Calculation method of cable wrapping tape material consumption and construction method of calculation model

Abstract

The invention discloses a construction method of a cable wrapping tape material consumption calculation model. The construction method comprises the following steps: 1) establishing a calculation model application scene; 2) deducing a calculation model; and 3) judging the reasonability of the model. In the step 2), single-layer equation derivation is firstly carried out, then layered calculation, superposition and summation are carried out, a calculation model # imgabs0 # is finally obtained, and the cable wrapping tape material consumption is calculated by adopting the calculation model. Compared with a design thought of a conventional calculation method, the method is more in line with engineering practice, and calculation differences caused by outer diameter changes due to layered wrapping are fully considered. Meanwhile, through function analysis, the calculation model is more accurate, and calculation errors caused by increase of the number of wrapping layers can be reduced.

Description

Technical Field

[0001] The invention relates to the technical field of cable manufacturing, and in particular to a method for calculating the material consumption of a cable wrapping tape and a method for constructing a calculation model. Background Art

[0002] Cable wrapping tape plays many important roles in cable manufacturing and use. For example, it can enhance the insulation performance of the cable. By tightly wrapping around the cable core or the outer insulation layer, it can prevent current leakage and electromagnetic interference, and ensure stable signal transmission. The wrapping tape can also significantly improve the mechanical strength of the cable, enhance its compression, tension and torsion resistance, protect the cable from use in harsh environments, extend its service life and reduce the failure rate. In certain occasions, the wrapping tape can also achieve special functions. For example, the flame-retardant wrapping tape significantly improves safety in complex environments such as coal mines; the temperature-resistant wrapping tape meets the safe operation requirements in high temperature environments. In addition, the wrapping tape can also play a role in heat insulation, corrosion resistance, and anti-aging, protecting the insulation layer or inner sheath layer of the cable.

[0003] Because of this, the amount of cable wrapping tape used is relatively large, and the material cost of the cable is not low. In cable design and manufacturing, the consumption of wrapping tape materials can refer to the commonly used calculation formula for cable wrapping tape material consumption mentioned in "Wu Changshun. Wire and Cable Handbook. Volume 2 [M]. Beijing: Machinery Industry Press, 2017.8:754.":

[0004]

[0005] Where W is the weight of the wrapping tape (kg / km); d is the diameter of the tape before wrapping (wrapped cable) (mm); n is the number of layers of the wrapping tape; t is the thickness of the wrapping tape (mm); ρ is the density of the wrapping tape (g / cm 3 ); k is the wrapping gap ratio or wrapping overlap ratio, the overlapping wrapping method adopts 1-k, and the gap wrapping method adopts 1+k.

[0006] At the same time, the document also provides the outer diameter formula D of the strip after overlapping wrapping n =D n-1 +3t,D n-1 It indicates the outer diameter of the n-1th layer of strip after wrapping.

[0007] In actual production, the wrapping tape is wrapped layer by layer, and the calculated outer diameter d is different for each layer. The weight W of the wrapping tape is accumulated for each layer. When the weight W of the wrapping tape is calculated according to formula (1), the product of the number of wrapping tape layers n and the thickness t of the wrapping tape is used as the overall thickness of the wrapping tape. At the same time, d is the diameter before wrapping, which is a constant and has a large difference from the actual value. The weight difference caused by the change of the outer diameter caused by the layered wrapping is not fully considered, so there is a certain error in calculating the material consumption.

[0008] When the number of wrapping layers is small, the influence of formula (1) on the calculation result is small. When the number of wrapping layers gradually increases, the error of the calculation result also increases. For example, the number of wrapping layers of mica tape used in mica tape mineral insulated cable is usually 4 to 12. When formula (1) is used to calculate material consumption, the error is large, which has a great impact on material cost control and material production utilization rate in the large-scale production process. Summary of the invention

[0009] In order to solve the problems existing in the prior art, the present invention proposes a new calculation modeling and calculation method for cable wrapping tape material consumption, specifically:

[0010] A method for calculating the material consumption of cable wrapping tape, using a calculation model If the cable is wrapped in an overlapping manner, the model is (1-k), where k is the wrapping overlap rate; if the cable is wrapped in an intermittent manner, the model is (1+k), where k is the wrapping intermittent rate.

