JP5962443B2 - Method and apparatus for predicting cable breakage life - Google Patents
Method and apparatus for predicting cable breakage life Download PDFInfo
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Description
本発明は、複数の導体素線からなる導体を有するケーブルの屈曲断線寿命予測方法および装置に関するものである。 The present invention relates to a method and an apparatus for predicting a bent wire breakage life of a cable having a conductor composed of a plurality of conductor wires.
複数の導体素線からなる導体を有するケーブルの屈曲断線寿命予測方法として、ケーブルの屈曲条件と導体構造から導体素線に作用する歪振幅（あるいは応力振幅）を求め、導体素線単線の屈曲疲労寿命データベース（所謂ＳＮ線図）を参照して、求めた歪振幅（あるいは応力振幅）に対応する導体素線が破断するサイクル数（寿命）を求めることで、当該サイクル数をケーブルの屈曲断線寿命として予測する方法が知られている（例えば、特許文献１，２参照）。 As a method for predicting the bending breakage life of a cable having a conductor composed of a plurality of conductor strands, the strain fatigue (or stress amplitude) acting on the conductor strand is obtained from the cable bending condition and the conductor structure, and the bending fatigue of the conductor strand single wire By referring to the life database (so-called SN diagram), the number of cycles (life) at which the conductor wire corresponding to the obtained strain amplitude (or stress amplitude) breaks is obtained, and the number of cycles is calculated as the bending break life of the cable. (For example, refer patent documents 1 and 2).
しかしながら、繰り返し屈曲を受けるケーブルでは、屈曲疲労だけでなく導体素線同士の摩耗によって早期断線に至るケースがある。上述の従来のケーブルの屈曲断線寿命予測方法では、導体素線同士の摩耗を考慮していないため、実際よりも長い危険側の屈曲断線寿命を予測してしまう場合があり、導体素線同士の摩耗を考慮したケーブル屈曲断線寿命の予測が望まれる。 However, in a cable that is repeatedly bent, there are cases in which not only bending fatigue but also early breakage occurs due to wear between conductor wires. In the above-mentioned conventional method for predicting the bending breakage of a cable, since the wear between the conductor strands is not taken into account, the bending disconnection life on the danger side longer than the actual may be predicted. Prediction of cable bending breakage life considering wear is desired.
本発明は上記事情に鑑み為されたものであり、複数の導体素線からなる導体を有するケーブルの屈曲断線寿命を精度よく予測することが可能なケーブルの屈曲断線寿命予測方法および装置を提供することを目的とする。 The present invention has been made in view of the above circumstances, and provides a method and apparatus for predicting the bending breakage life of a cable capable of accurately predicting the bending breakage life of a cable having a conductor composed of a plurality of conductor strands. For the purpose.
本発明は上記目的を達成するために創案されたものであり、複数の導体素線からなる導体を有するケーブルの屈曲断線寿命を予測する方法であって、前記ケーブルの屈曲条件と導体構造から、摩耗していない初期の前記導体素線に生じる初期の応力振幅と平均応力を求め、前記ケーブルを屈曲した際の前記導体素線同士の摩耗を考慮して屈曲回数ごとに前記導体素線の断面積を求め、当該求めた断面積と前記導体素線の初期の断面積の比、および初期の応力振幅と平均応力から、屈曲回数ごとの応力振幅と平均応力を求め、当該屈曲回数ごとの応力振幅と平均応力と、前記導体素線の材料特性とを基に、屈曲回数ごとの疲労損傷度を求め、当該屈曲回数ごとの疲労損傷度を累積することで、前記導体素線が破断する屈曲回数を求め、当該求めた屈曲回数を前記ケーブルの屈曲断線寿命として予測し、予め求めておいた前記ケーブルの曲げ半径に対する導体素線間の接触荷重の関係、および曲げ半径に対する導体素線間の摺動距離の関係と、前記ケーブルの屈曲条件である曲げ半径とから、前記導体素線間の接触荷重および摺動距離を求め、当該求めた導体素線間の接触荷重および摺動距離と、予め求めておいた接触荷重ごとの総摺動距離に対する摩耗痕の深さの関係とから、屈曲回数に対する摩耗痕の深さの関係を求め、当該屈曲回数に対する摩耗痕の深さの関係から、屈曲回数ごとの摩耗痕の深さを求め、当該求めた摩耗痕の深さから前記導体素線の断面積を求めることで、屈曲回数ごとに前記導体素線の断面積を求め、前記接触荷重ごとの総摺動距離に対する摩耗痕の深さの関係を、前記導体素線を模した試験線同士を接触させ前記接触荷重に相当する荷重を印加した状態で摺動させることにより、求めるケーブルの屈曲断線寿命予測方法である。 The present invention was devised in order to achieve the above object, and is a method for predicting the bending disconnection life of a cable having a conductor composed of a plurality of conductor strands, from the bending condition and conductor structure of the cable, The initial stress amplitude and average stress generated in the initial conductor wire that is not worn are obtained, and the conductor strands are cut for each number of bendings in consideration of wear of the conductor wires when the cable is bent. Obtain the area, determine the stress amplitude and average stress for each number of flexures from the ratio of the obtained cross-sectional area to the initial cross-sectional area of the conductor wire, and the initial stress amplitude and average stress. Based on the amplitude, average stress, and material properties of the conductor strand, the fatigue damage degree for each number of flexures is obtained, and the fatigue damage degree for each flexion count is accumulated, whereby the conductor strand is bent. Ask for the number of times Predicting bending times as bending breakage life of the cable, the relationship between the sliding distance between the conductors strands relationship contact load between the conductors strands to bending radius of the cable obtained in advance, and bending to the radius, The contact load and sliding distance between the conductor strands are determined from the bending radius that is the bending condition of the cable, and the contact load and sliding distance between the conductor strands thus determined and the contact load determined in advance. From the relationship of the depth of the wear mark with respect to the total sliding distance for each, the relationship of the depth of the wear mark with respect to the number of bends is obtained. By obtaining the depth, and obtaining the cross-sectional area of the conductor wire from the obtained depth of the wear scar, the cross-sectional area of the conductor wire is obtained for each number of bends, and the total sliding distance for each contact load Depth of wear marks And by sliding while applying a load corresponding to the contact load contacting the test line between imitating the conductor wire, it is bent disconnection life prediction method for a cable to be obtained.
