JP2023044265A - Fatigue limit estimation method - Google Patents

Fatigue limit estimation method Download PDF

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JP2023044265A
JP2023044265A JP2021152195A JP2021152195A JP2023044265A JP 2023044265 A JP2023044265 A JP 2023044265A JP 2021152195 A JP2021152195 A JP 2021152195A JP 2021152195 A JP2021152195 A JP 2021152195A JP 2023044265 A JP2023044265 A JP 2023044265A
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秀樹 上田
Hideki Ueda
英介 中山
Eisuke Nakayama
浩 白水
Hiroshi Shiromizu
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Nippon Steel Corp
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Abstract

To provide a method for accurately estimating the fatigue limit of an object to be measured based on a dissipation energy distribution of the object to be measured that is measured by using an infrared imaging apparatus.SOLUTION: A method according to the present invention has: a relationship calculation step S1 of picking up an image of an object to be measured by using an infrared imaging apparatus while sequentially adding repeated loads different in load width P to the object to be measured, thereby measuring a temporal change of the temperature distribution of the object to be measured for each of the repeated loads, based on the temporal change, calculating the dissipation energy distribution of the object to be measured for each of the repeated loads, and based on the dissipation energy distribution, calculating the relationship between the load widths P and dissipation energy q; and a fatigue limit estimation step S2 of estimating, as the fatigue limit of the object to be measured, the load width P at which the maximum value of at least one parameter is obtained, the parameter of three parameters: a first-order differential value d for each of the load widths P obtained by performing first-order differentiation on the relationship at the load width P; a second-order differential value d2 for each of the load widths P obtained by performing second-order differentiation; and the product dα of the first-order differential value d and the second-order differential value d2 for each of the load widths P.SELECTED DRAWING: Figure 2

Description

本発明は、赤外線撮像装置を用いて測定した被測定物の散逸エネルギー分布に基づき、被測定物の疲労限度を精度良く推定する方法に関する。 The present invention relates to a method for accurately estimating the fatigue limit of an object to be measured based on the dissipated energy distribution of the object measured using an infrared imaging device.

被測定物に発生する応力分布を非接触で測定する方法として、赤外線撮像装置（サーモグラフィ）を用いた熱弾性応力測定法が提案されている（例えば、非特許文献１参照）。
熱弾性応力測定法は、被測定物が断熱的に弾性変形する際に温度変化が生じるという熱弾性効果を利用し、繰り返し荷重が付加される被測定物を赤外線撮像装置を用いて撮像することで被測定物の温度分布の時間的変化（所定時間内における温度分布の変化）を測定し、この測定した温度分布の時間的変化を被測定物の応力分布の時間的変化（所定時間内における応力分布の変化）に換算する方法である。応力分布の初期値を把握していれば（実際に応力分布を測定して把握している場合のみならず、想定可能な場合も含む）、この初期値に応力分布の時間的変化を加算することで、所定時間経過後の応力分布を測定可能である。 A thermoelastic stress measurement method using an infrared imaging device (thermography) has been proposed as a method for non-contact measurement of stress distribution generated in an object to be measured (see, for example, Non-Patent Document 1).
The thermoelastic stress measurement method utilizes the thermoelastic effect, in which temperature changes occur when an object undergoes adiabatic elastic deformation. Measure the temporal change in the temperature distribution of the object to be measured (change in temperature distribution within a predetermined time), and measure the temporal change in the measured temperature distribution with the temporal change in the stress distribution of the object to be measured (in the predetermined time change in stress distribution). If the initial value of the stress distribution is known (not only when the stress distribution is actually measured and grasped, but also when it can be assumed), the time change of the stress distribution is added to this initial value. Thus, it is possible to measure the stress distribution after a predetermined time has elapsed.

この熱弾性応力測定法を用いて被測定物の温度分布の時間的変化を測定する際、例えば、被測定物の周囲の熱（赤外線）が被測定物の表面で反射し、赤外線撮像装置で受光される場合がある。換言すれば、赤外線撮像装置を用いて測定した被測定物の温度分布の時間的変化に、上記のような外乱要因の他、被測定物内での熱伝導や、後述のエネルギー散逸に起因した発熱のように、熱弾性効果によって生じる温度変化（被測定物から放射される赤外線の強度変化）以外の要因で生じた温度変化が含まれる場合がある。 When measuring temporal changes in the temperature distribution of an object to be measured using this thermoelastic stress measurement method, for example, heat (infrared rays) around the object to be measured is reflected on the surface of the object to be measured, and an infrared imaging device may be received. In other words, the temporal change in the temperature distribution of the object to be measured measured using the infrared imaging device may be affected by heat conduction in the object and energy dissipation, which will be described later, in addition to the above disturbance factors. Temperature changes caused by factors other than temperature changes caused by the thermoelastic effect (intensity changes of infrared rays radiated from the object to be measured) may be included, such as heat generation.

このため、非特許文献１に記載の技術では、赤外線撮像装置から出力された画像信号から、測定対象とする熱弾性効果によって生じる温度変化に応じた信号波形をロックイン処理している。すなわち、赤外線撮像装置から出力された画像信号から、所定の周波数成分のみを抽出している。
具体的には、例えば、被測定物に繰り返し荷重を付加する疲労試験機から出力され、付加する繰り返し荷重と同じ周波数の参照信号を利用する。この参照信号で画像信号を同期検波し、参照信号に応じた周波数帯域の画像信号成分のみ（参照信号と同じ周波数を有する画像信号成分のみ又は参照信号と同じ周波数を含む狭周波数帯域の画像信号のみ）を抽出することで、測定すべき熱弾性効果によって生じる温度変化のＳ／Ｎ比を向上させている。そして、抽出した画像信号成分の大きさと、予め記憶されている画像信号成分の大きさ及び温度の対応関係とに応じて、被測定物の温度分布の時間的変化（赤外線撮像装置で撮像した撮像画像を構成する画素毎の温度の時間的変化）を算出する。次に、被測定物の温度分布の時間的変化と、温度の時間的変化及び応力の時間的変化の間の所定の関係式とに基づき、被測定物の応力分布の時間的変化を算出する。具体的には、被測定物の温度分布の時間的変化と、以下の式（１）で表される関係式とに基づき、被測定物の応力分布の時間的変化を算出する。
Δσ＝－１／Ｋ・ΔＴ／Ｔ ・・・（１）
上記の式（１）において、ΔＴは温度の時間的変化を、Δσは応力の時間的変化を、Ｔは被測定物の温度を、Ｋは熱弾性係数を意味する。熱弾性係数Ｋは被測定物の材質によって決まる物性値であり、例えば被測定物が鉄鋼材料から形成されている場合、Ｋ＝３．５×１０－１２［Ｐａ－１］となる。
このように、ロックイン処理を用いれば、被測定物の応力分布の時間的変化、ひいては被測定物の応力分布を精度良く算出することが可能である。 For this reason, in the technique described in Non-Patent Document 1, a lock-in process is performed on a signal waveform corresponding to a temperature change caused by a thermoelastic effect to be measured from an image signal output from an infrared imaging device. That is, only predetermined frequency components are extracted from the image signal output from the infrared imaging device.
Specifically, for example, a reference signal that is output from a fatigue tester that applies a repeated load to the object to be measured and that has the same frequency as that of the applied repeated load is used. The image signal is synchronously detected with this reference signal, and only the image signal component in the frequency band corresponding to the reference signal (only the image signal component with the same frequency as the reference signal or only the narrow frequency band image signal containing the same frequency as the reference signal) is detected. ) improves the S/N ratio of the temperature change caused by the thermoelastic effect to be measured. Then, according to the magnitude of the extracted image signal component and the correspondence relationship between the magnitude and temperature of the image signal component stored in advance, the temporal change in the temperature distribution of the object to be measured (image captured by the infrared imaging device) Temporal change in temperature for each pixel constituting an image) is calculated. Next, the temporal change in the stress distribution of the object to be measured is calculated based on the temporal change in the temperature distribution of the object to be measured and a predetermined relational expression between the temporal change in temperature and the temporal change in stress. . Specifically, the temporal change in the stress distribution of the object to be measured is calculated based on the temporal change in the temperature distribution of the object to be measured and the relational expression represented by the following equation (1).
Δσ=−1/K・ΔT/T (1)
In the above equation (1), ΔT is the temporal change in temperature, Δσ is the temporal change in stress, T is the temperature of the object to be measured, and K is the thermoelastic coefficient. The thermoelastic coefficient K is a physical property value determined by the material of the object to be measured.
In this way, by using the lock-in process, it is possible to accurately calculate the temporal change in the stress distribution of the object to be measured, and thus the stress distribution of the object to be measured.

被測定物に繰り返し荷重を付加することによって、上記の熱弾性効果に起因した温度分布の時間的変化とは別に、エネルギー散逸に起因した温度分布の時間的変化も発生する。
非特許文献２に記載のように、エネルギー散逸に起因した温度分布の時間的変化は、被測定物に最大応力と最小応力とが作用した際に、それぞれ発熱成分として発生すると考えられており、散逸エネルギーは、温度の時間的変化における、被測定物に付加する繰り返し荷重の周波数の２倍の周波数成分として定義される。この散逸エネルギーをΔＴＤとし、赤外線撮像装置を用いて測定した温度の時間的変化（ロックイン処理前の温度の時間的変化）をΔＴＭとし、熱弾性効果に起因した温度の時間的変化（ロックイン処理後の温度の時間的変化）をΔＴＥとすると、外乱要因や熱伝導を考慮しない場合、以下の式（２）が成立する。
ΔＴＤ＝ΔＴＭ－ΔＴＥ ・・・（２）
したがって、散逸エネルギー分布は、赤外線撮像装置を用いて測定可能である。具体的には、例えば、赤外線撮像装置を用いて測定した温度分布の時間的変化から、前述のようにロックイン処理によって算出した熱弾性効果に起因した温度分布の時間的変化を減算することによって算出可能である。 By repeatedly applying a load to the object to be measured, a temporal change in temperature distribution due to energy dissipation occurs in addition to the temporal change in temperature distribution due to the thermoelastic effect.
As described in Non-Patent Document 2, temporal changes in temperature distribution due to energy dissipation are thought to occur as heat generation components when maximum stress and minimum stress act on the object to be measured. Dissipated energy is defined as a frequency component that is twice the frequency of the cyclic load applied to the object to be measured in the temperature change over time. This dissipated energy is ΔT D , the temporal change in temperature measured using an infrared imaging device (temporal change in temperature before lock-in processing) is ΔT M , and the temporal change in temperature due to the thermoelastic effect ( Assuming that ΔT E is the temporal change in temperature after the lock-in process, the following equation (2) holds if disturbance factors and heat conduction are not considered.
ΔT D =ΔT M −ΔT E (2)
Therefore, the dissipated energy distribution can be measured using an infrared imager. Specifically, for example, by subtracting the temporal change in temperature distribution due to the thermoelastic effect calculated by the lock-in process as described above from the temporal change in temperature distribution measured using an infrared imaging device, It is calculable.

また、非特許文献２には、赤外線撮像装置を用いて測定した被測定物の散逸エネルギーに基づき、被測定物の疲労限度を推定することが提案されている。
具体的には、被測定物に荷重幅（＝最大荷重－最小荷重）の異なる繰り返し荷重を順次付加（例えば、付加する繰り返し荷重の荷重幅を段階的に増加させ、各荷重幅の繰り返し荷重を数千サイクル程度付加）しながら、赤外線撮像装置を用いて被測定物を撮像することで、繰り返し荷重毎に被測定物の温度分布の時間的変化を測定する。そして、繰り返し荷重毎に測定した被測定物の温度分布の時間的変化に基づき、繰り返し荷重毎に被測定物の散逸エネルギー分布を算出し、この繰り返し荷重毎に算出した被測定物の散逸エネルギー分布に基づき、荷重幅と散逸エネルギーとの関係を算出する。 Non-Patent Document 2 proposes estimating the fatigue limit of an object to be measured based on the dissipation energy of the object measured using an infrared imaging device.
Specifically, cyclic loads with different load widths (=maximum load - minimum load) are sequentially applied to the object to be measured. By taking an image of the object to be measured using an infrared imaging device while applying about several thousand cycles, the temporal change in the temperature distribution of the object to be measured is measured for each repeated load. Then, the dissipated energy distribution of the measured object is calculated for each repeated load based on the temporal change in the temperature distribution of the measured object measured for each repeated load, and the dissipated energy distribution of the measured object calculated for each repeated load Based on, the relationship between the load width and the dissipated energy is calculated.