[0011] The input parameters of the calculation model include: density ρ of the wrapping tape, thickness t of the wrapping tape, number of wrapping layers n, outer diameter d of the cable before wrapping, wrapping gap ratio or wrapping overlap ratio k.

[0012] The method for constructing the computational model comprises the following steps:

[0013] 1) Establishing computing model application scenarios

[0014] For the wrapping layer obtained by wrapping the wrapping tape on the outside of the cable, first cut off a wrapping layer of the wrapping pitch, and unfold the wrapping tape of the corresponding part on the plane; then, derive the formula of the calculation model on the plane according to the quantitative relationship obtained on the unfolded diagram; the cut line is perpendicular to the axis of the cable;

[0015] The planar expansion diagram of the wrapping layer includes two congruent right triangles; the length of the first right-angled side of the right triangle is 1 pitch; the first right-angled sides of the two right triangles coincide, the hypotenuses of the two right triangles are parallel, and the second right-angled sides of the two right triangles are two cutting lines respectively; a parallelogram is connected to the hypotenuse of the first right triangle; of the two adjacent sides of the parallelogram, one side coincides with the hypotenuse of the first right triangle, and the other side is on the extension line of the second right-angled side of the first right triangle; the length of one height of the parallelogram is the wrapping overlap width; the first right-angled side is parallel to the axis of the cable;

[0016] 2) Derivation of computational model

[0017] 2.1) Single-layer formula derivation

[0018] In the application scenario of step 1), assume that: L1 is a pitch of the wrapping layer, b1 is the wrapping overlap width, r is the radius of the cable after wrapping, L2 is the unfolded length of the wrapping tape, b is the width of the wrapping tape, L4 is the wrapping circumference of the wrapping tape, α is the wrapping angle (i.e., the angle between the hypotenuse of the right triangle and the first right angle), S is the unfolded area of ​​the wrapping layer per pitch, P is the mass per unit area of ​​the wrapping tape, W is the mass per unit length of the wrapping tape, ρ is the density of the wrapping tape, and t is the thickness of the wrapping tape. Then there is a quantitative relationship:

[0019] P=ρt, L3=(1-k)b, L4=2πr,

[0020] so,

[0021]

[0022] In the formula, k is the wrapping overlap ratio, and (1-k) indicates the use of overlapping wrapping method;

[0023] According to the specifications of the wrapping tape, the length of the wrapping tape with different widths under area S Then L2=L5;

[0024] so,

[0025]

[0026] so,

[0027]

[0028] When L1 takes the value of 1 unit length, the formula is simplified to

[0029]

[0030] Formula (2) represents the weight when wrapping one layer of wrapping tape;

[0031] 2.2) Layered calculation and superposition summation

[0032] In actual production, the wrapping tape is wrapped layer by layer, and after wrapping, the outer diameter 2r is calculated to change layer by layer;

[0033] According to the outer diameter formula D after overlapping wrapping of the strip n =D n-1 +3t, then:

[0034] After wrapping the first layer, 2r1=d+t,

[0035] After wrapping the second layer, 2r2=D1+t=d+3t+t=d+4t,

[0036] After wrapping the third layer, 2r3=D2+t=d+3t+3t+t=d+7t,

[0037] ………

[0038] After wrapping the nth layer, 2r n =d+3t(n-1)+t=d+(3n-2)t;

[0039] Where t is the thickness of the wrapping tape, r n is the radius of the line with the wrapped layer after wrapping the nth layer; d is the outer diameter of the cable before wrapping;

[0040] Therefore, combined with formula (2), the weight W of n layers of overlapping wrapping tape is n总 for:

