JP2016024056A - Fatigue limit stress specification system and method for specifying fatigue limit stress - Google Patents
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本発明は、繰り返し応力振幅を測定対象物に加えて、材料内部のエネルギー散逸によって生じる平均温度上昇量の一定領域内における分布を赤外線サーモグラフィによって測定する散逸エネルギー測定手段を用いた疲労限度応力特定システムおよび疲労限度応力特定方法に関するものである。 The present invention relates to a fatigue limit stress identification system using a dissipative energy measuring means for applying a repeated stress amplitude to an object to be measured and measuring a distribution of an average temperature rise caused by energy dissipation within a material within a certain region by infrared thermography. And a fatigue limit stress identification method.
従来、疲労限度応力の特定方法としては、例えば、非特許文献１〜５、特許文献１，２に記載されているようなものが報告されている。
図１３は、非特許文献１に示された疲労限度応力の特定方法を示している。
Conventionally, methods for identifying fatigue limit stress have been reported, for example, as described in Non-Patent Documents 1 to 5 and Patent Documents 1 and 2.
FIG. 13 shows a method for specifying the fatigue limit stress shown in Non-Patent Document 1.
これは、ＸＣ５５スチール試験片に加えられる周期的な引張−圧縮荷重を段階的に変化させて、温度上昇量を赤外線サーモグラフィで測定した結果を示す。荷重３８０Ｍｐａ付近で、荷重に対する温度上昇量の傾きが変化する様子を示している。非特許文献１では、この傾きが変化する点がＸＣ５５スチール試験片の疲労限度応力荷重とほぼ一致することを述べている。 This shows the result of measuring the amount of temperature increase by infrared thermography by changing the periodic tensile-compressive load applied to the XC55 steel test piece stepwise. A state is shown in which the gradient of the temperature rise with respect to the load changes in the vicinity of the load of 380 Mpa. Non-Patent Document 1 describes that the point at which the slope changes substantially matches the fatigue limit stress load of the XC55 steel specimen.
非特許文献２では、焼鈍された鋳物（ＵＮＩ３５４５−６８）でノッチなしの試験片、および棒溶接接合された自動車部品に対して、非特許文献１と同様の報告がされている。
非特許文献３では、クランクシャフトなど自動車部品への適応例が示されている。
In Non-Patent Document 2, a report similar to that in Non-Patent Document 1 is reported for an annealed casting (UNI 3545-68) and a test piece without a notch, and an automobile part joined by bar welding.
Non-Patent Document 3 shows an application example to automobile parts such as a crankshaft.
非特許文献４では、ＸＣ４８（カーボン含有量０．４８％の炭素鋼）スチール、残留応力を除去したステンレス鋼ＳＵＳ３１６Ｌ、及びアルミニウムＡｌ７０１０、Ａｌ２０２４（Ａｌ−Ｃｕ系）について、試験片レベルであるが非特許文献１と同様の疲労限度応力の特定方法が述べられている。 In Non-Patent Document 4, although XC48 (carbon steel with a carbon content of 0.48%) steel, stainless steel SUS316L from which residual stress has been removed, and aluminum Al7010 and Al2024 (Al-Cu system) are at the test piece level, A method for specifying the fatigue limit stress similar to that of Patent Document 1 is described.
また、非特許文献５では、鋼のエネルギー散逸を疲労限度応力以下の荷重では擬弾性変化に関連付け、応力の二乗に比例するとして二次の関数による近似線を用い、疲労限度応力以上の荷重ではミクロな塑性変形と関連付け、応力を負荷したときにミクロな塑性変形が単位体積あたりいくつの粒子において発生するのかを確率分布を求めることによって、応力の累乗に比例することが述べられている。
特許文献１では、応力集中係数を評価する工程、散逸エネルギーを測定する工程、疲労限度を特定する工程から構成される。応力集中係数を評価する工程では応力集中係数３を基準値として、それ以上、未満であることを判断する。散逸エネルギーを測定する工程では、撮影された温度画像を加振周波数の２〜３倍の周波数で高速フーリエ変換することで得られる温度振幅画像、または応力分布画像を用いて、温度振幅または応力振幅の分布画像の最大を示すピクセルに着目し、散逸エネルギー曲線を作成することが記載されている。疲労限度を特定する工程では、作成された散逸エネルギー曲線を構成する測定点の内、少なくとも３点以上用いて、統計処理によって引かれる近似線の交点によって求められることが記載されている。更に、応力集中係数を評価する工程で求められた情報をもとに、応力集中係数が３以上であれば散逸エネルギー曲線の屈曲点の初段を疲労限度とし、それ未満では初段以降の屈曲点を疲労限度とすることが記載されている。また、特許文献１で示される疲労限度応力の特定方法は、少なくとも１つ以上のボルトまたはネジからなる締結体と、締結体によって締結される１つ以上の被締結体から構成される金属締結体へも適応可能で、それらを構成する材料は主成分が主に鉄からなる、炭素鋼、オーステナイト系ステンレス鋼であることが記載されている。
In Non-Patent Document 5, the energy dissipation of steel is related to pseudoelastic change for loads below the fatigue limit stress, and an approximate line based on a quadratic function is used as proportional to the square of the stress. In connection with micro plastic deformation, it is stated that the probability distribution is proportional to the power of stress by obtaining the probability distribution of how many particles per unit volume the micro plastic deformation occurs when stress is applied.
Patent Document 1 includes a step of evaluating a stress concentration factor, a step of measuring dissipation energy, and a step of specifying a fatigue limit. In the step of evaluating the stress concentration factor, the stress concentration factor 3 is used as a reference value, and it is determined that the stress concentration factor is more than or less than that. In the step of measuring the dissipated energy, the temperature amplitude or the stress amplitude is obtained by using a temperature amplitude image or a stress distribution image obtained by performing a fast Fourier transform on the photographed temperature image at a frequency two to three times the excitation frequency. It is described that a dissipative energy curve is created by focusing on a pixel indicating the maximum of the distribution image. It is described that, in the step of specifying the fatigue limit, it is determined by the intersection of approximate lines drawn by statistical processing using at least three or more measurement points constituting the created dissipation energy curve. Furthermore, based on the information obtained in the process of evaluating the stress concentration factor, if the stress concentration factor is 3 or more, the first stage of the inflection point of the dissipative energy curve is set as the fatigue limit. It is stated that it is a fatigue limit. In addition, the method for specifying the fatigue limit stress disclosed in Patent Document 1 is a metal fastening body including a fastening body composed of at least one bolt or screw and one or more fastened bodies fastened by the fastening body. It is described that the materials constituting them are carbon steel and austenitic stainless steel whose main component is mainly iron.
特許文献２では、散逸エネルギーを測定する工程、疲労限度を特定する工程から構成される。散逸エネルギーを測定する工程では、散逸エネルギーを測定するタイミングについて具体的に記載され、散逸エネルギーとひずみ量で表されるグラフのヒステリシスループの面積が一定、もしくは、発生応力範囲の周波数成分の１倍、２倍、３倍の周波数成分が一定変化になるタイミングで測定することが記載されている。また、この時着目するピクセルについては主応力和もしくは、発生応力範囲の周波数成分が最大を示すピクセルである。疲労限度を特定する工程では、疲労限度の特定に用いるデータ範囲について、高サイクル疲労である荷重領域か、横軸を荷重、縦軸を温度変化量もしくは主応力和のグラフ、横軸を主応力和、縦軸を散逸エネルギーとしたグラフで急激な変化をしない領域と記載されている。更に、疲労限度の特定に用いる近似線は、２本の近似線と近似に用いるデータ点の残差の二乗和が最小となるように引かれることが記載されている。 Patent Document 2 includes a process for measuring dissipated energy and a process for specifying a fatigue limit. In the process of measuring the dissipated energy, the timing for measuring the dissipated energy is specifically described, and the area of the hysteresis loop of the graph represented by the dissipated energy and the strain amount is constant, or 1 time the frequency component of the generated stress range It is described that the measurement is performed at a timing at which the frequency components of 2 times and 3 times become constant changes. Further, the pixel of interest at this time is a pixel in which the main stress sum or the frequency component of the generated stress range is maximum. In the process of specifying the fatigue limit, the data range used to specify the fatigue limit is the load region that is high cycle fatigue, the horizontal axis is the load, the vertical axis is the graph of temperature change or principal stress sum, and the horizontal axis is the principal stress. It is described as a region where there is no sudden change in the graph with the sum and dissipated energy on the vertical axis. Furthermore, it is described that the approximate line used for specifying the fatigue limit is drawn so that the sum of squares of the residuals of the two approximate lines and the data point used for the approximation is minimized.
しかしながら、散逸エネルギー測定による疲労限度応力の特定方法については、以前から多くの報告がなされているものの、その多くは研究者各々が独自の主観的判断に基づいた測定および疲労限度応力特定を行っていた。例えば、散逸エネルギーを抽出するピクセルの選択方法や近似線の求め方、使用するデータ範囲など基本的な条件についての決定方法である。 However, although there have been many reports on how to identify fatigue limit stress by measuring dissipative energy, many researchers have made measurements based on their own subjective judgments and identified fatigue limit stress. It was. For example, it is a method for determining basic conditions such as a method for selecting a pixel for extracting dissipated energy, a method for obtaining an approximate line, and a data range to be used.