図１は、荷重幅と散逸エネルギーとの関係を模式的に示す図である。図１において「◆」でプロットした点が、荷重幅の異なる繰り返し荷重毎に算出した散逸エネルギーである。図１に示すように、両者の関係には、ある荷重幅を境にして散逸エネルギーが急増する急増点が本来的に生じる。そして、この急増点における繰り返し荷重の荷重幅が、いわゆるＳ－Ｎ線図によって求められる疲労限度に対応すると考えられている。
したがって、荷重幅と散逸エネルギーとの関係を算出し、散逸エネルギーが急増する急増点を検出すれば、この急増点における繰り返し荷重の荷重幅を疲労限度として推定可能である。 FIG. 1 is a diagram schematically showing the relationship between load width and dissipated energy. The points plotted with “♦” in FIG. 1 are the dissipated energy calculated for each repeated load with different load widths. As shown in FIG. 1, in the relationship between the two, there is inherently an abrupt point at which the dissipated energy abruptly rises beyond a certain load range. It is believed that the load width of the repeated load at this rapid increase point corresponds to the fatigue limit obtained from the so-called SN diagram.
Therefore, by calculating the relationship between the load width and the dissipated energy and detecting the point where the dissipated energy sharply increases, it is possible to estimate the load width of the repeated load at the point of rapid increase as the fatigue limit.

しかしながら、赤外線撮像装置を用いて測定される散逸エネルギー分布から得られる、荷重幅と散逸エネルギーとの関係は、実際には、図１に示した通りのものになるとは限らず、被測定物が残留応力を含む熱処理材や溶接材である場合や、測定時に外乱要因の影響が大きい場合には、散逸エネルギーのばらつきが大きくなったり、全体的に散逸エネルギーが一定の勾配で単調増加してしまい、疲労限度を精度良く推定できる急増点が明確に生じない場合がある。 However, the relationship between the load width and the dissipated energy obtained from the dissipated energy distribution measured using the infrared imaging device is not always as shown in FIG. If the material is a heat-treated or welded material that contains residual stress, or if the influence of disturbance factors during measurement is large, the dispersion of the dissipated energy becomes large, and the overall dissipated energy monotonously increases at a constant gradient. , there is a case where there is no clear sharp point at which the fatigue limit can be accurately estimated.

なお、特許文献１、２には、赤外線カメラから得られた温度画像から、測定対象物に関する、加振の基本周波数の成分の温度振幅に対する第二高調波成分の温度振幅の関係を求め、前記関係を、二次曲線である第一の近似線と二次曲線である第二の近似線によりフィッティングし、前記第一の近似線と前記第二の近似線の交点に基づき前記測定対象物の疲労限度応力を求める方法が提案されている。
しかしながら、特許文献１、２に記載の方法は、図１に示すような荷重幅と散逸エネルギーとの関係において、疲労限度に対応すると考えられる散逸エネルギーの急増点を検出するものではない。 In addition, in Patent Documents 1 and 2, from the temperature image obtained from the infrared camera, the relationship between the temperature amplitude of the fundamental frequency component of the excitation and the temperature amplitude of the second harmonic component regarding the measurement object is obtained. The relationship is fitted by a first approximation line that is a quadratic curve and a second approximation line that is a quadratic curve, and the measurement object is measured based on the intersection of the first approximation line and the second approximation line. A method for determining the fatigue limit stress has been proposed.
However, the methods described in Patent Literatures 1 and 2 do not detect the sharp point of dissipated energy, which is considered to correspond to the fatigue limit, in the relationship between the load width and the dissipated energy as shown in FIG.

矢尾板達也、他２名、「赤外線カメラによる応力測定と疲労限界点の予測測定」、自動車技術会秋季学術講演会、Ｎｏ．９８－０３、（２００３）Tatsuya Yaoita, 2 others, "Stress measurement by infrared camera and prediction measurement of fatigue limit point", Society of Automotive Engineers of Japan Autumn Meeting, No. 98-03, (2003) 塩澤大輝、他６名、「散逸エネルギ計測に基づいたＴｉ－６Ａｌ－４Ｖ合金の疲労限度推定」、日本材料学会第６９期学術講演会講演論文集、Ｎｏ．１３２、（２０２０）Daiki Shiozawa, 6 others, "Estimation of Fatigue Limit of Ti-6Al-4V Alloy Based on Dissipated Energy Measurement", Proc. 132, (2020)

特開２０１８－１０５７０９号公報JP 2018-105709 A 特開２０１９－１４８５０７号公報JP 2019-148507 A

本発明は、上記のような従来技術の問題点を解決するためになされたものであり、赤外線撮像装置を用いて測定した被測定物の散逸エネルギー分布に基づき、被測定物の疲労限度を精度良く推定する方法を提供することを課題とする。 The present invention has been made to solve the problems of the prior art as described above. An object of the present invention is to provide a method of estimating well.

前記課題を解決するため、本発明者らは鋭意検討した結果、従来と同様に、被測定物に付加する繰り返し荷重の荷重幅と散逸エネルギーとの関係を算出した後、この関係を荷重幅で１階微分して得られる１階微分値、荷重幅で２階微分して得られる２階微分値、及び、１階微分値と前記２階微分値との積の３つのパラメータのうち、いずれか１つのパラメータに着目すれば、このパラメータの最大値が得られた荷重幅が被測定物の疲労限度に精度良く対応することを知見した。換言すれば、被測定物の残留応力や外乱要因の影響により、荷重幅と散逸エネルギーとの関係を図示するだけでは明確な急増点が生じていない場合であっても、上記３つのパラメータのうちのいずれか１つのパラメータの最大値が得られた荷重幅が本来の急増点に相当するものになることを知見した。 In order to solve the above-mentioned problems, the present inventors conducted intensive studies and found that after calculating the relationship between the load width of the repeated load applied to the object to be measured and the dissipated energy in the same manner as in the prior art, this relationship was expressed by the load width. One of the three parameters of the first differential value obtained by the first differential, the second differential value obtained by second differential with the load width, and the product of the first differential value and the second differential value It has been found that if one parameter is focused, the load width at which the maximum value of this parameter is obtained corresponds to the fatigue limit of the object to be measured with high accuracy. In other words, due to the residual stress of the object to be measured and the influence of disturbance factors, even if a clear rapid increase point does not occur only by showing the relationship between the load width and the dissipated energy, It was found that the load width at which the maximum value of any one of the parameters is obtained corresponds to the original rapid increase point.

本発明は、本発明者らの上記の知見に基づき完成したものである。
すなわち、前記課題を解決するため、本発明は、被測定物に荷重幅Ｐの異なる繰り返し荷重を順次付加しながら、赤外線撮像装置を用いて前記被測定物を撮像することで、前記繰り返し荷重毎に前記被測定物の温度分布の時間的変化を測定し、前記繰り返し荷重毎に測定した前記被測定物の温度分布の時間的変化に基づき、前記繰り返し荷重毎に前記被測定物の散逸エネルギー分布を算出し、前記繰り返し荷重毎に算出した前記被測定物の散逸エネルギー分布に基づき、荷重幅Ｐと散逸エネルギーｑとの関係を算出する関係算出ステップと、前記関係算出ステップで算出した関係を前記荷重幅Ｐで１階微分して得られる前記荷重幅Ｐ毎の１階微分値ｄ、前記関係算出ステップで算出した関係を前記荷重幅Ｐで２階微分して得られる前記荷重幅Ｐ毎の２階微分値ｄ２、及び、前記荷重幅Ｐ毎の前記１階微分値ｄと前記２階微分値ｄ２との積ｄαの３つのパラメータのうち、いずれか１つのパラメータの最大値が得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定する疲労限度推定ステップと、を有する、疲労限度推定方法を提供する。 The present invention has been completed based on the above findings of the present inventors.
That is, in order to solve the above-mentioned problems, the present invention captures an image of the object to be measured using an infrared imaging device while sequentially applying repeated loads having different load widths P to the object to be measured, thereby obtaining Measure the temporal change in the temperature distribution of the object to be measured, and dissipate energy distribution of the object to be measured for each cyclic load based on the temporal change in the temperature distribution of the object to be measured measured for each cyclic load and calculating the relationship between the load width P and the dissipated energy q based on the dissipated energy distribution of the object to be measured calculated for each repetitive load; A first-order differential value d for each load width P obtained by first-order differentiation with the load width P, and a first-order differential value d for each load width P obtained by second-order differentiation with the load width P of the relationship calculated in the relationship calculation step The maximum value of any one of the three parameters of the second differential value d2 and the product dα of the first differential value d and the second differential value d2 for each load width P is obtained. and a fatigue limit estimation step of estimating the load width P as the fatigue limit of the object to be measured.

本発明によれば、関係算出ステップにおいて、従来と同様に、荷重幅Ｐと散逸エネルギーｑとの関係を算出する。そして、疲労限度推定ステップにおいて、１階微分値ｄ、２階微分値ｄ２、及び、１階微分値ｄと２階微分値ｄ２との積ｄαの３つのパラメータのうち、いずれか１つのパラメータの最大値が得られた荷重幅Ｐを被測定物の疲労限度として推定する。このため、本発明者らが知見した通り、被測定物の疲労限度を精度良く推定可能である。 According to the present invention, in the relation calculation step, the relation between the load width P and the dissipated energy q is calculated as in the conventional case. Then, in the fatigue limit estimation step, any one of the three parameters of the first derivative value d, the second derivative value d2, and the product dα of the first derivative value d and the second derivative value d2 The load width P at which the maximum value is obtained is estimated as the fatigue limit of the object to be measured. Therefore, as the inventors have found out, it is possible to accurately estimate the fatigue limit of the object to be measured.

本発明者らの知見によれば、３つのパラメータのうち、１階微分値ｄと２階微分値ｄ２との積ｄαの最大値が、本来の急増点に相当する可能性が最も高く、被測定物の疲労限度と最も精度良く対応する場合が多い。
このため、前記疲労限度推定ステップにおいて、前記１階微分値ｄと前記２階微分値ｄ２との積ｄαの最大値ｄαｍａｘが得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定することが好ましい。 According to the findings of the present inventors, among the three parameters, the maximum value of the product dα of the first derivative value d and the second derivative value d2 is most likely to correspond to the original rapid increase point. In many cases, it corresponds to the fatigue limit of the measured object with the highest accuracy.
Therefore, in the fatigue limit estimation step, the load width P for which the maximum value dα max of the product dα of the first differential value d and the second differential value d2 is obtained is estimated as the fatigue limit of the object to be measured. preferably.

