Method for calculating broadening of Bi-2223 superconducting tape after rolling

Abstract

The invention discloses a method for calculating broadening of a Bi-2223 superconducting tape after rolling, which comprises the following steps of: 1, rolling the Bi-2223 superconducting tape, and recording data; secondly, the recorded data are substituted into a formula for calculation, and # imgabs0 # and # imgabs1 # are obtained; thirdly, # imgabs2 # and # imgabs3 # are substituted into the formula, and then a calculation formula for broadening of the Bi-2223 superconducting tape after rolling is obtained; 4, the Bi-2223 superconducting tape is rolled, and data are recorded; and 5, substituting the recorded data into a formula to obtain the broadening of the Bi-2223 superconducting tape after rolling. Based on the relation that the volume moving in the width and height directions in the rolling process is in direct proportion to the consumed work, the influence of the relative rolling reduction, the length of the deformation area and the shape of the roller on the broadening is considered, the method for calculating the broadening of the Bi-2223 superconducting strip after rolling is established, basic parameters are easy to obtain, the broadening calculation process is simple, and the calculation accuracy is high. And rapid broadening calculation is facilitated.

Description

Technical Field

[0001] The invention belongs to the technical field of high-temperature superconducting material calculation, and in particular relates to a method for calculating the width expansion of a Bi-2223 superconducting strip after rolling. Background Art

[0002] During the rolling process, the strip is compressed in the height direction by the rollers. The compressed volume will move longitudinally and transversely according to the law of least resistance. The change in the strip width caused by the transversely moving volume is called widening. During the flat roll rolling process of Bi-2223 superconducting strip, the strip widening is free widening. Its biggest feature is that during the rolling process, the pressed part of the strip is compressed in the thickness direction and has the possibility of moving freely in both directions perpendicular to the rolling direction. At this time, the deformation of the strip is not affected by any other obstacles and restrictions except the contact friction. Therefore, generally speaking, the size of the strip increases significantly in the width direction.

[0003] A large number of studies have shown that for Bi-2223 strips, reasonable width expansion during rolling is not only conducive to the densification of powders and the texturing arrangement of particles in the core wire, but also can increase the silver / super interface and improve the area of ​​high current-carrying area, so it has a positive significance for the final current-carrying performance of the strip. At present, the calculation of Bi-2223 strip width expansion is based on empirical data, which has great limitations in use.

[0004] Therefore, a method is needed to calculate the width expansion of Bi-2223 superconducting tape after rolling. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for calculating the width of Bi-2223 superconducting strip after rolling in view of the shortcomings of the above-mentioned prior art. The method is based on the relationship that the volume moved in the width and height directions during the rolling process is proportional to the work consumed, determines the constant a and friction coefficient f in the formula for calculating the width of Bi-2223 superconducting strip during rolling, and establishes a formula for calculating the width of Bi-2223 superconducting strip after rolling based on relative reduction, roller radius and reduction, which provides a useful reference for accurately controlling the width of Bi-2223 superconducting strip and improving the current carrying performance of Bi-2223 superconducting strip.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for calculating the width expansion of Bi-2223 superconducting strip after rolling, characterized in that the method comprises the following steps:

[0007] Step 1, rolling 6 to 10 groups of Bi-2223 superconducting strips, and recording the thickness H before rolling, the difference Δh between the thickness of the Bi-2223 superconducting strip before and after rolling, the difference Δb between the width of the Bi-2223 superconducting strip before and after rolling, and the roller radius R, all in mm;

[0008] Step 2: Substitute the data recorded in step 1 into the formula Calculations were performed, where a is a constant during the rolling of the Bi-2223 superconducting strip, and f is the friction coefficient. Three to five sets of two-variable linear equations about a and f were obtained. Then, three to five sets of a and f were calculated by solving two-variable linear equations. The average values ​​of a and f in the three to five sets were calculated to obtain accurate and

[0009] Step 3: The data obtained in step 2 and Substituting the formula into the formula, we get the calculation formula for the width expansion of Bi-2223 superconducting strip after rolling:

