Method for predicting the breaking strength of steel cords

Abstract

The present invention aims to provide a method for predicting the breaking strength of a steel cord that can predict the breaking strength of a steel cord with a new structure with high accuracy. [Solution] The present invention provides a method for predicting the breaking strength of a steel cord, comprising the steps of: obtaining the breaking strength t of the filaments constituting the steel cord; obtaining the contact force I of the steel cord based on the cord structure of the steel cord; obtaining the relationship between the twist loss rate δ and the contact force I' of another steel cord, which uses the same type of steel as the steel cord but has a different cord structure than the steel cord; and predicting the breaking strength T of the steel cord based on the obtained breaking strength t of the filaments, the obtained contact force I, and the obtained relationship.

Description

[Technical Field]

[0001] This invention relates to a method for predicting the breaking strength of steel cords. [Background technology]

[0002] The breaking strength of steel cord is not simply the sum of the breaking strengths of the filaments because the filaments are twisted. This can be expressed using the twist loss rate δ, where T is the breaking strength of the steel cord and t is the breaking strength of the filaments, as shown in equation A below. (Equation A) T = (1-δ)Σt Conventionally, the breaking strength of new steel cord structures was predicted using the following equation B. Specifically, the filament twist angle was α, and the approximation was (1-δ)=cosα. (Formula B)T=Σt*cosα [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2018-189555 [Overview of the project] [Problems that the invention aims to solve]

[0004] However, the method using equation B described above does not take into account the premature breakage of filaments due to interactions between filaments within the steel cord. Therefore, the actual breaking strength of the steel cord tends to be lower than the predicted value using the prediction method of equation B, and the prediction accuracy is insufficient.

[0005] Therefore, the present invention aims to provide a method for predicting the breaking strength of a steel cord that can predict the breaking strength of a steel cord with a new structure with high accuracy. [Means for solving the problem]

[0006] The gist configuration of the present invention is as follows. (1) A method for predicting the breaking strength T of a steel cord, comprising: a step of obtaining the breaking strength t of the filaments constituting the steel cord; a step of obtaining the contact force I of the steel cord based on the cord structure of the steel cord; a step of obtaining the relationship between the twist reduction rate δ and the contact force I' of another steel cord having a cord structure different from that of the steel cord, using the same type of steel material as the steel cord; a step of predicting the breaking strength T of the steel cord based on the obtained breaking strength t of the filaments, the obtained contact force I, and the obtained relationship. A method for predicting the breaking strength of a steel cord, characterized by including the above steps.

[0007] Here, for the "another steel cord", "using the same type of steel material as the steel cord" means that the steel cord whose breaking strength T is to be predicted and the another steel cord have the same grade of steel defined by ISO. Also, for the "another steel cord", "having a cord structure different from that of the steel cord" means that the steel cord whose breaking strength T is to be predicted and the another steel cord have the same number of core filaments, but different numbers of sheath filaments.

[0008] (2) The method for predicting the breaking strength of a steel cord according to (1) above, wherein in the step of obtaining the contact force I of the steel cord, the contact force I is calculated by calculating the contact force within the layer and the contact force between the layers, respectively.

[0009] (3) The method for predicting the breaking strength of a steel cord according to (1) or (2) above, wherein in the step of obtaining the contact force I of the steel cord, the contact force I is calculated using a calculation formula corresponding to the number of core filaments constituting the steel cord.

[0010] (4) The method for predicting the breaking strength of a steel cord according to any one of (1) to (3), wherein the relationship is a linear relationship between the twisting rate δ and the contact force I'.

[0011] (5) A method for predicting the breaking strength of a steel cord according to any one of (1) to (4) above, wherein in the step of obtaining the relationship between the twist loss rate δ and the contact force I' of the other steel cord, the relationship is calculated using a data series of the twist loss rate δ and the contact force I' of the other steel cord stored in a database.

[0012] (6) A method for predicting the breaking strength of a steel cord according to any one of (1) to (5) above, wherein in the step of obtaining the relationship between the twist loss rate δ of the other steel cord and the contact force I', the relationship is calculated using regression analysis. [Effects of the Invention]

[0013] According to the present invention, it is possible to provide a method for predicting the breaking strength of a steel cord that can predict the breaking strength of a steel cord with a new structure with high accuracy. [Brief explanation of the drawing]

[0014] [Figure 1] This is a cross-sectional view of a steel cord with a (3+9) structure in the embodiment. [Figure 2] This is a cross-sectional view of a steel cord with a (1+6) structure in the embodiment. [Modes for carrying out the invention]

[0015] The embodiments of the present invention will be described in detail below.