好ましくは、前記疲労限度推定ステップにおいて、前記１階微分値ｄの最大値ｄｍａｘに対する前記１階微分値ｄの比ｄ＿ｒａｔｅを前記荷重幅Ｐ毎に算出し、前記最大値ｄｍａｘについての前記比ｄ＿ｒａｔｅを除く全ての前記比ｄ＿ｒａｔｅが第１しきい値以下である場合には、前記最大値ｄｍａｘが得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定し、前記最大値ｄｍａｘについての前記比ｄ＿ｒａｔｅを除くいずれかの前記比ｄ＿ｒａｔｅが前記第１しきい値を超える場合には、前記２階微分値ｄ２の最大値ｄ２ｍａｘに対する前記２階微分値ｄ２の比ｄ２＿ｒａｔｅを前記荷重幅Ｐ毎に算出し、前記最大値ｄ２ｍａｘについての前記比ｄ２＿ｒａｔｅを除く全ての前記比ｄ２＿ｒａｔｅが第２しきい値以下である場合には、前記最大値ｄ２ｍａｘが得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定し、前記最大値ｄｍａｘについての前記比ｄ＿ｒａｔｅを除くいずれかの前記比ｄ＿ｒａｔｅが前記第１しきい値を超え、且つ、前記最大値ｄ２ｍａｘについての前記比ｄ２＿ｒａｔｅを除くいずれかの前記比ｄ２＿ｒａｔｅが前記第２しきい値を超える場合には、前記１階微分値ｄと前記２階微分値ｄ２との積ｄαの最大値ｄαｍａｘが得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定する。 Preferably, in the fatigue limit estimation step, a ratio d_rate of the first differential value d to the maximum value d max of the first differential value d is calculated for each load width P, and the ratio of the maximum value d max When all the ratios d_rate except d_rate are equal to or less than the first threshold value, the load width P at which the maximum value dmax is obtained is estimated as the fatigue limit of the object to be measured, and the maximum value d If any of the ratios d_rate except the ratio d_rate for max exceeds the first threshold, the ratio d2_rate of the second derivative d2 to the maximum value d2max of the second derivative d2 is set to the Calculated for each load width P, when all the ratios d2_rate except the ratio d2_rate for the maximum value d2 max are equal to or less than a second threshold value, the load width from which the maximum value d2 max is obtained estimating P as the fatigue limit of the object under test, any of the ratios d_rate excluding the ratio d_rate for the maximum value d max exceeds the first threshold value, and for the maximum value d2 max When any of the ratios d2_rate other than the ratio d2_rate exceeds the second threshold, the maximum value dα max of the product dα of the first differential value d and the second differential value d2 is obtained. The load width P is estimated as the fatigue limit of the object to be measured.

上記の好ましい方法では、１階微分値ｄの最大値ｄｍａｘに対する１階微分値ｄの比ｄ＿ｒａｔｅを荷重幅Ｐ毎に算出し、最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除く全ての比ｄ＿ｒａｔｅが第１しきい値以下であるか否かを判定する。最大値ｄｍａｘについての比ｄ＿ｒａｔｅは１であるため、第１しきい値としては、０より大きく１より小さな値（例えば、０．５）が設定される。最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除く全ての比ｄ＿ｒａｔｅが第１しきい値以下であれば（換言すれば、最大値ｄｍａｘが他の１階微分値ｄに比べて十分に大きければ）、最大値ｄｍａｘが得られた荷重幅Ｐが本来の急増点に相当する可能性が高いといえる。このため、上記の好ましい方法では、最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除く全ての比ｄ＿ｒａｔｅが第１しきい値以下である場合には、最大値ｄｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定する。 In the preferred method described above, the ratio d_rate of the first differential value d to the maximum value d max of the first differential value d is calculated for each load width P, and all ratios d_rate except the ratio d_rate for the maximum value d max It is determined whether or not it is equal to or less than 1 threshold. Since the ratio d_rate for the maximum value d max is 1, a value greater than 0 and less than 1 (for example, 0.5) is set as the first threshold. If all the ratios d_rate except the ratio d_rate for the maximum value d max are less than or equal to the first threshold (in other words, if the maximum value d max is sufficiently larger than the other first derivative values d), It can be said that there is a high possibility that the load width P at which the maximum value d max is obtained corresponds to the original rapid increase point. For this reason, in the preferred method described above, if all the ratios d_rate except the ratio d_rate for the maximum value dmax are equal to or less than the first threshold, the load width P at which the maximum value dmax is obtained is measured. Estimated as the fatigue limit of the object.

一方、最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除くいずれかの比ｄ＿ｒａｔｅが第１しきい値を超える場合には、最大値ｄｍａｘが得られた荷重幅Ｐが本来の急増点に相当しない可能性がある。このため、上記の好ましい方法では、上記の場合に、２階微分値ｄ２の最大値ｄ２ｍａｘに対する２階微分値ｄ２の比ｄ２＿ｒａｔｅを荷重幅Ｐ毎に算出し、最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除く全ての比ｄ２＿ｒａｔｅが第２しきい値以下であるか否かを判定する。最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅは１であるため、第２しきい値としては、０より大きく１より小さな値（例えば、０．５）が設定される。第２しきい値は第１しきい値と同じ値であってもよいし、異なる値であってもよい。最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除く全ての比ｄ２＿ｒａｔｅが第２しきい値以下であれば（換言すれば、最大値ｄ２ｍａｘが他の２階微分値ｄ２に比べて十分に大きければ）、最大値ｄ２ｍａｘが得られた荷重幅Ｐが本来の急増点に相当する可能性が高いといえる。このため、上記の好ましい方法では、最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除く全ての比ｄ２＿ｒａｔｅが第２しきい値以下である場合には、最大値ｄ２ｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定する。 On the other hand, if any of the ratios d_rate other than the ratio d_rate for the maximum value dmax exceeds the first threshold, there is a possibility that the load width P at which the maximum value dmax is obtained does not correspond to the original rapid increase point. There is Therefore, in the above preferred method, in the above case, the ratio d2_rate of the second derivative value d2 to the maximum value d2 max of the second derivative value d2 is calculated for each load width P, and the ratio d2_rate of the maximum value d2 max is less than or equal to the second threshold. Since the ratio d2_rate for the maximum value d2 max is 1, a value greater than 0 and less than 1 (for example, 0.5) is set as the second threshold. The second threshold may be the same value as the first threshold, or may be a different value. If all ratios d2_rate except the ratio d2_rate for the maximum value d2 max are less than or equal to the second threshold (in other words, if the maximum value d2 max is sufficiently greater than the other second derivative values d2), It can be said that there is a high possibility that the load width P at which the maximum value d2 max is obtained corresponds to the original rapid increase point. Therefore, in the preferred method described above, if all the ratios d2_rate except the ratio d2_rate for the maximum value d2 max are equal to or less than the second threshold, the load width P at which the maximum value d2 max is obtained is measured. Estimated as the fatigue limit of the object.

そして、上記の好ましい方法では、最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除くいずれかの比ｄ＿ｒａｔｅが第１しきい値を超え、且つ、最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除くいずれかの比ｄ２＿ｒａｔｅが第２しきい値を超える場合には、前述のように、本来の急増点に相当する可能性が最も高い、１階微分値ｄと２階微分値ｄ２との積ｄαの最大値ｄαｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定する。 Then, in the above preferred method, any ratio d_rate except the ratio d_rate for the maximum value d max exceeds the first threshold, and any ratio d2_rate except the ratio d2_rate for the maximum value d2 max exceeds When the second threshold value is exceeded, as described above, the maximum value dα max of the product dα of the first differential value d and the second differential value d2, which is most likely to correspond to the original sharp increase point, is The obtained load width P is estimated as the fatigue limit of the object to be measured.

以上のように、上記の好ましい方法によれば、１階微分値ｄの最大値ｄｍａｘ、２階微分値ｄ２の最大値ｄ２ｍａｘ、１階微分値ｄと２階微分値ｄ２との積ｄαの最大値ｄαｍａｘの順に、被測定物の疲労限度を推定するのに用いるパラメータを検討するため、例えば、１階微分値ｄの最大値ｄｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定することになった場合（最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除く全ての比ｄ＿ｒａｔｅが第１しきい値以下である場合）には、２階微分値ｄ２や、１階微分値ｄと２階微分値ｄ２との積ｄαを算出する必要がなく、推定の効率を高めることが可能である。同様に、２階微分値ｄ２の最大値ｄ２ｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定することになった場合（最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除く全ての比ｄ２＿ｒａｔｅが第２しきい値以下である場合）には、１階微分値ｄと２階微分値ｄ２との積ｄαを算出する必要がなく、推定の効率を高めることが可能である。 As described above, according to the above preferable method, the maximum value d max of the first differential value d, the maximum value d2 max of the second differential value d2, the product dα of the first differential value d and the second differential value d2 In order to examine the parameters used for estimating the fatigue limit of the object to be measured in the order of the maximum value dα max of When estimating as the fatigue limit (when all ratios d_rate excluding the ratio d_rate for the maximum value d max are equal to or less than the first threshold value), the second derivative value d2 and the first derivative value Since it is not necessary to calculate the product dα of d and the second derivative value d2, the estimation efficiency can be improved. Similarly, when the load width P at which the maximum value d2 max of the second derivative value d2 is obtained is estimated as the fatigue limit of the object to be measured (all ratios d2_rate is equal to or less than the second threshold value), it is not necessary to calculate the product dα of the first derivative value d and the second derivative value d2, and the estimation efficiency can be improved.

好ましくは、前記疲労限度推定ステップにおいて、前記１階微分値ｄの最大値ｄｍａｘに対する前記１階微分値ｄの比ｄ＿ｒａｔｅを前記荷重幅Ｐ毎に算出すると共に、前記２階微分値ｄ２の最大値ｄ２ｍａｘに対する前記２階微分値ｄ２の比ｄ２＿ｒａｔｅを前記荷重幅Ｐ毎に算出し、前記最大値ｄｍａｘについての前記比ｄ＿ｒａｔｅを除く全ての前記比ｄ＿ｒａｔｅが第１しきい値以下であり、前記最大値ｄ２ｍａｘについての前記比ｄ２＿ｒａｔｅを除く全ての前記比ｄ２＿ｒａｔｅが第２しきい値以下であり、なお且つ、前記最大値ｄｍａｘが得られた前記荷重幅Ｐと前記最大値ｄ２ｍａｘが得られた前記荷重幅Ｐとが等しいという条件を満足する場合には、前記最大値ｄｍａｘ及び前記最大値ｄ２ｍａｘが得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定し、前記条件を満足しない場合には、前記１階微分値ｄと前記２階微分値ｄ２との積ｄαの最大値ｄαｍａｘが得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定する。 Preferably, in the fatigue limit estimation step, the ratio d_rate of the first differential value d to the maximum value d max of the first differential value d is calculated for each load width P, and the maximum value of the second differential value d2 A ratio d2_rate of the second derivative value d2 to the value d2 max is calculated for each load width P, and all the ratios d_rate excluding the ratio d_rate for the maximum value d max are equal to or less than a first threshold; All the ratios d2_rate except the ratio d2_rate for the maximum value d2 max are equal to or less than a second threshold, and the load width P and the maximum value d2 max from which the maximum value d max is obtained are When the condition that the obtained load width P is equal is satisfied, the load width P for which the maximum value d max and the maximum value d2 max are obtained is estimated as the fatigue limit of the object to be measured, If the condition is not satisfied, the load width P at which the maximum value dα max of the product dα of the first differential value d and the second differential value d2 is obtained is estimated as the fatigue limit of the object to be measured. .