これらの理由として、散逸エネルギー測定による疲労限度応力の特定方法については、測定対象物の疲労試験から求められた疲労限度応力と散逸エネルギー測定から求められた疲労限度応力の比較による現象論から特定可能かどうかの議論が殆どであった。また、特定に用いられる近似線の引き方も疲労限度応力以下の荷重では擬弾性変化に関連付けられることから二次関数で示されているが、測定データによる裏付けは示されず、鋼が擬似弾性的な変化をしているであろうという推測をもとに二次関数での近似が述べられている。 For these reasons, the method for specifying the fatigue limit stress by measuring the dissipative energy can be specified from the phenomenology by comparing the fatigue limit stress obtained from the fatigue test of the object to be measured and the fatigue limit stress obtained from the dissipated energy measurement. There was almost no debate about whether or not. In addition, the method of drawing the approximate line used for identification is shown by a quadratic function because it is related to the pseudoelastic change at loads below the fatigue limit stress, but it is not supported by the measurement data, and the steel is pseudoelastic. Approximation with a quadratic function is described based on the assumption that it is likely to change.
一方、疲労限度応力以上では、応力を負荷したときにミクロな塑性変形が単位体積あたりいくつの結晶粒において発生するのかを確率分布として求めた結果から、応力の累乗に比例するとしてｎ次の多項式で近似するとしているが、測定データに対して次数を高くすることによってフィッティング性を高めているだけで、決して疲労のメカニズムであるミクロな塑性変形の発生を反映したものではない。 On the other hand, when the stress is greater than the fatigue limit stress, the nth order polynomial is assumed to be proportional to the power of the stress from the result of obtaining the probability distribution of how many crystal grains per unit volume when micro plastic deformation occurs when stress is applied. However, it does not reflect the occurrence of micro plastic deformation, which is a fatigue mechanism, by merely increasing the fitting property by increasing the order of the measurement data.
更に、応用面においても引張、圧縮など荷重の負荷方法によっても異なる結果が得られるなど不明な点が多く、物性値として定性的あるいは定量的に適応可能な範囲が不明である点などが挙げられる。 In addition, there are many unclear points such as different results depending on the load method such as tension and compression in terms of application, and the range that can be applied qualitatively or quantitatively as physical property values is unknown. .
このため、単品部品や非常に単純な部品および複雑な構成の応力集中部に関して疲労限度応力を客観的に特定できる方法およびシステムは無かった。
本発明は、応力集中を有する材料や部品の疲労限度応力を客観的に特定可能な方法およびそれらを実現するシステムを提供することを目的とする。
For this reason, there has been no method and system that can objectively specify the fatigue limit stress for a single component, a very simple component, or a stress concentration portion having a complicated configuration.
It is an object of the present invention to provide a method capable of objectively specifying the fatigue limit stress of a material or part having a stress concentration and a system for realizing the method.
それ故に、本発明の目的は、上記課題を解決するものであり、散逸エネルギーを抽出するピクセルの選択から近似線を表現する関数の次数など基本的な散逸エネルギーによる疲労限度応力特定プロセスや測定対象物の適応可能な範囲を明確にすると共に、高精度に散逸エネルギー測定が可能な疲労限度応力特定システム、および疲労限度応力特定方法を提供することである。 Therefore, an object of the present invention is to solve the above-mentioned problem, and to identify a fatigue limit stress by a basic dissipative energy such as the order of a function expressing an approximate line from selection of a pixel from which the dissipated energy is extracted and a measurement target. It is to provide a fatigue limit stress identification system and a fatigue limit stress identification method capable of clarifying the applicable range of an object and measuring a dissipated energy with high accuracy.
本発明は、疲労限度応力特定システムおよび疲労限度応力特定方法に向けられている。そして、上記目的を達成するために、本発明の疲労限度応力特定システムは、測定対象物に作用させる荷重を段階的に増加させ、前記荷重毎に発生する前記測定対象物の温度振幅を測定する疲労限度応力特定システムであって、測定対象物に対して荷重を繰り返し加える加振機と、前記測定対象物の温度画像を得る赤外線カメラと、前記赤外線カメラから得た前記測定対象物の温度画像を処理するフーリエ変換手段を有する情報処理装置とを備え、前記情報処理装置は、散逸エネルギーを測定する散逸エネルギー測定工程と、前記散逸エネルギー測定工程から得られた測定結果から疲労限度応力を特定する疲労限度応力特定工程を有し、前記散逸エネルギー測定工程は、前記赤外線カメラが撮影した温度画像より、加振の基本周波数の成分および第２高調波の成分の温度振幅画像を取得し、前記第２高調波の成分の温度振幅画像の最大を示す領域内において、前記基本周波数の成分の温度振幅画像に対する荷重特性の傾きが最大であるピクセル領域の散逸エネルギーを抽出する、ことを特徴とする。 The present invention is directed to a fatigue limit stress identification system and a fatigue limit stress identification method. And in order to achieve the said objective, the fatigue limit stress specific system of this invention increases the load made to act on a measurement object in steps, and measures the temperature amplitude of the said measurement object generate | occur | produced for every said load. A fatigue limit stress identification system, a vibrator that repeatedly applies a load to a measurement object, an infrared camera that obtains a temperature image of the measurement object, and a temperature image of the measurement object obtained from the infrared camera An information processing device having a Fourier transform means for processing the energy, and the information processing device specifies a dissipated energy measuring step for measuring the dissipated energy and a fatigue limit stress from the measurement result obtained from the dissipated energy measuring step. A fatigue limit stress specifying step, and the dissipative energy measuring step includes a component of a fundamental frequency of excitation from a temperature image taken by the infrared camera. Temperature amplitude image of the second harmonic component is acquired, and the gradient of the load characteristic with respect to the temperature amplitude image of the fundamental frequency component is maximum in the region indicating the maximum of the temperature amplitude image of the second harmonic component. Extracting the dissipated energy of a pixel region.
前記疲労限度応力特定システムの概要を、一例として図１（ａ）（ｂ）に示す。加振機１ａに固定した測定対象物としての試験片１ｂの温度を赤外線カメラ１ｃによって測定する。赤外線カメラ１ｃから得た温度画像を処理する情報処理装置１ｄは、散逸エネルギー測定工程２１と疲労限度応力特定工程２２を有している。情報処理装置１ｄにはモニタ１ｅが接続されている。 An outline of the fatigue limit stress specifying system is shown in FIGS. 1A and 1B as an example. The temperature of the test piece 1b as the measurement object fixed to the vibration exciter 1a is measured by the infrared camera 1c. The information processing apparatus 1d that processes the temperature image obtained from the infrared camera 1c has a dissipated energy measurement step 21 and a fatigue limit stress identification step 22. A monitor 1e is connected to the information processing apparatus 1d.
散逸エネルギー測定工程２１は、加振の基本周波数ｆの成分およびその２倍の周波数２ｆ（これを第２高調波と称す）の成分の温度振幅画像を取得し、図３（ａ）に示されるように第２高調波の成分の温度振幅画像の最大を示す領域２３内において、図３（ｂ）に示す基本周波数成分の温度振幅画像に対する荷重特性の傾きが最大であるピクセルを選択する。なお、図３（ａ）における仮想線２４は、測定対象物としての試験片１ｂの輪郭を示している。 The dissipative energy measurement step 21 acquires temperature amplitude images of the component of the fundamental frequency f of the vibration and the component of the frequency 2f (referred to as the second harmonic) that is twice that, as shown in FIG. In this way, in the region 23 indicating the maximum temperature amplitude image of the second harmonic component, a pixel having the maximum inclination of the load characteristic with respect to the temperature amplitude image of the fundamental frequency component shown in FIG. 3B is selected. In addition, the virtual line 24 in Fig.3 (a) has shown the outline of the test piece 1b as a measuring object.
疲労限度応力特定工程２２は、横軸に前記加振の基本周波数の成分である温度振幅、縦軸に第２高調波の成分である温度振幅をプロットすることを特徴とする。 The fatigue limit stress specifying step 22 is characterized in that the horizontal axis plots the temperature amplitude that is a component of the fundamental frequency of the excitation, and the vertical axis plots the temperature amplitude that is a second harmonic component.
