JP5847625B2 - Finite element model creation method, finite element model creation program and finite element model creation device for twisted cord - Google Patents

Description

  The present invention relates to a twisted cord finite element model creating method, a finite element model creating program, and a finite element model creating device for creating a finite element model of a twisted cord by a computer.

  Conventionally, in a belt such as a transmission belt, rubber and other polymer materials are reinforced by using a twisted cord obtained by twisting a metal, glass, or other polymer material as a core. The twisted cord used for the belt is mainly subjected to three deformations of “tensile” in the longitudinal direction, “bending” by bending the belt, and “compressing in the radial direction” when the pulley is engaged. Therefore, in the structural analysis by the finite element method, it is necessary to use a finite element model having appropriate rigidity against these deformations.

  Here, the twist cord used for the belt has a low bending rigidity with respect to the tensile rigidity (that is, it is strong against tension and is easily bent). Further, when the V-belt bites into the pulley, the belt is compressed in the width direction. At this time, the inner core wire (twisted cord) is also compressed in the core wire radial direction, and the radial compression rigidity is larger than the bending rigidity. Even lower. Thus, the rigidity in each deformation form of the core wire is “tensile rigidity”> “bending rigidity”> “radial compression rigidity” in order from the largest, but these are large differences of about two digits each. Become. Therefore, a device is required for the construction of the finite element model.

  Further, a technique for creating a finite element model by handling a twisted cord in a cylindrical shape or a polygonal column shape has been developed. For example, in the technique shown in Patent Document 1, a finite element model is created with only twisted cords, and in the technique shown in Patent Document 2, reinforcing elements such as trusses and beams are added in the longitudinal direction in addition to the solid elements. A finite element model is created by additional placement. The technology shown in Patent Document 3 creates a finite element model by independently adjusting the rigidity in each direction with the material properties of the solid element as anisotropic. doing.

  However, the conventional finite element model cannot accurately represent all three stiffnesses of “tensile stiffness”, “bending stiffness”, and “radial compression stiffness”. For example, in the finite element model having only solid elements shown in Patent Document 1, the rigidity can be adjusted to only one of the above three when the isotropic material is used. In addition, the finite element model including the truss element shown in Patent Document 2 can be adjusted only to one of “tension stiffness” in the longitudinal direction and “bending stiffness” or “radial compression stiffness”, that is, two stiffnesses. Absent. Furthermore, if the anisotropic material properties shown in Patent Document 3 are used, there is a possibility that the three stiffnesses can be adjusted. However, it is difficult to adjust the anisotropic material properties, and the conventional technology also uses anisotropic properties. In addition, there are no examples that match the three stiffnesses, and simple finite element method analysis software may not be able to set anisotropic physical properties, so it lacks versatility. Accordingly, none of the exemplified Patent Documents 1 to 3 refers to combining all the above three stiffnesses, and even combining the techniques of Patent Documents 1 to 3 does not combine all the above three stiffnesses. I can't.

JP 2004-102424 A JP 2006-164113 A JP 2007-34728 A

  Therefore, all three stiffnesses of “tensile stiffness”, “bending stiffness”, and “radial compression stiffness” are set to the target values (values measured in the test, values set at the code design stage) by the computer. A finite element model creation method, a finite element model creation program, and a finite element model creation apparatus for a twisted cord that can create a finite element method model of a matching twisted cord are provided.

Finite element model creation method of the twisted cord according to the present invention is a finite element modeling methods twisted cord to create a finite element model of Oite twisted cord on a computer, processing executed by the computer, the twisted cord Dividing the outermost hollow cylinder into an outer member, a solid cylinder or hollow cylinder inside the outer member as an inner member, and creating a finite element model by modeling with a solid element; and Based on a theoretical formula and an approximate formula set in advance so that the tensile stiffness in the longitudinal direction of the twisted cord, the bending stiffness associated with the bending of the twisted cord, and the radial compression stiffness of the twisted cord match the target value, And a step of setting a physical property value of the outer member, a physical property value of the inner member, and a diameter of the inner member of a finite element model.

  A twisted cord finite element model creating program according to the present invention is a twisted cord finite element model creating program for creating a stranded element finite element model, and the twisted cord is divided into two concentric layers, and the outermost hollow A step of creating a finite element model by modeling with a solid element using a cylinder as an outer member, a solid cylinder or a hollow cylinder inside the outer member as an inner member, and a tensile rigidity in the longitudinal direction of the twisted cord, the twisted cord The physical properties of the outer member of the finite element model based on the theoretical and approximate expressions set in advance so that the bending stiffness accompanying the bending of the wire and the radial compression stiffness of the twisted cord match the target value, And a step of setting a physical property value of the inner member and a diameter of the inner member.

  The twisted cord finite element model creation device according to the present invention is a twisted cord finite element model creation device that is mounted on a computer and creates a finite element model of a twisted cord. The twisted cord is composed of two concentric circular layers. The outermost hollow cylinder as an outer member, the solid cylinder or hollow cylinder inside the outer member as an inner member, a means for modeling with a solid element to create a finite element model, and a longitudinal direction of the twisted cord The external of the finite element model is based on a theoretical formula and an approximate formula set in advance so as to match the tensile stiffness, the bending stiffness associated with the bending of the twisted cord, and the radial compression stiffness of the twisted cord with a target value. Means for setting a physical property value of the material, a physical property value of the inner member, and a diameter of the inner member.