[0016] <Method for predicting the breaking strength of steel cords> In the method for predicting the breaking strength of steel cord according to this embodiment, first, the breaking strength t of the filaments constituting the steel cord is obtained (step S101). It is preferable to obtain the breaking strength t of the filaments by using data of the breaking strength t of filaments stored in a database, for example. On the other hand, the breaking strength t of the filaments can also be obtained by measurement. Furthermore, the breaking strength t of the filaments may be obtained by calculation using theoretical formulas, etc.

[0017] Next, the contact force I of the steel cord is obtained based on the cord structure of the steel cord (step S102). It is preferable to obtain the contact force I of the steel cord by calculation. In this case, it is even more preferable to calculate the contact force I using a calculation formula that corresponds to the number of core filaments constituting the steel cord. As an example, the case where there are 3 core filaments ((3+N) structure, where N is the number of sheath filaments) and the case where there is 1 core filament ((1+N) structure, where N is the number of sheath filaments) will be described below.

[0018] (Calculation of contact force I in the case of a (3+N) structure) As an example, the contact force I of a (3+N) structured cord can be expressed by the following equation 1, where X2 is the radial contact force per unit length of the core filament, Q2 is the circumferential contact force of the core filament, X3' is the radial contact force per unit length of the sheath filament, Q3 is the circumferential contact force of the sheath filament, and A is the cross-sectional area of ​​the steel cord. (Equation 1) I = [(X² + X³') + (Q² ​​+ Q³)] / A

[0019] The quantities related to the core filament can be determined as follows: First, the axial strain ε of the core filament when the steel cord is pulled is defined by the following equation 2, where h is the original length of the core filament and h' is the length of the core filament after pulling. (Formula 2)ε=(h´-h) / h

[0020] The helix radius r2 of the core filament before deformation is expressed by the following Equation 3. (Equation 3) r2 = R2(1 + s) 1 / 2 Here, R2 is the core filament diameter, and s is expressed by the following Equation 4. (Equation 4) s = cot 2 (π / m2) csc 2 (α2) Here, m2 is the number of core filaments, and α2 is the twist angle of the core filament.

[0021] The axial strain ξ2 acting on the core filament is expressed by the following Equation 5. (Equation 5) ξ2 = ε - Δα2 / tanα2

[0022] At this time, taking the bending moment in the y direction as G´´2, the elastic modulus as E, and the curvature change as R2Δκ´2, it can be expressed as the following Equation 6. (Equation 6) G´´2 / ER2 3 = π / 4(R2Δκ´2) Also, taking the torsional moment in the y direction as H´´2, the Poisson's ratio as ν, and the change in torsion rate as R2Δτ2, it can be expressed as the following Equation 7. (Equation 7) H´´2 / ER2 3 = π / 4(1 + ν)*R2Δτ2

[0023] Also, taking the shear force in the y direction as N2´, it can be expressed as the following Equation 8. (Equation 8) N2´ / ER2 2 =(H2 / ER2 3 ) cos 2 α2 / (r2 / R2) - (G2´´ / ER2 3 ) sinα2 cosα2 / (r2 / R2) Also, taking the axial force of the filament as T2, it can be expressed as the following Equation 9. (Equation 9) T2 / ER2 2 = πξ2

[0024] And the radial contact force X2 per unit length of the core filament can be expressed as the following Equation 10. (Formula 10)X2 / ER2=(N2´ / ER2 2 )sinα2cosα2 / (r2 / R2)-(T2 / ER2 2 )cos 2 α2 / (r2 / R2)

[0025] Furthermore, the circumferential contact force Q2 of the core filaments can be expressed as shown in Equation 11 below, where m2 is the number of core filaments. (Formula 11)Q2=-X2 / 2cosγ2 However, cosγ2 = 1 / cos 2 α2[[(1+tan 2 (π / 2-π / m2)] / sin 2 α2]-1 / cos 2 α2[tan 2 (π / 2-π / m2)*[1+1 / tan 2 α2cos 2 (π / 2-π / m2)[sin 2 α2+tan 2 (π / 2-π / m2)]+sin 4 α2] 1 / 2