図４は、横軸に基本周波数の成分の主応力和（Δσ＝−ΔＴ／（ｋｍ・Ｔ）、ΔＴ：温度変化量，ｋｍ：熱弾性係数，Ｔ：絶対温度）、縦軸に加振の基本周波数の第２高調波の成分である温度振幅をプロットした図である。試験片など単純な形状をした測定対象物であれば、加振機などから負荷された荷重と測定対象物に発生する応力は比例するが、実物の測定対象物は接合部や切り欠きなど複雑な形状をしているため、加振機で負荷された荷重と実物に発生する応力は必ずしも比例するとは限らない。一方、第２高調波の成分の温度振幅が得られる部分の基本周波数の成分の温度振幅成分は、測定対象物に発生する応力成分に依存している。そのため、横軸に荷重ではなく、基本周波数の成分の温度振幅を用いることが望ましい。 4, the main stress sum of components of the fundamental frequency on the horizontal axis (Δσ = -ΔT / (k m · T), ΔT: temperature change, k m: thermoelastic coefficient, T: absolute temperature), the longitudinal axis It is the figure which plotted the temperature amplitude which is a component of the 2nd harmonic of the fundamental frequency of excitation. In the case of a measurement object with a simple shape such as a test piece, the load applied from a shaker or the like is proportional to the stress generated in the measurement object, but the actual measurement object is complex, such as a joint or notch. Therefore, the load applied by the vibrator and the stress generated in the actual product are not always proportional. On the other hand, the temperature amplitude component of the fundamental frequency component where the temperature amplitude of the second harmonic component is obtained depends on the stress component generated in the measurement object. Therefore, it is desirable to use the temperature amplitude of the fundamental frequency component instead of the load on the horizontal axis.
疲労限度応力特定工程２２では、自由度調整済み決定係数およびGauss - Newton法によって求められる２本の近似線の交点から疲労限度応力を特定する。
また、疲労限度応力特定工程２２で用いられる近似線は、ｙ＝ａｘｎ＋ｂで表される多項式と直線であることを特徴とする。
In the fatigue limit stress specifying step 22, the fatigue limit stress is specified from the intersection of two approximate lines obtained by the determination coefficient adjusted for the degree of freedom and the Gauss-Newton method.
The approximate line used in the fatigue limit stress specifying step 22 is characterized by a polynomial and a straight line represented by y = ax n + b.
また、疲労限度応力特定工程２２において、前記ｙ＝ａｘｎ＋ｂで表される多項式の次数ｎは２であることを特徴とする。
測定対象物に加えられる荷重が低い領域、すなわち疲労限度応力以下の領域において、内部摩擦によって生じるエネルギー散逸が熱として発生しているという仮定のもとに行ったシミュレーションの結果と赤外線カメラによって測定された実験結果とを比較検証するとともに、実験結果に対して関数の次数を変えてフィッティングすることで適切な次数を求めるために検証した。その結果、散逸されるエネルギーの荷重振幅に対する増加が次数ｎ＝２とする２次関数で表されることを導き出した。ここで前記ｙ＝ａｘｎ＋ｂで表される多項式の切片ｂは赤外線カメラで測定された散逸エネルギーのノイズに相当する。
In the fatigue limit stress specifying step 22, the degree n of the polynomial represented by y = ax n + b is 2.
In the region where the load applied to the object to be measured is low, that is, in the region below the fatigue limit stress, the result of the simulation conducted under the assumption that the energy dissipation caused by internal friction is generated as heat and measured by an infrared camera. The test results were compared and verified, and verification was performed in order to obtain an appropriate order by fitting the test results by changing the order of the function. As a result, it was derived that the increase of the energy dissipated with respect to the load amplitude is expressed by a quadratic function with the order n = 2. Here, the intercept b of the polynomial expressed by y = ax n + b corresponds to noise of dissipated energy measured by an infrared camera.
また、疲労限度応力特定工程２２において、前記直線はｙ＝ｃｘ＋ｄで表されることを特徴とする。
測定対象物に加えられる荷重が高い領域、すなわち疲労限度応力以上の領域において、３次元の弾塑性解析を行うことで荷重振幅に比例して増加し、直線で近似できることを導き出した。また、その弾塑性解析で得られた結果は、赤外線カメラを用いた散逸エネルギー測定の結果と非常に良く一致する結果が得られることからもｙ＝ｃｘ＋ｄで表される直線で近似することが望ましい。
In the fatigue limit stress specifying step 22, the straight line is expressed by y = cx + d.
In the region where the load applied to the object to be measured is high, that is, in the region exceeding the fatigue limit stress, the three-dimensional elasto-plastic analysis increased in proportion to the load amplitude, and it was derived that it can be approximated by a straight line. In addition, the result obtained by the elasto-plastic analysis is preferably approximated by a straight line represented by y = cx + d because a result that matches the result of the dissipated energy measurement using an infrared camera very well is obtained. .
また、疲労限度応力特定工程２２で用いられる自由度調整済み決定係数およびGauss - Newton法によって求められる２本の近似線は、２本の近似線とデータのフィッティングによって求められる残差の二乗和が最小になるように近似されることを特徴とする。 In addition, the degree-of-freedom-adjusted coefficient of determination used in the fatigue limit stress specifying step 22 and the two approximate lines obtained by the Gauss-Newton method are the sum of squares of the residuals obtained by fitting the two approximate lines and the data. It is characterized by being approximated to be minimized.
詳細には、荷重または主応力和の低い方から最低３点の実験データをｙ＝ａｘ２＋ｂの２次関数に対してGauss - Newton法で近似し、残りのデータを用いてｙ＝ｃｘ＋ｄでGauss - Newton法を用い近似し、２つの近似線の残差の二乗和を求める。次に２次関数ｙ＝ａｘ２＋ｂで近似するデータを１つ増やして近似し、残りのデータを直線ｙ＝ｃｘ＋ｄで近似し、２つの近似線の残渣の二乗和を求める。その作業を繰り返すことによって図５の荷重振幅の境界に対する残差の二乗和の値が得られる。この残差の二乗和が最小になる近似線の組み合わせが最も実験結果に対してフィッティングされた近似線となる。 Specifically, the experimental data of at least three points from the lower load or principal stress sum is approximated by a Gauss-Newton method for a quadratic function of y = ax 2 + b, and y = cx + d is used with the remaining data. Approximate using Gauss-Newton method and find the sum of squares of the residuals of two approximate lines. Next, the approximation is performed by increasing the data approximated by the quadratic function y = ax 2 + b, and the remaining data is approximated by a straight line y = cx + d to obtain the sum of squares of the residues of the two approximate lines. By repeating this operation, the value of the sum of squares of the residual with respect to the boundary of the load amplitude in FIG. 5 is obtained. The combination of approximate lines that minimizes the sum of squares of the residuals is the approximate line that is most fitted to the experimental results.
また、疲労限度応力特定工程２２で用いられる前記２本の近似線は、２本の近似曲線の自由度調整済み決定係数Ｒ２の相乗平均が最大になる場合のデータ範囲を用いることによって求められることを特徴とする。 The two approximate lines used in the fatigue limit stress specifying step 22 are obtained by using a data range when the geometric mean of the degree-of-freedom adjusted determination coefficient R2 of the two approximate curves is maximized. It is characterized by that.
上記残差の二乗和が最小値となる２つの近似線を求め、その２つの近似線の交点から疲労限度応力を特定することは可能であるが、データの使用範囲によっては、異なる疲労限度応力が求まる場合がある。そこで、２つの近似線の残差の二乗和の最小を求め、同時に２つの近似線の自由度調整済み決定係数の相乗平均が最大となる近似線を求めることで適切な疲労限度応力を特定できる。 It is possible to obtain two approximate lines where the sum of squares of the residuals is the minimum value and specify the fatigue limit stress from the intersection of the two approximate lines, but depending on the range of use of the data, different fatigue limit stresses May be found. Therefore, it is possible to identify an appropriate fatigue limit stress by obtaining the minimum of the sum of squares of the residuals of the two approximate lines and simultaneously obtaining the approximate line that maximizes the geometric mean of the coefficients of determination adjusted for the degrees of freedom of the two approximate lines. .
自由度調整済み決定係数とは、多項式回帰モデルに対する決定係数（寄与率）の自由度を調整して、多項式回帰モデルを安定させる手法である。例えば、多項式の次数を大きくすると、自由度は増えるがモデルが不安定になる。一方、次数を減らせば自由度は減るが、モデルは安定する。 The degree-of-freedom-adjusted determination coefficient is a method of stabilizing the polynomial regression model by adjusting the degree of freedom of the determination coefficient (contribution rate) to the polynomial regression model. For example, if the degree of the polynomial is increased, the degree of freedom increases but the model becomes unstable. On the other hand, decreasing the order reduces the degree of freedom but stabilizes the model.
多項式回帰モデルに対する決定係数Ｒ２は回帰曲線を The coefficient of determination R 2 for the polynomial regression model is a regression curve
本発明によれば、測定対象物に対して加振機によって荷重を繰り返し加え、そのときの測定対象物を赤外線カメラで撮影し、これを散逸エネルギー測定工程と、疲労限度応力特定工程によって処理して疲労限度応力を特定するので、疲労限度応力特定プロセスを標準化し、応力集中を有する材料や部品の疲労限度応力を、主観的な判断に頼ることなく客観的に疲労限度応力を正確に求めることができる。 According to the present invention, a load is repeatedly applied to an object to be measured by a shaker, and the object to be measured at that time is photographed with an infrared camera, and this is processed by a dissipative energy measurement process and a fatigue limit stress identification process. Since the fatigue limit stress is specified, the fatigue limit stress identification process should be standardized to accurately determine the fatigue limit stress objectively without relying on subjective judgment of the fatigue limit stress of stress-concentrated materials and parts. Can do.