上記の好ましい方法によれば、１階微分値ｄの最大値ｄｍａｘ及び２階微分値ｄ２の最大値ｄ２ｍａｘ、１階微分値ｄと２階微分値ｄ２との積ｄαの最大値ｄαｍａｘの順に、被測定物の疲労限度を推定するのに用いるパラメータを検討するため、例えば、１階微分値ｄの最大値ｄｍａｘ及び２階微分値ｄ２の最大値ｄ２ｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定することになった場合（最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除く全ての比ｄ＿ｒａｔｅが第１しきい値以下であり、最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除く全ての比ｄ２＿ｒａｔｅが第２しきい値以下であり、なお且つ、最大値ｄｍａｘが得られた荷重幅Ｐと最大値ｄ２ｍａｘが得られた荷重幅Ｐとが等しい場合）には、１階微分値ｄと２階微分値ｄ２との積ｄαを算出する必要がなく、推定の効率を高めることが可能である。 According to the above preferred method, the maximum value dmax of the first differential value d, the maximum value d2max of the second differential value d2, and the maximum value dαmax of the product dα of the first differential value d and the second differential value d2 In order to examine the parameters used for estimating the fatigue limit of the object to be measured, for example, the maximum value dmax of the first derivative value d and the maximum value d2max of the second derivative value d2 If P is to be estimated as the fatigue limit of the object to be measured (all ratios d_rate except the ratio d_rate for the maximum value dmax are less than or equal to the first threshold, and the ratio d2_rate for the maximum value d2max is All ratios except d2_rate are equal to or less than the second threshold, and the load width P at which the maximum value dmax is obtained is equal to the load width P at which the maximum value d2max is obtained), 1 Since it is not necessary to calculate the product dα of the differential value d and the second differential value d2, the estimation efficiency can be improved.

本発明によれば、赤外線撮像装置を用いて測定した被測定物の散逸エネルギー分布に基づき、被測定物の疲労限度を精度良く推定することが可能である。 According to the present invention, it is possible to accurately estimate the fatigue limit of an object to be measured based on the dissipation energy distribution of the object measured using an infrared imaging device.

荷重幅と散逸エネルギーとの関係を模式的に示す図である。It is a figure which shows typically the relationship between load width and dissipation energy. 第１実施形態に係る疲労限度推定方法のステップを概略的に示すフロー図である。FIG. 4 is a flow diagram schematically showing steps of a fatigue limit estimation method according to the first embodiment; 図２に示す関係算出ステップＳ１で算出される、被測定物の散逸エネルギー分布及び荷重幅Ｐと散逸エネルギーｑとの関係の一例を示す図である。3 is a diagram showing an example of the relationship between the dissipated energy distribution of the object to be measured, the load width P, and the dissipated energy q calculated in the relation calculation step S1 shown in FIG. 2; FIG. 図３（ｂ）に示す荷重幅Ｐと散逸エネルギーｑとの関係と、この関係から算出した１階微分値ｄとを示す図である。It is a figure which shows the relationship between the load width P and the dissipation energy q which are shown in FIG.3(b), and the 1st order differential value d calculated from this relationship. 図３（ｂ）に示す荷重幅Ｐと散逸エネルギーｑとの関係と、この関係から算出した２階微分値ｄ２とを示す図である。It is a figure which shows the relationship between the load width P and the dissipation energy q which are shown in FIG.3(b), and the 2nd order differential value d2 calculated from this relationship. 図３（ｂ）に示す荷重幅Ｐと散逸エネルギーｑとの関係と、この関係から算出した１階微分値ｄと２階微分値ｄ２との積ｄαを示す図である。It is a figure which shows the product d(alpha) of the 1st-order differential value d calculated from this relationship between the load width P and the dissipation energy q which are shown in FIG.3(b), and the 2nd-order differential value d2. 第２実施形態に係る疲労限度推定方法のステップを概略的に示すフロー図である。FIG. 5 is a flow diagram schematically showing steps of a fatigue limit estimation method according to a second embodiment; 第１実施形態に係る疲労限度推定方法の実施例の概要を説明する説明図である。It is an explanatory view explaining the outline of the example of the fatigue limit estimation method concerning a 1st embodiment.

以下、添付図面を適宜参照しつつ、本発明の実施形態（第１実施形態及び第２実施形態）に係る疲労限度推定方法について説明する。 Hereinafter, a fatigue limit estimation method according to embodiments (first embodiment and second embodiment) of the present invention will be described with appropriate reference to the accompanying drawings.

＜第１実施形態＞
図２は、第１実施形態に係る疲労限度推定方法のステップを概略的に示すフロー図である。
図２に示すように、第１実施形態に係る疲労限度推定方法は、関係算出ステップＳ１と、疲労限度推定ステップＳ２と、を有する。以下、各ステップＳ１、Ｓ２について順に説明する。 <First embodiment>
FIG. 2 is a flow diagram schematically showing the steps of the fatigue limit estimation method according to the first embodiment.
As shown in FIG. 2, the fatigue limit estimation method according to the first embodiment has a relation calculation step S1 and a fatigue limit estimation step S2. The steps S1 and S2 will be described in order below.

［関係算出ステップＳ１］
関係算出ステップＳ１では、疲労試験機等によって、被測定物に荷重幅（＝最大荷重－最小荷重）Ｐの異なる繰り返し荷重を順次付加しながら、赤外線撮像装置を用いて被測定物を撮像することで、繰り返し荷重毎に被測定物の温度分布の時間的変化を測定する。具体的には、被測定物に付加する繰り返し荷重の荷重幅Ｐを、応力比（＝最小応力／最大応力＝最小荷重／最大荷重）を一定にした条件で段階的に増加させ、各荷重幅Ｐの繰り返し荷重を数千サイクル程度付加しながら、赤外線撮像装置を用いて被測定物を撮像することで、繰り返し荷重毎に被測定物の温度分布の時間的変化を測定する。そして、繰り返し荷重毎に測定した被測定物の温度分布の時間的変化に基づき、繰り返し荷重毎に被測定物の散逸エネルギー分布を算出する。
具体的には、赤外線撮像装置から出力された画像信号から、熱弾性効果によって生じる温度変化に応じた信号波形をロックイン処理する（付加する繰り返し荷重と同じ周波数の参照信号で画像信号を同期検波し、参照信号に応じた周波数帯域の画像信号成分のみを抽出する）。そして、赤外線撮像装置から出力された画像信号（ロックイン処理前の画像信号）によって得られた被測定物の温度分布の時間的変化から、ロックイン処理によって抽出した画像信号成分によって得られた熱弾性効果に起因した被測定物の温度分布の時間的変化を減算することで、被測定物の散逸エネルギー分布を算出する。
なお、関係算出ステップＳ１の上記の手順を実行するための赤外線撮像装置としては、例えば、ＦＬＩＲ社製のＸ６５８０シリーズ（冷却式、温度分解能０．０２℃、画素数最大６４０×５１２ピクセル、フレームレート最大３５０Ｈｚ）を、散逸エネルギー分布の算出用ソフトウェアとしては、同社製のＡｌｔａｉｒＬＩを用いることができる。 [Relationship calculation step S1]
In the relationship calculation step S1, the object to be measured is imaged using an infrared imaging device while sequentially applying repeated loads with different load widths (= maximum load - minimum load) P to the object to be measured by a fatigue tester or the like. , the temporal change in the temperature distribution of the object to be measured is measured for each repeated load. Specifically, the load width P of the cyclic load applied to the object to be measured is increased stepwise under the condition that the stress ratio (= minimum stress/maximum stress = minimum load/maximum load) is kept constant, and each load width By taking an image of the object to be measured using an infrared imaging device while applying a repeated load of P for several thousand cycles, the temporal change in the temperature distribution of the object to be measured is measured for each repeated load. Then, the dissipated energy distribution of the object to be measured is calculated for each repeated load based on the temporal change in the temperature distribution of the object to be measured measured for each repeated load.
Specifically, from the image signal output from the infrared imaging device, the signal waveform corresponding to the temperature change caused by the thermoelastic effect is lock-in processed (the image signal is synchronously detected with a reference signal having the same frequency as the repeated load to be applied). and extracts only the image signal component in the frequency band corresponding to the reference signal). Then, the heat obtained by the image signal component extracted by lock-in processing from the temporal change in the temperature distribution of the object to be measured obtained by the image signal (image signal before lock-in processing) output from the infrared imaging device. By subtracting the temporal change in the temperature distribution of the object due to the elastic effect, the dissipated energy distribution of the object is calculated.
As an infrared imaging device for executing the above procedure of the relationship calculation step S1, for example, FLIR X6580 series (cooling type, temperature resolution 0.02 ° C., maximum number of pixels 640 × 512 pixels, frame rate 350 Hz at maximum), and AltairLI manufactured by the same company can be used as the software for calculating the dissipated energy distribution.

次に、関係算出ステップＳ１では、上記のようにして、繰り返し荷重毎に算出した被測定物の散逸エネルギー分布に基づき、荷重幅Ｐと散逸エネルギーｑとの関係を算出する。
図３は、関係算出ステップＳ１で算出される、被測定物の散逸エネルギー分布及び荷重幅Ｐと散逸エネルギーｑとの関係の一例を示す図である。図３（ａ）は散逸エネルギー分布（散逸エネルギー分布を示す画像）の一例を、図３（ｂ）は荷重幅Ｐと散逸エネルギーｑとの関係の一例を示す。図３（ａ）に示す散逸エネルギー分布は、濃度の濃い（黒い）画素ほど、散逸エネルギーが大きいことを示している。図３（ｂ）に示す関係は、図３（ａ）に示すような散逸エネルギー分布を繰り返し荷重毎に（段階的に増加させた異なる荷重幅Ｐ毎に）算出し、散逸エネルギー分布において、破壊起点が発生し得ると考えられる応力集中部（図３（ａ）に示す破線Ｓで囲んだ縦横数～十数ピクセルずつの画素領域）における散逸エネルギーの代表値（具体的には、平均値）を繰り返し荷重毎にプロットしたものである。なお、代表値としては、平均値に限るものではなく、例えば、最大値を用いることも可能である。 Next, in the relation calculation step S1, the relation between the load width P and the dissipated energy q is calculated based on the dissipated energy distribution of the object to be measured calculated for each repeated load as described above.
FIG. 3 is a diagram showing an example of the relationship between the dissipated energy distribution of the object to be measured, the load width P, and the dissipated energy q calculated in the relation calculation step S1. FIG. 3(a) shows an example of the dissipated energy distribution (image showing the dissipated energy distribution), and FIG. 3(b) shows an example of the relationship between the load width P and the dissipated energy q. The dissipated energy distribution shown in FIG. 3(a) indicates that the darker (blacker) the pixel, the greater the dissipated energy. The relationship shown in FIG. 3(b) is calculated by calculating the dissipated energy distribution as shown in FIG. A representative value (specifically, an average value) of the dissipated energy in the stress concentration part where the starting point can be generated (the pixel area surrounded by the dashed line S shown in FIG. is plotted for each repeated load. Note that the representative value is not limited to the average value, and for example, the maximum value can also be used.

[疲労限度推定ステップＳ２]
図３（ｂ）に示す荷重幅Ｐと散逸エネルギーｑとの関係は、図１に示す関係に比べれば、全体的に散逸エネルギーが一定の勾配で単調増加しており、急増点が明確ではない。
そこで、第１実施形態に係る疲労限度推定方法の疲労限度推定ステップＳ２では、関係算出ステップＳ１で算出した関係を荷重幅Ｐで１階微分して得られる荷重幅Ｐ毎の１階微分値ｄ、関係算出ステップＳ１で算出した関係を荷重幅Ｐで２階微分して得られる荷重幅Ｐ毎の２階微分値ｄ２、及び、荷重幅Ｐ毎の１階微分値ｄと２階微分値ｄ２との積ｄαの３つのパラメータのうち、いずれか１つのパラメータの最大値が得られた荷重幅Ｐを被測定物の疲労限度として推定する。 [Fatigue limit estimation step S2]
Compared to the relationship shown in FIG. 1, the relationship between the load width P and the dissipated energy q shown in FIG. .
Therefore, in the fatigue limit estimation step S2 of the fatigue limit estimation method according to the first embodiment, the first-order differential value d for each load width P obtained by first-order differentiating the relationship calculated in the relationship calculation step S1 with the load width P , the second-order differential value d2 for each load width P obtained by second-order differentiation of the relationship calculated in the relationship calculation step S1 with respect to the load width P, and the first-order differential value d and second-order differential value d2 for each load width P The load width P at which the maximum value of any one of the three parameters of the product dα is obtained is estimated as the fatigue limit of the object to be measured.