[0010] Step 4: Roll a group of Bi-2223 superconducting strips, and record the thickness H before rolling, the difference Δh between the thickness of the Bi-2223 superconducting strips before and after rolling, the difference Δb between the width of the Bi-2223 superconducting strips before and after rolling, and the roller radius R, all in mm;

[0011] Step 5: Substitute the data recorded in step 4 into the calculation formula of the width expansion of the Bi-2223 superconducting strip after rolling obtained in step 3 to obtain the width expansion of the Bi-2223 superconducting strip after rolling in step 4.

[0012] The present invention is based on the relationship that the volume of Bi-2223 superconducting strip moving in the width and height directions during rolling is proportional to the work consumed, and takes into account the relative reduction The length of the deformation zone, i.e. the horizontal projection length of the arc where the strip contacts the roll, the friction coefficient f and the roll shape have an influence on the width expansion. The formula is proposed: Then, through multiple tests, the average value of the constants of the Bi-2223 superconducting tape during rolling was obtained. and the average value of the friction coefficient Then and Substituting the above formula into the calculation formula of the width expansion of Bi-2223 superconducting strip after rolling: The subsequent rolling of the Bi-2223 superconducting strip can be calculated according to the calculation formula of the width expansion, and the width expansion of the Bi-2223 superconducting strip after rolling can be quickly obtained, which provides a useful reference for accurately controlling the width expansion of the strip and improving the current carrying performance of the strip.

[0013] The above method for calculating the width of Bi-2223 superconducting strip after rolling is characterized in that the rolling speeds in step 1 and step 4 are both 1m / min to 7m / min, and the temperatures are both room temperature. The present invention limits the rolling speed and room temperature to prevent the width of Bi-2223 superconducting strip after rolling from being affected, so that the calculation of the friction coefficient is more accurate.

[0014] The above-mentioned method for calculating the width of Bi-2223 superconducting strip after rolling is characterized in that the rolling described in step 1 and step 4 is performed by flat rolls, and the width of Bi-2223 superconducting strip is free width. In the present invention, the rolling of Bi-2223 superconducting strip belongs to flat roll rolling, and the width of the strip is free width. Free width means that during the rolling process of Bi-2223 superconducting strip, the metal volume pressed down and its metal particles have the possibility of freely moving in both sides perpendicular to the rolling direction when moving laterally. At this time, the flow of the strip is not affected by any other obstacles and restrictions, such as the side wall of the hole, the vertical roll, etc., except for the influence of contact friction. The result clearly shows the increase of the linear dimension of the strip width, which is called free width.

[0015] The above method for calculating the width of Bi-2223 superconducting strip after rolling is characterized in that when 10 groups of Bi-2223 superconducting strips are rolled in step 1, the width calculated in step 2 is The calculation formula for the width expansion of Bi-2223 superconducting strip after rolling in step 3 is: The present invention obtains accurate and The obtained formula calculates the spread more accurately.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] 1. Based on the relationship that the volume moved in the width and height directions during the rolling process is proportional to the work consumed, the present invention determines the constant a and friction coefficient f in the formula for calculating the width expansion of Bi-2223 superconducting strip during rolling, and establishes a formula for calculating the width expansion of Bi-2223 superconducting strip after rolling based on relative reduction, roller radius and reduction. This formula provides a useful reference for accurately controlling the width expansion of Bi-2223 superconducting tapes and improving the current carrying performance of Bi-2223 superconducting tapes.

[0018] 2. The present invention calculates the constants of Bi-2223 superconducting strip rolling through the data of multiple experiments. Friction coefficient The calculation formula for the width expansion of Bi-2223 superconducting strip after rolling is obtained:

[0019]

[0020] 3. The free width expansion of flat roll rolling calculated by the width expansion calculation formula in the present invention can obtain a result close to the actual result, which verifies the accuracy of the formula. Therefore, it can be used in actual deformation calculation, solving the problem that many current formulas for calculating the width expansion are compiled according to empirical data and have great limitations in use.