以下に、本発明の各実施の形態について、図面を参照しながら説明する。
（実施の形態１）
図１〜図１０は本発明の実施の形態１を示す。
Embodiments of the present invention will be described below with reference to the drawings.
(Embodiment 1)
1 to 10 show Embodiment 1 of the present invention.
図１（ａ）（ｂ）は、本発明の実施の形態１における疲労限度応力特定システムを示す。疲労限度応力特定システムは、加振機１ａに固定した測定対象物としての試験片１ｂの温度を、高精度赤外線カメラ（以下、単に赤外線カメラと記す）１ｃによって測定する。 1 (a) and 1 (b) show a fatigue limit stress identification system according to Embodiment 1 of the present invention. The fatigue limit stress identification system measures the temperature of a test piece 1b as an object to be measured fixed to a vibrator 1a by a high-precision infrared camera (hereinafter simply referred to as an infrared camera) 1c.
試験片１ｂは、図６に示すように幅Ｂで厚みｔの短冊状で、長さ方向の中央には両側から中心に向かって深くなるノッチ２５が形成されている。ノッチ２５は曲率半径ｒｈ０で、ノッチ２５の深さがｄ、ｂは、応力集中部の最小断面の幅の半分である。 As shown in FIG. 6, the test piece 1b has a strip shape with a width B and a thickness t, and a notch 25 is formed at the center in the length direction so as to deepen from both sides toward the center. The notch 25 has a radius of curvature rh 0 and the depth of the notch 25 is d and b are half the width of the minimum cross section of the stress concentration portion.
加振機１ａとしては、油圧サーボ疲労試験機（島津製作所，サーボパルサ，最大試験能力：１０ｋＮ）を用いた。加振機１ａの荷重振幅は、荷重制御により０ｋＮ〜８．５ｋＮまで０．１ｋＮ毎に引張荷重を変えて測定した。加振による基本周波数ｆは２５Ｈｚ一定とした。 As the vibrator 1a, a hydraulic servo fatigue tester (Shimadzu Corporation, servo pulser, maximum test capacity: 10 kN) was used. The load amplitude of the vibrator 1a was measured by changing the tensile load every 0.1 kN from 0 kN to 8.5 kN by load control. The fundamental frequency f due to vibration was constant at 25 Hz.
赤外線カメラ１ｃとしては、Cedip社のSilver480Mを用いた。赤外線カメラ１ｃで測定した温度画像は、フーリエ変換手段を有する情報処理装置１ｄでデータ処理する。情報処理装置１ｄには、モニタ１ｅが接続されている。 As the infrared camera 1c, Silver480M manufactured by Cedip was used. The temperature image measured by the infrared camera 1c is processed by the information processing apparatus 1d having Fourier transform means. A monitor 1e is connected to the information processing apparatus 1d.
情報処理装置１ｄには、後述するピクセル選択法のフローチャートが構築されている。
散逸エネルギー測定の原理について図７を用いて説明する。
繰り返し負荷を受けた試験片１ｂは、熱弾性効果によって、加振機１ａによる加振周波数と同一周波数の繰り返し温度変化２ａを生じるが、それに加えて材料内部のエネルギー散逸によって平均温度上昇２ｃを生じる。ただし、熱弾性効果による温度変化２ａおよび散逸エネルギーによる平均温度上昇２ｃは、外乱の温度変化２ｂに比べて小さい。このため試験片１ｂの温度変化量ΔＴを表すと下記（式１）のようになる。
In the information processing apparatus 1d, a flowchart of a pixel selection method described later is constructed.
The principle of dissipated energy measurement will be described with reference to FIG.
The test piece 1b that has been subjected to repeated loads generates a repeated temperature change 2a having the same frequency as the excitation frequency by the vibration exciter 1a due to the thermoelastic effect, but in addition, an average temperature rise 2c is generated due to energy dissipation inside the material. . However, the temperature change 2a due to the thermoelastic effect and the average temperature rise 2c due to the dissipative energy are smaller than the temperature change 2b due to disturbance. For this reason, when the temperature variation ΔT of the test piece 1b is expressed, the following (formula 1) is obtained.
ΔＴ＝ｒｅ−Ｔｃ＋Ｄ＋Ｔｅ ・・・・・・ （式１）
ΔＴ：温度変化量
ｒｅ：外的要因（風や周囲の温度変化）
Ｔｃ：熱の伝導（温度の高い箇所と低い箇所が均一化を図る働き）
Ｄ ：散逸エネルギー（繰り返しサイクルにおける温度上昇量）
Ｔｅ：熱弾性効果
実際の散逸エネルギーの測定では、赤外線カメラで試験片１ｂの温度測定を行うと同時に、疲労試験機１ａからの制御信号である同期入力信号を取り込み、同期入力信号に基づく特定の周波数成分についてフーリエ変換による赤外線応力画像処理を行うことで外乱の影響を除外して、試験片１ｂの熱弾性効果による温度変化だけを測定する。
ΔT = r e −T c + D + T e (Equation 1)
ΔT: Temperature change
r e : External factor (wind and ambient temperature change)
Tc : heat conduction (high temperature and low temperature work to make uniform)
D : Dissipated energy (temperature rise in repeated cycles)
T e : Thermoelastic effect In the actual measurement of dissipated energy, the temperature of the test piece 1b is measured with an infrared camera, and at the same time, a synchronous input signal that is a control signal from the fatigue testing machine 1a is taken in and specified based on the synchronous input signal The influence of the disturbance is excluded by performing infrared stress image processing by Fourier transform for the frequency component of, and only the temperature change due to the thermoelastic effect of the test piece 1b is measured.
熱弾性効果による温度上昇・下降から、更に小さな繰り返しサイクル毎の機械的現象に基づく材料内部の散逸エネルギーによる温度上昇量を分離して測定すると、繰り返しサイクルにおける温度上昇量の散逸エネルギーＤの測定画像が描かれる。 When the temperature rise amount due to the dissipated energy inside the material is separated from the temperature rise / fall due to the thermoelastic effect and measured based on the mechanical phenomenon for each smaller repetitive cycle, the dissipated energy D of the temperature rise amount in the repetitive cycle is measured. Is drawn.
赤外線カメラ１ｃを用いて、試験片１ｂの散逸エネルギーを測定した結果を図３（ａ）に示す。
図３（ａ）を見て分かるように、試験片１ｂのノッチ２５の付近に非常に温度が高くなっている部分が見られる。この温度振幅が高く示される部分を含む領域２３に着目し、領域２３内の各ピクセルにおいて図３（ｂ）に示すような荷重振幅に対する加振による基本周波数の温度振幅グラフを作成し、傾きを求める。
The result of measuring the dissipated energy of the test piece 1b using the infrared camera 1c is shown in FIG.
As can be seen from FIG. 3A, a portion where the temperature is very high is seen in the vicinity of the notch 25 of the test piece 1b. Focusing on the region 23 including the portion where the temperature amplitude is shown high, create a temperature amplitude graph of the fundamental frequency by excitation with respect to the load amplitude as shown in FIG. Ask.
この傾きが最大のピクセルは主応力和の大きさが最大であり、最大応力集中部のピクセルである。よって、加振の基本周波数ｆの２倍の周波数２ｆ（第２高調波と称す）の成分の温度振幅が大きく、かつ荷重振幅と加振による基本周波数の温度振幅のグラフの傾きが最大のピクセルを選択することにより、疲労損傷と応力集中の両方が発生しているピクセルを選択できる。 The pixel having the largest inclination has the largest principal stress sum and is the pixel of the maximum stress concentration portion. Accordingly, a pixel having a large temperature amplitude of a component of a frequency 2f (referred to as a second harmonic) that is twice the fundamental frequency f of the excitation, and a maximum slope of the graph of the load amplitude and the temperature amplitude of the fundamental frequency due to the excitation. By selecting, it is possible to select a pixel in which both fatigue damage and stress concentration occur.
この処理は情報処理装置１ｄの散逸エネルギー測定工程２１において図２のように演算処理されている。
ステップＳ１では、各荷重振幅における第２高調波の成分の温度振幅の分布画像を作成する。
This process is performed as shown in FIG. 2 in the dissipated energy measurement step 21 of the information processing apparatus 1d.
In step S1, a distribution image of the temperature amplitude of the second harmonic component at each load amplitude is created.
ステップＳ２では、加振の基本周波数の第２高調波の成分の温度振幅が大きい領域である領域２３に注目する。
ステップＳ３では、着目した領域内のすべてのピクセルにおいて加振振幅に対する加振周波数の温度振幅のグラフを作成する。
In step S2, attention is paid to a region 23 in which the temperature amplitude of the second harmonic component of the fundamental frequency of excitation is large.
In step S3, a graph of the temperature amplitude of the excitation frequency with respect to the excitation amplitude is created for all pixels in the focused region.
ステップＳ４では、ステップＳ３で求めたグラフの傾きが最大のものを疲労限度推定に用いるピクセルに決定する。
図８（ａ）（ｂ）は確認のため行った疲労試験の前後の試験片を示す。図８（ｂ）に示される疲労試験後の試験片の破断箇所も、図３（ａ）に示された散逸エネルギーにより温度振幅が大きくかつ荷重振幅と加振周波数の温度振幅のグラフの傾きが最大である部分である。
In step S4, the pixel having the maximum slope obtained in step S3 is determined as a pixel used for fatigue limit estimation.