[0026] Here, the curvature change R2Δκ2' is expressed by the following equation 12. (Formula 12) R2Δκ2′=-2cosα2sinα2 / (r2 / R2)Δα2+A2 / (r2 / R2)cos 2 α2 Furthermore, the change in torsion R2Δτ2 is expressed by the following equation 13. (Equation 13) R²Δτ² = cos 2 α2 / (r2 / R2)Δα2+A2 / (r2 / R2)sinα2cosα2 However, A2=νξ2+t / (1+t)Δα2cotα2

[0027] Next, the helical radius r3 of the sheath filament can be expressed by the following equation 14, where R3 is the diameter of the sheath filament. (Formula 14)r3=r2+R2+R3 Furthermore, the twist angle of the sheath filament can be expressed as shown in Equation 15 below, where α3 is the twist angle. (Equation 15) ξ3 = ξ2 - Δα3 / tanα3

[0028] Let G''3 be the bending moment in the y-direction. This can be expressed as shown in equation 16 below. (Formula 16) G´´3 / ER3 3 =π / 4(R3Δκ'3) Let H''² be the torsional moment in the y-direction. This can be expressed as shown in Equation 17 below. (Formula 17) H´´3 / ER3 3 =π / 4(1+ν)*R3Δτ3

[0029] Furthermore, the shear force in the y-direction can be expressed as shown in Equation 18 below, where N3' is the shear force. (Equation 18) N3' / ER3 2 =(H3 / ER3 3 )cos 2 α3 / (r3 / R3)-(G3´´ / ER3 3 )sinα3cosα3 / (r3 / R3) Furthermore, the axial force of the filament can be expressed as shown in Equation 19 below, where T3 is the axial force of the filament. (Formula 19) T3 / ER3 2 =πξ3

[0030] X3 can then be expressed as shown in equation 20 below. (Equation 20) X3 / ER3 = (N3' / ER3) 2 )sinα3cosα3 / (r3 / R3)-(T3 / ER3 2 )cos 2 α3 / (r3 / R3)

[0031] Furthermore, the circumferential contact force Q3 of the sheath filaments can be expressed as shown in Equation 21 below, where m3 is the number of sheath filaments. (Equation 21) Q3 = -X3 / 2cosγ3 However, cosγ3 = 1 / cos 2 α3[{(1+tan 2 (π / 2-π / m3) / sin 2 α3]-1 / cos 2α3[tan 2 (π / 2-π / m3)*[1+1 / tan 2 α3cos 2 (π / 2-π / m3)[sin 2 α3+tan 2 (π / 2-π / m³)]+sin 4 α3]1 / 2

[0032] Here, the curvature change R3Δκ3' is expressed by the following equation 22. (Formula 22) R3Δκ3′=-2cosα3sinα3 / (r3 / R3)Δα3+(B3 / r3) / (r3 / R3)cos 2 α3 Furthermore, the change in torsion R3Δτ3 is expressed by the following equation 23. (Equation 23) R3Δτ3 = cos 2 α3 / (r3 / R3)Δα3+(B3 / r3) / (r3 / R3)sinα3cosα3

[0033] Furthermore, the torsional strain B3 acting on the sheath filament is expressed by the following equation 24. (Formula 24)B3=ξ3 / tanα3-Δα3+B3 / r3cotα3

[0034] The radial contact force X3' per unit length of the sheath filament is expressed by the following equation 25. (Equation 25) X3' = l3 / (2π / Θ3) * X3 However, l3 = 2πr3 / cosα3, Θ3=2πr2tanα2 / m3(r2tanα2+r3tanα3)

[0035] (Calculation of contact force I in the case of a (1+N) structure) Next, we will explain how to calculate the contact force in a (1+N) structure. Regarding the sheath filament, the only difference compared to the (3+N) structure is the following formula. (Formula 26) R3Δκ3′=-2cosα3sinα3 / (r3 / R3)Δα3+(A3 / r3) / (r3 / R3)cos 2 α3 (Formula 27) R3Δτ3=(1-2sin 2α3) / (R3 / r3)Δα3+(A3 / r3) / (r3 / R3)sinα3cosα3 (Equation 28) A3 = ν(R2ξ2 + R3ξ3) Finally, the contact force I can be expressed by the following equation 29. (Equation 29) I = (X3 + Q3) / A

[0036] As in the example above, in the process of obtaining the contact force I of the steel cord, it is preferable to calculate the contact force I by calculating the contact force within the layer (Q2, Q3 in the example above) and the contact force between layers (X2, X3 in the example above), respectively.