１階微分値ｄは、隣り合うプロット点の荷重幅Ｐの変化量をΔＰとし、隣り合うプロット点の散逸エネルギーの変化量をΔｑとすると、以下の式（３）で算出される（図３（ｂ）参照）。
ｄ＝Δｑ／ΔＰ ・・・（３）
すなわち、小さい方からｎ番目のプロット点の１階微分値ｄをｄｎとし、小さい方からｎ番目のプロット点の荷重幅ＰをＰｎ、散逸エネルギーｑをｑｎとし、小さい方からｎ＋１番目のプロット点の荷重幅ＰをＰｎ＋１、散逸エネルギーｑをｑｎ＋１とすれば、１階微分値ｄｎは、例えば、以下の式（３）’で算出される。
ｄｎ＝（ｑｎ＋１－ｑｎ）／（Ｐｎ＋１－Ｐｎ） ・・・（３）’ The first-order differential value d is calculated by the following formula (3), where ΔP is the amount of change in the load width P of the adjacent plot points, and Δq is the amount of change in the dissipated energy of the adjacent plot points (Fig. 3 (b)).
d=Δq/ΔP (3)
That is, the first derivative value d of the n-th plot point from the smallest is dn , the load width P of the n-th plot point from the smallest is Pn , the dissipation energy q is qn , and the n+1th from the smallest Assuming that the load width P of the plotted points of is P n+1 and the dissipation energy q is q n+1 , the first derivative value d n is calculated by, for example, the following equation (3)′.
dn =(qn +1 - qn )/(Pn +1 - Pn ) (3)'

２階微分値ｄ２は、隣り合うプロット点の１階微分値ｄの変化量をΔｄとすれば、以下の式（４）で算出される（図３（ｂ）参照）。
ｄ２＝Δｄ／ΔＰ ・・・（４）
すなわち、小さい方からｎ番目のプロット点の２階微分値ｄ２をｄ２ｎとし、小さい方からｎ＋１番目のプロット点の１階微分値ｄをｄｎ＋１とすれば、２階微分値ｄ２ｎは、例えば、以下の式（４）’で算出される。
ｄ２ｎ＝（ｄｎ＋１－ｄｎ）／（Ｐｎ＋１－Ｐｎ）＝｛（ｑｎ＋２－ｑｎ＋１）／（Ｐｎ＋２－Ｐｎ＋１）－（ｑｎ＋１－ｑｎ）／（Ｐｎ＋１－Ｐｎ）｝／（Ｐｎ＋１－Ｐｎ）・・・（４）’
上記の式（４）’において、ｑｎ＋２は小さい方からｎ＋２番目のプロット点の散逸エネルギーｑであり、Ｐｎ＋２は小さい方からｎ＋２番目のプロット点の荷重幅Ｐである。 The second-order differential value d2 is calculated by the following equation (4), where Δd is the amount of change in the first-order differential value d between adjacent plot points (see FIG. 3B).
d2=Δd/ΔP (4)
That is, if the second differential value d2 of the n-th plot point from the smallest is d2n , and the first differential value d of the n+1th plot point from the smallest is dn +1 , then the second differential value d2n is For example, it is calculated by the following formula (4)'.
d2 n = (d n+1 −d n )/(P n+1 −P n )={(q n+2 −q n+1 )/(P n+2 −P n+1 )−(q n+1 −q n )/(P n+1 −P n )}/(Pn +1 - Pn ) (4)'
In the above equation (4)′, q n+2 is the dissipated energy q of the n+2th smallest plot point, and P n+2 is the load width P of the n+2th smallest plot point.

１階微分値ｄと２階微分値ｄ２との積ｄαは、以下の式（５）で算出される（図３（ｂ）参照）。
ｄα＝ｄ・ｄ２ ・・・（５）
すなわち、小さい方からｎ番目のプロット点の積ｄαをｄαｎとすれば、積ｄαｎは、以下の式（５）’で算出される。
ｄαｎ＝ｄｎ・ｄ２ｎ ・・・（５）’ The product dα of the first-order differential value d and the second-order differential value d2 is calculated by the following equation (5) (see FIG. 3B).
dα=d·d2 (5)
That is, if the product dα of the n-th plot point from the smallest is dαn , the product dαn is calculated by the following equation (5)′.
dαn = dn · d2n (5)'

前述のように、疲労限度推定ステップＳ２では、以上に説明した、荷重幅Ｐ毎の１階微分値ｄ、荷重幅Ｐ毎の２階微分値ｄ２、及び、荷重幅Ｐ毎の１階微分値ｄと２階微分値ｄ２との積ｄαの３つのパラメータのうち、いずれか１つのパラメータの最大値が得られた荷重幅Ｐを被測定物の疲労限度として推定するが、具体的には、以下に説明する各ステップを実行する。 As described above, in the fatigue limit estimation step S2, the first differential value d for each load width P, the second differential value d2 for each load width P, and the first differential value for each load width P are calculated. Among the three parameters of the product dα of d and the second derivative value d2, the load width P at which the maximum value of any one parameter is obtained is estimated as the fatigue limit of the object to be measured. Execute each step described below.

図２に示すように、疲労限度推定ステップＳ２では、まず、関係算出ステップＳ１で算出した関係（図３（ｂ）参照）を荷重幅Ｐで１階微分して荷重幅Ｐ毎の１階微分値ｄを算出し、１階微分値ｄの最大値ｄｍａｘに対する１階微分値ｄの比ｄ＿ｒａｔｅを荷重幅Ｐ毎に算出する（図２のステップＳ２１）。
すなわち、小さい方からｎ番目のプロット点の１階微分値ｄｎについての比ｄ＿ｒａｔｅをｄ＿ｒａｔｅｎとすると、比ｄ＿ｒａｔｅｎは、以下の式（６）で算出される。
ｄ＿ｒａｔｅｎ＝ｄｎ／ｄｍａｘ ・・・（６）
そして、最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除く全ての比ｄ＿ｒａｔｅが第１しきい値Ｔｈ１以下であるか否かを判定する（図２のステップＳ２２）。最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除く全ての比ｄ＿ｒａｔｅが第１しきい値Ｔｈ１以下である場合（図２のステップＳ２２において「Ｙｅｓ」の場合）には、最大値ｄｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定する（図２のステップＳ２３）。一方、最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除くいずれかの比ｄ＿ｒａｔｅが第１しきい値Ｔｈ１を超える場合（図２のステップＳ２２において「Ｎｏ」の場合）には、ステップＳ２４に進む。 As shown in FIG. 2, in the fatigue limit estimation step S2, first, the relationship calculated in the relationship calculation step S1 (see FIG. 3(b)) is first differentiated by the load width P, and the first derivative for each load width P A value d is calculated, and a ratio d_rate of the first differential value d to the maximum value d max of the first differential value d is calculated for each load width P (step S21 in FIG. 2).
That is, when the ratio d_rate for the first differential value dn of the n-th plot point from the smallest is d_rate n , the ratio d_rate n is calculated by the following equation (6).
d_raten= dn / dmax (6)
Then, it is determined whether or not all the ratios d_rate except the ratio d_rate for the maximum value d max are equal to or less than the first threshold value Th1 (step S22 in FIG. 2). When all the ratios d_rate except the ratio d_rate for the maximum value d max are equal to or less than the first threshold value Th1 (“Yes” in step S22 of FIG. 2), the load at which the maximum value d max is obtained The width P is estimated as the fatigue limit of the object to be measured (step S23 in FIG. 2). On the other hand, if any ratio d_rate other than the ratio d_rate for the maximum value d max exceeds the first threshold value Th1 ("No" in step S22 of FIG. 2), the process proceeds to step S24.

図４は、図３（ｂ）に示す荷重幅Ｐと散逸エネルギーｑとの関係と、この関係から算出した１階微分値ｄとを示す図である。図４において、１階微分値ｄは「×」でプロットしている。
図４に示すように、荷重幅Ｐ８において、１階微分値ｄが最大値ｄｍａｘとなっている。このため、荷重幅Ｐ８が本来の急増点に相当すると考えることもできる。しかしながら、荷重幅Ｐ１０及びＰ１６においても１階微分値ｄが大きくなっているため、荷重幅Ｐ８が本来の急増点に相当すると断定するのは困難である。そこで、上記のように、最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除く全ての比ｄ＿ｒａｔｅが第１しきい値Ｔｈ１以下であるか否かを判定することにしている。図４に示す例では、荷重幅Ｐ１０における１階微分値ｄ１０についての比ｄ＿ｒａｔｅ１０、荷重幅Ｐ１４における１階微分値ｄ１４についての比ｄ＿ｒａｔｅ１４及び荷重幅Ｐ１６における１階微分値ｄ１６についての比ｄ＿ｒａｔｅ１６のいずれもが０．５よりも大きい。このため、第１しきい値Ｔｈ１＝０．５とすると、最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除くいずれかの比ｄ＿ｒａｔｅが第１しきい値Ｔｈ１を超えることになるため、ステップＳ２４に進むことになる。 FIG. 4 is a diagram showing the relationship between the load width P and the dissipated energy q shown in FIG. 3(b), and the first order differential value d calculated from this relationship. In FIG. 4, the first derivative value d is plotted with "x".
As shown in FIG. 4, the first differential value d is the maximum value dmax at the load width P8 . Therefore, it can be considered that the load width P8 corresponds to the original rapid increase point. However, since the first derivative value d is also large in the load widths P10 and P16 , it is difficult to conclude that the load width P8 corresponds to the original rapid increase point. Therefore, as described above, it is determined whether or not all the ratios d_rate excluding the ratio d_rate for the maximum value d max are equal to or less than the first threshold value Th1. In the example shown in FIG. 4, the ratio d_rate 10 for the first differential value d 10 in the load width P 10 , the ratio d_rate 14 for the first differential value d 14 in the load width P 14, and the first differential value in the load width P 16 Any of the ratios d_rate 16 for d 16 are greater than 0.5. Therefore, if the first threshold value Th1=0.5, any ratio d_rate other than the ratio d_rate for the maximum value d max exceeds the first threshold value Th1, so the process proceeds to step S24. become.

疲労限度推定ステップＳ２のステップＳ２４では、関係算出ステップＳ１で算出した関係（図３（ｂ）参照）を荷重幅Ｐで２階微分して荷重幅Ｐ毎の２階微分値ｄ２を算出し、２階微分値ｄ２の最大値ｄ２ｍａｘに対する２階微分値ｄの比ｄ２＿ｒａｔｅを荷重幅Ｐ毎に算出する。
すなわち、小さい方からｎ番目のプロット点の２階微分値ｄ２ｎについての比ｄ２＿ｒａｔｅをｄ２＿ｒａｔｅｎとすると、比ｄ２＿ｒａｔｅｎは、以下の式（７）で算出される。
ｄ２＿ｒａｔｅｎ＝ｄ２ｎ／ｄ２ｍａｘ ・・・（７）
そして、最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除く全ての比ｄ２＿ｒａｔｅが第２しきい値Ｔｈ２以下であるか否かを判定する（図２のステップＳ２５）。最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除く全ての比ｄ２＿ｒａｔｅが第２しきい値Ｔｈ２以下である場合（図２のステップＳ２５において「Ｙｅｓ」の場合）には、最大値ｄ２ｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定する（図２のステップＳ２６）。一方、最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除くいずれかの比ｄ２＿ｒａｔｅが第２しきい値Ｔｈ２を超える場合（図２のステップＳ２５において「Ｎｏ」の場合）には、ステップＳ２７に進む。 In step S24 of the fatigue limit estimation step S2, the relationship calculated in the relationship calculation step S1 (see FIG. 3B) is second-order differentiated by the load width P to calculate the second-order differential value d2 for each load width P, A ratio d2_rate of the second differential value d to the maximum value d2 max of the second differential value d2 is calculated for each load width P.
That is, when the ratio d2_rate for the second derivative value d2n of the n-th plot point from the smallest is d2_raten , the ratio d2_raten is calculated by the following equation (7).
d2_raten = d2n / d2max (7)
Then, it is determined whether or not all the ratios d2_rate except the ratio d2_rate for the maximum value d2 max are equal to or less than the second threshold value Th2 (step S25 in FIG. 2). When all the ratios d2_rate except the ratio d2_rate for the maximum value d2 max are equal to or less than the second threshold value Th2 ("Yes" in step S25 in FIG. 2), the load at which the maximum value d2 max is obtained The width P is estimated as the fatigue limit of the object to be measured (step S26 in FIG. 2). On the other hand, if any ratio d2_rate other than the ratio d2_rate for the maximum value d2 max exceeds the second threshold Th2 (“No” in step S25 of FIG. 2), the process proceeds to step S27.

