A method for quickly determining the mold temperature field based on interpolation

Abstract

A method for quickly determining the temperature field of a crystallizer based on an interpolation method comprises measuring the crystallizer cross-section data, summarizing the temperature gradient in the crystallizer wall thickness direction based on the temperature field data from finite element simulation and actual testing, embedding thermocouples at four quadrant points on the centerline of the crystallizer cross-section, and obtaining temperature values, interpolating the centerline temperature using a piecewise sine function to obtain the temperature distribution of the centerline represented by the piecewise sine function curve and outputting it using a computer, fitting the piecewise sine function curve using an interpolation method in a cylindrical coordinate system, obtaining the temperature field of the cross-section and outputting it using a computer, and using the same method to obtain the temperature field of another cross-section on the crystallizer, thereby interpolating the surface between the two cross-sections to obtain the temperature field between the two cross-sections. Advantages of the present invention include being able to address the need for quickly obtaining a temperature field, realizing a method for quickly calculating a temperature field even in a field environment, and improving work efficiency.

Description

Technical Field

[0001] The invention relates to the field of temperature distribution calculation of a horizontal continuous casting crystallizer, and in particular to a method for quickly determining the crystallizer temperature field based on an interpolation method. Background Art

[0002] During horizontal continuous casting, copper billets can exhibit quality issues such as deformation, porosity, and cracks. To address these quality issues and meet market demand for high-quality continuous casting billets, researchers studied the temperature field and solidification heat transfer process within the horizontal continuous casting mold, optimizing it to improve billet quality. To calculate the mold temperature field, a physical model is first established, divided into microelements according to specific requirements, boundary conditions are determined, and a computer is used to solve the temperature field. However, using finite element software to calculate the temperature field requires considerable time and resources, and this method of determining the temperature field is inefficient, significantly impacting the optimization of the continuous casting mold to improve billet quality. Summary of the Invention

[0003] The present invention aims to provide a method for rapidly calculating the temperature field. This method can obtain the temperature field distribution along a continuous circumferential surface of a mold and rapidly determine the temperature values at each point in the mold's working zone. This method effectively addresses the difficulties in obtaining the mold temperature field on-site and the low efficiency of traditional simulation calculations, providing a new approach for extending mold life and optimizing processes.

[0004] To achieve the above object, a method for quickly calculating the temperature field of a crystallizer is provided, wherein the method comprises the following steps:

[0005] A method for quickly determining a mold temperature field based on an interpolation method, characterized in that it comprises the following steps:

[0006] Step 1: Measure the cross-sectional data of the crystallizer and summarize the temperature gradient in the thickness direction of the crystallizer based on the temperature field data of the finite element simulation and actual tests;

[0007] Step 2: Pre-embed thermocouples at the four quadrants of the center line of the crystallizer cross section and obtain temperature values;

[0008] Step 3: Interpolate the centerline temperature using a piecewise sine function to obtain the temperature distribution of the centerline represented by the piecewise sine function curve and output it using a computer;

[0009] Step 4: Use the interpolation method to fit the piecewise sine function curve in the cylindrical coordinate system to obtain the temperature field of the cross section and output it using a computer;

[0010] Step 5: Use the same method to calculate the temperature field of another section on the crystallizer. The temperature field between the two sections can be calculated by interpolating the surface between the two sections.

[0011] The target cross-section data in step 1 are specifically: centerline diameter D, temperature gradient GT in the direction of the mold wall thickness; the quadrant point temperature in step 2 is the value Ti (i=1, 2, 3, 4) measured by the thermocouple;

[0012] The basic form of the piecewise sine function in step 3 is:

[0013] Ts=A*sin(w*X+B)+C

[0014] Ai=0.5*abs(Ti-Ti+1)

[0015] Ci=0.5*(Ti+Ti+1)

[0016] W=2π / (L / 2)

[0017] L=π*D

[0018] Bi is the independent variable of the expression, the expression is: Ai*sin(w*Xi+Bi)+Ci-Ti=0(i=1,2,3,4)

[0019] Where: A is the amplitude, Ci is the offset, B is the initial phase, L / 2 is the period, and abs represents the absolute value.

[0020] The fourth step is to establish a correlation between the arc length in the cylindrical coordinate system and the piecewise sine function.

