KR101865270B1 - Methiod for counting fatigue damage in frequency domain applicable to multi-spectral loading pattern - Google Patents

Abstract

The present invention relates to a method of calculating fatigue damage in a frequency domain for vibration testing of a mechanical system. According to the present invention, a strain gauge is attached to measure fatigue damage in a time domain, Conventional methods for calculating fatigue damage using a zero-crossing peak count method are accurate, but for a mechanical system with an irregular random signal, a large amount of time-domain data However, the conventional methods of calculating in the frequency domain to solve such a difficulty have solved the problems of the conventional methods of calculating fatigue damage which have limitations applicable only to harmonic excitations, Utilizing acceleration data in a condition with sine-on-random (SOR) representing the spectrum We propose a method to calculate the fatigue damage degree in the random excitation state and calculate the fatigue damage degree in the random, harmonic and SOR excited state in connection with the fatigue calculation method in the existing harmonic excitation state. There is provided a method of calculating a fatigue damage degree in a frequency region capable of coping with a variety of vibration spectrum patterns configured to be capable of both.

Description

[0001] The present invention relates to a method for calculating fatigue damage in a frequency region capable of coping with various vibration spectrum patterns,

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of calculating a fatigue damage degree in a frequency domain for vibration testing of a mechanical system such as an automobile part, The conventional methods of calculating the fatigue damage using the zero-crossing peak count method after measuring the strain by attaching the strain gauges are accurate, but in a mechanical system acting as a circle with an irregular random signal It is difficult to process a large amount of data in the time domain. Conventional methods of calculating in the frequency domain in order to solve such a difficulty include the conventional method of calculating the fatigue damage by the harmonic method In order to solve the problem of random and harmonic oscillations, Calculate the fatigue damage in the frequency domain that can cope with various vibration spectrum patterns that are calculated so that the linear system can calculate the fatigue damage degree under the condition of sine-on-random (SOR) ≪ / RTI >

Further, in order to calculate the fatigue damage degree in the random, harmonic, and SOR-excited states as described above, the present invention is characterized in that, in order to calculate the fatigue damage degrees in the random, In this paper, we propose a method to calculate the fatigue damage degree in the state of fatigue damage, and in connection with the fatigue calculation method in the existing harmonic fatigue state, ultimately calculate the fatigue damage degree in the random, And more particularly to a method of calculating fatigue damage in a frequency region capable of coping with various vibration spectrum patterns to be constructed.

In general, the vibration test of a mechanical system can be roughly divided into harmonic excitation and random excitation, and the frequency components are determined according to the type of vibration pattern of the target system being exposed to the operating state.

For example, in the case of automotive parts, which are representative mechanical systems, we propose a systematic vibration profile according to the target parts in the international (see ISO 16750-3: 2007 (E)) or domestic (see KS R 1034 For a system that exhibits a composite vibration pattern in which both harmonic and random components occur at the same time, a test method for a vibration profile named SOR (sine-on-random) is proposed in the US National Defense Standard (MIL-STD- 810G).

In addition, in the conventional research, it is suggested that the SOR test should be performed when the target system shows a complex spectrum pattern by performing comparative analysis in terms of the SOR vibration test, the existing harmonic test, the random excitation test, and the fatigue damage have.

That is, in the vibration environment, since the target system is exposed to a high-frequency excitation, the reliability of the strain component is low due to noise and the like even though the measurement site is very weak. In the acceleration response, However, since the acceleration physical quantity can not directly derive the fatigue damage value, an indirect method using energy contour or the like or pseudo damage is used.

In addition, since the counting method in the time domain and the frequency domain method are all possible in the process of predicting the fatigue damage degree by using the acceleration data, there are differences in the result values depending on which method is selected. In particular, The fatigue damage prediction method utilizing strain is based on the strain - based physical fatigue damage and normalizes the input vibration. Therefore, high reliability can be guaranteed in comparing and evaluating fatigue damage degrees.

Here, as an example of the prior art relating to a method for calculating the degree of fatigue damage of the above-described parts or structures, for example, according to Korean Patent Registration No. 10-1414520, Converting the response of the structure generated by the vibration into a digital signal, removing the harmonic response and the linear response of the frequency signals from the digital signal, extracting the primary modulated signal by synchronously demodulating the signals, Extracting the primary modulated signals by continuously varying the frequencies of the signals of the different frequencies and combining the primary modulated signals to generate a first sideband spectrogram and generating a first sideband spectrogram from the first sideband spectrogram And determining whether or not the damage is caused even if the voltage level of the ultrasonic wave is very small, It can be determined, it is shown the description of the method for assessing the safety of a structure using a non-linear ultrasonic modulation technique that is configured to be capable of reducing the power consumption of the sensor bar.