図５は、図３（ｂ）に示す荷重幅Ｐと散逸エネルギーｑとの関係と、この関係から算出した２階微分値ｄ２とを示す図である。図５において、２階微分値ｄ２は「＋」でプロットしている。
図５に示すように、荷重幅Ｐ８において、２階微分値ｄ２が最大値ｄ２ｍａｘとなっている。このため、荷重幅Ｐ８が本来の急増点に相当すると考えることもできる。しかしながら、荷重幅Ｐ６及びＰ１０においても２階微分値ｄ２が大きくなっているため、荷重幅Ｐ８が本来の急増点に相当すると断定するのは困難である。そこで、上記のように、最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除く全ての比ｄ２＿ｒａｔｅが第２しきい値Ｔｈ２以下であるか否かを判定することにしている。図５に示す例では、荷重幅Ｐ６における２階微分値ｄ２６についての比ｄ２＿ｒａｔｅ６、及び、荷重幅Ｐ１０における２階微分値ｄ２１０についての比ｄ２＿ｒａｔｅ１０のいずれもが０．５よりも大きい。このため、第２しきい値Ｔｈ２＝０．５とすると、最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除くいずれかの比ｄ２＿ｒａｔｅが第２しきい値Ｔｈ２を超えることになるため、ステップＳ２７に進むことになる。 FIG. 5 is a diagram showing the relationship between the load width P and the dissipated energy q shown in FIG. 3B, and the second order differential value d2 calculated from this relationship. In FIG. 5, the second derivative value d2 is plotted with "+".
As shown in FIG. 5, the second derivative value d2 is the maximum value d2max at the load width P8 . Therefore, it can be considered that the load width P8 corresponds to the original rapid increase point. However, since the second derivative value d2 is also large in the load widths P6 and P10 , it is difficult to conclude that the load width P8 corresponds to the original rapid increase point. Therefore, as described above, it is determined whether or not all the ratios d2_rate excluding the ratio d2_rate for the maximum value d2 max are equal to or smaller than the second threshold Th2. In the example shown in FIG. 5, both the ratio d2_rate 6 for the second derivative value d2_6 in the load width P6 and the ratio d2_rate10 for the second derivative value d2_10 in the load width P10 are less than 0.5 is also big. Therefore, if the second threshold value Th2=0.5, any ratio d2_rate other than the ratio d2_rate for the maximum value d2 max exceeds the second threshold value Th2, so the process proceeds to step S27. become.

疲労限度推定ステップＳ２のステップＳ２７は、前述のように、１階微分値ｄの最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除くいずれかの比ｄ＿ｒａｔｅが第１しきい値Ｔｈ１を超え、且つ、２階微分値ｄ２の最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除くいずれかの比ｄ２＿ｒａｔｅが第２しきい値Ｔｈ２を超える場合に実行される。ステップＳ２７では、１階微分値ｄと２階微分値ｄ２との積ｄαを算出し、この積ｄαの最大値ｄαｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定する。
なお、１階微分値ｄと２階微分値ｄ２とが共に負の値である場合には、１階微分値ｄと２階微分値ｄ２との積ｄαの算出結果は、強制的にｄα＝０とする。 As described above, step S27 of the fatigue limit estimation step S2 is performed when any ratio d_rate other than the ratio d_rate for the maximum value d max of the first derivative value d exceeds the first threshold Th1 and when the second-order It is executed when any ratio d2_rate except the ratio d2_rate for the maximum value d2 max of the differential value d2 exceeds the second threshold Th2. In step S27, the product dα of the first differential value d and the second differential value d2 is calculated, and the load width P at which the maximum value dα max of the product dα is obtained is estimated as the fatigue limit of the object to be measured.
Note that when both the first-order differential value d and the second-order differential value d2 are negative values, the calculation result of the product dα of the first-order differential value d and the second-order differential value d2 is forced to be dα= 0.

図６は、図３（ｂ）に示す荷重幅Ｐと散逸エネルギーｑとの関係と、この関係から算出した１階微分値ｄと２階微分値ｄ２との積ｄαを示す図である。図６において、積ｄαは「＊」でプロットしている。
図６に示すように、荷重幅Ｐ８において、積ｄαが最大値ｄαｍａｘとなっているため、荷重幅Ｐ８が被測定物の疲労限度として推定されることになる。荷重幅Ｐ８における積ｄαｍａｘと他の荷重幅Ｐにおける積ｄαとの差は、図４に示す荷重幅Ｐ８における１階微分値ｄｍａｘと他の荷重幅Ｐにおける１階微分値ｄとの差や、図５に示す荷重幅Ｐ８における２階微分値ｄ２ｍａｘと他の荷重幅Ｐにおける２階微分値ｄ２との差に比べて大きい。このため、荷重幅Ｐ８が本来の急増点に相当する可能性が高いといえる。 FIG. 6 is a diagram showing the relationship between the load width P and the dissipated energy q shown in FIG. In FIG. 6, the product dα is plotted with "*".
As shown in FIG. 6, the product dα is the maximum value dα max in the load width P8 , so the load width P8 is estimated as the fatigue limit of the object to be measured. The difference between the product dα max at the load width P 8 and the product dα at the other load width P is the first derivative value d max at the load width P 8 and the first derivative value d at the other load width P shown in FIG. and the difference between the second derivative value d2 max in the load width P8 and the second derivative value d2 in the other load width P shown in FIG. Therefore, it can be said that there is a high possibility that the load width P8 corresponds to the original rapid increase point.

以上に説明した第１実施形態に係る疲労限度推定方法によれば、疲労限度推定ステップＳ２において、１階微分値ｄ、２階微分値ｄ２、及び、１階微分値ｄと２階微分値ｄ２との積ｄαの３つのパラメータのうち、いずれか１つのパラメータの最大値が得られた荷重幅Ｐを被測定物の疲労限度として推定するため、被測定物の疲労限度を精度良く推定可能である。
特に、第１実施形態に係る疲労限度推定方法によれば、１階微分値ｄの最大値ｄｍａｘ、２階微分値ｄ２の最大値ｄ２ｍａｘ、１階微分値ｄと２階微分値ｄ２との積ｄαの最大値ｄαｍａｘの順に、被測定物の疲労限度を推定するのに用いるパラメータを検討するため、例えば、１階微分値ｄの最大値ｄｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定することになった場合（最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除く全ての比ｄ＿ｒａｔｅが第１しきい値Ｔｈ１以下である場合）には、２階微分値ｄ２や、１階微分値ｄと２階微分値ｄ２との積ｄαを算出する必要がなく、推定の効率を高めることが可能である。同様に、２階微分値ｄ２の最大値ｄ２ｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定することになった場合（最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除く全ての比ｄ２＿ｒａｔｅが第２しきい値Ｔｈ２以下である場合）には、１階微分値ｄと２階微分値ｄ２との積ｄαを算出する必要がなく、推定の効率を高めることが可能である。 According to the fatigue limit estimation method according to the first embodiment described above, in the fatigue limit estimation step S2, the first differential value d, the second differential value d2, and the first differential value d and the second differential value d2 Since the load width P at which the maximum value of any one of the three parameters of the product dα is obtained is estimated as the fatigue limit of the object to be measured, the fatigue limit of the object to be measured can be accurately estimated. be.
In particular, according to the fatigue limit estimation method according to the first embodiment, the maximum value d max of the first differential value d, the maximum value d2 max of the second differential value d2, the first differential value d and the second differential value d2 In order to consider the parameters used for estimating the fatigue limit of the object to be measured in order of the maximum value dα max of the product dα of When estimating as the fatigue limit of the measured object (when all ratios d_rate except the ratio d_rate for the maximum value d max are equal to or less than the first threshold Th1), the second derivative value d2, Since it is not necessary to calculate the product dα of the first derivative value d and the second derivative value d2, the estimation efficiency can be improved. Similarly, when the load width P at which the maximum value d2 max of the second derivative value d2 is obtained is estimated as the fatigue limit of the object to be measured (all ratios d2_rate is equal to or less than the second threshold value Th2), it is not necessary to calculate the product dα of the first-order differential value d and the second-order differential value d2, and the estimation efficiency can be improved.

＜第２実施形態＞
図７は、第２実施形態に係る疲労限度推定方法のステップを概略的に示すフロー図である。
図７に示すように、第２実施形態に係る疲労限度推定方法も、第１実施形態と同様に、関係算出ステップＳ１と、疲労限度推定ステップＳ２’と、を有する。ただし、疲労限度推定ステップＳ２’の内容が第１実施形態の疲労限度推定ステップＳ２と異なる。以下、疲労限度推定ステップＳ２’について、第１実施形態の疲労限度推定ステップＳ２と同じ点については適宜説明を省略し、主として第１実施形態と異なる点を説明する。 <Second embodiment>
FIG. 7 is a flow diagram schematically showing the steps of the fatigue limit estimation method according to the second embodiment.
As shown in FIG. 7, the fatigue limit estimation method according to the second embodiment also has a relationship calculation step S1 and a fatigue limit estimation step S2', like the first embodiment. However, the contents of the fatigue limit estimation step S2' differ from the fatigue limit estimation step S2 of the first embodiment. Hereinafter, regarding the fatigue limit estimation step S2', description of the same points as the fatigue limit estimation step S2 of the first embodiment will be omitted as appropriate, and differences from the first embodiment will be mainly described.

[疲労限度推定ステップＳ２’]
疲労限度推定ステップＳ２’でも、第１実施形態の疲労限度推定ステップＳ２と同様に、荷重幅Ｐ毎の１階微分値ｄ、荷重幅Ｐ毎の２階微分値ｄ２、及び、荷重幅Ｐ毎の１階微分値ｄと２階微分値ｄ２との積ｄαの３つのパラメータのうち、いずれか１つのパラメータの最大値が得られた荷重幅Ｐを被測定物の疲労限度として推定するが、具体的には、以下に説明する各ステップを実行する。 [Fatigue limit estimation step S2']
In the fatigue limit estimation step S2', similarly to the fatigue limit estimation step S2 of the first embodiment, the first derivative value d for each load width P, the second derivative value d2 for each load width P, and each load width P Among the three parameters of the product dα of the first derivative value d and the second derivative value d2, the load width P at which the maximum value of any one parameter is obtained is estimated as the fatigue limit of the object to be measured. Specifically, each step described below is executed.