According to this, the twisted cord is concentrically divided into two layers, the outer hollow cylinder is the outer member, the inner hollow cylinder or the solid cylinder is the inner member, and the outer member and the inner member have different dimensions and physical property values. The material is a finite element model, and based on a theoretical formula and approximation formula set in advance, the physical property value of the outer member (in the case of linear elasticity, Young's modulus and Poisson's ratio), the physical property value of the inner member, the diameter of the inner member ( That is, three diameters (the diameter of the cylindrical surface serving as a boundary between the inner member and the outer member) (Note that the diameter of the outer member is the diameter of the twisted cord, and thus is fixed to that value and cannot be changed). By appropriately setting the three values of the tensile strength in the longitudinal direction of the twisted cord, the bending stiffness accompanying bending, and the radial compressive stiffness, all the target values (actual values of the twisted cord measured in the test) Value and twisted cord design stage In can be tailored to, etc.) set value, it is possible to match the actual no practical problem on the value level.
That is, in order to identify physical property values from tests on three deformation modes (tensile, bending, and radial compression) of twisted cords and determine the dimensions of the finite element model, the following two theories are used for each deformation mode. An expression is required.
1. Formula to calculate rigidity from test (each data of twisted cord dimensions, external force, displacement).
2. Formula to calculate stiffness from physical property data of finite element model dimensions and physical property values (Young's modulus, etc.).
In other words, using the three stiffness values calculated from Equation 1 from the test as the reference (target value), and matching the finite element model dimensions and physical property values to match them, the finiteness that matches all three stiffnesses An element model can be constructed.

  The twisted cord finite element model creation method, the finite element model creation program, and the finite element model creation device according to the present invention are characterized in that the physical property values are linear isotropic elastic material, linear anisotropic elastic material, and superelastic material. Alternatively, a plastic material may be used.

  According to this, the physical property value of the outer member and the physical property value of the inner member are basically linear isotropic elastic material (Young's modulus and Poisson's ratio), but besides that, linear anisotropic elastic material, super elastic material, Or there exists an advantage that material behavior other than linear isotropic elasticity can be expressed by using a plastic material.

  In addition, the twisted cord finite element model creation method, the finite element model creation program, and the finite element model creation device according to the present invention may divide the twisted cord into three or more concentric layers.

  According to this, the twisted cord is concentrically divided into three or more layers, the outermost hollow cylinder is the outer member, the inner hollow cylinder or the solid cylinder is the inner member, and the outer member and the plurality of inner members have different dimensions. By using a finite element model with materials having different physical property values, there is an advantage that the degree of freedom of adjustment increases.

  Further, in the finite element model creation method, the finite element model creation program, and the finite element model creation apparatus for the twisted cord according to the present invention, the finite element model may be modeled by combining a truss element or a beam element with a solid element. .

  According to this, there is an advantage that the degree of freedom of adjustment is increased by combining the truss element (bar element not having bending rigidity) or the beam element (bar element having bending rigidity) with the solid element.

  Note that the finite element model creation program for twisted cords according to the present invention can be recorded and distributed on a fixed recording medium such as a removable recording medium or a hard disk, or can be communicated by the wired or wireless telecommunication means such as the Internet. Distribution is possible via a network.

  The twisted cord finite element model creating method, the finite element model creating program, and the finite element model creating device according to the present invention divide the twisted cord into two layers concentrically, the outer hollow cylinder as the outer member, the inner hollow cylinder or the middle A real cylinder is used as the inner member, and the outer member and inner member are made of finite element models with different dimensions and physical property values. Based on preset theoretical and approximate equations, the physical properties of the outer member (linear elasticity problem) In this case, the twisted cord is set by appropriately setting three of the Young's modulus and Poisson's ratio), the physical property value of the inner member, and the diameter of the inner member (that is, the diameter of the cylindrical surface serving as the boundary between the inner member and the outer member). The three values of tensile stiffness in the longitudinal direction, bending stiffness associated with bending, and radial compression stiffness are all set at the same time (the actual value of the twisted cord measured in the test and the design phase of the twisted cord). The Can be adjusted to a value, etc.), it can be combined with no actual values practical problem level.

It is a flowchart figure which shows the procedure of the process of the finite element model creation method of the twisted cord which concerns on this embodiment. It is a block diagram which shows the function structure of the finite element model production apparatus of the twisted cord which concerns on this embodiment. It is a figure which shows the state which divided | segmented the twist cord into the outer member and the inner member as a finite element model of the twist cord which concerns on this embodiment. It is a figure which shows the tensile rigidity of the twisted cord which concerns on this embodiment. It is a figure which shows the bending rigidity of the twisted cord which concerns on this embodiment. It is a figure which shows the radial direction compression rigidity of the twisted cord which concerns on this embodiment. It is a figure which shows the finite element method analysis model for deriving | requiring the approximate expression of the radial direction compression rigidity of the twisted cord which concerns on this embodiment. It is a figure which shows the finite element method analysis result of radial direction compression rigidity of the twisted cord which concerns on this embodiment. It is a figure which shows the relationship between the radial direction compression rigidity of the twisted cord which concerns on this embodiment, and the ratio of the diameter of an outer member and an inner member. It is a figure which shows the finite element model of the twisted cord which concerns on this embodiment. There are three methods for deforming the finite element model of the twisted cord according to the present embodiment when the finite element method is analyzed: (a) tension, (b) bending, and (c) radial compression. It is a figure which shows the test which calculates | requires the bending rigidity of the aramid core wire used in a present Example.

  DESCRIPTION OF EMBODIMENTS Hereinafter, embodiments for implementing a finite element model creation method, a finite element model creation program, and a finite element model creation apparatus for a twisted cord according to the present invention will be described based on a specific example with reference to the drawings. . In addition, what is demonstrated below is only what was illustrated and does not show the application limit of the finite element model creation method of a twisted cord, a finite element model creation program, and a finite element model creation apparatus concerning the present invention. That is, the finite element model creation method, the finite element model creation program, and the finite element model creation device of the twisted cord according to the present invention are not limited to the following embodiments, and various as long as they are described in the claims. Can be changed.

First, a method for creating a finite element model of a twisted cord according to the present embodiment will be described with reference to FIG. FIG. 1 is a flowchart showing a processing procedure of a finite element model creation method for twisted cords according to the present embodiment.
Note that the processing of the twisted cord finite element model creating method according to the present embodiment described below can be similarly read and executed by the CPU as a twisted cord finite element model creating program in a computer. Further, the finite element model creation program for the twisted cord can be installed in storage devices of various computers by recording it on a removable storage medium.