[0041]

[0042] 3) Determine the rationality of the model and determine the calculation model

[0043] Formula (3) and the existing commonly used formula The difference is that the overall thickness of the wrap is not nt, but Then, through function analysis, we can judge the rationality of formula (3):

[0044] Assuming function f(n) is formula (3) / formula (1), we have:

[0045]

[0046] From the function f(n), we can know that:

[0047] When the number of wrapping layers n = 1, f(n) = 1 is always true, and formula (3) is always equal to formula (1); then when n = 1, the derivation of formula (3) is correct;

[0048] When the number of wrapping layers n>1, f(n)>1, the result calculated by formula (3) is greater than that calculated by formula (1); when n>1, the accuracy of weight calculated by formula (3) is higher;

[0049] Taking the derivative of the function f(n), we have:

[0050]

[0051] Therefore, f(n) is an increasing function, and the curve shows an upward trend;

[0052] It can be seen that as the number of wrapping layers n increases, the calculation result of formula (3) is more accurate and reasonable than that of formula (1);

[0053] Therefore, the calculation model of cable overlapping wrapping tape material consumption is expressed as:

[0054]

[0055] For formula (4), considering the gap wrapping, the calculation model of cable overlapping wrapping tape material consumption is expressed as:

[0056]

[0057] If the cable is wrapped in an overlapping manner, the model takes (1-k), where k is the wrapping overlap ratio; if the cable is wrapped in a gap manner, the model takes (1+k), where k is the wrapping gap ratio.

[0058] The present invention derives the calculation model based on the wrapping tape overlap rate being ≤50%.

[0059] Advantages of the invention:

[0060] 1. The present invention establishes a calculation model through an unfolded diagram of a wrapping pitch to obtain a weight calculation formula for a single-layer wrapping tape, and then uses the principle of layer-by-layer wrapping calculation superposition to derive a weight calculation formula for a multi-layer wrapping tape. Compared with the design idea of ​​a conventional calculation formula, the design idea of ​​the present invention is more practical and more reasonable, and fully considers the calculation difference caused by the change in outer diameter caused by layered wrapping.

[0061] 2. With the increase of the number of wrapping layers, the derived formula is more accurate through function analysis, which can reduce the calculation error caused by the increase of the number of wrapping layers. At the same time, using this formula to calculate the weight of the wrapping tape can reduce the impact of actual production on material cost control and material production utilization. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 The schematic diagram of wrapping the wrapping tape on the conductor in this example is shown. In the figure, a cable 1 and a wrapping layer 2 formed by wrapping the wrapping tape around the cable are shown.

[0063] Figure 2 The figure shows an expanded view of a wrapping pitch taken along cutting lines A and B in this example.

[0064] Figure 3 Represents the construction process of this computational model. DETAILED DESCRIPTION

[0065] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0066] The specific implementation process of the present invention is as follows:

[0067] 1. Establish a calculation model. In actual production, the overlap rate of the wrapping tape is generally ≤50%. Considering the practicality of the formula, the overlap rate of ≤50% is used as the model for deduction.

[0068] refer to Figure 1 , L1 is the pitch of one wrapping tape (mm); b1 is the overlapping width of the wrapping tape (mm).

[0069] refer to Figure 2 , a wrapping pitch intercepted along the dotted lines A and B is unfolded to obtain a calculation model, and the formula is derived based on the quantitative relationship on the unfolded diagram.