図７に示すように、疲労限度推定ステップＳ２’では、まず、関係算出ステップＳ１で算出した関係（図３（ｂ）参照）を荷重幅Ｐで１階微分して荷重幅Ｐ毎の１階微分値ｄを算出し、１階微分値ｄの最大値ｄｍａｘに対する１階微分値ｄの比ｄ＿ｒａｔｅを荷重幅Ｐ毎に算出すると共に、関係算出ステップＳ１で算出した関係（図３（ｂ）参照）を荷重幅Ｐで２階微分して荷重幅Ｐ毎の２階微分値ｄ２を算出し、２階微分値ｄ２の最大値ｄ２ｍａｘに対する２階微分値ｄの比ｄ２＿ｒａｔｅを荷重幅Ｐ毎に算出する（図７のステップＳ２１’）。
そして、以下の条件（ａ）～（ｃ）を満足するか否かを判定する（図７のステップＳ２２’）。
（ａ）最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除く全ての比ｄ＿ｒａｔｅが第１しきい値Ｔｈ１以下である。
（ｂ）最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除く全ての比ｄ２＿ｒａｔｅが第２しきい値Ｔｈ２以下である。
（ｃ）最大値ｄｍａｘが得られた荷重幅Ｐと最大値ｄ２ｍａｘが得られた荷重幅Ｐとが等しい。
上記の条件（ａ）～（ｃ）を全て満足する場合（図７のステップＳ２２’において「Ｙｅｓ」の場合）には、最大値ｄｍａｘ及び最大値ｄ２ｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定する（図２のステップＳ２３’）。一方、上記の条件（ａ）～（ｃ）のいずれかを満足しない場合（図２のステップＳ２２’において「Ｎｏ」の場合）には、ステップＳ２４’に進む。 As shown in FIG. 7, in the fatigue limit estimation step S2′, first, the relationship calculated in the relationship calculation step S1 (see FIG. 3B) is first-order differentiated by the load width P, and the first-order The differential value d is calculated, the ratio d_rate of the first differential value d to the maximum value d max of the first differential value d is calculated for each load width P, and the relationship calculated in the relationship calculation step S1 (Fig. 3 (b) ) is second-order differentiated with the load width P to calculate the second-order differential value d2 for each load width P, and the ratio d2_rate of the second-order differential value d to the maximum value d2 max of the second-order differential value d2 is calculated for each load width P (step S21' in FIG. 7).
Then, it is determined whether or not the following conditions (a) to (c) are satisfied (step S22' in FIG. 7).
(a) All the ratios d_rate except the ratio d_rate for the maximum value d max are less than or equal to the first threshold Th1.
(b) all ratios d2_rate except the ratio d2_rate for the maximum value d2 max are less than or equal to the second threshold Th2;
(c) The load width P at which the maximum value dmax is obtained is equal to the load width P at which the maximum value d2max is obtained.
When all of the above conditions (a) to (c) are satisfied (“Yes” in step S22′ of FIG. 7), the load width P for which the maximum value d max and the maximum value d2 max are obtained is applied. It is estimated as the fatigue limit of the measured object (step S23' in FIG. 2). On the other hand, if any of the above conditions (a) to (c) is not satisfied ("No" in step S22' of FIG. 2), the process proceeds to step S24'.

前述の図４に示す例では、荷重幅Ｐ１０における１階微分値ｄ１０についての比ｄ＿ｒａｔｅ１０、荷重幅Ｐ１４における１階微分値ｄ１４についての比ｄ＿ｒａｔｅ１４及び荷重幅Ｐ１６における１階微分値ｄ１６についての比ｄ＿ｒａｔｅ１６のいずれもが０．５よりも大きい。このため、第１しきい値Ｔｈ１＝０．５とすると、最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除くいずれかの比ｄ＿ｒａｔｅが第１しきい値Ｔｈ１を超えることになるため、上記の条件（ａ）を満足しないことになる。
また、前述の図５に示す例では、荷重幅Ｐ６における２階微分値ｄ２６についての比ｄ２＿ｒａｔｅ６、及び、荷重幅Ｐ１０における２階微分値ｄ２１０についての比ｄ２＿ｒａｔｅ１０のいずれもが０．５よりも大きい。このため、第２しきい値Ｔｈ２＝０．５とすると、最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除くいずれかの比ｄ２＿ｒａｔｅが第２しきい値Ｔｈ２を超えることになるため、上記の条件（ｂ）を満足しないことになる。
さらに、前述の図４及び図５に示す例では、最大値ｄｍａｘが得られた荷重幅Ｐと最大値ｄ２ｍａｘが得られた荷重幅Ｐとが共に荷重幅Ｐ８で等しいため、上記の条件（ｃ）を満足することになる。
したがって、前述の図４及び図５に示す例では、上記の条件（ａ）～（ｃ）のうち、条件（ａ）及び（ｂ）を満足しないため、ステップＳ２４’に進むことになる。 In the example shown in FIG. 4 described above, the ratio d_rate 10 for the first differential value d 10 in the load width P 10 , the ratio d_rate 14 for the first differential value d 14 in the load width P 14, and the first order in the load width P 16 Any of the ratios d_rate 16 for the differential value d 16 is greater than 0.5. Therefore, if the first threshold value Th1=0.5, any ratio d_rate other than the ratio d_rate for the maximum value d max exceeds the first threshold value Th1. ) is not satisfied.
Further, in the example shown in FIG. 5 described above, both the ratio d2_rate 6 for the second derivative value d2 6 in the load width P 6 and the ratio d2_rate 10 for the second derivative value d2 10 in the load width P 10 are Greater than 0.5. Therefore, if the second threshold Th2=0.5, any ratio d2_rate other than the ratio d2_rate for the maximum value d2 max exceeds the second threshold Th2. ) is not satisfied.
Furthermore, in the examples shown in FIGS. 4 and 5, the load width P at which the maximum value dmax is obtained and the load width P at which the maximum value d2max is obtained are both equal to the load width P8 . Condition (c) is satisfied.
Therefore, in the example shown in FIGS. 4 and 5, of the above conditions (a) to (c), conditions (a) and (b) are not satisfied, so the process proceeds to step S24'.

疲労限度推定ステップＳ２’のステップＳ２４’では、第１実施形態の疲労限度推定ステップＳ２のステップＳ２７と同様に、１階微分値ｄと２階微分値ｄ２との積ｄαを算出し（１階微分値ｄと２階微分値ｄ２とが共に負の値である場合には、１階微分値ｄと２階微分値ｄ２との積ｄαの算出結果は、強制的にｄα＝０とする）、この積ｄαの最大値ｄαｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定する。
前述の図６に示す例では、荷重幅Ｐ８において、積ｄαが最大値ｄαｍａｘとなっているため、荷重幅Ｐ８が被測定物の疲労限度として推定されることになる。 In step S24' of fatigue limit estimation step S2', similarly to step S27 of fatigue limit estimation step S2 of the first embodiment, the product dα of the first derivative value d and the second derivative value d2 is calculated (first order When both the differential value d and the second differential value d2 are negative values, the calculation result of the product dα of the first differential value d and the second differential value d2 is forcibly set to dα=0) , the load width P at which the maximum value dα max of the product dα is obtained is estimated as the fatigue limit of the object to be measured.
In the example shown in FIG. 6 described above, the product dα is the maximum value dα max in the load width P8 , so the load width P8 is estimated as the fatigue limit of the object to be measured.

以上に説明した第２実施形態に係る疲労限度推定方法によれば、疲労限度推定ステップＳ２’において、１階微分値ｄ、２階微分値ｄ２、及び、１階微分値ｄと２階微分値ｄ２との積ｄαの３つのパラメータのうち、いずれか１つのパラメータの最大値が得られた荷重幅Ｐを被測定物の疲労限度として推定するため、被測定物の疲労限度を精度良く推定可能である。
特に、第２実施形態に係る疲労限度推定方法によれば、１階微分値ｄの最大値ｄｍａｘ及び２階微分値ｄ２の最大値ｄ２ｍａｘ、１階微分値ｄと２階微分値ｄ２との積ｄαの最大値ｄαｍａｘの順に、被測定物の疲労限度を推定するのに用いるパラメータを検討するため、例えば、１階微分値ｄの最大値ｄｍａｘ及び２階微分値ｄ２の最大値ｄ２ｍａｘが得られた荷重幅Ｐを被測定物の疲労限度として推定することになった場合（最大値ｄｍａｘについての比ｄ＿ｒａｔｅを除く全ての比ｄ＿ｒａｔｅが第１しきい値Ｔｈ１以下であり、最大値ｄ２ｍａｘについての比ｄ２＿ｒａｔｅを除く全ての比ｄ２＿ｒａｔｅが第２しきい値Ｔｈ２以下であり、なお且つ、最大値ｄｍａｘが得られた荷重幅Ｐと最大値ｄ２ｍａｘが得られた荷重幅Ｐとが等しい場合）には、１階微分値ｄと２階微分値ｄ２との積ｄαを算出する必要がなく、推定の効率を高めることが可能である。 According to the fatigue limit estimation method according to the second embodiment described above, in the fatigue limit estimation step S2', the first differential value d, the second differential value d2, and the first differential value d and the second differential value Among the three parameters of the product dα with d2, the load width P at which the maximum value of any one of the parameters is obtained is estimated as the fatigue limit of the object to be measured, so the fatigue limit of the object to be measured can be accurately estimated. is.
In particular, according to the fatigue limit estimation method according to the second embodiment, the maximum value d max of the first differential value d and the maximum value d2 max of the second differential value d2, the first differential value d and the second differential value d2 In order to consider the parameters used for estimating the fatigue limit of the object to be measured in the order of the maximum value dα max of the product dα of When estimating the load width P for which d2 max is obtained as the fatigue limit of the object to be measured (all ratios d_rate except the ratio d_rate for the maximum value d max are less than or equal to the first threshold Th1, All the ratios d2_rate except the ratio d2_rate for the maximum value d2 max are equal to or less than the second threshold value Th2, and the load width P at which the maximum value d max is obtained and the load width at which the maximum value d2 max is obtained is equal to P), there is no need to calculate the product dα of the first-order differential value d and the second-order differential value d2, and the estimation efficiency can be improved.

なお、本発明に係る疲労限度推定方法は、以上に説明した第１実施形態又は第２実施形態に係る疲労限度推定方法に限るものではない。荷重幅Ｐと散逸エネルギーｑとの関係から得られる、１階微分値ｄ、２階微分値ｄ２、及び、１階微分値ｄと２階微分値ｄ２との積ｄαの３つのパラメータのうち、いずれか１つのパラメータの最大値が得られた荷重幅Ｐを被測定物の疲労限度として推定する限りにおいて、種々の態様を採用可能である。 In addition, the fatigue limit estimation method according to the present invention is not limited to the fatigue limit estimation method according to the first embodiment or the second embodiment described above. Among the three parameters of the first differential value d, the second differential value d2, and the product dα of the first differential value d and the second differential value d2 obtained from the relationship between the load width P and the dissipated energy q, Various modes can be adopted as long as the load width P at which the maximum value of any one parameter is obtained is estimated as the fatigue limit of the object to be measured.