  As shown in FIG. 1, in a computer, based on the finite element model of the twisted cord 3 shown in FIG. 3, the physical property value and dimension value (that is, diameter) of the outer member 1, and the physical property value and dimension value of the inner member 2 (that is, An initial value of (diameter) is set (step S1). Here, the finite element model of the twisted cord according to the present embodiment will be described with reference to FIG. FIG. 3 is a diagram showing a state in which the twisted cord is divided into an outer member and an inner member as a finite element model of the twisted cord according to the present embodiment. As shown in FIG. 3, the twisted cord 3 according to the present embodiment is a finite element model made of solid elements as two concentric circular cylinders, the outer hollow cylindrical part is the outer member 1, and the inner solid cylindrical part Is called the inner member 2. The outer member 1 and the inner member 2 are made of materials having different physical property values. Further, the physical property value of the outer member 1 and the physical property value of the inner member 2 of the twisted cord 3 according to this embodiment are a Young's modulus and a Poisson's ratio, which are linear isotropic elastic materials. Moreover, the diameter of the outer member 1 is a fixed value, and is equal to the diameter of the twisted cord. Here, as a fixing condition, in addition to the diameter of the outer member 1, a part of the physical property value of the outer member 1 or the inner member 2 may be set as a fixed value. In this step, the physical property value of the outer member 1 of the twisted cord 3, the physical property value of the inner member 2, and the initial value of the diameter of the inner member 2 need not be set.

  Next, target values for tensile rigidity, bending rigidity and radial compression rigidity are set (step S2). The target value is a value obtained by measuring each rigidity of an actual twisted cord by a test, a value set at the design stage of the twisted cord, or the like. In the test, a belt having a twisted cord as a cord may be used.

  And the physical property value of the outer member 1 of the twisted cord 3, the physical property value of the inner member 2, and the value of the diameter of the inner member 2 are varied (step S3). As a variable condition, a ratio of a plurality of types of the diameter of the inner member 2 to a diameter of the fixed outer member 1 and a ratio of a plurality of types of physical property values of the inner member 2 to the physical property values of the outer member 1 are set. Here, the ratio of the plurality of types of the diameter of the inner member 2 to the diameter of the fixed outer member 1 is preferably 0.2 or more and 0.7 or less. This is because if the ratio of the plurality of types of the diameter of the inner member 2 to the diameter of the fixed outer member 1 is smaller than 0.2, the finite element mesh becomes too fine and the analysis efficiency decreases. Further, when the ratio of the plurality of types of the diameter of the inner member 2 to the diameter of the fixed outer member 1 is larger than 0.7, it is outside the range of the approximate expression of the radial compression rigidity described later.

Next, the tensile stiffness, the bending stiffness, and the radial compression stiffness are calculated based on a preset theoretical formula and approximate formula (step S4).
Here, based on the physical property data of the twisted cord according to the present embodiment, in order to calculate the tensile stiffness, bending stiffness and radial compression stiffness of the twisted cord according to the present embodiment, The definition will be described below with reference to FIGS. FIG. 4 is a diagram showing the tensile rigidity of the twisted cord according to the present embodiment. FIG. 5 is a diagram showing the bending rigidity of the twisted cord according to the present embodiment. FIG. 6 is a diagram showing the radial compression stiffness of the twisted cord according to the present embodiment. As will be described later, formulas for calculating the tensile stiffness and bending stiffness of the twisted cord from the physical property data of the twisted cord can be expressed by theoretical equations, and the radial compression stiffness of the twisted cord is calculated from the physical property data of the twisted cord. The expression for this is expressed by an approximate expression.
Further, in the finite element model of the twisted cord according to this embodiment shown in FIG. 3, the Young's modulus of the outer member 1 is E ₁ , the Poisson's ratio is ν ₁ , the Young's modulus of the inner member 2 is E ₂ , and the Poisson's ratio is ν. ₂ .

[Tensile rigidity of twisted cord]
Regarding the tensile rigidity of the twisted cord, as shown in FIG. 4, it is assumed that the length of the twisted cord 3 whose original length is L ₀ is pulled by the force of F _{S in} the longitudinal direction and the length becomes L. The cross-sectional area of the outer member 1 is A ₁ and the cross-sectional area of the inner member 2 is A ₂ .
First, consider the formula for calculating stiffness from the test. When the twisted cord 3 having the original length L ₀ is pulled in the longitudinal direction by the force of F _S and the engineering strain when the length becomes L is ε _S , ε _S is as follows.
ε _S = (L−L ₀ ) / L ₀ formula (1.1)
If the tensile stiffness of the time and K _S, K _S is a next "force causes the unit strain", the formula shown in Equation 1 (1.2). The unit is a unit of force ([N] in the SI unit system).

Next, the formula for calculating the stiffness from the physical property data is examined. The force F acting on the entire twisted cord 3 is divided into the force F ₁ that the outer member 1 takes and the force F ₂ that the inner member 2 takes, and the stress and strain equation “σ = E · ε”, the definition of stress In consideration of “σ = F / A”, the force F is expressed by Equation (1.3) shown in Formula 2.

Therefore, when the formula (1.3) is substituted into the formula (1.2), the formula (1.4) shown in Equation 3 is obtained for the tensile stiffness K _S , from the physical property value (E) and the dimension (A). Stiffness can be calculated. D ₁ is the diameter of the outer member 1 and is a constant.

[Bending rigidity of twisted cord]
Regarding the bending rigidity of the twisted cord, as shown in FIG. 5, it is assumed that the originally straight twisted cord is bent at a moment of force M and the radius of curvature of the central axis of the twisted cord becomes R. Further, the cross-sectional secondary moment of the outer member 1 is I ₁ , and the cross-sectional secondary moment of the inner member 2 is I ₂ .
First, consider the formula for calculating stiffness from the test. In this case, when the bending rigidity and _{K B, K B} from the test results obtained by the following equation (2.1). The unit is force unit × length unit × length unit ([N · m ² ] in the SI unit system).
K _B = M · R Formula (2.1)

Next, the formula for calculating the stiffness from the physical property data is examined. Flexural rigidity of the entire twisted cord 3 K _B is the bending stiffness K _B1 of the outer member 1, the sum of the flexural rigidity K _B2 of the inner member 2, the bending rigidity is the product of the Young's modulus E and geometrical moment of inertia I Therefore, the overall bending rigidity is expressed by the following equation (2.2) shown in the following equation 4. Note that in Formula (2.2) shown in Expression 4, the second moment of the circular cross-section the formula "I = [pi] D ^4/64" used.