[0021] Arc length (arclen) is equal to the product of radian and radius. Determine the range of arc length and determine the corresponding function curve:

[0022] 0<=arclen<0.25*L then Ts=A1*sin(w*arclen+B1)+C1

[0023] 0.25*L<=arclen<0.5*L then Ts=A2*sin(w*arclen+B2)+C2

[0024] 0.5*L<=arclen<0.75*L then Ts=A3*sin(w*arclen+B3)+C3

[0025] 0.75*L<=arclen<=L then Ts=A4*sin(w*arclen+B4)+C4

[0026] The temperature value Ts can be determined based on the arc length, and the temperature distribution in the thickness direction of the point can be determined based on T=Ts+(0.5*Dr)*GT; where r is the distance from any point on the cross section to the center of the circle, that is, the radius.

[0027] In step 5, the temperature T3 of a point a3 between two cross sections, i.e., cross section 1 and cross section 2, is determined. First, the curvature and radius of the cross section where the point is located are determined. Once these are determined, the temperatures T1 and T2 of the corresponding points a1 and a2 on cross sections 1 and 2 can be obtained using steps 1-4. Then, the temperature T3 of point a3 can be determined using the lever principle: (T3 = T1*Q1 + T2*Q2).

[0028] In the formula: Q1 = d2 / (d1+d2), Q2 = d1 / (d1+d2), d1 is the distance from section 3 to section 1, and d2 is the distance from section 3 to section 2.

[0029] Advantages of the present invention:

[0030] The method for quickly determining the mold temperature field based on the interpolation method described in the present invention improves the calculation efficiency of the mold temperature field, can solve the problem of quickly obtaining the temperature field demand, and realizes a method for quickly calculating the temperature field in the field environment, thereby improving work efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments:

[0032] Figure 1 Schematic diagram of a simplified model for calculating the cross-sectional temperature field;

[0033] Figure 2 It is a schematic diagram of the temperature distribution of the midline represented by the piecewise sinusoidal function curve;

[0034] Figure 3 The figure is a flow chart of the computer-based rapid calculation method of the temperature field in the cross section of the crystallizer. DETAILED DESCRIPTION

[0035] Example 1

[0036] like Figure 1 As shown, the center line is a curve on the temperature measurement section with equal distances to both ends of the temperature measurement surface, and D is the center line diameter; thermocouples are embedded at the four quadrant points P1 (P5), P2, P3, and P4, where P1 and P5 coincide; T1 (T5), T2, T3, and T4 are their temperature values, where T1 = T5.

[0037] To make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the following will be combined with the appended drawings of the embodiments of the present invention. Figure 1 , attached Figure 2 , attached Figure 3, the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are 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 making creative work are within the scope of protection of the present invention.

[0038] Step 1: Measure the target cross-section data and summarize the temperature gradient based on the temperature field data simulated by finite element simulation and actual test. The cross-section data includes: the diameter of the cross-section centerline D (mm) and the temperature gradient in the direction of the mold wall thickness: GT (℃ / m).

[0039] Step 2: Pre-embed thermocouples at the four quadrant points of the center line of the target section, and obtain the temperature numerical parameters T1 (T5), T2, T3, T4 (℃) of the quadrant points P1 (P5), P2, P3, P4.

[0040] Step 3: Determine the basic form of the sine function as Ts=A*sin(w*X+B)+C, and perform piecewise function interpolation through the measured temperatures of the four quadrant points. Taking two of the quadrant points P1(0, T1) and P2(0.25L, T2) as examples, by calculating A1, B1, C1, the sine function curve of this section can be directly determined, and then the sine function curves between P2 and P3, P3 and P4, and P4 and P5 are determined in turn, among which P5 (because the circumference is L, point P5 coincides with point P1, and the coordinates of point P5 are (L, T1)). Finally, the temperature distribution of the midline is represented by the piecewise sine function curve and the computer output is as follows: Figure 2 shown.

[0041] Step 4: Use the interpolation method to fit the generated piecewise sine function curve in the cylindrical coordinate system to obtain the temperature field of the section and output it using a computer. Specifically: in the cylindrical coordinate system, input the radian (θ) and radius (r) values, and use arclen = θ * 0.5 * D to preferentially calculate the temperature of the point θ on the center line; according to the range of the arc length occupied by the circumference, automatically determine the corresponding piecewise function and calculate the temperature value, and you can directly obtain the temperature Ts of the point θ on the center line:

[0042] 0<=arclen<0.25*L then Ts=A1*sin(w*arclen+B1)+C1

[0043] 0.25*L<=arclen<0.5*L then Ts=A2*sin(w*arclen+B2)+C2

[0044] 0.5*L<=arclen<0.75*L then Ts=A3*sin(w*arclen+B3)+C3

[0045] 0.75*L<=arclen<=L then Ts=A4*sin(w*arclen+B4)+C4

[0046] Since the input point (θ, r) and the point corresponding to θ on the center line are on the same straight line, the corresponding temperature value is calculated by interpolation according to T=Ts+(0.5*Dr)*GT and output by computer.