＜実施例＞
以下、第１実施形態に係る疲労限度推定方法を実行した実施例について説明する。
図８は、本実施例の概要を説明する説明図である。図８（ａ）は本実施例で用いた試験片を模式的に示す図であり、図８（ｂ）は図８（ａ）に示す試験片の疲労試験を行って求めたＳ－Ｎ線図である。
図８（ａ）に示すように、試験片としては、２枚の鋼板の一部を重ね、この重ね代にスポット溶接を施して２枚の鋼板を接合したものを用いた。
本実施例の関係算出ステップＳ１では、この試験片を、繰り返し荷重を付加する疲労試験機に取り付け、荷重幅Ｐ＝０．８～２．４ｋＮ（応力比：０．０５、繰り返し周波数：７Ｈｚ）の範囲で段階的に荷重幅Ｐを増加させ、各荷重幅Ｐの繰り返し荷重を２０００サイクルずつ付加した。この状態で、赤外線撮像装置を用いて試験片のスポット溶接部の周辺を撮像することで、繰り返し荷重毎に試験片の温度分布の時間的変化を測定した。赤外線撮像装置としては、ＦＬＩＲ社製のＸ６５８０シリーズを用い、フレームレートを１４９Ｈｚに設定して、繰り返し荷重毎に１０ｓｅｃ間の測定を行なった（１０ｓｅｃ間における温度分布の変化を測定した）。そして、ＦＬＩＲ社製のＡｌｔａｉｒＬＩを用いて、散逸エネルギー分布を算出した。前述の図３（ａ）は、上記の手順で算出した散逸エネルギー分布である。前述の図３（ｂ）の縦軸は、図３（ａ）に示す破線Ｓで囲んだ１５×１５ピクセルの画素領域（破壊起点が発生し得ると考えられるスポット溶接部（応力集中部）に相当する画素領域）における散逸エネルギーの平均値である。 <Example>
An example in which the fatigue limit estimation method according to the first embodiment is executed will be described below.
FIG. 8 is an explanatory diagram for explaining the outline of this embodiment. FIG. 8(a) is a diagram schematically showing the test piece used in this example, and FIG. 8(b) is an SN line obtained by performing a fatigue test on the test piece shown in FIG. 8(a) It is a diagram.
As shown in FIG. 8( a ), as a test piece, two steel plates were partially overlapped and spot-welded in the overlapping portion to join the two steel plates.
In the relationship calculation step S1 of the present embodiment, this test piece is attached to a fatigue tester that applies a repeated load, and the load width P = 0.8 to 2.4 kN (stress ratio: 0.05, repetition frequency: 7 Hz). The load width P was increased stepwise within the range of , and a repeated load of each load width P was applied for 2000 cycles each. In this state, the area around the spot-welded portion of the test piece was imaged using an infrared imaging device to measure the temporal change in the temperature distribution of the test piece for each repeated load. FLIR's X6580 series was used as the infrared imaging device, the frame rate was set to 149 Hz, and measurement was performed for 10 seconds for each repeated load (change in temperature distribution was measured for 10 seconds). Then, the dissipated energy distribution was calculated using AltairLI manufactured by FLIR. FIG. 3(a) described above is the dissipated energy distribution calculated by the above procedure. The vertical axis of FIG. 3(b) described above is the pixel area of 15×15 pixels surrounded by the dashed line S shown in FIG. is the average value of the dissipated energy in the corresponding pixel area).

前述の図４に示す１階微分値ｄは、本実施例の疲労限度推定ステップＳ２で算出した１階微分値ｄである。
前述の図５に示す２階微分値ｄ２は、本実施例の疲労限度推定ステップＳ２で算出した２階微分値ｄ２である。
前述の図６に示す積ｄαは、本実施例の疲労限度推定ステップＳ２で算出した積ｄαである。
したがって、本実施例では、荷重幅Ｐ８が被測定物の疲労限度として推定されることになる。 The first-order differential value d shown in FIG. 4 described above is the first-order differential value d calculated in the fatigue limit estimation step S2 of this embodiment.
The second-order differential value d2 shown in FIG. 5 described above is the second-order differential value d2 calculated in the fatigue limit estimation step S2 of this embodiment.
The product dα shown in FIG. 6 described above is the product dα calculated in the fatigue limit estimation step S2 of this embodiment.
Therefore, in this embodiment, the load width P8 is estimated as the fatigue limit of the object to be measured.

図８（ｂ）に示すように、疲労試験の結果、荷重幅Ｐ７では試験片は未破断であったが、荷重幅Ｐ９に増加することで破断した。このため、荷重幅Ｐ７と荷重幅Ｐ９との中間の値である荷重幅Ｐ８が疲労限度であることが分かる。したがって、第１実施形態に係る疲労限度推定方法で推定した疲労限度は、Ｓ－Ｎ線図から求めた疲労限度と一致し、精度良く推定可能であることが確認できた。 As shown in FIG. 8(b), as a result of the fatigue test, the test piece was not fractured at the load width P7 , but was fractured when the load width was increased to P9 . Therefore, it can be seen that the load width P8, which is an intermediate value between the load width P7 and the load width P9 , is the fatigue limit. Therefore, it was confirmed that the fatigue limit estimated by the fatigue limit estimation method according to the first embodiment matches the fatigue limit obtained from the SN diagram, and can be estimated with high accuracy.

ｄ・・・１階微分値
ｄ２・・・２階微分値
ｄα・・・１階微分値と２階微分値との積
Ｐ・・・荷重幅
ｑ・・・散逸エネルギー
Ｓ１・・・関係算出ステップ
Ｓ２、Ｓ２’・・・疲労限度推定ステップ d... 1st order differential value d2... 2nd order differential value dα... Product of 1st order differential value and 2nd order differential value P... Load width q... Dissipated energy S1... Relationship calculation Step S2, S2' ... fatigue limit estimation step

Claims (4)

被測定物に荷重幅Ｐの異なる繰り返し荷重を順次付加しながら、赤外線撮像装置を用いて前記被測定物を撮像することで、前記繰り返し荷重毎に前記被測定物の温度分布の時間的変化を測定し、前記繰り返し荷重毎に測定した前記被測定物の温度分布の時間的変化に基づき、前記繰り返し荷重毎に前記被測定物の散逸エネルギー分布を算出し、前記繰り返し荷重毎に算出した前記被測定物の散逸エネルギー分布に基づき、荷重幅Ｐと散逸エネルギーｑとの関係を算出する関係算出ステップと、
前記関係算出ステップで算出した関係を前記荷重幅Ｐで１階微分して得られる前記荷重幅Ｐ毎の１階微分値ｄ、前記関係算出ステップで算出した関係を前記荷重幅Ｐで２階微分して得られる前記荷重幅Ｐ毎の２階微分値ｄ２、及び、前記荷重幅Ｐ毎の前記１階微分値ｄと前記２階微分値ｄ２との積ｄαの３つのパラメータのうち、いずれか１つのパラメータの最大値が得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定する疲労限度推定ステップと、を有する、
疲労限度推定方法。 By taking an image of the object to be measured using an infrared imaging device while sequentially applying repeated loads having different load widths P to the object to be measured, temporal changes in the temperature distribution of the object to be measured for each of the repeated loads can be obtained. Based on the temporal change in the temperature distribution of the object measured for each repeated load, the dissipated energy distribution of the object to be measured is calculated for each repeated load, and the measured object calculated for each repeated load a relationship calculation step of calculating the relationship between the load width P and the dissipated energy q based on the dissipated energy distribution of the measured object;
A first-order differential value d for each load width P obtained by first-order differentiating the relationship calculated in the relationship calculation step with the load width P, and second-order differentiation of the relationship calculated in the relationship calculation step with the load width P and the product dα of the first differential value d and the second differential value d2 for each load width P, which are obtained by a fatigue limit estimation step of estimating the load width P for which the maximum value of one parameter is obtained as the fatigue limit of the object to be measured;
Fatigue limit estimation method. 前記疲労限度推定ステップにおいて、前記１階微分値ｄと前記２階微分値ｄ２との積ｄαの最大値ｄαｍａｘが得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定する、
請求項１に記載の疲労限度推定方法。 In the fatigue limit estimation step, the load width P for which the maximum value dα max of the product dα of the first differential value d and the second differential value d2 is obtained is estimated as the fatigue limit of the object to be measured.
The fatigue limit estimation method according to claim 1. 前記疲労限度推定ステップにおいて、
前記１階微分値ｄの最大値ｄｍａｘに対する前記１階微分値ｄの比ｄ＿ｒａｔｅを前記荷重幅Ｐ毎に算出し、前記最大値ｄｍａｘについての前記比ｄ＿ｒａｔｅを除く全ての前記比ｄ＿ｒａｔｅが第１しきい値以下である場合には、前記最大値ｄｍａｘが得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定し、
前記最大値ｄｍａｘについての前記比ｄ＿ｒａｔｅを除くいずれかの前記比ｄ＿ｒａｔｅが前記第１しきい値を超える場合には、前記２階微分値ｄ２の最大値ｄ２ｍａｘに対する前記２階微分値ｄ２の比ｄ２＿ｒａｔｅを前記荷重幅Ｐ毎に算出し、前記最大値ｄ２ｍａｘについての前記比ｄ２＿ｒａｔｅを除く全ての前記比ｄ２＿ｒａｔｅが第２しきい値以下である場合には、前記最大値ｄ２ｍａｘが得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定し、
前記最大値ｄｍａｘについての前記比ｄ＿ｒａｔｅを除くいずれかの前記比ｄ＿ｒａｔｅが前記第１しきい値を超え、且つ、前記最大値ｄ２ｍａｘについての前記比ｄ２＿ｒａｔｅを除くいずれかの前記比ｄ２＿ｒａｔｅが前記第２しきい値を超える場合には、前記１階微分値ｄと前記２階微分値ｄ２との積ｄαの最大値ｄαｍａｘが得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定する、
請求項１に記載の疲労限度推定方法。 In the fatigue limit estimation step,
A ratio d_rate of the first differential value d to the maximum value d max of the first differential value d is calculated for each load width P, and all the ratios d_rate except the ratio d_rate for the maximum value d max are If it is equal to or less than 1 threshold, estimate the load width P for which the maximum value d max is obtained as the fatigue limit of the object to be measured,
If any of the ratios d_rate except the ratio d_rate for the maximum value dmax exceeds the first threshold value, the second derivative d2 for the maximum value d2max of the second derivative d2 A ratio d2_rate is calculated for each load width P, and when all the ratios d2_rate except the ratio d2_rate for the maximum value d2 max are equal to or less than a second threshold value, the maximum value d2 max is obtained. Estimate the load width P as the fatigue limit of the object to be measured,
any ratio d_rate other than the ratio d_rate for the maximum value d max exceeds the first threshold and any ratio d2_rate other than the ratio d2_rate for the maximum value d2 max exceeds the When the second threshold value is exceeded, the load width P at which the maximum value dα max of the product dα of the first differential value d and the second differential value d2 is obtained is taken as the fatigue limit of the object to be measured. presume,
The fatigue limit estimation method according to claim 1. 前記疲労限度推定ステップにおいて、
前記１階微分値ｄの最大値ｄｍａｘに対する前記１階微分値ｄの比ｄ＿ｒａｔｅを前記荷重幅Ｐ毎に算出すると共に、前記２階微分値ｄ２の最大値ｄ２ｍａｘに対する前記２階微分値ｄ２の比ｄ２＿ｒａｔｅを前記荷重幅Ｐ毎に算出し、前記最大値ｄｍａｘについての前記比ｄ＿ｒａｔｅを除く全ての前記比ｄ＿ｒａｔｅが第１しきい値以下であり、前記最大値ｄ２ｍａｘについての前記比ｄ２＿ｒａｔｅを除く全ての前記比ｄ２＿ｒａｔｅが第２しきい値以下であり、なお且つ、前記最大値ｄｍａｘが得られた前記荷重幅Ｐと前記最大値ｄ２ｍａｘが得られた前記荷重幅Ｐとが等しいという条件を満足する場合には、前記最大値ｄｍａｘ及び前記最大値ｄ２ｍａｘが得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定し、
前記条件を満足しない場合には、前記１階微分値ｄと前記２階微分値ｄ２との積ｄαの最大値ｄαｍａｘが得られた前記荷重幅Ｐを前記被測定物の疲労限度として推定する、
請求項１に記載の疲労限度推定方法。 In the fatigue limit estimation step,
A ratio d_rate of the first differential value d to the maximum value d max of the first differential value d is calculated for each load width P, and the second differential value d2 to the maximum value d2 max of the second differential value d2 A ratio d2_rate of is calculated for each load width P, and all the ratios d_rate except the ratio d_rate for the maximum value dmax are equal to or less than a first threshold value, and the ratio d2_rate for the maximum value d2max is equal to or less than the second threshold, and the load width P at which the maximum value dmax is obtained is equal to the load width P at which the maximum value d2max is obtained. When the condition is satisfied, the load width P for which the maximum value d max and the maximum value d2 max are obtained is estimated as the fatigue limit of the object to be measured,
If the condition is not satisfied, the load width P at which the maximum value dα max of the product dα of the first differential value d and the second differential value d2 is obtained is estimated as the fatigue limit of the object to be measured. ,
The fatigue limit estimation method according to claim 1.
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