前記導体素線の半径をｒ、屈曲回数ｎ回目の摩耗痕の深さをｈnとしたとき、屈曲回数ｎ回目の前記導体素線の断面積Ｓnを、下式（１）
Ｓn＝ｒ2（π−θn）＋ｒ（ｒ−ｈn）ｓｉｎθn ・・・（１）
但し、θn＝ｃｏｓ-1｛（ｒ−ｈn）／ｒ｝
により求めてもよい。
Assuming that the radius of the conductor wire is r and the depth of the wear mark having the number of flexing times n is h n , the cross-sectional area Sn of the conductor wire having the number of flexing times n is expressed by the following equation (1)
S n = r 2 (π−θ n ) + r (r−h n ) sin θ n (1)
However, θ n = cos −1 {(r−h n ) / r}
You may ask for.
また、本発明は、複数の導体素線からなる導体を有するケーブルの屈曲断線寿命を予測する装置であって、前記ケーブルの屈曲条件と導体構造から、摩耗していない初期の前記導体素線に生じる初期の応力振幅と平均応力を求める初期応力演算部と、前記ケーブルを屈曲した際の前記導体素線同士の摩耗を考慮して屈曲回数ごとに前記導体素線の断面積を求める導体素線断面積演算部と、当該導体素線断面積演算部で求めた断面積と前記導体素線の初期の断面積の比、および前記初期応力演算部で求めた初期の応力振幅と平均応力から、屈曲回数ごとの応力振幅と平均応力を求める屈曲回数毎応力演算部と、当該屈曲回数毎応力演算部で求めた屈曲回数ごとの応力振幅と平均応力と、前記導体素線の材料特性とを基に、屈曲回数ごとの疲労損傷度を求める疲労損傷度演算部と、当該疲労損傷度演算部で求めた屈曲回数ごとの疲労損傷度を累積することで、前記導体素線が破断する屈曲回数を求め、当該求めた屈曲回数を前記ケーブルの屈曲断線寿命として予測する屈曲断線寿命予測部と、を備え、前記導体素線断面積演算部は、予め求めておいた前記ケーブルの曲げ半径に対する導体素線間の接触荷重の関係、および曲げ半径に対する導体素線間の摺動距離の関係と、前記ケーブルの屈曲条件である曲げ半径とから、前記導体素線間の接触荷重および摺動距離を求め、当該求めた導体素線間の接触荷重および摺動距離と、予め求めておいた接触荷重ごとの総摺動距離に対する摩耗痕の深さの関係とから、屈曲回数に対する摩耗痕の深さの関係を求め、当該屈曲回数に対する摩耗痕の深さの関係から、屈曲回数ごとの摩耗痕の深さを求め、当該求めた摩耗痕の深さから前記導体素線の断面積を求めることで、屈曲回数ごとに前記導体素線の断面積を求め、前記接触荷重ごとの総摺動距離に対する摩耗痕の深さの関係は、前記導体素線を模した試験線同士を接触させ前記接触荷重に相当する荷重を印加した状態で摺動させることにより、求められているケーブルの屈曲断線寿命予測装置である。 Further, the present invention is an apparatus for predicting the bending disconnection life of a cable having a conductor composed of a plurality of conductor strands, wherein the initial conductor strand that is not worn is determined from the bending conditions and the conductor structure of the cable. An initial stress calculation unit for obtaining an initial stress amplitude and an average stress to be generated, and a conductor strand for obtaining a cross-sectional area of the conductor strand for each number of bends in consideration of wear of the conductor strands when the cable is bent From the cross-sectional area calculation unit, the ratio of the cross-sectional area obtained by the conductor wire cross-sectional area calculation unit and the initial cross-sectional area of the conductor strand, and the initial stress amplitude and average stress obtained by the initial stress calculation unit, Based on the stress calculation unit for each bend number for obtaining the stress amplitude and average stress for each bend number, the stress amplitude and average stress for each bend number obtained by the stress calculation unit for each bend number, and the material properties of the conductor wire. In addition, fatigue loss for each flexion By calculating the fatigue damage degree calculation unit for determining the degree and the fatigue damage degree for each bend number obtained by the fatigue damage degree calculation unit, the number of bends at which the conductor strand breaks is obtained. A bending breakage life prediction unit for predicting the bending breakage life of the cable, the conductor strand cross-sectional area calculation unit, the relationship of the contact load between the conductor strands to the bending radius of the cable that has been obtained in advance, The contact load and sliding distance between the conductor strands are determined from the relationship of the sliding distance between the conductor strands with respect to the bending radius and the bending radius which is the bending condition of the cable. From the relationship between the contact load and sliding distance and the relationship between the wear trace depth and the total sliding distance for each contact load obtained in advance, the relationship between the wear trace depth and the number of flexures is determined. Wear scar From the relationship, the depth of the wear trace for each number of flexures is obtained, and the cross-sectional area of the conductor strand is obtained from the obtained depth of the wear trace, thereby obtaining the cross-sectional area of the conductor strand for each flexion count. The relationship of the depth of the wear scar with respect to the total sliding distance for each contact load is determined by contacting the test wires simulating the conductor strands and applying a load corresponding to the contact load. Thus, the cable breakage life prediction device is required .
本発明によれば、複数の導体素線からなる導体を有するケーブルの屈曲断線寿命を精度よく予測することが可能なケーブルの屈曲断線寿命予測方法および装置を提供できる。 ADVANTAGE OF THE INVENTION According to this invention, the bending disconnection lifetime prediction method and apparatus of a cable which can estimate the bending disconnection lifetime of the cable which has the conductor which consists of a some conductor strand with high precision can be provided.
以下、本発明の実施の形態を添付図面にしたがって説明する。 Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.
