefficient, and the Nu number of the heat exchange process between the solid and water sides inside the casting roller.

[0044] Step 5: Obtain the heat transfer resistance of each part to calculate the total heat transfer coefficient of the casting roller.

[0045] Step 6: Calculate the water temperature in the flow channel according to the general control equation of convection heat transfer, calculate the shell surface temperature difference according to the energy conservation equation, extract the shell surface temperature difference and the length of the casting roller, and calculate the casting roller shell temperature slope to reflect the temperature uniformity of the casting roller.

[0046] like Figure 2 As shown in the figure, the surface temperature value of the casting roller shell in the length direction of the casting roller is extracted through three-dimensional simulation calculation and drawn into a scatter plot. It can be seen that in the central area of ​​the shell temperature distribution, each data point is distributed inside the area composed of two straight lines with the same slope. By calculating the slope of the straight line, it can be further calculated through the formula

[0047] ΔT s =kL to calculate the extreme difference in roller surface temperature.

[0048] In the step 1, the designed physical parameters are the universal gas constant gravitational acceleration g = 9.8 m / s 2 、The density of liquid water ρ=965.8kg / m 3 , liquid water constant pressure specific heat capacity c p =4208 J / (kg·K), kinematic viscosity of liquid water at 90°C ν = 0.326×10 -6 m2 / s, thermal conductivity of liquid water K H20 =0.68W / (m·K), thermal conductivity of metal k metal = 51.5W / (m·K), Planck number Pr of liquid water at 90°C f =1.95.

[0049] Among them, Figure 3 As shown, the calculation formula of the pitch of the spiral flow channel and the total length of the spiral line in step 2 is:

[0050] S G =πDtanα

[0051]

[0052] Where D is the inner end diameter of the casting roller, S G is the helix pitch and L is the length of the casting roller.

[0053] The calculation formula of the spiral flow channel width is:

[0054]

[0055] like Figure 3 As shown, the spiral flow channel is approximated as a cuboid flow channel with a rectangular cross section, and its hydraulic diameter is:

[0056]

[0057] Wherein, dx is the height of the spiral channel, and dy is the width of the spiral channel.

[0058] The calculation formula for the liquid flow rate in the flow channel is:

[0059]

[0060] Among them, u in is the inlet flow rate.

[0061] Wherein, the calculation formula of the Reynolds number of the water flow in step 3 is:

[0062]

[0063] Here, ν is the kinematic viscosity of the fluid.

[0064] Wherein, the calculation formula of Nu number in step 4 is:

[0065]

[0066] f=(1.82lgRe-1.64) -2

[0067]

[0068] Among them, Pr f is the Planck number of the fluid, f is the Darcy drag coefficient of the turbulent flow in the tube, C t is the inlet effect correction factor, D w It is the outer diameter of the end face of the casting roll.

[0069] Among them, Figure 4 As shown, the heat exchange resistance involved in the casting roller in step 5 has three parts R1, R2, and R3. Among them:

[0070]

[0071]

[0072]

[0073] The overall heat transfer coefficient is:

[0074]

[0075] Among them, R1, R2, and R3 are the heat transfer resistances of each part; h1 is the heat transfer coefficient between the roller surface and the air side, δ is the thickness of the casting roller shell, λ is the thermal conductivity of the casting roller shell, and h3 is the heat transfer coefficient between the solid inside the casting roller and the water side. The calculation formula is:

[0076]

[0077] λ f is the thermal conductivity of liquid water.

[0078] Among them, the general control equation of convective heat transfer involved in step six is:

[0079]

[0080] in,

[0081] make but:

[0082]

[0083] The calculation formula of roller surface temperature is:

[0084]

[0085] The energy conservation equation involved is:

[0086]

[0087] L is the length of the casting roller, D0 is the outer cross-sectional diameter of the casting roller, T0 is the hot water inlet temperature, T ∞ is the ambient temperature, c p is the constant pressure specific heat capacity of liquid water, ρ is the density of liquid water, q v is the volume flow rate of liquid water; the temperature slope equation is:

[0088]

[0089] Compared with the finite element analysis method, the method for predicting the surface temperature uniformity of the casting roller provided by the present invention has a faster analysis speed and more flexible and universal applicability. There are many factors that affect the temperature uniformity of the casting roller. Through this method, the slope value of the outer shell temperature can be directly calculated by using the formula to directly reflect the temperature uniformity of the casting roller. Figure 5 As shown, this method is highly consistent with the three-dimensional simulation calculation results and has good accuracy. Therefore, it can save calculation time, facilitate subsequent casting roller flow channel design and structural optimization, and save the manufacturing cost of the casting roller.