[Radial compression stiffness of twisted cord]
Regarding the radial compression stiffness of the twisted cord, there is no definition in terms of material mechanics, but a practical definition is as follows. As shown in FIG. 6, the twisted cord is sandwiched between rigid plates in the radial direction, and compressed in the radial direction with a force of _Fr per unit length of the twisted cord. This original twisted cord diameter D ₀ is to become D. Here, the unit length is the length of the twisted cord and is the length in the vertical direction of FIG.
First, consider the formula for calculating stiffness from the test. The radial strain ε _r when the twisted cord diameter D ₀ becomes D when compressed in the radial direction with a force of F _r per unit length of the twisted cord is defined as follows. Since compression changes, if the original strain of definition, epsilon _r is a negative value, to simplify the subsequent computation, so that a positive value at the time of compression.
ε _r = (D−D ₀ ) / D ₀ formula (3.1)
The radial compression stiffness at this time is defined as _Kr , and _Kr is defined by the following equation. This stiffness is defined as “radial compression stiffness per unit length of twisted cord”. The unit is a unit of force ([N] in the SI unit system).
_{K r = F r / ε r} = FD 0 / (D-D 0) Equation (3.2)

Next, the formula for calculating the stiffness from the physical property data is examined. Regarding the deformed state of FIG. 6, it is difficult to theoretically derive the relational expression between the force F _r and the strain ε _r . Therefore, an approximate expression is obtained using finite element method analysis. That is, to simulate the deformed state of FIG. 6 in finite element analysis to determine the radial stiffness K _r from the force F _r and the radial strain epsilon _r. Then, the physical properties and dimensions of the outer member 1 and the inner member 2 are varied and analyzed, and regularity is found from the results and generalized as an approximate expression.
FIG. 7 shows a finite element method analysis model for deriving an approximate expression of radial compression stiffness.
The analysis method of the finite element method analysis was as follows.
-Due to symmetry of shape and load, a quarter circle model was used.
-A plane strain element was used as the element, and the thickness was a unit thickness (1 mm).
・ There was no friction between the rigid surface and the core wire (contact without friction).
-The material properties were linear elastic materials (defined by Young's modulus and Poisson's ratio).
・ The large deformation option was turned on because it included contact.
The conditions for the finite element method analysis were as follows.
<Fixed conditions>
・ Outer member 1 diameter: 2 mm (radius 1 mm)
-Outer member 1 Young's modulus: 1.0 [MPa]
-Radial strain: 0.1 (10%)
<Variable conditions>
The diameter and Young's modulus of the inner member 2 were expressed as a ratio with respect to the outer member 1 and varied.
Inner member 2 diameter / outer member 1 diameter (D ₂ / D ₁ ): 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7 (0. 7 and above could not be calculated due to the large collapse of the outer member)
Inner member 2 Young's modulus / outer member 1 Young's modulus (E ₂ / E ₁ ): 1, 2, 5, 10, 20, 50, 100, 1000, 10000

Under the above conditions, the finite element method analysis is performed, and based on the analysis result, the radial compression stiffness (K _r ) per unit length of the twisted cord is calculated. The horizontal axis represents E ₂ / E ₁ , and the vertical axis represents FIG. 8 shows a graph in which _Kr is taken and plotted for each D ₂ / D ₁ (the horizontal axis of FIG. 8 is a logarithmic scale). FIG. 8 is a diagram showing a finite element method analysis result of the radial compression stiffness of the twisted cord according to the present embodiment.
FIG. 8 shows that there is almost no change in _Kr in the region where E ₂ / E ₁ is about 50 or more. That is, if the inner member 2 is 50 times or more greater Young's modulus than the outer member 1, the values are that it does not affect the K _r be much. Since the inner member mainly has a role of adjusting the tensile rigidity, it usually has a Young's modulus several orders of magnitude greater than that of the outer member. Therefore, the constraint condition of “50 times larger” is not a problem, and E ₂ becomes irrelevant to K _r (independence is increased). Therefore, E ₂ / E ₁ is not included in the approximate expression.

Next, an approximate expression of radial compression stiffness is derived. FIG. 9 is a diagram showing the relationship between the radial compression stiffness of the twisted cord according to this embodiment and the ratio of the diameters of the outer member and the inner member. FIG. 9 is a result of plotting the relationship between D ₂ / D ₁ and K _r using a value of E ₂ / E ₁ = 10000, and approximating a quadratic equation using the Excel graph function. From FIG. 9, the radial compression stiffness when D ₁ = 2 [mm] and E ₁ = 1.0 [MPa] can be approximated by the equation (3.3) expressed by Equation 5.

Until now, the diameter (D ₁ ) and Young's modulus (E ₁ ) of the outer member 1 have been fixed. Next, arbitrary D ₁ and E ₁ will be considered. First, regarding the Young's modulus E ₁ , when E ₂ / E ₁ is fixed, if E ₁ becomes A times, E ₂ also becomes A times, so the Young's modulus of the entire finite element model is A Doubled. Accordingly, the radial compressive stiffness K _r also may be simply A multiplied by. Since the above equation (3.3) is a formula in the case of _E 1 = 1.0 [MPa], in the case of any _{E 1} may be multiplied by _{E 1.} Next, D ₁ is fixed, but if D ₂ / D ₁ is fixed, if D ₁ becomes A times, D ₂ also becomes A times, so that the entire model is enlarged to A times in a similar shape ( The thickness of the plane strain element remains the unit thickness). Accordingly, the radial compression rigidity is also A times. Since the above equation (3.3) is a formula in case of _D 1 = 2 [mm], in the case of any _{D 1} may be multiplied by _(D 1/2).
From the above, the approximate expression of the radial compression stiffness Kr for any E ₁ , E ₂ , D ₁ , D ₂ is _expressed by the following expression (3.4) shown in Equation 6. In Expression (3.4), a unit of _{K r:} N, the unit of _{E 1:} MPa, the _{D 1} and _{D 2} Unit: it is in mm.