図１は、本実施の形態に係るケーブルの屈曲断線寿命予測方法のフロー図である。なお、本実施の形態で屈曲断線寿命の予測対象となるケーブルは、複数の導体素線からなる導体を有するケーブルである。導体素線は撚り合わされていてもよいし、撚り合わされていなくてもよい。 FIG. 1 is a flowchart of a method for predicting the bending breakage life of a cable according to the present embodiment. In addition, the cable which is the object of prediction of the bending disconnection life in the present embodiment is a cable having a conductor composed of a plurality of conductor strands. The conductor strands may be twisted or may not be twisted.
図１に示すように、本実施の形態に係るケーブルの屈曲断線寿命予測方法では、まず、ステップＳ１にて、ケーブルの屈曲条件と導体構造から、摩耗していない初期の導体素線に生じる初期の応力振幅σa0と平均応力σm0を求める。 As shown in FIG. 1, in the cable bending breakage life prediction method according to the present embodiment, first, in step S1, the initial state generated in the unworn initial conductor wire from the cable bending condition and the conductor structure. The stress amplitude σ a0 and the average stress σ m0 are obtained.
ケーブルの曲げ半径をＲ、ケーブルの外径をａ、導体全体の外径をｂ、導体素線の外径をｃとすると、下式（２）
ε＝（ｂ−ｃ）／（２Ｒ＋ａ） ・・・（２）
により導体素線に生じる歪εを求めることができ、さらに、導体素線の材料特性である歪−応力特性を用いて歪εを応力σに換算することができる。図２に示すように、ケーブル２１を曲げ半径Ｒmin〜Ｒmax間で繰り返し屈曲する場合、最大曲げ半径Ｒmaxに対応する歪・応力が初期の最小歪εmin・最小応力σminとなり、最小曲げ半径Ｒminに対応する歪・応力が初期の最大歪εmax・最大応力σmaxとなる。
When the bending radius of the cable is R, the outer diameter of the cable is a, the outer diameter of the entire conductor is b, and the outer diameter of the conductor wire is c, the following equation (2)
ε = (b−c) / (2R + a) (2)
Thus, the strain ε generated in the conductor strand can be obtained, and further, the strain ε can be converted into the stress σ using the strain-stress characteristic which is the material property of the conductor strand. As shown in FIG. 2, when the cable 21 is repeatedly bent between the bending radii R min to R max , the strain / stress corresponding to the maximum bending radius R max becomes the initial minimum strain ε min / minimum stress σ min , and the minimum The strain / stress corresponding to the bending radius R min is the initial maximum strain ε max and maximum stress σ max .
初期の最小応力σminと最大応力σmaxを求めれば、下式（３），（４）
σa0＝（σmax−σmin）／２ ・・・（３）
σm0＝（σmax＋σmin）／２ ・・・（４）
により、初期の応力振幅σa0と平均応力σm0を求めることができる。
If the initial minimum stress σ min and maximum stress σ max are obtained, the following equations (3), (4)
σ a0 = (σ max −σ min ) / 2 (3)
σ m0 = (σ max + σ min ) / 2 (4)
Thus, the initial stress amplitude σ a0 and average stress σ m0 can be obtained.
ステップＳ１にて初期の応力振幅σa0と平均応力σm0を求めた後、ステップＳ２〜Ｓ４にて、ケーブルを屈曲した際の導体素線同士の摩耗を考慮して屈曲回数ｎごとに導体素線の断面積Ｓnを求める。 After obtaining the initial stress amplitude σ a0 and the average stress σ m0 in step S1, in steps S2 to S4, the conductor element is taken for each number of times n in consideration of the wear of the conductor wires when the cable is bent. determining the cross-sectional area S n of the line.
まず、ステップＳ２にて、ケーブルの屈曲条件と導体構造から、導体素線間の接触荷重および摺動距離を求める。 First, in step S2, the contact load and the sliding distance between the conductor wires are obtained from the cable bending conditions and the conductor structure.
導体素線間の接触荷重および摺動距離を求める際には、予め、図３（ａ）に示すケーブルの曲げ半径Ｒに対する導体素線間の接触荷重Ｗの関係、および、図３（ｂ）に示す曲げ半径Ｒに対する導体素線間の摺動距離の関係を予め求めておき、これらの関係を用いて、ケーブルの屈曲条件である曲げ半径Ｒ（Ｒmin，Ｒmax）から、導体素線間の接触荷重および摺動距離を求める。図３（ａ），（ｂ）の関係は、事前に試験やシミュレーションを行うことにより得ることができる。 When obtaining the contact load and the sliding distance between the conductor strands, the relationship between the contact load W between the conductor strands and the bending radius R of the cable shown in FIG. The relationship of the sliding distance between the conductor strands with respect to the bending radius R shown in FIG. 2 is obtained in advance, and using these relationships, the conductor strands are obtained from the bending radius R (R min , R max ) which is the cable bending condition. Obtain the contact load and sliding distance. The relationship between FIGS. 3A and 3B can be obtained by conducting tests and simulations in advance.
なお、図３（ａ）の関係を用いて曲率半径Ｒmin，Ｒmaxに対応する２つの接触荷重Ｗを得ることができるが、本実施の形態では、安全側の評価とするため、最小曲率半径Ｒminに対応する最大接触荷重Ｗmaxを接触荷重として用いる。 Although the two contact loads W corresponding to the curvature radii R min and R max can be obtained using the relationship shown in FIG. 3A, in this embodiment, the minimum curvature is used for evaluation on the safe side. The maximum contact load W max corresponding to the radius R min is used as the contact load.
また、図３（ｂ）の縦軸はケーブルを直線状態から曲げたときに生じる導体素線間の摺動距離を示しており、最小曲げ半径Ｒminに対応する最大摺動距離Ｌmaxから、最大曲げ半径Ｒmaxに対応する最小摺動距離Ｌminを減じた値が、ケーブルを曲げ半径Ｒmin〜Ｒmax間で屈曲した際の摺動距離Ｌとなる。 The vertical axis in FIG. 3 (b) indicates the sliding distance between the conductor wires generated when the cable is bent from the straight state, and from the maximum sliding distance L max corresponding to the minimum bending radius R min , A value obtained by subtracting the minimum sliding distance L min corresponding to the maximum bending radius R max is the sliding distance L when the cable is bent between the bending radii R min to R max .