[0070] 2. Formula derivation

[0071] Assume r is the calculated radius after wrapping (mm); L2 is the unfolded length of the wrapping tape (mm); b is the width of the wrapping tape (mm); L4 is the circumference of the wrapping tape (mm); S is the unfolded area of ​​the wrapping tape m 2 , P is the weight of the wrapping tape (g / m 2 ), W is the weight of the wrapping tape (kg / km). Then there is a quantitative relationship:

[0072] P=ρt, L3=(1-k)b, L4=2πr

[0073] so,

[0074] The specifications of the wrapping tapes used in actual production are different. The corresponding lengths of wrapping tapes with different widths of S square meters Then L2=L5. So, so,

[0075] When L1 is 1 km, after unit conversion, the formula is simplified to

[0076]

[0077] Formula (2) is the weight formula for wrapping one layer of wrapping tape. In actual production, the wrapping tape is wrapped layer by layer, and the outer diameter r calculated after wrapping changes layer by layer. According to the outer diameter formula D after overlapping wrapping of the tape n =D n-1 +3t, (reference "Wu Changshun. Wire and Cable Handbook. Volume 2 [M]. Beijing: Machinery Industry Press, 2017.8:754."), so:

[0078] At the first layer, 2r1=d+t,

[0079] In the second layer, 2r2=D1+t=d+3t+t=d+4t,

[0080] At the third layer, 2r3=D2+t=d+3t+3t+t=d+7t,

[0081] ………

[0082] At the nth layer, 2r n =d+3t(n-1)+t=d+(3n-2)t.

[0083] Therefore, the weight of n layers of overlapping wrapping tape is W n总 for:

[0084]

[0085] 3. Establishment of calculation method

[0086] The formula (3) obtained by the modeling idea of ​​calculating the consumption of layered wrapping and superimposing the summary is different from the formula (1) in that the total thickness of the wrapping is not nt, but The rationality of formula (3) is explained below through function analysis.

[0087] Assuming function f(n) is formula (3) / formula (1), we have:

[0088]

[0089] From the function f(n), we can know that:

[0090] When the number of wrapping layers is n=1, f(n)=1 is always true, and equation (3) is always equal to equation (1), so the derivation of equation (3) is correct.

[0091] When the number of wrapping layers n>1, f(n)>1, so the calculation result of formula (3) is greater than the calculation result of the commonly used formula (1), and the accuracy of the calculated weight is higher.

[0092] Taking the derivative of the function f(n), we have:

[0093]

[0094] Therefore, f(n) is an increasing function, and the curve shows an upward trend. It can be seen that as the number of wrapping layers n increases, the material consumption calculated by formula (3) is more accurate and reasonable than formula (1), which can reduce the calculation error caused by the increase in the number of wrapping layers, and at the same time reduce the impact of actual production on material cost control and material production utilization.

[0095] Therefore, the calculation formula for the cable overlapping wrapping tape material consumption can be expressed as:

[0096]

[0097] Furthermore, considering the gap wrapping, equation (4) can be supplemented as

[0098]

[0099] Therefore, the calculation formula for the cable wrapping tape material consumption can be expressed as formula (5).