  Then, it is determined whether or not the calculated values of tensile rigidity, bending rigidity, and radial compression rigidity coincide with the target values within a predetermined error range (step S5). Here, the ratio of the difference between the calculated value with respect to the target value and the target value is set as an error, and a range allowable as a predetermined error (for example, a range of ± 5%) is set in advance.

  If it is determined that the calculated tensile stiffness, bending stiffness, and radial compression stiffness do not match the target value within a predetermined error range (step S5: NO), the process returns to step S3.

  On the other hand, when it is determined that the calculated values of tensile stiffness, bending stiffness, and radial compression stiffness match the target values within a predetermined error range (step S5: YES), the values calculated in step S4 are calculated. The physical property value of the outer member 1 of the twisted cord 3, the physical property value of the inner member 2, and the value of the diameter of the inner member 2 are output (step S6). When there are multiple cases where the calculated tensile stiffness, bending stiffness, and radial compression stiffness are consistent with the target value within a predetermined error range, the calculated tensile stiffness, bending stiffness, and diameter The physical property value of the outer member 1, the physical property value of the inner member 2, and the diameter value of the inner member 2 with the smallest error between the value of the directional compression stiffness and the target value are output.

  As described above, a finite element model of a twisted cord in which the three stiffnesses of the tensile strength in the longitudinal direction of the twisted cord, the bending stiffness accompanying bending, and the radial compression stiffness are all adjusted to the target value at the same time is created.

  Next, a twisted cord finite element model creating apparatus according to the present embodiment will be described with reference to FIG. FIG. 2 is a block diagram of a twisted cord finite element model creation device according to the present embodiment. The twisted cord finite element model creation device 10 includes an arithmetic unit, a storage unit, an input unit, and an output unit, and is mounted on a computer. Here, each unit (arithmetic unit, storage unit, input unit, and output unit) of the twisted cord finite element model creation device 10 shown in FIG. 2 is configured by a computer such as a general-purpose personal computer. Yes. Such a computer stores hardware such as a CPU, ROM, RAM, hard disk, and CD-ROM drive, and the hard disk stores a program (this program is recorded on a removable storage medium). Can be installed on a variety of computers). And the above-mentioned each part is constructed | assembled by combining these hardware and software.

  The apparatus 10 for creating a finite element model of a twisted cord includes a physical property value of an outer member, a physical property value of an inner member, and an initial value 11 of a diameter of the inner member, a target value 12 of tensile stiffness, bending stiffness, and radial compression stiffness, Variable part 21 of material physical property value, internal member physical property value and inner member diameter, tensile stiffness, bending stiffness and radial compression stiffness calculation unit 22 by theoretical formula / approximation formula, tensile stiffness, bending stiffness and radial direction A compression stiffness comparison unit 23 and a tensile stiffness, bending stiffness and radial compression stiffness output unit 24 are provided.

  The physical property value of the outer member, the physical property value of the inner member, and the initial value 11 of the inner member diameter are based on the finite element model of the twisted cord 3 shown in FIG. The initial values of the physical property value and the dimension value (that is, the diameter) of the inner member 2 are input and stored via an input unit or a network. In addition, the effect | action of the physical property value of an outer member, the physical property value of an inner member, and the initial value 11 of the diameter of an inner member is the same as the process of step S1 of the finite element model preparation method of the twisted cord mentioned above, Detailed description Omitted.

  The target values 12 of the tensile stiffness, the bending stiffness, and the radial compression stiffness are for inputting and storing the target values of the tensile stiffness, the bending stiffness, and the radial compression stiffness via the input unit or the network. In addition, the effect | action of the target value 12 of tensile rigidity, bending rigidity, and radial direction compression rigidity is the same as the process of step S2 of the finite element model preparation method of the twisted cord mentioned above, and detailed description is abbreviate | omitted.

  The variable part 21 of the physical property value of the external material, the physical property value of the internal member, and the diameter of the internal member, the physical property value of the external member 1 of the twisted cord 3, the physical property value of the internal member 2, and the value of the diameter of the internal member 2 It is for variable. In addition, the effect | action of the physical property value of an outer member, the physical property value of an inner member, and the variable part 21 of the diameter of an inner member is the same as the process of step S3 of the finite element model creation method of the twisted cord mentioned above, and detailed description is given. Omitted.

  The tensile stiffness, bending stiffness and radial compression stiffness calculation unit 22 based on theoretical and approximate equations is used to calculate tensile stiffness, bending stiffness and radial compression stiffness based on preset theoretical and approximate equations. is there. Note that the operations of the tensile stiffness, bending stiffness, and radial compression stiffness calculation unit 22 by the finite element method are the same as the processing in step S4 of the finite element model creation method of the twisted cord described above, and detailed description thereof is omitted.

  The tensile stiffness, bending stiffness, and radial compression stiffness comparison unit 23 determines whether the calculated tensile stiffness, bending stiffness, and radial compression stiffness values match the target value within a predetermined error range. Is. If the tensile rigidity, bending rigidity, and radial compression rigidity comparison unit 23 does not determine that they match, the result is output to the variable part 21 of the physical property value of the outer member, the physical property value of the inner member, and the diameter of the inner member. Is done. The action of the tensile rigidity, bending rigidity, and radial compression rigidity comparison unit 23 is the same as the processing in step S5 of the above-described twisted cord finite element model creation method, and detailed description thereof is omitted.