ステップＳ２にて導体素線間の接触荷重Ｗmaxおよび摺動距離Ｌを求めた後、ステップＳ３にて、接触荷重Ｗmaxおよび摺動距離Ｌから屈曲回数ｎに対する摩耗痕の深さｈの関係を求める。 After determining the contact load W max and sliding distance L between the conductors strands at step S2, at step S3, the relationship of the contact load W max and a sliding distance L of the wear scar for bending count n depth h Ask for.
屈曲回数ｎに対する摩耗痕の深さｈの関係を求める際には、予め、図４（ａ）に示す接触荷重Ｗごとの総摺動距離に対する摩耗痕の深さｈの関係を求めておき、この関係を用い、ステップＳ２で求めた接触荷重Ｗmaxに対応する総摺動距離に対する摩耗痕の深さｈの関係（図４（ａ）における実線）を求める。この関係における横軸の総摺動距離は、つまり（屈曲回数ｎ）×（１回の屈曲での摺動距離Ｌ）と等しいので、総摺動距離をステップＳ２で求めた摺動距離Ｌで除すれば、図４（ｂ）に示すような屈曲回数ｎに対する摩耗痕の深さｈの関係を得ることができる。 When determining the relationship of the depth h of the wear mark with respect to the number of bendings n, the relationship of the depth h of the wear mark to the total sliding distance for each contact load W shown in FIG. Using this relationship, a relationship (solid line in FIG. 4A) of the depth h of the wear scar with respect to the total sliding distance corresponding to the contact load W max obtained in step S2 is obtained. Since the total sliding distance of the horizontal axis in this relationship is equal to (number of bendings n) × (sliding distance L in one bending), the total sliding distance is the sliding distance L obtained in step S2. Except for this, it is possible to obtain the relationship of the depth h of the wear scar with respect to the number of bendings n as shown in FIG.
なお、図４（ａ）の関係は、図５に示すような導体素線摩耗試験装置５１を用いて事前に試験を行うことにより得ることができる。導体素線摩耗試験装置５１は、導体素線を模した２本の試験線５２が交差した状態で載置される第１試験線固定治具５３と、第１試験線固定治具５３との間で両試験線５２を挟み込み、両試験線５２に接触荷重を印可する第２試験線固定治具５４と、第１試験線固定治具５３を水平方向にスライドさせることで、両試験線固定治具５３，５４で両試験線５２に接触荷重を加えた状態で両試験線５２を互いに摺動させるアクチュエータ５５と、を備えている。 4A can be obtained by conducting a test in advance using a conductor wire wear test apparatus 51 as shown in FIG. The conductor wire wear test apparatus 51 includes a first test line fixing jig 53 and a first test line fixing jig 53 placed in a state where two test lines 52 simulating conductor wires intersect each other. Both test lines 52 are sandwiched between them, and a second test line fixing jig 54 for applying a contact load to both test lines 52 and a first test line fixing jig 53 are horizontally slid to fix both test lines. And an actuator 55 that slides the test lines 52 with each other in a state in which a contact load is applied to the test lines 52 with the jigs 53 and 54.
図５の導体素線摩耗試験装置５１により試験を行ったときの試験線５２の断面形状は、図６に示すように、円形状の一部を切り欠いた形状となる。この切り欠きの半径方向に沿った深さが、摩耗痕の深さｈである。つまり、摩耗痕の深さｈとは、屈曲断線寿命の予測対象となるケーブルの導体素線に形成される実際の摩耗痕の深さではなく、屈曲断線寿命の予測対象となるケーブルの導体素線と同じ応力状態で導体素線摩耗試験装置５１により試験を行ったときに、試験線５２に形成される摩耗痕の深さを意味している。以下、ｎ回屈曲後に相当する摩耗痕の深さをｈnと表示する。 As shown in FIG. 6, the cross-sectional shape of the test line 52 when the test is performed by the conductor strand wear test apparatus 51 of FIG. 5 is a shape in which a part of a circular shape is cut out. The depth along the radial direction of this notch is the depth h of the wear scar. That is, the depth h of the wear scar is not the actual depth of the wear scar formed on the conductor wire of the cable to be predicted for the bending break life, but the conductor conductor of the cable to be predicted for the flex break life. This means the depth of wear marks formed on the test line 52 when a test is performed by the conductor strand wear test apparatus 51 in the same stress state as the line. Hereinafter, the depth of the corresponding wear mark after n times of bending is denoted as h n .
その後、ステップＳ４にて、ステップＳ３で求めた屈曲回数ｎに対する摩耗痕の深さｈの関係から、屈曲回数ｎごとの導体素線の断面積Ｓnを求める。 Then, at step S4, from the relationship of the depth h of the wear track with respect to bending count n obtained at step S3, determining the cross-sectional area S n of the conductor wire of each bending number n.
図６に示すように、導体素線の半径をｒ、屈曲回数ｎ回目の摩耗痕の深さをｈnとしたとき、屈曲回数ｎ回目の導体素線の断面積Ｓnは、下式（１）
Ｓn＝ｒ2（π−θn）＋ｒ（ｒ−ｈn）ｓｉｎθn ・・・（１）
但し、θn＝ｃｏｓ-1｛（ｒ−ｈn）／ｒ｝
により求めることができる。屈曲回数ｎ回目の導体素線の断面積Ｓnは、導体素線の初期の断面積Ｓ0（＝πｒ2）よりも減少する。
As shown in FIG. 6, when the radius of the conductor wire is r and the depth of the wear mark of the nth bending is h n , the cross-sectional area Sn of the nth conductor wire is expressed by the following formula ( 1)
S n = r 2 (π−θ n ) + r (r−h n ) sin θ n (1)
However, θ n = cos −1 {(r−h n ) / r}
It can ask for. Sectional area S n of the bending count n-th conductor element wire is reduced from the initial cross-sectional area S 0 of the conductor wires (= πr 2).