[0090] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0091] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A method for predicting the surface temperature uniformity of a casting roll, characterized in that: The prediction method includes the following steps: Step 1: Obtain the geometric dimensions of the casting roll as the data basis for subsequent calculations; Step 2: extract the rise angle, diameter and number of the casting roll to calculate the pitch, total length of the spiral line, width of the spiral channel, hydraulic diameter and water flow rate in the spiral channel of the casting roll; The formula for calculating the pitch is: S G =πDtanα; S G is the pitch, D is the inner end diameter of the casting roll, and α is the rise angle of the casting roll; The total length of the spiral is calculated as: L S is the total length of the spiral line, L is the length of the casting roller; The flow channel width calculation formula is: dy is the flow channel width, n is the number of casting rollers; The hydraulic diameter calculation formula is: D lx is the hydraulic diameter, dx is the flow channel height; The calculation formula of water flow velocity in the spiral flow channel is: u is the water flow velocity in the spiral flow channel, u in is the inlet flow rate; Step 3: extracting the water flow velocity, kinematic viscosity and hydraulic diameter in the spiral flow channel of the casting roller to calculate the Reynolds number of the water flow; The Reynolds number calculation formula for water is: Re is the Reynolds number of water, ν is the kinematic viscosity of the fluid; Step 4: Extract the Reynolds number of water flow, the hydraulic diameter of the spiral flow channel, and the inner end diameter of the casting roller, and calculate the Darcy drag coefficient of the turbulent flow in the spiral flow channel, the inlet effect correction coefficient, and the Nu number of the heat exchange process between the solid and water sides inside the casting roller; The calculation formula of Nu number is: Nu number is the Nusselt number, Pr f is the Planck number of the fluid, f is the Darcy drag coefficient, C t is the inlet effect correction factor; The calculation formula of Darcy's drag coefficient is: f = (1.82lgRe-1.64) -2 ; The calculation formula of the inlet effect correction factor is: D w is the outer diameter of the end face of the casting roller; Step 5: Obtain the heat transfer resistance of each part to calculate the total heat transfer coefficient of the casting roller; the heat transfer resistance of each part includes R1, R2, and R3, where: R1, R2, and R3 are the heat transfer resistances of each part, h1 is the heat transfer coefficient between the roller surface and the air side, δ is the thickness of the casting roller shell, λ is the thermal conductivity of the casting roller shell, and h3 is the heat transfer coefficient between the solid inside the casting roller and the water side; The total heat transfer coefficient is calculated as follows: h is the total heat transfer coefficient; Step 6: Calculate the water temperature in the flow channel according to the general control equation of convection heat transfer, calculate the shell surface temperature difference according to the energy conservation equation, extract the shell surface temperature difference and the casting roller length, and calculate the casting roller shell temperature slope to reflect the casting roller temperature uniformity; The energy conservation equation is calculated as: D0 is the outer cross-sectional diameter of the casting roll, T0 is the hot water inlet temperature, T ∞ is the ambient temperature, c p is the constant pressure specific heat capacity of liquid water, ρ is the density of liquid water, q v is the volume flow rate of liquid water, ΔT is the change in water temperature; The temperature slope calculation formula is: k is the temperature slope.

2. The method for predicting the surface temperature uniformity of a casting roll according to claim 1, characterized in that: The geometric dimensions of the casting roll include the thickness, diameter, rise angle, length, number of heads, water flow parameters and thermal conductivity of the metal. The water flow parameters include density, kinematic viscosity, specific heat capacity, thermal conductivity and Planck number.

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