  When the tensile stiffness, bending stiffness and radial compression stiffness output unit 24 determines that the tensile stiffness, bending stiffness and radial compression stiffness comparison unit 23 match, the result is input, and the tensile stiffness, bending stiffness and radial direction are input. This is for outputting the physical property value of the outer member 1, the physical property value of the inner member 2, and the diameter value of the inner member 2 calculated by the finite element method of the compression rigidity calculation unit 22. Note that the operations of the tensile rigidity, bending rigidity, and radial compression rigidity output unit 24 are the same as the processing in step S6 of the above-described twisted cord finite element model creation method, and detailed description thereof is omitted.

  In addition, the physical property value / dimension value of the finite element model of the twisted cord 3 created by applying the finite element model creating method, the finite element model creating program, and the finite element model creating apparatus of the twisted cord of the present embodiment described above. Using the physical property value of the outer member 1 of the twisted cord 3, the physical property value of the inner member 2, and the value of the diameter of the inner member 2, the effect may be actually verified by performing a finite element method analysis.

  More specifically, as shown in FIG. 10, the finite element model of the twisted cord 3 has a semicircular shape that is half in the radial direction depending on the shape and load conditions, and the symmetry plane is constrained in the plane. Moreover, the area | region of the predetermined length of a twisted cord longitudinal direction is modeled, and a cut surface is restrained in a surface. A hexahedral primary element (solid element) is used as the finite element model of the twisted cord according to the present embodiment, and the element at the center is degenerated into a pentahedron for convenience of shape. As the analysis option, only the large deformation nonlinear option is set to ON, and nonlinear analysis by the update Lagrangian method is performed. This is because contact between the rigid body and the twisted cord occurs under the radial compression condition, and this needs to be taken into consideration. The material is a linear isotropic elastic material.

  Then, a finite element analysis was performed on the finite element model of the twisted cord to perform three kinds of deformation as shown in FIG. The three types of deformation are the three types of tension shown in FIG. 11 (a), bending shown in FIG. 11 (b), and radial compression shown in FIG. 11 (c). In these three types of deformation, the symmetry plane under the symmetry condition and the cut surface in the longitudinal direction give a constraint that “always keep the plane but allow the deformation in the plane”. In addition, tensile strain, radius of curvature, and radial strain are set as individual conditions for the deformation shown in FIG. 11 (a), bending shown in FIG. 11 (b), and radial compression shown in FIG. 11 (c). To do.

  Under the above conditions, the above-described three deformation behaviors generated in the twisted cord 3 are analyzed by simulating with the finite element method analysis software. From the obtained deformation state, the above formula (1.4) (2 .2) Using (3.4), calculate each stiffness of tensile stiffness, bending stiffness and radial compression stiffness. Based on the errors between the analyzed tensile stiffness, bending stiffness and radial compression stiffness and the target value, it was confirmed that finite element analysis considering the three stiffnesses of the twisted cord 3 was possible within the practical range. To do.

  As described above, the finite element model creation method, the finite element model creation program, and the finite element model creation device for the twisted cord according to the present embodiment divide the twisted cord into two or more layers concentrically, and use the outermost hollow cylinder as the outer member. The inner hollow cylinder or solid cylinder is the inner member, and the outer member and inner member are finite element models with different physical property values, and the physical properties of the outer member are based on preset theoretical and approximate equations. (In the case of linear elasticity, Young's modulus and Poisson's ratio), the physical properties of the inner member, and the diameter of the inner member (that is, the diameter of the cylindrical surface that serves as the boundary between the inner member and the outer member) should be set appropriately. Therefore, the three values of the tensile stiffness in the longitudinal direction of the twisted cord, the bending stiffness accompanying bending, and the radial compressive stiffness are all simultaneously set to the target values (the actual value of the twisted cord measured in the test, design Can be matched to a value, etc.) set in the floor, it can be combined with the actual no practical problem on the value level.

  The preferred embodiments of the present invention have been described above. However, the present invention is not limited to the above-described embodiments, and various modifications can be made as long as they are described in the claims.

  In the above embodiment, the finite element model is created by concentrically dividing the twisted cord into two layers of cylinders. However, the finite element model may be created by concentrically dividing it into three or more layers of cylinders. In that case, the theoretical formula / approximation formula set in advance is calculated from the physical property values of the outermost outer member, the physical property values and diameters of two or more inner members inside the outer member, and in the longitudinal direction of the twisted cord. Three stiffnesses are set such as tensile stiffness, bending stiffness associated with bending, and radial compression stiffness. Thereby, the freedom degree of adjustment can be increased.

  In the above embodiment, the finite element model is created by the solid element. However, the finite element model is obtained by combining the solid element with a truss element (bar element having no bending rigidity) or a beam element (bar element having bending rigidity). You may create it. In that case, in addition to the physical property value of the solid element, set the shape characteristics such as the cross-sectional area and cross-sectional shape of the truss element or beam element to be combined, and the physical property value, and then twist when adding the truss element or beam element. Create theoretical and approximate formulas for the tensile stiffness in the longitudinal direction of the cord, the bending stiffness associated with bending, and the radial compression stiffness. Thus, the degree of freedom of adjustment can be increased by increasing the number of shape characteristics and physical property values that can be adjusted.

  Furthermore, the physical property value of the outer member 1 and the physical property value of the inner member 2 of the twisted cord 3 according to the above embodiment are the Young's modulus and Poisson's ratio, which are linear isotropic elastic materials, but are not limited thereto. For example, a linear isotropic elastic material other than Young's modulus and Poisson's ratio may be used, or a linear anisotropic elastic material, a super elastic material, or a plastic material may be used. In that case, to obtain the three stiffnesses of the tensile strength in the longitudinal direction of the twisted cord, the bending stiffness accompanying bending, and the radial compression stiffness from the physical property value of the outer member, the physical property value of the inner member, and the diameter of the inner member. Are set based on a linear isotropic elastic material other than Young's modulus and Poisson's ratio, a linear anisotropic elastic material, a superelastic material, or a plastic material. Thereby, there exists an advantage that material behaviors other than the linear isotropic elastic material defined by Young's modulus and Poisson's ratio can be expressed.