[0021] 4. The geometric theory based on the Bi-2223 strip rolling width calculation formula established in the present invention is simple and easy to understand, the basic parameters are easy to obtain, and the width calculation process is simple, which is conducive to accurately calculating the width of the Bi-2223 superconducting strip.

[0022] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a schematic diagram of the thickness direction of the Bi-2223 superconducting strip in the present invention when it is rolled by flat rolls.

[0024] Figure 2 It is a schematic diagram of the width direction of the Bi-2223 superconducting strip in the present invention when it is rolled by flat rolls. DETAILED DESCRIPTION

[0025] Figure 1 Schematic diagram of the thickness direction of the Bi-2223 superconducting strip in the present invention when it is rolled by flat rolls. Figure 1 It can be seen that the thickness of Bi-2223 superconducting tape becomes smaller after flat roll rolling.

[0026] Figure 2 Schematic diagram of the width direction of the Bi-2223 superconducting strip in the present invention when it is rolled by flat rolls. Figure 2 It can be seen that the width of the Bi-2223 superconducting tape increases after flat roll rolling.

[0027] Example 1

[0028] This embodiment includes the following steps:

[0029] Step 1: Roll 10 groups of Bi-2223 superconducting strips, and record the thickness H before rolling, the difference Δh between the thickness of the Bi-2223 superconducting strip before and after rolling, the difference Δb between the width of the Bi-2223 superconducting strip before and after rolling, and the roller radius R, all in mm;

[0030] Step 2: Substitute the data recorded in step 1 into the formula Calculations were performed, where a is a constant during the rolling of the Bi-2223 superconducting strip, and f is the friction coefficient. Five sets of two-variable linear equations about a and f were obtained. Then, five sets of a and f were calculated by solving two-variable linear equations. Then, the average values ​​of the five sets of a and f were calculated, and the obtained values ​​were and

[0031] Step 3: The and Substituting the formula into the formula, we get the calculation formula for the width expansion of Bi-2223 superconducting strip after rolling:

[0032] The calculation formula for the width expansion of the Bi-2223 superconducting strip obtained in Example 1 after rolling is: Applied to the calculations of Examples 2 to 4.

[0033] Example 2

[0034] This embodiment includes the following steps:

[0035] Step 1: Roll a Bi-2223 superconducting strip with a thickness of 1.38 mm and a width of 2.55 mm on a flat roll mill with a flat roll diameter of 300 mm at a downward pressure of 0.19 mm, a rolling speed of 1 m / min, a rolling temperature of room temperature, and a free widening of the Bi-2223 superconducting strip, to obtain a thickness H before rolling of 1.38 mm, a difference Δh between the thickness of the Bi-2223 superconducting strip before and after rolling of 0.19 mm, and a roller radius R of 150 mm;

[0036] Step 2: Substitute the data recorded in step 1 into the formula get That is, the width of the Bi-2223 superconducting strip after rolling is 0.286 mm.

[0037] The Bi-2223 superconducting strip after rolling in this embodiment was measured, and the width was 0.270 mm. The absolute error of the width of 0.286 mm obtained by the calculation formula of the width in this embodiment is 0.016 mm, and the relative error is 5.9%. It can be seen that the method of calculating the width of the Bi-2223 superconducting strip after rolling in this application is basically consistent with the actual width.

[0038] Example 3

[0039] This embodiment includes the following steps:

[0040] Step 1: Roll a Bi-2223 superconducting strip with a thickness of 1.19 mm and a width of 2.9 mm on a flat roll mill with a flat roll diameter of 300 mm at a downward pressure of 0.13 mm, a rolling speed of 4 m / min, a rolling temperature of room temperature, and a free widening of the Bi-2223 superconducting strip, to obtain a thickness H before rolling of 1.19 mm, a difference Δh between the thickness of the Bi-2223 superconducting strip before and after rolling of 0.13 mm, and a roller radius R of 150 mm;

[0041] Step 2: Substitute the data recorded in step 1 into the formula get That is, the width of the Bi-2223 superconducting strip after rolling is 0.213 mm.