FIGS. 8A and 8B show test pieces before and after the fatigue test performed for confirmation. The fracture location of the specimen after the fatigue test shown in FIG. 8B also has a large temperature amplitude due to the dissipative energy shown in FIG. This is the largest part.
図６に示されるような切欠き形状を有する試験片の切欠き部の曲率半径ｒｈ０を１ｍｍと２ｍｍの２種類の試験片を用いた。なお、試験片の幅Ｂ、切欠き深さ（ノッチ）ｄ、応力集中部の最小断面の幅の半分ｂ、厚みｔはそれぞれ３ｍｍ一定とした。 Two types of test pieces having a radius of curvature rh 0 of 1 mm and 2 mm at the notch of the test piece having a notch shape as shown in FIG. 6 were used. Note that the width B, the notch depth (notch) d, the half width b of the minimum cross section of the stress concentration portion, and the thickness t were fixed to 3 mm, respectively.
それらの試験片に対して、荷重振幅を変化させて測定を行った散逸エネルギーの測定結果から求めた変曲点と、同様の試験片を用いて機械的疲労試験から求めた疲労限度荷重を比較した結果の一例を図９及び図１０に示す。 Compare the inflection point obtained from the measurement result of the dissipated energy measured by changing the load amplitude for those specimens and the fatigue limit load obtained from the mechanical fatigue test using the same specimen. An example of the results is shown in FIGS.
図９（ａ）（ｂ）は、切欠き部の曲率半径がｒｈ０＝２ｍｍ、１ｍｍの試験片を疲労試験機１ａに取付け、荷重を徐々に上げながら散逸エネルギー測定を行った結果を示す。図１０（ａ）（ｂ）は、切欠き部の曲率半径がｒｈ０＝２ｍｍ、１ｍｍの試験片を加振機１ａに取付け、求めた疲労ＳＮ曲線である。 9 (a) and 9 (b) show the results of dissipating energy measurement while attaching a test piece having a notch radius of curvature of rh 0 = 2 mm and 1 mm to the fatigue testing machine 1a and gradually increasing the load. FIGS. 10A and 10B are fatigue SN curves obtained by attaching a test piece having a radius of curvature of a notch portion of rh 0 = 2 mm and 1 mm to the vibrator 1a.
散逸エネルギー測定の結果および疲労試験による疲労ＳＮ曲線から求めた疲労限界荷重振幅の結果を表１に示す。 Table 1 shows the results of the measurement of dissipated energy and the results of the fatigue limit load amplitude obtained from the fatigue SN curve by the fatigue test.
（実施の形態２）
本発明の実施の形態２では、横軸に加振の基本周波数の成分である温度振幅、縦軸に第２高調波の成分である温度振幅をプロットする散逸エネルギー曲線を用いる疲労限度応力特定システムおよび疲労限度応力特定方法について説明する。実施の形態１の図１に示した装置を使用して、加振機１ａの荷重振幅は、荷重制御により０ｋＮ〜９．０ｋＮまで０．１ｋＮ毎に引張荷重を変えて測定した。加振による基本周波数は２５Ｈｚ一定とした。
(Embodiment 2)
In Embodiment 2 of the present invention, a fatigue limit stress identification system using a dissipative energy curve in which the horizontal axis represents the temperature amplitude that is a component of the fundamental frequency of vibration and the vertical axis represents the temperature amplitude that is the second harmonic component. The fatigue limit stress identification method will be described. Using the apparatus shown in FIG. 1 according to the first embodiment, the load amplitude of the vibrator 1a was measured by changing the tensile load every 0.1 kN from 0 kN to 9.0 kN by load control. The fundamental frequency by excitation was constant at 25 Hz.
疲労限度応力特定方法に用いられる散逸エネルギー曲線は、横軸が荷重振幅、縦軸が平均温度上昇量もしくは加振の基本周波数の第２高調波の成分の温度振幅のグラフから疲労限度応力特定を行うことが一般的である。しかし、実製品のような複雑な形状をしている場合、試験機により負荷された荷重に対応した応力が生じているとは限らない。また、切欠き試験片のように応力集中部がある場合、塑性変形が起きると応力の再分配が起き応力分布が荷重ごとに変化する可能性があるため、横軸を荷重振幅にすると実際に生じている応力や応力分布の変化の影響を無視した第２高調波の成分である温度振幅のグラフから疲労限度応力特定を行うことになる。そこで横軸に加振の基本周波数の成分の温度振幅をとることにより、第２高調波の成分である温度振幅の挙動を忠実に表すことが可能になる。 The dissipation energy curve used in the fatigue limit stress identification method is to specify the fatigue limit stress from the graph of the load amplitude on the horizontal axis and the temperature amplitude of the second harmonic component of the average temperature rise or the fundamental frequency of vibration on the vertical axis. It is common to do. However, in the case of a complicated shape such as an actual product, a stress corresponding to the load applied by the testing machine is not always generated. In addition, when there is a stress concentration part like a notched specimen, stress redistribution occurs when plastic deformation occurs, and the stress distribution may change for each load. The fatigue limit stress is specified from the graph of the temperature amplitude which is the second harmonic component ignoring the influence of the generated stress and the change of the stress distribution. Therefore, by taking the temperature amplitude of the component of the fundamental frequency of vibration on the horizontal axis, it becomes possible to faithfully represent the behavior of the temperature amplitude that is the second harmonic component.
図１１（ａ）は、荷重振幅に対する第２高調波の成分である温度振幅をプロットした図である。図１１（ｂ）は、加振の基本周波数の成分の主応力和に対する第２高調波の成分である温度振幅をプロットした図を示す。図１１（ａ）は、応力集中部１６ａと１６ａから１ｍｍ離れた部分１６ｂの散逸エネルギー曲線を示し、測定から得られるデータは殆ど重なっていて差が見られない。一方、図１１（ｂ）では、基本周波数の成分の主応力和に対する第２高調波の成分である温度振幅が応力集中部１６ａと１ｍｍ離れた１６ｂの部分では傾きが顕著に異なり、想定される応力集中部１６ａの傾きがのほうが大きい傾向が見られる。また、図１１（ａ）（ｂ）で求めた疲労限度応力の特定値を比べると、図１１（ｂ）の１６ａで求めた疲労限度応力が疲労試験により求めた疲労限度応力に近い値が得られた。 FIG. 11A is a diagram in which the temperature amplitude that is a component of the second harmonic with respect to the load amplitude is plotted. FIG. 11B shows a diagram in which the temperature amplitude, which is the second harmonic component, is plotted against the principal stress sum of the fundamental frequency component of excitation. FIG. 11A shows the dissipated energy curves of the stress concentrated portions 16a and the portion 16b 1 mm away from the 16a, and the data obtained from the measurements are almost overlapped and no difference is seen. On the other hand, in FIG. 11B, the slope of the temperature amplitude, which is the second harmonic component with respect to the principal stress sum of the fundamental frequency component, is remarkably different in the portion 16b that is 1 mm away from the stress concentration portion 16a. There is a tendency that the inclination of the stress concentration portion 16a is larger. 11A and 11B, the fatigue limit stress obtained in 16a of FIG. 11B is close to the fatigue limit stress obtained by the fatigue test. It was.
以上の結果から、横軸に加振の基本周波数の成分の主応力和、縦軸に第２高調波の成分である温度振幅をプロットする散逸エネルギー曲線を用いることで、疲労限度応力を正確に求めることが可能なのは明らかである。 From the above results, the fatigue limit stress can be accurately determined by using the dissipative energy curve in which the horizontal axis represents the principal stress sum of the fundamental frequency components and the vertical axis represents the temperature amplitude, which is the second harmonic component. It is clear that it can be sought.
（実施の形態３）
本発明の実施の形態３では、自由度調整済み決定係数もしくはGauss - Newton法によって求められる２本の近似線の交点から疲労限度応力を特定する疲労限度応力特定方法および疲労限度応力特定システムについて説明する。実施の形態１の図１に示した装置を使用して、加振機１ａの荷重振幅は、荷重制御により０ｋＮ〜９．０ｋＮまで０．１ｋＮ毎に引張荷重を変えて測定した。加振による基本周波数は２５Ｈｚ一定とした。
(Embodiment 3)
In the third embodiment of the present invention, a fatigue limit stress specifying method and a fatigue limit stress specifying system for specifying a fatigue limit stress from the intersection of two approximate lines obtained by a coefficient of freedom adjusted for the degree of freedom or the Gauss-Newton method will be described. To do. Using the apparatus shown in FIG. 1 according to the first embodiment, the load amplitude of the vibrator 1a was measured by changing the tensile load every 0.1 kN from 0 kN to 9.0 kN by load control. The fundamental frequency by excitation was constant at 25 Hz.