その後、ステップＳ５にて、ステップＳ４で求めた屈曲回数ｎごとの導体素線の断面積Ｓnから、断面積減少により増加する屈曲回数ｎごとの応力振幅σanと平均応力σmnを求める。 Then, at step S5, the sectional area S n of the conductor wire of each bending count n obtained in step S4, obtaining the stress amplitude sigma an, and the average stress sigma mn per bending count n to increase the cross-sectional area decreases.
より詳細には、ステップＳ４で求めた屈曲回数ｎごとの導体素線の断面積Ｓnと導体素線の初期の断面積Ｓ0の比（Ｓ0／Ｓn）、および初期の応力振幅σa0と平均応力σm0から、下式（５），（６）
σan＝（Ｓ0／Ｓn）・σa0 ・・・（５）
σmn＝（Ｓ0／Ｓn）・σm0 ・・・（６）
により屈曲回数ｎごとの応力振幅σanと平均応力σmnを求める。
More particularly, the initial ratio of the cross-sectional area S 0 of the sectional area S n and the conductor wire of the conductor wire of each bending number n calculated in step S4 (S 0 / S n), and the initial stress amplitude σ From a0 and average stress σ m0 , the following equations (5), (6)
σ an = (S 0 / S n ) · σ a0 (5)
σ mn = (S 0 / S n ) · σ m0 (6)
Thus, the stress amplitude σ an and the average stress σ mn for each bending number n are obtained.
屈曲回数ｎに対する応力振幅σanの関係、および、屈曲回数ｎに対する平均応力σmnの関係は、図７（ａ），（ｂ）のようになる。図７（ａ），（ｂ）に示すように、屈曲回数ｎが増えるほど、導体素線に生じる応力振幅σanと平均応力σmnは増加する。 The relationship of the stress amplitude σ an to the number of bendings n and the relationship of the average stress σ mn to the number of bendings n are as shown in FIGS. As shown in FIGS. 7A and 7B, the stress amplitude σ an and the average stress σ mn generated in the conductor wire increase as the number of bendings n increases.
その後、ステップＳ６にて、ステップＳ５で求めた屈曲回数ｎごとの応力振幅σanと平均応力σmnから、屈曲回数ｎごとの疲労損傷度（１／Ｎｆn）を求める。 Thereafter, in step S6, the fatigue damage degree (1 / Nf n ) for each number of flexing times n is obtained from the stress amplitude σ an for each number of flexing times n and the average stress σ mn obtained in step S5.
より詳細には、ステップＳ５で求めた屈曲回数ｎごとの応力振幅σanと平均応力σmnと、導体素線の材料特性であるＳＮ線図を基に、屈曲回数ｎごとの疲労損傷度（１／Ｎｆn）を求める。 More specifically, based on the stress amplitude σ an and average stress σ mn for each bending number n obtained in step S5, and the SN diagram that is the material property of the conductor wire, the fatigue damage degree for each bending number n ( 1 / Nf n ).
図８に示すように、ＳＮ線図は、応力振幅σaに対する破断サイクル数（寿命）Ｎｆの関係であり、この関係は平均応力σmによって変化する。上述のように、屈曲回数ｎごとに平均応力σmnは変化するので、屈曲回数ｎごとに、ステップＳ５で求めた平均応力σmnに対応するＳＮ線図を用いて、応力振幅σanに対応する破断サイクル数Ｎｆnを求め、この破断サイクル数Ｎｆnの逆数をとることで、屈曲回数ｎごとの疲労損傷度（１／Ｎｆn）を求める。なお、低サイクル数におけるＳＮ線図は下式（７）
σa＝Ｃ・Ｎｆ-α ・・・（７）
のＣｏｆｆｉｎ−Ｍａｎｓｏｎ則の弾性項で表すことができる。この式（７）におけるＣとαは平均応力σmにより決定される係数であり、事前に平均応力σmと係数Ｃ，αの関係を求めておけば、式（７）を用いて各平均応力σmnに対応するＳＮ線図を作成することができる。
As shown in FIG. 8, the SN diagram shows the relationship of the number of fracture cycles (life) Nf to the stress amplitude σ a , and this relationship changes depending on the average stress σ m . As described above, since the average stress σ mn changes for each bending number n, it corresponds to the stress amplitude σ an using the SN diagram corresponding to the average stress σ mn obtained in step S5 for each bending number n. The number of fracture cycles Nf n to be obtained is obtained, and the fatigue damage degree (1 / Nf n ) for each number of flexures n is obtained by taking the reciprocal of the number of fracture cycles Nf n . The SN diagram at the low cycle number is expressed by the following equation (7).
σ a = C · Nf −α (7)
It can be expressed by the elastic term of Coffin-Manson rule. The equation (7) is C and alpha in a coefficient determined by the mean stress sigma m, pre-mean stress sigma m and the coefficient C, if seeking relationship alpha, the average using the formula (7) An SN diagram corresponding to the stress σ mn can be created.
その後、ステップＳ７にて、屈曲回数ｎごとの疲労損傷度（１／Ｎｆn）を累積することで、導体素線が破断する屈曲回数ｎcableを求め、当該求めた屈曲回数ｎcableをケーブルの屈曲断線寿命として予測する。 Thereafter, in step S7, by accumulating fatigue damage degree of each bend number n (1 / Nf n), obtains the number of bends n cable conductor wire is broken, the number of bends n cable obtained the cable Predicted as bent wire break life.
屈曲回数ｎに対する疲労損傷度（１／Ｎｆn）の関係は、図９のようになる。この疲労損傷度（１／Ｎｆn）の累積値が１となる屈曲回数ｎcableが、導体素線が破断する屈曲回数、すなわちケーブルの屈曲断線寿命となる。つまり、［数１］に示す式（８）の関係を満たすｎcableがケーブルの屈曲断線寿命となる。ケーブルの屈曲断線寿命ｎcableを求めた後、処理を終了する。 The relationship of the degree of fatigue damage (1 / Nf n ) with respect to the number of bends n is as shown in FIG. The number of bends n cable at which the cumulative value of the fatigue damage degree (1 / Nf n ) is 1 is the number of bends at which the conductor strand breaks, that is, the cable bend break life. That is, the n cable satisfying the relationship of the equation (8) shown in [Equation 1] is the cable breakage life. After obtaining the cable breakage life n cable , the process is terminated.