[0047] Step 5: Determine the temperature of a point between two sections (Section 1, Section 2). First, determine the curvature and radius of the section where the point is located. Once determined, the temperatures T1 and T2 of the corresponding points on Section 1 and Section 2 can be obtained. Then, according to the lever law: (T3 = T1*Q1+T2*Q2), the temperature value T3 of point a3 can be determined, thereby obtaining the temperature field between the two sections.

[0048] Matters not covered by the present invention are known technologies.

[0049] The above embodiments are intended only to illustrate the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. They are not intended to limit the scope of protection of the present invention. Any equivalent changes or modifications made in accordance with the spirit of the present invention are intended to be covered by the scope of protection of the present invention.

Claims

1. A method for quickly determining the mold temperature field based on interpolation method, characterized by: The steps include: Step 1: Measure the cross-sectional data of the crystallizer and summarize the temperature gradient in the thickness direction of the crystallizer based on the temperature field data of the finite element simulation and actual tests; Step 2: Pre-embed thermocouples at the four quadrants of the center line of the crystallizer cross section and obtain temperature values; Step 3: Interpolate the centerline temperature using a piecewise sine function to obtain the temperature distribution of the centerline represented by the piecewise sine function curve and output it using a computer; Step 4: Use the interpolation method to fit the piecewise sine function curve in the cylindrical coordinate system to obtain the temperature field of the cross section and output it using a computer; Step 5: Use the same method to find the temperature field of another section on the crystallizer. Then, interpolate the surface between the two sections to find the temperature field between the two sections. The target cross-section data in step 1 are specifically: centerline diameter D, temperature gradient GT in the direction of the mold wall thickness; the quadrant point temperature in step 2 is the value Ti measured by the thermocouple, where i=1, 2, 3, 4; The basic form of the piecewise sine function in step 3 is: Ts=A*sin(w*X+B)+C Ai=0.5*abs(Ti-Ti+1) Ci=0.5*(Ti+Ti+1) w=2π / (L / 2) L=π*D Bi is the independent variable of the expression, and the expression is: Ai*sin(w*Xi+Bi)+Ci-Ti=0 Where: A is the amplitude, Ci is the offset, B is the initial phase, L / 2 is the period, and abs represents the absolute value.

2. The method for quickly determining the mold temperature field based on the interpolation method according to claim 1, characterized in that: In step 4, the arc length in the cylindrical coordinate system is associated with the piecewise sine function. The arc length arclen is equal to the product of the radian and the radius. The arc length range is determined to determine the corresponding function curve: 0<=arclen<0.25*L then Ts=A1*sin(w*arclen+B1)+C1 0.25*L<=arclen<0.5*L then Ts=A2*sin(w*arclen+B2)+C2 0.5*L<=arclen<0.75*L then Ts=A3*sin(w*arclen+B3)+C3 0.75*L<=arclen<=L then Ts=A4*sin(w*arclen+B4)+C4 The temperature value Ts can be determined based on the arc length, and the temperature distribution in the thickness direction of the point can be determined based on T = Ts+(0.5*Dr)*GT; where r is the distance from any point on the cross section to the center of the circle, that is, the radius.

3. The method for quickly determining the mold temperature field based on the interpolation method according to claim 1, characterized in that: In step 5, the temperature T3 of a point a3 between two cross sections, i.e., cross section 1 and cross section 2, is determined. First, the arc and radius of the cross section where the point is located are determined. Once these are determined, the temperatures T1 and T2 of the corresponding points a1 and a2 on cross sections 1 and 2 can be obtained using steps 1 to 4. Then, according to the lever principle: T3 = T1*Q1 + T2*Q2, the temperature value T3 of point a3 can be determined. In the formula: Q1=d2 / (d1+d2), Q2=d1 / (d1+d2), d1 is the distance from section 3 to section 1, and d2 is the distance from section 3 to section 2.

Images