[0042] The width of the Bi-2223 superconducting strip after rolling in this embodiment was measured to be 0.202 mm. The absolute error of the width of 0.213 mm obtained by the calculation formula of the width in this embodiment is 0.011 mm, and the relative error is 5.4%. It can be seen that the method of calculating the width of the Bi-2223 superconducting strip after rolling in this application is basically consistent with the actual width.

[0043] Example 4

[0044] This embodiment includes the following steps:

[0045] Step 1: Roll a Bi-2223 superconducting strip with a thickness of 0.87 mm and a width of 3.51 mm on a flat roll mill with a flat roll diameter of 300 mm at a downward pressure of 0.13 mm, a rolling speed of 7 m / min, a rolling temperature of room temperature, and a free widening of the Bi-2223 superconducting strip, to obtain a thickness H before rolling of 0.87 mm, a difference Δh between the thickness of the Bi-2223 superconducting strip before and after rolling of 0.13 mm, and a roller radius R of 150 mm;

[0046] Step 2: Substitute the data recorded in step 1 into the formula get That is, the width of the Bi-2223 superconducting strip after rolling is 0.292 mm.

[0047] The Bi-2223 superconducting strip after rolling in this embodiment was measured to have a width of 0.320 mm, which has a relative error of 0.028 mm and 8.8% from the width calculation formula of 0.292 mm in this embodiment. This shows that the method used in this application to calculate the width of the Bi-2223 superconducting strip after rolling is basically consistent with the actual width.

[0048] The above is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent change made to the above embodiment according to the technical essence of the present invention still falls within the protection scope of the technical solution of the present invention.

Claims

1. A method for calculating the width of Bi-2223 superconducting strip after rolling, characterized in that: The method comprises the following steps: Step 1, rolling 6 to 10 groups of Bi-2223 superconducting strips, and recording the thickness H before rolling, the difference Δh between the thickness of the Bi-2223 superconducting strip before and after rolling, the difference Δb between the width of the Bi-2223 superconducting strip before and after rolling, and the roller radius R, all in mm; Step 2: Substitute the data recorded in step 1 into the formula Calculations were performed, where a is a constant during the rolling of the Bi-2223 superconducting strip, and f is the friction coefficient. Three to five sets of two-variable linear equations about a and f were obtained. Then, three to five sets of a and f were calculated by solving two-variable linear equations. The average values ​​of a and f in the three to five sets were calculated to obtain accurate and Step 3: The data obtained in step 2 and Substituting the formula into the formula, we get the calculation formula for the width expansion of Bi-2223 superconducting strip after rolling: Step 4: Roll a group of Bi-2223 superconducting strips, and record the thickness H before rolling, the difference Δh between the thickness of the Bi-2223 superconducting strips before and after rolling, the difference Δb between the width of the Bi-2223 superconducting strips before and after rolling, and the roller radius R, all in mm; Step 5: Substitute the data recorded in step 4 into the calculation formula of the width expansion of the Bi-2223 superconducting strip after rolling obtained in step 3 to obtain the width expansion of the Bi-2223 superconducting strip after rolling in step 4.

2. A method for calculating the width of Bi-2223 superconducting strip after rolling according to claim 1, characterized in that: The rolling speeds in step 1 and step 4 are both 1 m / min to 7 m / min, and the temperatures are both room temperature.

3. The method for calculating the width of Bi-2223 superconducting strip after rolling according to claim 1, characterized in that: The rolling in step 1 and step 4 is performed by flat rolls, and the widening of the Bi-2223 superconducting tape is free widening.

4. The method for calculating the width expansion of Bi-2223 superconducting strip after rolling according to claim 1, characterized in that: When 10 groups of Bi-2223 superconducting strips are rolled in step 1, the calculated The calculation formula for the width expansion of Bi-2223 superconducting strip after rolling in step 3 is:

Images