[0037] In the examples above, we illustrated the cases with 3 core filaments and 1 core filament, but the same theoretical formula can be appropriately constructed to calculate the contact force in cases with 2 or 4 or more core filaments.

[0038] The above formulas are illustrative examples, and known theories or their applications concerning cord contact force, such as Hertz's contact formula, can be used as appropriate.

[0039] The above calculations can be performed by hand or using a computer.

[0040] Furthermore, while the above example shows how to calculate and obtain the contact force I, if such data already exists, you may obtain it from a database.

[0041] Next, in this embodiment, the relationship between the twist loss rate δ and the contact force I' of a different steel cord, which uses the same type of steel material as the steel cord but has a different cord structure, is obtained (step S103). In this case, the relationship between the twist loss rate δ and the contact force I' of the alternative steel cord must be similar to the relationship between the twist loss rate δ and the contact force I in the new steel cord structure used to predict the fracture strength T. Therefore, the same type of steel material (steel cord of the same grade) is used, and the number of core filaments is the same. On the other hand, the number of sheath filaments is different.

[0042] The relationship described above is preferably a linear relationship between the twisting rate δ and the contact force I'. That is, for example, the relationship can be assumed by the following equation 30. (Equation 30) δ = aI + b (a and b are coefficients)

[0043] Furthermore, it is preferable to calculate the relationship using data sequences of the twist loss rate δ and contact force I' of other steel cords stored in the database. It is also preferable to calculate the relationship using regression analysis. In other words, by substituting the data series for the twisting rate δ and contact force I' from the database into Equation 30, the constants a and b can be determined, for example, by the least squares method. By considering equation 30, in which constants a and b have been determined in this way, as the relationship between the twist loss rate δ and the contact force I in the steel cord of the new structure, once the contact force I of the steel cord is obtained in step S102, the twist loss rate δ can be determined by substituting the contact force I into equation 30.

[0044] In the example above, a linear relationship was assumed between the twisting rate δ and the contact force I', but various other relationships, such as those involving polynomials or other equations, can be assumed.

[0045] Steps S101 to S103 may be performed in any order, or two or more steps may be performed simultaneously.

[0046] In step S101, the breaking strength t of the filament is obtained, and in steps S102 and S103, (if the contact force I is obtained, the twist loss rate δ can be calculated by substituting the contact force I into equation 30), the breaking strength of the steel cord can be calculated using equation A by obtaining the contact force I and then calculating the twist loss rate δ. Thus, in this embodiment, the breaking strength T of the steel cord is predicted based on the obtained filament breaking strength t, the obtained contact force I, and the obtained relationship (step S104). The following describes the effects and advantages of the method for predicting the breaking strength of steel cord according to this embodiment.

[0047] In the method for predicting the breaking strength of a steel cord according to this embodiment, by focusing on the contact force I of the steel cord and dividing the prediction of the breaking strength T into obtaining the contact force I of the steel cord (step S102) and obtaining the relationship between the twist loss rate δ and the contact force I' (step S103), it is possible to predict the breaking strength T without using an extremely complex theoretical formula that would directly determine the breaking strength T. Furthermore, by using the relationship between the twist loss rate δ and the contact force I' of a different steel cord with a different cord structure but using the same type of steel material as the steel cord, highly accurate analogy becomes possible, and as a result, the predicted breaking strength T can also be highly accurate (as shown in the embodiments described later). As described above, the method for predicting the breaking strength of steel cords according to this embodiment allows for highly accurate prediction of the breaking strength of steel cords with a new structure.

[0048] In the step of obtaining the contact force I of the steel cord (step S102), it is preferable to calculate the contact force I by calculating the contact forces within the layers (Q2, Q3 in the above example) and the contact forces between layers (X2, X3 in the above example). This is because a more accurate calculation of the contact force I allows for a more accurate prediction of the breaking strength.

[0049] In the step of obtaining the contact force I of the steel cord (step S102), it is preferable to calculate the contact force I using a formula that corresponds to the number of core filaments constituting the steel cord. This is because a more accurate calculation of the contact force I allows for a more accurate prediction of the breaking strength.