Claims

1. A method for constructing a calculation model for cable wrapping tape material consumption, characterized in that Includes steps: 1) Establishing computing model application scenarios For the wrapping layer obtained by wrapping the wrapping tape on the outside of the cable, first cut off a wrapping layer of the wrapping pitch, and unfold the wrapping tape of the corresponding part on the plane; then, derive the formula of the calculation model on the plane according to the quantitative relationship obtained on the unfolded diagram; the cut line is perpendicular to the axis of the cable; The planar expansion diagram of the wrapping layer includes two congruent right triangles; the length of the first right-angled side of the right triangle is 1 pitch; the first right-angled sides of the two right triangles coincide, the hypotenuses of the two right triangles are parallel, and the second right-angled sides of the two right triangles are two cutting lines respectively; a parallelogram is connected to the hypotenuse of the first right triangle; of the two adjacent sides of the parallelogram, one side coincides with the hypotenuse of the first right triangle, and the other side is on the extension line of the second right-angled side of the first right triangle; the length of one height of the parallelogram is the wrapping overlap width; the first right-angled side is parallel to the axis of the cable; 2) Derivation of computational model 2.1) Single-layer formula derivation In the application scenario of step 1), assume that: L1 is one pitch of the wrapping layer, b1 is the wrapping overlap width, r is the radius of the cable after wrapping, L2 is the unfolded length of the wrapping tape, b is the width of the wrapping tape, L4 is the wrapping circumference of the wrapping tape, α is the wrapping angle (i.e. the angle between the hypotenuse of the right triangle and the first right angle), S is the unfolded area of ​​one pitch wrapping layer, P is the mass per unit area of ​​the wrapping tape, W is the mass per unit length of the wrapping tape, ρ is the density of the wrapping tape, and t is the thickness of the wrapping tape. Then there is a quantitative relationship: P=ρt, L3=(1-k)b, L4=2πr, so, In the formula, k is the wrapping overlap ratio, and (1-k) indicates the use of overlapping wrapping method; According to the specifications of the wrapping tape, the length of the wrapping tape with different widths under area S Then L2=L5; so, so, When L1 takes the value of 1 unit length, the formula is simplified to Formula (2) represents the weight when wrapping one layer of wrapping tape; 2.2) Layered calculation and superposition summation In actual production, the wrapping tape is wrapped layer by layer, and after wrapping, the outer diameter 2r is calculated to change layer by layer; According to the outer diameter formula D after overlapping wrapping of the strip n =D n-1 +3t, then: After wrapping the first layer, 2r1=d+t, After wrapping the second layer, 2r2=D1+t=d+3t+t=d+4t, After wrapping the third layer, 2r3=D2+t=d+3t+3t+t=d+7t, ……… After wrapping the nth layer, 2r n =d+3t(n-1)+t=d+(3n-2)t; Where t is the thickness of the wrapping tape, r n is the radius of the line with the wrapped layer after wrapping the nth layer; d is the outer diameter of the cable before wrapping; Therefore, combined with formula (2), the weight W of n layers of overlapping wrapping tape is n总 for: 3) Determine the rationality of the model and determine the calculation model Formula (3) and the existing commonly used formula Compared with formula (1), the difference is that the overall thickness of the package is not nt, but Then, through function analysis, we can judge the rationality of formula (3): Assuming function f(n) is formula (3) / formula (1), we have: From the function f(n), we know that: When the number of wrapping layers n = 1, f(n) = 1 is always true, and formula (3) is always equal to formula (1); then when n = 1, the derivation of formula (3) is correct; When the number of wrapping layers n>1, f(n)>1, the result calculated by formula (3) is greater than that calculated by formula (1); when n>1, the accuracy of weight calculated by formula (3) is higher; Taking the derivative of the function f(n), we have: Therefore, f(n) is an increasing function, and the curve shows an upward trend; It can be seen that as the number of wrapping layers n increases, the calculation result of formula (3) is more accurate and reasonable than that of formula (1); Therefore, the calculation model of cable overlapping wrapping tape material consumption is expressed as:

2. The method for constructing a calculation model for cable wrapping tape material consumption according to claim 1 is characterized in that for formula (4), considering gap wrapping, the calculation model for cable overlapping wrapping tape material consumption is expressed as: If the cable is wrapped in an overlapping manner, the model takes (1-k), where k is the wrapping overlap ratio; if the cable is wrapped in a gap manner, the model takes (1+k), where k is the wrapping gap ratio.

3. The method for constructing a calculation model for cable wrapping tape material consumption according to claim 1 or 2, characterized in that The calculation model is derived with the wrapping tape overlap ratio ≤50%.

4. A method for calculating the material consumption of cable wrapping tape, characterized in that Using computational models If the cable is wrapped in an overlapping manner, the model is (1-k), where k is the wrapping overlap rate; if the cable is wrapped in an intermittent manner, the model is (1+k), where k is the wrapping intermittent rate. The input parameters of the calculation model include: density ρ of the wrapping tape, thickness t of the wrapping tape, number of wrapping layers n, outer diameter d of the cable before wrapping, wrapping gap ratio or wrapping overlap ratio k.

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