横軸が加振による基本周波数の温度振幅、縦軸が加振の第２高調波の成分の温度振幅のグラフから屈曲点決定をするための関数として、疲労限度応力以下の荷重振幅の値が低い領域について、適切な関数の次数を検討した。検討した関数は、１次関数ｙ＝ａｘ＋ｂ、２次関数ｙ＝ａｘ２＋ｂ、３次関数ｙ＝ａｘ３＋ｂ、４次関数ｙ＝ａｘ４＋ｂとした。適切な関数の次数を選択するための方法として、自由度調整済み決定係数とGauss - Newton法を用いて検討を行った。使用した試験片はノッチ半径２ｍｍを３本用いて荷重４ｋＮまで散逸エネルギーを測定し、その時の自由度調整済み決定係数の値を求めた。その結果を表２に示す。 The horizontal axis is the temperature amplitude of the fundamental frequency due to vibration, and the vertical axis is the function for determining the bending point from the graph of the temperature amplitude of the second harmonic component of the vibration. Appropriate function orders were examined for the low region. The function examined was a linear function y = ax + b, a quadratic function y = ax 2 + b, a cubic function y = ax 3 + b, and a quartic function y = ax 4 + b. As a method for selecting an appropriate function order, the coefficient of freedom adjusted for the degree of freedom and the Gauss-Newton method were used. The test piece used was measured for dissipated energy up to a load of 4 kN using three notch radii of 2 mm, and the value of the coefficient of determination after adjusting the degree of freedom was obtained. The results are shown in Table 2.
以上の結果から、加振の荷重振幅が低い弾性領域の近似線は、次数ｎ＝２とする２次関数が最適であり、その関数の形はｙを第２高調波の成分の温度振幅、ｘを荷重振幅とするｙ＝ａｘ２＋ｂが最適なのは明らかである。 From the above results, the approximate line of the elastic region where the load amplitude of excitation is low is optimally a quadratic function with the order n = 2, and the form of the function is that y is the temperature amplitude of the second harmonic component, Clearly, y = ax 2 + b, where x is the load amplitude, is optimal.
（実施の形態４）
本発明の実施の形態４では、散逸エネルギーを測定工程２１で抽出された結果から疲労限度応力を特定する疲労限度応力特定工程２２で用いられる近似線は、ｙ＝ａｘｎ＋ｂで表される多項式と直線の交点から疲労限度応力を特定する疲労限度応力特定方法および疲労限度応力特定システムについて説明する。実施の形態１の図１に示した装置を使用して、加振機１ａの荷重振幅は、荷重制御により０ｋＮ〜９．０ｋＮまで０．１ｋＮ毎に引張荷重を変えて測定した。ここで加振による基本周波数は２５Ｈｚ一定とした。多項式ｙ＝ａｘｎ＋ｂは、実施の形態３において、次数ｎ＝２が最適であることが求められたので、ここでは疲労限度応力以上の荷重振幅における近似線について１次関数、２次関数、３次関数、４次関数での近似を行い、どの次数の関数で近似した場合が、フィッティングが最適か検証した。そして、荷重振幅が増加すると、エネルギーの散逸も増加し、測定される第２高調波の成分の温度振幅も増加すると考えられるので、近似する関数はｙを第２高調波の成分の温度振幅、ｘを荷重振幅とすると、１次関数はｙ＝ａｘ＋ｂ、２次関数はｙ＝ａｘ２＋ｂ、３次関数はｙ＝ａｘ３＋ｂ、４次関数はｙ＝ａｘ４＋ｂとした。試験片はノッチ半径５ｍｍを３本用いて散逸エネルギーを測定した。なお、使用したデータ範囲は６．４ｋＮ〜９．０ｋＮである。またそれぞれの近似関数のデータに対する自由度調整済み決定係数もしくはGauss - Newton法により、最適な関数の次数および多項式を求めた。表４に近似関数のデータに対する自由度調整済み決定係数の相乗平均を示す。
(Embodiment 4)
In the fourth embodiment of the present invention, the approximate line used in the fatigue limit stress specifying step 22 for specifying the fatigue limit stress from the result of extracting the dissipated energy in the measurement step 21 is a polynomial represented by y = ax n + b. A fatigue limit stress specifying method and a fatigue limit stress specifying system for specifying the fatigue limit stress from the intersection of the line and the straight line will be described. Using the apparatus shown in FIG. 1 according to the first embodiment, the load amplitude of the vibrator 1a was measured by changing the tensile load every 0.1 kN from 0 kN to 9.0 kN by load control. Here, the fundamental frequency by excitation was constant at 25 Hz. Since the polynomial y = ax n + b has been determined that the order n = 2 is optimal in the third embodiment, a linear function, a quadratic function, and an approximate line at a load amplitude equal to or greater than the fatigue limit stress are used here. Approximation with a cubic function and a quartic function was performed, and it was verified with which order of function the fitting was optimal. As the load amplitude increases, the energy dissipation increases, and the temperature amplitude of the measured second harmonic component also increases. Therefore, the function to be approximated expresses y as the temperature amplitude of the second harmonic component, When x is a load amplitude, the linear function is y = ax + b, the quadratic function is y = ax 2 + b, the cubic function is y = ax 3 + b, and the quartic function is y = ax 4 + b. The test piece was measured for dissipated energy using three notch radii of 5 mm. The data range used is 6.4 kN to 9.0 kN. In addition, the optimum function order and polynomial were obtained by the coefficient of freedom adjusted for each approximate function data or the Gauss-Newton method. Table 4 shows the geometric mean of the coefficient of determination adjusted for the degree of freedom for the data of the approximate function.
（実施の形態５）
本発明の実施の形態５では、２本の近似線は、２本の近似線とデータのフィッティングによって求められる残渣の二乗和が最小になるように近似される疲労限度応力特定方法および疲労限度応力特定システムについて説明する。実施の形態１の図１に示した装置を使用して、加振機１ａの荷重振幅は、荷重制御により０ｋＮ〜９．０ｋＮまで０．１ｋＮ毎に引張荷重を変えて測定した。加振による基本周波数は２５Ｈｚ一定とした。試験片１ｂはノッチ半径５．０ｍｍ、２．０ｍｍ、１．０ｍｍを用いて検証した。疲労限度応力特定に用いた近似線は、実施の形態３および実施の形態４で最適な関数の形態として求めたｙ＝ａｘ２＋ｂで表されるｎ＝２の多項式と直線はｙ＝ｃｘ＋ｄである。２つの近似線は荷重振幅の低い方から最低３つのデータとその他のデータに対してフィッティングされ残差の二乗和を求める。次に荷重振幅の低い方から一つデータを加えた４つのデータとその他のデータに対してフィッティングされ残差の二乗和を求める。このようにデータを一つずつ増やしながら残差の二乗和を求めた。残差の二乗和が最小となる近似線の組み合わせが取得データに対して最適な近似線の組み合わせであり、この手法によって求められた２つの近似線の交点から求められた疲労限度応力の特定値と疲労試験によって求められた疲労限度応力を表６に示す。また参考までに従来方法である２本の直線による近似線の交点によって求められた疲労限度応力とCuraらによる多項式と直線の近似線の交点によって求められた疲労限度応力を示す。
(Embodiment 5)
In the fifth embodiment of the present invention, the two approximate lines are the fatigue limit stress specifying method and the fatigue limit stress approximated so that the sum of squares of the residue obtained by fitting the data to the two approximate lines is minimized. A specific system will be described. Using the apparatus shown in FIG. 1 according to the first embodiment, the load amplitude of the vibrator 1a was measured by changing the tensile load every 0.1 kN from 0 kN to 9.0 kN by load control. The fundamental frequency by excitation was constant at 25 Hz. The test piece 1b was verified using notch radii of 5.0 mm, 2.0 mm, and 1.0 mm. The approximate line used for specifying the fatigue limit stress is the polynomial of n = 2 and y = cx + d represented by y = ax 2 + b obtained as the optimum function form in the third and fourth embodiments. is there. The two approximate lines are fitted to at least three data and other data from the lower load amplitude to obtain the sum of squares of the residuals. Next, four data obtained by adding one data from the lower load amplitude and other data are fitted to obtain the square sum of the residuals. Thus, the residual sum of squares was obtained while increasing the data one by one. The combination of the approximate lines that minimizes the sum of squares of the residuals is the optimal approximate line combination for the acquired data, and the specific value of the fatigue limit stress obtained from the intersection of the two approximate lines obtained by this method Table 6 shows the fatigue limit stress obtained by the fatigue test. For reference, the fatigue limit stress obtained by the intersection of the approximate lines of the two straight lines and the fatigue limit stress obtained by the intersection of the polynomial and the approximate line of the straight line by Cura et al. Are shown for reference.