[0050] The aforementioned relationship is preferably a linear relationship between the twist loss rate δ and the contact force I'. This is because it is a simple method and allows for accurate approximation of the relationship.

[0051] In the step of obtaining the relationship between the twist loss rate δ and the contact force I' of another steel cord (step S103), it is preferable to calculate the relationship using the data series of the twist loss rate δ and the contact force I' of the other steel cord stored in the database. This is because the relationship can be easily calculated by making effective use of existing data.

[0052] In the step (step S103) of obtaining the relationship between the twist loss rate δ of a separate steel cord and the contact force I', it is preferable to calculate the relationship using regression analysis because it is a simple method.

[0053] Although embodiments of the present invention have been described above, the present invention is not limited in any way to the embodiments described above. In particular, each formula is illustrative, and those skilled in the art may use alternative formulas without departing from the spirit of the present invention. Furthermore, the present invention is also applicable to so-called multi-strand cords. For example, in the case of a structure with 3 core strands + N sheath strands, the same method can be used by replacing "filament" with "strand" in the example of the (3+N) structure above. Similarly, in the case of a structure with 1 core strand + N sheath strands, the same method can be used by replacing "filament" with "strand" in the example of the (1+N) structure above. This can also be generalized and applied to a structure with M core strands + N sheath strands.

[0054] The following describes embodiments of the present invention, but the present invention is not limited in any way to the following embodiments. [Examples]

[0055] The coefficients a and b in (Equation 30)δ=aI+b were determined from levels 1 to 6 of the (3+N) structure shown in Table 1, and a=0.9146 and b=-1.0752 were obtained. For example level 7 shown in Table 2, the breaking strength of the steel cord was predicted by performing the above steps S101 to S104. The breaking strength of the steel cord was also measured. The difference between the measured and predicted values ​​is shown in Table 2. The coefficients a and b in (Equation 30)δ=aI+b were determined from levels 1 to 5 of the (1+N) structure shown in Table 3, and a=1.2686 and b=0.736 were obtained. For example level 6 shown in Table 4, the breaking strength of the steel cord was predicted by performing the above steps S101 to S104. The breaking strength of the steel cord was also measured. The difference between the measured and predicted values ​​is shown in Table 4. Figure 1 is a cross-sectional view of a steel cord with a (3+9) structure in an embodiment. Figure 2 is a cross-sectional view of a steel cord with a (1+6) structure in an embodiment.

[0056] [Table 1]

[0057] [Table 2]

[0058] [Table 3]

[0059] [Table 4]

[0060] As shown in Tables 2 and 4, the predictions made by this method are highly accurate (with an error of less than 1%, as shown in the table).

Claims

1. A method for predicting the breaking strength T of a steel cord, A step of obtaining the breaking strength t of the filaments constituting the steel cord, A step of obtaining the contact force I of the steel cord based on the cord structure of the steel cord, A step to obtain the relationship between the twist loss rate δ and the contact force I' of another steel cord, which uses the same type of steel material as the aforementioned steel cord but has a different cord structure than the aforementioned steel cord, A method for predicting the breaking strength of a steel cord, comprising the step of predicting the breaking strength T of the steel cord based on the obtained breaking strength t of the filament, the obtained contact force I, and the obtained relationship.

2. The method for predicting the breaking strength of a steel cord according to claim 1, wherein the contact force I of the steel cord is calculated by calculating the contact force I within the layers and the contact force between layers, respectively, in the step of obtaining the contact force I of the steel cord.

3. A method for predicting the breaking strength of a steel cord according to claim 1 or 2, wherein in the step of obtaining the contact force I of the steel cord, the contact force I is calculated using a calculation formula corresponding to the number of core filaments constituting the steel cord.

4. The method for predicting the breaking strength of a steel cord according to claim 1 or 2, wherein the relationship is a linear relationship between the twist reduction rate δ and the contact force I'.

5. A method for predicting the breaking strength of a steel cord according to claim 1 or 2, wherein, in the step of obtaining the relationship between the twist loss rate δ and the contact force I' of the other steel cord, the relationship is calculated using a data sequence of the twist loss rate δ and the contact force I' of the other steel cord stored in a database.

6. A method for predicting the breaking strength of a steel cord according to claim 1 or 2, wherein in the step of obtaining the relationship between the twist reduction rate δ of the aforementioned steel cord and the contact force I', the relationship is calculated using regression analysis.

Images