次に、本実施の形態に係るケーブルの屈曲断線寿命予測方法を実施するケーブルの屈曲断線寿命予測装置について説明する。 Next, a cable breakage life prediction apparatus for carrying out the cable breakage life prediction method according to the present embodiment will be described.
図１０に示すように、ケーブルの屈曲断線寿命予測装置１００は、ケーブルの屈曲条件や導体構造などを入力する入力部１０１と、ケーブルの屈曲条件と導体構造から、摩耗していない初期の導体素線に生じる初期の応力振幅σa0と平均応力σm0を求める初期応力演算部１０２と、ケーブルを屈曲した際の導体素線同士の摩耗を考慮して屈曲回数ｎごとに導体素線の断面積Ｓnを求める導体素線断面積演算部１０３と、導体素線断面積演算部１０３で求めた断面積Ｓnと導体素線の初期の断面積Ｓ0の比、および初期応力演算部１０２で求めた初期の応力振幅σa0と平均応力σm0から、上述の式（５），（６）により屈曲回数ｎごとの応力振幅σanと平均応力σmnを求める屈曲回数毎応力演算部１０４と、屈曲回数毎応力演算部１０４で求めた屈曲回数ｎごとの応力振幅σanと平均応力σmnと、導体素線の材料特性（ＳＮ線図）とを基に、屈曲回数ｎごとの疲労損傷度（１／Ｎｆn）を求める疲労損傷度演算部１０５と、疲労損傷度演算部１０５で求めた屈曲回数ｎごとの疲労損傷度（１／Ｎｆn）を累積することで、導体素線が破断する屈曲回数ｎcableを求め、当該求めた屈曲回数ｎcableをケーブルの屈曲断線寿命として予測する屈曲断線寿命予測部１０６と、屈曲断線寿命予測部１０６で求めたケーブルの屈曲断線寿命をモニタ等の表示器１０８に出力する出力部１０７と、を備えている。 As shown in FIG. 10, the cable bending / breaking life prediction apparatus 100 includes an input unit 101 for inputting a cable bending condition, a conductor structure, and the like, and an initial conductor element that is not worn from the cable bending condition and the conductor structure. The initial stress calculation unit 102 for obtaining the initial stress amplitude σ a0 and the average stress σ m0 generated in the wire, and the cross-sectional area of the conductor wire for every number of times n in consideration of the wear of the conductor wires when the cable is bent the conductor element wire cross-sectional area calculation section 103 for obtaining the S n, the initial ratio of the cross-sectional area S 0 of the sectional area S n and the conductor element wire determined by the conductor element wire cross-sectional area calculation section 103, and an initial stress calculation unit 102 From the obtained initial stress amplitude σ a0 and average stress σ m0 , the number-of-flexes stress calculation unit 104 for obtaining the stress amplitude σ an and mean stress σ mn for each number of flexures n according to the above formulas (5) and (6); The bend obtained by the stress calculation unit 104 for each bend number The stress amplitude sigma an, for each number n and mean stress sigma mn, based on the material properties of the conductive wire (SN diagram), the fatigue damage degree seeking fatigue damage degree of each bend number n (1 / Nf n) The number of bends n cable at which the conductor strand breaks is obtained by accumulating the fatigue damage degree (1 / Nf n ) for each bend number n obtained by the calculation unit 105 and the fatigue damage degree calculation unit 105, and the obtained number A bending breakage life prediction unit 106 that predicts the number of bendings n cable as a bending breakage life of the cable; an output unit 107 that outputs the bending breakage life of the cable obtained by the bending breakage life prediction unit 106 to a display 108 such as a monitor; It has.
また、ケーブルの屈曲断線寿命予測装置１００は、図３（ａ）の曲げ半径Ｒに対する導体素線間の接触荷重Ｗの関係，図３（ｂ）の曲げ半径Ｒに対する導体素線間の摺動距離の関係、図４（ａ）の接触荷重Ｗごとの総摺動距離に対する摩耗痕の深さの関係、図８のＳＮ線図、その他演算に必要な材料パラメータ等を記憶する材料特性等記憶部１０９を備えている。 Further, the apparatus 100 for predicting the cable breakage life of the cable includes the relationship of the contact load W between the conductor wires with respect to the bending radius R in FIG. 3A and the sliding between the conductor wires with respect to the bending radius R in FIG. The relationship of distance, the relationship of the depth of the wear mark with respect to the total sliding distance for each contact load W in FIG. 4A, the SN diagram of FIG. 8, and other material parameters such as material parameters required for calculation Part 109 is provided.
導体素線断面積演算部１０３は、材料特性等記憶部１０９に記憶した図３（ａ），（ｂ）および図４（ａ）の関係を用いて、屈曲回数ｎごとの導体素線の断面積Ｓnを求めるように構成される。また、疲労損傷度演算部１０５は、材料特性等記憶部１０９に記憶したＳＮ線図を用いて、屈曲回数ｎごとの疲労損傷度（１／Ｎｆn）を求めるように構成される。 The conductor wire cross-sectional area calculation unit 103 uses the relationship shown in FIGS. 3A, 3B, and 4A stored in the material property storage unit 109 to break the conductor wire for each number of times n. configured to determine the area S n. Further, the fatigue damage degree calculation unit 105 is configured to obtain the fatigue damage degree (1 / Nf n ) for each number of flexures n using the SN diagram stored in the material property etc. storage unit 109.
これら入力部１０１、初期応力演算部１０２、導体素線断面積演算部１０３、屈曲回数毎応力演算部１０４、疲労損傷度演算部１０５、屈曲断線寿命予測部１０６、出力部１０７、および材料特性等記憶部１０９は、パーソナルコンピュータ等の演算装置に搭載され、ＣＰＵ、ソフトウェア、インターフェイス、メモリ等を適宜組み合わせて実現される。 These input unit 101, initial stress calculation unit 102, conductor wire cross-sectional area calculation unit 103, stress calculation unit 104 for each number of flexing times, fatigue damage degree calculation unit 105, bending disconnection life prediction unit 106, output unit 107, material characteristics, etc. The storage unit 109 is mounted on an arithmetic device such as a personal computer, and is realized by appropriately combining a CPU, software, an interface, a memory, and the like.