（実施の形態６）
本発明の実施の形態６では、横軸に前記加振の基本周波数の成分である温度振幅、縦軸に前記第２高調波の成分である温度振幅をプロットすることによって求められる疲労限度応力特定方法および疲労限度応力特定システムについて説明する。赤外線カメラ１ｃは、Cedip社のSilver480Mを用いた。また、加振機１ａとしては、油圧サーボ疲労試験機（島津製作所，サーボパルサ，最大試験能力：１０ｋＮ）を用い、加振機１ａの荷重振幅は、荷重制御により０ｋＮ〜９．０ｋＮまで０．１ｋＮ毎に引張荷重を変えて測定した。加振による基本周波数は２５Ｈｚ一定とした。試験片１ｂはノッチ半径５．０ｍｍ、２．０ｍｍ、１．０ｍｍを用いて検証した。表７に、疲労試験から求めた疲労限度応力と横軸に加振荷重、縦軸に第２高調波の温度振幅成分でプロットしたグラフから求めた疲労限度応力と、横軸に基本周波数の温度振幅成分、縦軸に第２高調波の温度振幅成分をプロットしたグラフから求めた疲労限度応力を比較した結果を示す。なお、近似線はｙ＝ａｘ２＋ｂで表されるｎ＝２の多項式と直線はｙ＝ｃｘ＋ｄである２本の近似線を用いてフィッティングし、２本の近似線の最小二乗和が最小となる組み合わせの近似線の交点から疲労限度応力は求めた。
(Embodiment 6)
In Embodiment 6 of the present invention, the fatigue limit stress specified by plotting the temperature amplitude which is a component of the fundamental frequency of excitation on the horizontal axis and the temperature amplitude which is the component of the second harmonic on the vertical axis is plotted. The method and fatigue limit stress identification system are described. As the infrared camera 1c, Silver480M manufactured by Cedip was used. Further, as the shaker 1a, a hydraulic servo fatigue tester (Shimadzu Corporation, servo pulser, maximum test capacity: 10 kN) is used, and the load amplitude of the shaker 1a is 0.1 kN from 0 kN to 9.0 kN by load control. Measurement was performed by changing the tensile load every time. The fundamental frequency by excitation was constant at 25 Hz. The test piece 1b was verified using notch radii of 5.0 mm, 2.0 mm, and 1.0 mm. Table 7 shows the fatigue limit stress obtained from the fatigue test, the horizontal axis represents the excitation load, the vertical axis represents the temperature amplitude component of the second harmonic, and the horizontal axis represents the temperature of the fundamental frequency. The result of comparing the fatigue limit stress obtained from the graph plotting the amplitude component and the temperature amplitude component of the second harmonic on the vertical axis is shown. The approximate line is fitted using a polynomial of n = 2 represented by y = ax 2 + b and the straight line is fitted using two approximate lines y = cx + d, and the least square sum of the two approximate lines is the minimum. The fatigue limit stress was obtained from the intersection of the approximate lines of the combination.
（実施の形態７）
本発明の実施の形態７では、疲労限度応力を特定する疲労限度応力特定工程２２で用いられる前記２本の近似線は、２本の近似曲線の自由度調整済み決定係数Ｒ２の相乗平均が最大になる場合のデータ範囲を用いることによって求められる疲労限度応力特定方法および疲労限度応力特定システムについて説明する。実施の形態１の図１に示した装置を使用して、加振機１ａの荷重振幅は、荷重制御により０ｋＮ〜９．０ｋＮまで０．１ｋＮ毎に引張荷重を変えて測定した。加振による基本周波数は２５Ｈｚ一定とした。試験片１ｂはノッチ半径５．０ｍｍを用いて検証した。疲労限度応力特定に用いた近似線は、実施の形態３および実施の形態４で最適な関数の形態として求めたｙ＝ａｘ２＋ｂで表されるｎ＝２の多項式と直線はｙ＝ｃｘ＋ｄである。実施の形態５で用いた２本の近似線とデータのフィッティングによって求められる残渣の二乗和が最小になるように近似すると同時にデータの使用上限を１つずつ減らし、そのたび二本の直線の決定係数を求めていき、二本の近似線の自由度調整済み決定係数の相乗平均が最大の場合のデータの使用上限を求めることによって最適なデータ範囲を求めることが可能である。表８に二本の近似線の自由度調整済み決定係数の相乗平均と疲労試験で求めた疲労限度応力との差を示す。
(Embodiment 7)
In the seventh embodiment of the present invention, the two approximate lines used in the fatigue limit stress specifying step 22 for specifying the fatigue limit stress are the geometric mean of the coefficient of determination R 2 after adjusting the degrees of freedom of the two approximate curves. The fatigue limit stress specifying method and the fatigue limit stress specifying system required by using the data range when maximizing will be described. Using the apparatus shown in FIG. 1 according to the first embodiment, the load amplitude of the vibrator 1a was measured by changing the tensile load every 0.1 kN from 0 kN to 9.0 kN by load control. The fundamental frequency by excitation was constant at 25 Hz. The test piece 1b was verified using a notch radius of 5.0 mm. The approximate line used for specifying the fatigue limit stress is the polynomial of n = 2 and y = cx + d represented by y = ax 2 + b obtained as the optimum function form in the third and fourth embodiments. is there. The approximation is performed so that the sum of squares of the residue obtained by fitting the two approximate lines used in the fifth embodiment and the data is minimized, and at the same time, the upper limit of data use is reduced by one, and two straight lines are determined each time. It is possible to obtain the optimum data range by obtaining the coefficients and obtaining the upper limit of use of the data when the geometric mean of the determination coefficients adjusted for the degrees of freedom of the two approximate lines is maximum. Table 8 shows the difference between the geometric mean of the coefficient of determination after adjusting the degrees of freedom of the two approximate lines and the fatigue limit stress obtained by the fatigue test.
図１２（ａ）に過大な荷重振幅での微小き裂など不自然な第２高調波の成分の温度振幅の上昇を含んだ状態で残差の二乗和が最小になる近似線を引いた図を示す。また図１２（ｂ）に表８の結果を反映させて不自然な第２高調波の成分の温度振幅の上昇を除去した状態で残差の二乗和が最小になる近似線を引いた図を示す。この結果から、残差の二乗和が最小かつ自由度調整済み決定係数の相乗平均が最大になるような二本の近似線をフィッティングし、更に自由度調整済み決定係数の相乗平均が最大になるようなデータ範囲を用いることによって最適な近似線を引くことが可能であり、その２本の近似線の交点から疲労限度応力を特定可能であることは明らかである。 FIG. 12A is a drawing obtained by drawing an approximate line that minimizes the residual sum of squares in a state including an increase in the temperature amplitude of an unnatural second harmonic component such as a microcrack with an excessive load amplitude. Indicates. FIG. 12B is a diagram in which the result of Table 8 is reflected to draw an approximate line that minimizes the residual sum of squares in a state where the temperature amplitude increase of the unnatural second harmonic component is removed. Show. From this result, fitting two approximate lines that minimize the residual sum of squares and maximize the geometric mean of the coefficient of determination adjusted for the degree of freedom, and further maximize the geometric mean of the coefficient of determination adjusted for the degree of freedom. By using such a data range, it is possible to draw an optimal approximate line, and it is clear that the fatigue limit stress can be specified from the intersection of the two approximate lines.
（実施の形態８）
本発明の実施の形態８では、実施の形態１〜７まで説明した疲労限度応力特定方法をシステムとして構築した疲労限度応力特定システムを用いて疲労限度応力を特定した。実施の形態１の図１に示した装置を使用して、加振機１ａの荷重振幅は、荷重制御により０ｋＮ〜９．０ｋＮまで０．１ｋＮ毎に引張荷重を変えて測定した。加振による基本周波数は２５Ｈｚ一定とした。試験片１ｂはノッチ半径５．０ｍｍ、２．０ｍｍ、１．０ｍｍを用いて検証した。加振機１ａを用いて荷重を段階的に増加させ、荷重毎に発生する温度振幅を赤外線カメラ１ｃで取得し、取得した画像をフーリエ変換して、加振の基本周波数と第２高調波の温度振幅成分を抽出し、２次元画像としてデータ化した。次に第２高調波の成分の画像から温度振幅の高い領域について横軸に荷重、縦軸に基本周波数の温度振幅成分のグラフを作成し、その傾きが大きなピクセルを選び出す。選び出したピクセルについて、横軸に基本周波数である主応力和、縦軸に第２高調波の成分を荷重の低い順番にプロットする。プロットされたデータについて、荷重の低い領域は、ｙ＝ａｘ２＋ｂで表されるｎ＝２の多項式と直線ｙ＝ｃｘ＋ｄでデータに対しGauss - Newton法を用いてフィッティングを行い、２つの近似線の残差の二乗和が最小でかつ自由度調整済み決定係数の相乗平均が最大になる条件を満たす近似線を求めた。その２つの近似線の交点から疲労限度応力を求めた。このような手法で求めた疲労限度応力を疲労試験の結果の比較を表９に示す。
(Embodiment 8)
In the eighth embodiment of the present invention, the fatigue limit stress is specified using the fatigue limit stress specifying system in which the fatigue limit stress specifying method described in the first to seventh embodiments is constructed as a system. Using the apparatus shown in FIG. 1 according to the first embodiment, the load amplitude of the vibrator 1a was measured by changing the tensile load every 0.1 kN from 0 kN to 9.0 kN by load control. The fundamental frequency by excitation was constant at 25 Hz. The test piece 1b was verified using notch radii of 5.0 mm, 2.0 mm, and 1.0 mm. The load is increased step by step using the vibrator 1a, the temperature amplitude generated for each load is acquired by the infrared camera 1c, the acquired image is Fourier transformed, and the fundamental frequency of the excitation and the second harmonic are The temperature amplitude component was extracted and converted into data as a two-dimensional image. Next, a graph of the temperature amplitude component of the fundamental frequency is created on the horizontal axis with the load on the horizontal axis and the vertical axis on the region of high temperature amplitude from the image of the second harmonic component, and a pixel having a large inclination is selected. For the selected pixels, the principal stress sum, which is the fundamental frequency, is plotted on the horizontal axis, and the second harmonic component is plotted on the vertical axis in order of increasing load. In the plotted data, the low-load region is obtained by fitting the data with a polynomial of n = 2 represented by y = ax 2 + b and a straight line y = cx + d using the Gauss-Newton method, and using two approximate lines. The approximate line that satisfies the condition that the sum of the squares of the residuals of the two is the smallest and the geometric mean of the coefficient of determination adjusted for the degrees of freedom is maximized was obtained. The fatigue limit stress was determined from the intersection of the two approximate lines. Table 9 shows a comparison of the fatigue limit stress obtained by such a method with the results of the fatigue test.