  Next, specific examples to which the finite element model creation method, the finite element model creation program and the finite element model creation apparatus of the above-described twisted cord according to this embodiment are applied will be described below. Below, it explains based on the concrete Example which applied the finite element model creation method (refer FIG. 1) of the twisted cord of this embodiment, and the finite element model creation program and finite element creation of the twisted cord of this embodiment The description of the apparatus is the same and will be omitted. An example in which the above-described finite element model creation method, finite element model creation program, and finite element model creation apparatus for a twisted cord according to this embodiment are applied to an aramid core wire will be described.

First, in the computer, based on the finite element model of the twisted cord 3 shown in FIG. 3, the physical property value and diameter of the outer member 1 and the initial physical property value and diameter of the inner member 2 are set (step S1). Here, in this embodiment, the physical property value of the outer member 1 and the physical property value of the inner member 2 of the aramid core wire are linear isotropic elastic materials (defined by Young's modulus and Poisson's ratio). The diameter _{D 1} of the outer member 1, and 1.19 [mm] (fixed value). As for the physical property values, only the Young's modulus was adjusted, and the Poisson's ratio of the outer member 1 and the inner member 2 was fixed at 0.3. Further, the Young's modulus and the diameter of the inner member 2 are represented by the ratio of the Young's modulus and the diameter of the outer member, respectively.

Next, target values for tensile rigidity, bending rigidity and radial compression rigidity are set (step S2). In the present embodiment, the target value is the average diameter (diameter outer member 1) D ₁ is the actual value measured by testing each rigidity of aramid core wire belt of 1.19 [mm] . For this aramid cord, measured values of tensile rigidity and bending rigidity are already required. The tensile stiffness is derived from the treated rope SS (stress-strain curve) using a linear approximation between 0 and 2%. The bending stiffness was measured with a sample in which an aramid core wire used in this example shown in FIG. 12 was sandwiched between rubbers using an Olsen-type bending tester (one end of the test piece was fixed to a chuck and bent at a predetermined bending angle. Sometimes the bending stiffness is calculated from the bending moment applied to the other end and the bending angle), and the bending stiffness of the core is obtained by subtracting the bending stiffness of the rubber.
Tensile rigidity K _s : 31187.27 [N]
Bending stiffness ^{_{K B: 115.171 [N · mm}} 2]

Regarding the radial compression stiffness, a test for the deformation mode of FIG. Therefore, as an alternative data, the radial compression stiffness was calculated using the finite element analysis described when obtaining the approximate expression of the radial compression stiffness of the above-described twisted cord from the elastic modulus in the radial direction. The radial elastic modulus of the aramid core wire was 20 [MPa], and the radial stiffness K _r (per core wire length of 1 mm) by finite element analysis was as follows.
K _r = 8.24 [N]

In summary, the rigidity in each deformation mode test of the aramid core wire used in this example is as follows.
Tensile rigidity K _s : 31187.27 [N]
Bending stiffness ^{_{K B: 115.171 [N · mm}} 2]
Radial compressive stiffness K _r: 8.24 [N] (per cord length 1mm)

  Then, the physical property value of the outer member 1 of the twisted cord 3, the physical property value of the inner member 2, and the value of the diameter of the inner member 2 are varied (step S3), and tension is determined based on preset theoretical and approximate equations. Rigidity, bending stiffness and radial compression stiffness are calculated (step S4), and it is determined that the calculated tensile stiffness, bending stiffness and radial compression stiffness values agree with the target value within a predetermined error range. (Step S5), the processing from Step S3 is repeated.

In this embodiment, the diameters and Young's moduli of the outer and inner members of the two-layer solid element model are matched so as to match all the rigidity of the three deformation modes summarized in step S2. In this example, the Excel solver function was used. Since the diameter (D ₁ ) of the external material is fixed as the core wire outer diameter (1.19 [mm]), the variables to be adjusted are the inner member diameter (D ₂ ), the outer member Young's modulus (E ₁ ), The inner member Young's modulus (E ₂ ) is three. From these three variables, the rigidity of each deformation mode is calculated by the above-described theoretical formula and approximate formula.

Then, (residual / target value) ² is calculated from the difference (residual) between the target value and the adjustment result. It is summed up in each deformation mode so that it becomes the minimum value.
Further, as a constraint condition, “the diameter of the inner member / the diameter of the outer member” is set larger than 0.2 and smaller than 0.7. Furthermore, “E ₂ / E ₁ > 50”, which is a condition for establishing an approximate expression of radial compression stiffness, is also included as a constraint condition. By executing the Excel solver under this condition, the Young's modulus of the outer member 1, the Young's modulus of the inner member 2, and the diameter of the inner member 2 in the present embodiment are output as follows.
External material Young's modulus E ₁ : 18.60 [MPa]
Inner member Young's modulus E ₂ : 616517 [MPa]
Inner member diameter D ₂ : 0.248 [mm]

  In addition, the estimated value of each deformation mode rigidity by the adjustment result of the calculated aramid cord in this embodiment is as shown in Table 1 below. In Table 1, it can be seen that although the error is slightly larger in the tensile rigidity, it can be adjusted well.

Here, using the physical property values and dimension values (E ₁ , E ₂ , D ₂ ) of the finite element model in the above embodiment, the finite element method analysis was actually performed to verify the effect. FIG. 10 shows a finite element model of a twisted cord for a belt. The finite element model has a half-circular shape in the radial direction due to the symmetry of the shape and load conditions, and the symmetry plane is constrained in the plane. Moreover, the area | region whose length of a twisted cord longitudinal direction is 0.5 mm was made into the finite element model, and the cut surface was restrained in the surface. As the finite element, a hexahedral primary element (solid element) was used, but the element at the center was reduced to a pentahedron for convenience of shape. The material properties were linear isotropic elasticity. The Young's modulus is as obtained in the above example, and the Poisson's ratio is 0.3 for both the outer member and the inner member. The dimensions are as follows calculated in the above example.
External material Young's modulus E ₁ : 18.60 [MPa]
Inner member Young's modulus E ₂ : 616517 [MPa]
Inner member diameter D ₂ : 0.248 [mm]