以上説明したように、本実施の形態に係るケーブルの屈曲断線寿命予測方法では、ケーブルの屈曲条件と導体構造から、摩耗していない初期の導体素線に生じる初期の応力振幅σa0と平均応力σm0を求め、ケーブルを屈曲した際の導体素線同士の摩耗を考慮して屈曲回数ｎごとに導体素線の断面積Ｓnを求め、求めた断面積Ｓnと導体素線の初期の断面積Ｓ0の比、および初期の応力振幅σa0と平均応力σm0から、屈曲回数ｎごとの応力振幅σanと平均応力σmnを求め、当該屈曲回数ｎごとの応力振幅σanと平均応力σmnと、導体素線の材料特性とを基に、屈曲回数ｎごとの疲労損傷度（１／Ｎｆn）を求め、当該屈曲回数ｎごとの疲労損傷度（１／Ｎｆn）を累積することで、導体素線が破断する屈曲回数ｎcableを求め、当該求めた屈曲回数ｎcableをケーブルの屈曲断線寿命として予測している。 As described above, in the cable bending break life prediction method according to the present embodiment, the initial stress amplitude σ a0 and the average stress generated in the initial conductor wire that is not worn out from the cable bending condition and the conductor structure. seeking sigma m0, obtains the cross-sectional area S n of conductor wires for each bending count n in consideration of the wear of the conductor wires between the time of bending the cable, the cross-sectional area S n and the conductor wire was determined early From the ratio of the cross-sectional area S 0 , the initial stress amplitude σ a0 and the average stress σ m0 , the stress amplitude σ an and the average stress σ mn for each number of flexing times n are obtained, and the stress amplitude σ an and the average for each number of flexing times n Based on the stress σ mn and the material properties of the conductor wire, the fatigue damage degree (1 / Nf n ) for each bending number n is obtained, and the fatigue damage degree (1 / Nf n ) for each bending number n is accumulated. doing, seek number of bends n cable conductor wire is broken, the obtained number of bends n cable Is estimated as the cable breakage life.
つまり、本実施の形態では、導体素線同士の摩耗による導体素線の応力状態の変化を考慮し、その上で累積損傷則（修正マイナー則）を適用してケーブルの屈曲断線寿命を予測している。 In other words, in the present embodiment, the change in the stress state of the conductor wires due to the wear of the conductor wires is taken into account, and then the cumulative breakage law (corrected minor law) is applied to predict the bending break life of the cable. ing.
導体素線同士の摩耗を考慮することにより、複数の導体素線からなる導体を有するケーブルの屈曲断線寿命を精度よく予測することが可能となる。その結果、顧客要求に応じた耐屈曲ケーブルを適切に、かつ、短期間で開発することが可能になる。また、開発期間の短縮により、コスト低減、サービス向上を図ることが可能になる。 By considering the wear between the conductor strands, it is possible to accurately predict the bending disconnection life of a cable having a conductor composed of a plurality of conductor strands. As a result, it is possible to appropriately and flexibly develop a bending resistant cable that meets customer requirements. In addition, shortening the development period makes it possible to reduce costs and improve services.
本発明は上記実施の形態に限定されるものではなく、本発明の趣旨を逸脱しない範囲で種々の変更を加え得ることは勿論である。 The present invention is not limited to the above-described embodiment, and it is needless to say that various modifications can be made without departing from the spirit of the present invention.
Claims (3)
前記ケーブルの屈曲条件と導体構造から、摩耗していない初期の前記導体素線に生じる初期の応力振幅と平均応力を求め、
前記ケーブルを屈曲した際の前記導体素線同士の摩耗を考慮して屈曲回数ごとに前記導体素線の断面積を求め、
当該求めた断面積と前記導体素線の初期の断面積の比、および初期の応力振幅と平均応力から、屈曲回数ごとの応力振幅と平均応力を求め、
当該屈曲回数ごとの応力振幅と平均応力と、前記導体素線の材料特性とを基に、屈曲回数ごとの疲労損傷度を求め、
当該屈曲回数ごとの疲労損傷度を累積することで、前記導体素線が破断する屈曲回数を求め、当該求めた屈曲回数を前記ケーブルの屈曲断線寿命として予測し、
予め求めておいた前記ケーブルの曲げ半径に対する導体素線間の接触荷重の関係、および曲げ半径に対する導体素線間の摺動距離の関係と、前記ケーブルの屈曲条件である曲げ半径とから、前記導体素線間の接触荷重および摺動距離を求め、
当該求めた導体素線間の接触荷重および摺動距離と、予め求めておいた接触荷重ごとの総摺動距離に対する摩耗痕の深さの関係とから、屈曲回数に対する摩耗痕の深さの関係を求め、
当該屈曲回数に対する摩耗痕の深さの関係から、屈曲回数ごとの摩耗痕の深さを求め、当該求めた摩耗痕の深さから前記導体素線の断面積を求めることで、屈曲回数ごとに前記導体素線の断面積を求め、
前記接触荷重ごとの総摺動距離に対する摩耗痕の深さの関係を、
前記導体素線を模した試験線同士を接触させ前記接触荷重に相当する荷重を印加した状態で摺動させることにより、
求める
ことを特徴とするケーブルの屈曲断線寿命予測方法。 A method for predicting the bending disconnection life of a cable having a conductor composed of a plurality of conductor strands,
From the bending condition and conductor structure of the cable, obtain the initial stress amplitude and average stress generated in the initial conductor wire that is not worn,
Taking into account the wear between the conductor strands when the cable is bent, obtain the cross-sectional area of the conductor strands for each number of bends,
From the obtained cross-sectional area and the ratio of the initial cross-sectional area of the conductor wire, and the initial stress amplitude and average stress, obtain the stress amplitude and average stress for each number of flexures,
Based on the stress amplitude and average stress for each number of bending times, and the material properties of the conductor element wire, determine the fatigue damage degree for each number of bending times,
By accumulating the degree of fatigue damage for each number of bends, the number of bends at which the conductor strand breaks is determined, and the obtained number of bends is predicted as the bending breakage life of the cable ,
From the relationship of the contact load between the conductor wires to the bending radius of the cable obtained in advance, the relationship of the sliding distance between the conductor wires to the bending radius, and the bending radius that is the bending condition of the cable, Find contact load and sliding distance between conductor wires,
From the contact load and sliding distance between the obtained conductor wires and the relationship of the depth of the wear trace to the total sliding distance for each contact load determined in advance, the relationship of the depth of the wear trace to the number of bendings Seeking
From the relationship of the depth of the wear trace with respect to the number of bending times, the depth of the wear mark for each number of bending times is obtained, and the cross-sectional area of the conductor wire is obtained from the obtained depth of the wear mark for each number of bending times. Obtain the cross-sectional area of the conductor wire,
The relationship of the depth of wear marks to the total sliding distance for each contact load,
By sliding the test wires imitating the conductor strands in contact with each other and applying a load corresponding to the contact load,
A method for predicting the bending breakage life of a cable, characterized in that it is obtained.