なお、上記の各実施の形態では、加振の基本周波数の成分およびその第２高調波の成分の温度振幅を取得し、前記第２高調波の成分の温度振幅画像の最大を示す領域内において、加振の基本周波数の成分の温度振幅画像に対する荷重特性の傾きが最大であるピクセル領域の散逸エネルギーを抽出したが、測定対象物の形状や材質、測定対象物の実際の使用条件などによっては、第３高調波あるいはそれよりも高次の高調波の成分の温度振幅画像に基づいて散逸エネルギーを抽出することも有効である。
In each of the above embodiments, the temperature amplitude of the fundamental frequency component of the excitation and the second harmonic component thereof are acquired, and the maximum amplitude of the temperature amplitude image of the second harmonic component is obtained. Extracted the energy dissipated in the pixel area where the gradient of the load characteristic with respect to the temperature amplitude image of the component of the fundamental frequency of excitation is the maximum, but depending on the shape and material of the measurement object, the actual use conditions of the measurement object, etc. It is also effective to extract the dissipated energy based on the temperature amplitude image of the third harmonic or higher-order harmonic components.
本発明にかかる疲労限度応力特定システムおよび疲労限度応力特定方法は、基本的な散逸エネルギーによる疲労限度応力特定プロセスを標準化し、システム化することで誰にでも高精度に散逸エネルギー測定が可能になり、従来の疲労試験と同等な精度かつ短時間で正確な疲労限度応力を求められるため、製品の強度における信頼性を効率よく向上させる上で有用である。 The fatigue limit stress identification system and the fatigue limit stress identification method according to the present invention standardize the fatigue limit stress identification process based on the basic dissipative energy and make it possible for anyone to measure the dissipated energy with high accuracy. Since an accurate fatigue limit stress can be obtained in a short time in the same accuracy as the conventional fatigue test, it is useful for efficiently improving the reliability of the product strength.
１ａ 加振機
１ｂ 試験片
１ｃ 赤外線カメラ
１ｄ 情報処理装置
１ｅ モニタ
２ａ 加振周波数と同一周波数の繰り返し温度変化
２ｂ 外乱の温度変化
２ｃ エネルギー散逸によって生じる平均温度上昇
２１ 散逸エネルギー測定工程
２２ 疲労限度応力特定工程
DESCRIPTION OF SYMBOLS 1a Exciter 1b Test piece 1c Infrared camera 1d Information processing apparatus 1e Monitor 2a Repeated temperature change of the same frequency as the excitation frequency 2b Temperature change of disturbance 2c Average temperature rise caused by energy dissipation 21 Dissipated energy measurement process 22 Fatigue limit stress identification Process
Claims (9)
測定対象物に対して荷重を繰り返し加える加振機と、
前記測定対象物の温度画像を得る赤外線カメラと、
前記赤外線カメラから得た前記測定対象物の温度画像を処理するフーリエ変換手段を有する情報処理装置とを備え、
前記情報処理装置は、
散逸エネルギーを測定する散逸エネルギー測定工程と、
前記散逸エネルギー測定工程から得られた測定結果から疲労限度応力を特定する疲労限度応力特定工程を有し、
前記散逸エネルギー測定工程は、
前記赤外線カメラが撮影した温度画像より、加振の基本周波数の成分および第２高調波成分の温度振幅画像を取得し、
前記第２高調波の成分の温度振幅画像の最大を示す領域内において、前記基本周波数の成分の温度振幅画像に対する荷重特性の傾きが最大であるピクセル領域の散逸エネルギーを抽出する、
疲労限度応力特定システム。 A fatigue limit stress identification system that gradually increases a load applied to a measurement object and measures a temperature amplitude of the measurement object generated for each load,
A vibrator that repeatedly applies a load to the measurement object;
An infrared camera for obtaining a temperature image of the measurement object;
An information processing apparatus having Fourier transform means for processing a temperature image of the measurement object obtained from the infrared camera;
The information processing apparatus includes:
Dissipated energy measuring process for measuring dissipated energy;
A fatigue limit stress specifying step for specifying a fatigue limit stress from the measurement result obtained from the dissipative energy measurement step;
The dissipated energy measuring step includes
From the temperature image taken by the infrared camera, obtain the temperature amplitude image of the fundamental frequency component and the second harmonic component of excitation,
Extracting the dissipated energy of the pixel region where the gradient of the load characteristic with respect to the temperature amplitude image of the fundamental frequency component is maximum within the region indicating the maximum of the temperature amplitude image of the second harmonic component;
Fatigue limit stress identification system.
横軸に前記加振の基本周波数の成分である温度振幅、縦軸に前記第２高調波の成分である温度振幅をプロットすることを特徴とする、
請求項１記載の疲労限度応力特定システム。 The fatigue limit stress specifying step includes:
The horizontal axis is a temperature amplitude that is a component of the fundamental frequency of the excitation, and the vertical axis is a temperature amplitude that is a component of the second harmonic,
The fatigue limit stress identification system according to claim 1.
自由度調整済み決定係数もしくはGauss - Newton法によって求められる２本の近似線の交点から疲労限度応力を特定することを特徴とする、
請求項２記載の疲労限度応力特定システム。 The fatigue limit stress specifying step includes:
Fatigue limit stress is specified from the intersection of two approximate lines obtained by the coefficient of determination adjusted for degrees of freedom or Gauss-Newton method.
The fatigue limit stress identification system according to claim 2.
請求項３記載の疲労限度応力特定システム。 The approximate line used in the fatigue limit stress identification step is a polynomial represented by y = ax n + b and a straight line,
The fatigue limit stress identification system according to claim 3.
請求項４記載の疲労限度応力特定システム。 The degree n of the polynomial represented by y = ax n + b is 2,
The fatigue limit stress identification system according to claim 4.
請求項４記載の疲労限度応力特定システム。 In the fatigue limit stress identification step, the straight line is represented by y = cx + d,
The fatigue limit stress identification system according to claim 4.
請求項３〜６の何れかに記載の疲労限度応力特定システム。 The two approximate lines are approximated so that the sum of squares of the residue obtained by fitting the data with the two approximate lines is minimized.
The fatigue limit stress identification system according to any one of claims 3 to 6.
請求項３〜７の何れかに記載の疲労限度応力特定システム。 The two approximate lines is characterized in that the geometric mean of freedom adjusted coefficient of determination R 2 of the two approximate curve is determined by using the data range when maximized,
The fatigue limit stress identification system according to any one of claims 3 to 7.
測定対象物に対して加振機によって荷重を繰り返し加え、そのときの前記測定対象物の温度画像を赤外線カメラで撮影し、
前記赤外線カメラから得た前記測定対象物の温度画像をフーリエ変換処理して、前記赤外線カメラが撮影した温度画像より加振の基本周波数の成分および第２高調波の成分の温度振幅画像を取得し、前記第２高調波の成分の温度振幅画像の最大を示す領域内において、前記基本周波数の成分の温度振幅画像に対する荷重特性の傾きが最大であるピクセル領域の散逸エネルギーを抽出する散逸エネルギー測定工程を実行し、
前記散逸エネルギー測定工程の測定結果から疲労限度応力を特定する疲労限度応力特定工程を実行する、
疲労限度応力特定方法。 A fatigue limit stress specifying method for gradually increasing a load applied to a measurement object and measuring a temperature amplitude of the measurement object generated for each load,
A load is repeatedly applied to the object to be measured by a vibrator, and a temperature image of the object to be measured at that time is taken with an infrared camera,
The temperature image of the measurement object obtained from the infrared camera is subjected to Fourier transform processing, and the temperature amplitude image of the fundamental frequency component and the second harmonic component is obtained from the temperature image captured by the infrared camera. A dissipated energy measuring step of extracting dissipated energy in a pixel region having a maximum inclination of a load characteristic with respect to the temperature amplitude image of the fundamental frequency component in a region indicating the maximum temperature amplitude image of the second harmonic component Run
Performing a fatigue limit stress specifying step of specifying a fatigue limit stress from the measurement result of the dissipative energy measurement step;
Fatigue limit stress identification method.
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