For this finite element model, a finite element method analysis was performed in which three types of deformation as shown in FIG. 11 were performed. These are three types: (a) tension, (b) bending, and (c) radial compression. In these three ways, the symmetry plane according to the symmetry condition and the cut surface in the longitudinal direction gave a constraint that “always keep the plane but allow deformation in the plane”.
The individual conditions are as follows.
(A) Tensile: Tensile strain 0.02
(B) Bending: radius of curvature 50mm
(C) radial compression: radial strain 0.1
The calculation environment is as follows.
・ Computer: Altix XE500, manufactured by SGI
CPU: Xeon 5570 x 2 manufactured by Intel Corporation Memory: 12 GB
OS: SuSE Linux (registered trademark) 10
-Finite element analysis software: “Marc2010.2” manufactured by MSC
・ Analysis option Only the large deformation nonlinear option was turned ON, and nonlinear analysis was performed by the updated Lagrangian method. This is because contact between the rigid body and the twisted cord occurs under the radial compression condition, and this needs to be taken into consideration. The material is a linear isotropic elastic material.

Under the above conditions, the above-described three deformation behaviors generated in the twisted cord 3 are analyzed by simulating with the finite element method analysis software. From the obtained deformation state, the above formula (1.4) (2 .2) Using (3.4), the respective stiffnesses (K _s , K _B , K _r ) of tensile stiffness, bending stiffness and radial compression stiffness were calculated. Table 2 below shows a comparison between the results of the respective stiffnesses K _s , K _B and K _r calculated in step S4 and the target values set in step S2.

  As shown in Table 2, it is confirmed that the finite element method analysis considering the three stiffnesses of the twisted cord can be performed within the practical range, although the bending stiffness error is slightly large (the result of the finite element method is more). did it.

DESCRIPTION OF SYMBOLS 1 External material 2 Internal member 3 Twisted cord 10 Twisted cord finite element model creation apparatus 11 Physical property value of external material, physical property value of internal member, and initial value of diameter of internal member 12 Tensile stiffness, bending stiffness and radial compression stiffness Target value 21 Physical property value of external member, physical property value of inner member, and diameter variable portion 22 of inner member Tension stiffness, bending stiffness and radial compression stiffness calculation unit 23 by theoretical and approximate equations Tension stiffness, bending stiffness and radial compression Rigidity comparison unit 24 Tensile stiffness, bending stiffness and radial compression stiffness output unit

Claims (12)

A finite element model how to create a twisted cord to create a finite element model of Oite twisted cord to the computer,
The process executed by the computer is
The process of creating a finite element model by dividing a twisted cord into two concentric layers, modeling the outermost hollow cylinder as an outer member, and using the solid cylinder or hollow cylinder inside the outer member as an inner member, and modeling with solid elements When,
Based on a theoretical formula and an approximate formula set in advance so that the tensile stiffness in the longitudinal direction of the twisted cord, the bending stiffness associated with the bending of the twisted cord, and the radial compression stiffness of the twisted cord match the target value, Setting the physical property value of the outer member, the physical property value of the inner member, and the diameter of the inner member of the finite element model;
A method for creating a finite element model of a twisted cord, comprising:   The method for creating a finite element model of a twisted cord according to claim 1, wherein the physical property value is a linear isotropic elastic material, a linear anisotropic elastic material, a superelastic material, or a plastic material.   The method of creating a finite element model of a twisted cord according to claim 1 or 2, wherein the twisted cord is divided into three or more concentric layers.   The method of creating a finite element model for a twisted cord according to any one of claims 1 to 3, wherein the finite element model is modeled by combining a truss element or a beam element with a solid element. A program for creating a finite element model of a twisted cord that creates a finite element model of a twisted cord,
The process of creating a finite element model by dividing a twisted cord into two concentric layers, modeling the outermost hollow cylinder as an outer member, and using the solid cylinder or hollow cylinder inside the outer member as an inner member, and modeling with solid elements When,
Based on a theoretical formula and an approximate formula set in advance so that the tensile stiffness in the longitudinal direction of the twisted cord, the bending stiffness associated with the bending of the twisted cord, and the radial compression stiffness of the twisted cord match the target value, Setting the physical property value of the outer member, the physical property value of the inner member, and the diameter of the inner member of the finite element model;
A computer program for creating a finite element model of a twisted cord, characterized by causing a computer to execute.   6. The program for creating a finite element model of a twisted cord according to claim 5, wherein the physical property value is a linear isotropic elastic material, a linear anisotropic elastic material, a super elastic material, or a plastic material.   The program for creating a finite element model of a twisted cord according to claim 5 or 6, wherein the twisted cord is divided into three or more concentric layers. The finite element model creation program for a twisted cord according to any one of claims 5 to 7 , wherein the finite element model is modeled by combining a solid element with a truss element or a beam element. A device for creating a finite element model of a twisted cord that is mounted on a computer and creates a finite element model of a twisted cord,
A method for creating a finite element model by dividing a twisted cord into two concentric layers, modeling the outermost hollow cylinder as an outer member, and using a solid cylinder or hollow cylinder inside the outer member as an inner member, and modeling with solid elements When,
Based on a theoretical formula and an approximate formula set in advance so that the tensile stiffness in the longitudinal direction of the twisted cord, the bending stiffness associated with the bending of the twisted cord, and the radial compression stiffness of the twisted cord match the target value, Means for setting a physical property value of the outer member, a physical property value of the inner member, and a diameter of the inner member of the finite element model;
An apparatus for creating a finite element model of a twisted cord, comprising:   The apparatus for creating a finite element model of a twisted cord according to claim 9, wherein the physical property value is a linear isotropic elastic material, a linear anisotropic elastic material, a superelastic material, or a plastic material.   The apparatus for creating a finite element model of a twisted cord according to claim 9 or 10, wherein the twisted cord is divided into three or more concentric layers.   The finite element model creation device for a twisted cord according to any one of claims 9 to 11, wherein the finite element model is modeled by combining a solid element with a truss element or a beam element.