Ｓn＝ｒ2（π−θn）＋ｒ（ｒ−ｈn）ｓｉｎθn ・・・（１）
但し、θn＝ｃｏｓ-1｛（ｒ−ｈn）／ｒ｝
により求める
請求項１記載のケーブルの屈曲断線寿命予測方法。 Assuming that the radius of the conductor wire is r and the depth of the wear mark having the number of flexing times n is h n , the cross-sectional area Sn of the conductor wire having the number of flexing times n is expressed by the following equation (1)
S n = r 2 (π−θ n ) + r (r−h n ) sin θ n (1)
However, θ n = cos −1 {(r−h n ) / r}
The method for predicting the bending breakage life of the cable according to claim 1 .
前記ケーブルの屈曲条件と導体構造から、摩耗していない初期の前記導体素線に生じる初期の応力振幅と平均応力を求める初期応力演算部と、
前記ケーブルを屈曲した際の前記導体素線同士の摩耗を考慮して屈曲回数ごとに前記導体素線の断面積を求める導体素線断面積演算部と、
当該導体素線断面積演算部で求めた断面積と前記導体素線の初期の断面積の比、および前記初期応力演算部で求めた初期の応力振幅と平均応力から、屈曲回数ごとの応力振幅と平均応力を求める屈曲回数毎応力演算部と、
当該屈曲回数毎応力演算部で求めた屈曲回数ごとの応力振幅と平均応力と、前記導体素線の材料特性とを基に、屈曲回数ごとの疲労損傷度を求める疲労損傷度演算部と、
当該疲労損傷度演算部で求めた屈曲回数ごとの疲労損傷度を累積することで、前記導体素線が破断する屈曲回数を求め、当該求めた屈曲回数を前記ケーブルの屈曲断線寿命として予測する屈曲断線寿命予測部と、
を備え、
前記導体素線断面積演算部は、
予め求めておいた前記ケーブルの曲げ半径に対する導体素線間の接触荷重の関係、および曲げ半径に対する導体素線間の摺動距離の関係と、前記ケーブルの屈曲条件である曲げ半径とから、前記導体素線間の接触荷重および摺動距離を求め、
当該求めた導体素線間の接触荷重および摺動距離と、予め求めておいた接触荷重ごとの総摺動距離に対する摩耗痕の深さの関係とから、屈曲回数に対する摩耗痕の深さの関係を求め、
当該屈曲回数に対する摩耗痕の深さの関係から、屈曲回数ごとの摩耗痕の深さを求め、当該求めた摩耗痕の深さから前記導体素線の断面積を求めることで、屈曲回数ごとに前記導体素線の断面積を求め、
前記接触荷重ごとの総摺動距離に対する摩耗痕の深さの関係は、
前記導体素線を模した試験線同士を接触させ前記接触荷重に相当する荷重を印加した状態で摺動させることにより、
求められていることを特徴とするケーブルの屈曲断線寿命予測装置。 An apparatus for predicting the bending disconnection life of a cable having a conductor composed of a plurality of conductor strands,
From the bending condition and the conductor structure of the cable, an initial stress calculation unit for obtaining an initial stress amplitude and an average stress generated in the initial conductor wire that is not worn;
Taking into account the wear between the conductor strands when the cable is bent, a conductor strand cross-sectional area calculation unit for obtaining the cross-sectional area of the conductor strand for each number of flexing times;
From the ratio of the cross-sectional area determined by the conductor wire cross-sectional area calculation unit to the initial cross-sectional area of the conductor wire, and the initial stress amplitude and average stress determined by the initial stress calculation unit, the stress amplitude for each number of flexures And a stress calculation unit for each bending number for obtaining an average stress,
Based on the stress amplitude and average stress for each bend obtained in the stress calculation unit for each bend number, and the material properties of the conductor wire, a fatigue damage degree calculation unit for obtaining the fatigue damage degree for each bend,
Bending to calculate the number of bendings at which the conductor wire breaks by accumulating the fatigue damage degree for each number of bendings obtained by the fatigue damage degree calculating unit, and predicting the obtained number of bendings as the bending breakage life of the cable Disconnection life prediction unit,
Equipped with a,
The conductor strand cross-sectional area calculation unit is
From the relationship of the contact load between the conductor wires to the bending radius of the cable obtained in advance, the relationship of the sliding distance between the conductor wires to the bending radius, and the bending radius that is the bending condition of the cable, Find contact load and sliding distance between conductor wires,
From the contact load and sliding distance between the obtained conductor wires and the relationship of the depth of the wear trace to the total sliding distance for each contact load determined in advance, the relationship of the depth of the wear trace to the number of bendings Seeking
From the relationship of the depth of the wear trace with respect to the number of bending times, the depth of the wear mark for each number of bending times is obtained, and the cross-sectional area of the conductor wire is obtained from the obtained depth of the wear mark for each number of bending times. Obtain the cross-sectional area of the conductor wire,
The relationship of the depth of the wear scar to the total sliding distance for each contact load is
By sliding the test wires imitating the conductor strands in contact with each other and applying a load corresponding to the contact load,
A cable breakage life prediction device characterized by what is required .
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