According to another example of the prior art relating to a method for calculating the degree of fatigue damage of a component or a structure as described above, for example, in JP-A-2014-44221, a corrosion medium The load is repeatedly applied to the surface of the introduced test piece, and the surface and / or the cross-section of the inner space of the test piece after the load is added are observed. Thus, the corrosion fatigue damage occurring in the inner cooling hole of the mold can be easily And a method of evaluating the corrosion fatigue damage constituted so as to be reproducible.

Another example of the prior art relating to a method for calculating the degree of fatigue damage of a component or a structure as described above is disclosed in, for example, International Publication No. WO 2013/160055, in which the rolling contact of a rolling- Measuring the magnitude and / or frequency of occurrence of a high frequency stress wave event which is divergent by the magnetic field, recording the measurement data as recording data, and recording data using the recording data and ISO (International Organization for Standardization) rolling-element bearing lifetime model Instead of using the value for the cumulative fatigue damage of the ISO rolling-element bearing lifetime model, including the step of predicting the remaining life of the rolling-element bearing, the size and / or frequency of the high frequency stress wave Which is configured to determine the cumulative fatigue damage from the measured values of the bearing life This technique has been suggested about the sintering method and system.

Further, as another example of the prior art relating to the method for calculating the degree of fatigue damage of the above-described parts or structures, for example, in Korean Patent Registration No. 10-0305723, in a power generation facility, A strain measuring sensor and a thermocouple are attached to the machinery where stress concentration and breakage are expected, and the stress and strain, which are detected and inputted from the temperature and strain measuring sensors detected and input from the thermocouple, are continuously measured, And then evaluating the fatigue life of the hysteresis loop using the real time fraction and the total number of creep and small deformation amounts from the hysteresis loop by analyzing the hysteresis loop through the plasticizing energy and the strain fractionation in the computer. Evaluating fatigue life using plastic deformation energy which is an internal area of the loop; Evaluating the fatigue life using the total strain at which the elastic deformation and the plastic deformation of the loop are summed; Evaluating the stress and temperature analyzed from the loop using creep parameters and creep lifetime consumption diagrams; And the creep-fatigue interaction index is calculated so that the lifetime of the mechanical equipment in which the complex load acts is accumulated and processed in real time. Thus, the lifetime of the mechanical equipment subjected to a complex load is accurately measured to ensure safe operation of the equipment And a method for evaluating the automatic life span of a mechanical equipment subjected to a combined load using a strain that is configured to accurately predict a replacement time of the mechanical equipment.

As described above, various techniques for calculating the degree of fatigue damage of a mechanical part or a structure have been proposed. However, the above-described conventional methods have the following problems.

More particularly, the present invention relates to a method of calculating fatigue damage in a frequency region for vibration testing of a mechanical system such as an automobile part, comprising the steps of measuring a strain by attaching a strain gauge, and then performing a zero-crossing peak count method The fatigue damage measurement method in the time domain in the prior art for calculating the fatigue damage degree using the above method can obtain the most accurate result value as compared with other methods. However, in the case of the mechanical system acting as a circle having an irregular random signal It has been difficult to process vast amounts of data in the time domain.

In order to solve the disadvantage of the calculation method in the time domain in which a large amount of data is required as described above, conventionally, in the frequency domain in which the strain (stress) data is PSD-converted and the physical damage degree is calculated in the frequency domain However, the frequency domain calculation methods of the prior art are applicable only when the object is in a harmonic excitation state, and in the frequency domain, the linear system The fatigue damage degree under the condition of sine-on-random (SOR) conditions showing different frequency spectra has a limit that can not be calculated.

Therefore, in order to solve the problems of the related art as described above, there is a need for a method and a system for estimating fatigue damage (hereinafter referred to as " fatigue ") in a condition having a random and harmonic excitation state as well as a sine- The calculation method of the fatigue damage in the time domain of the prior art in which it is difficult to process a large amount of data and the method of calculating the fatigue damage in the frequency domain of the prior art It is desirable to suggest a new fatigue damage calculation method which is configured to solve all of the problems of the fatigue damage calculation method. However, a device or a method that satisfies all of such requirements has not yet been provided.

1. Korean Registered Patent No. 10-1414520 (June 26, 2014) 2. JP-A-2014-44221 (Mar. 3. International Patent Publication No. WO 2013/160055 (Oct. 31, 2013). 4. Korean Patent Registration No. 10-0305723 (Aug. 01, 2001)

 SUMMARY OF THE INVENTION It is an object of the present invention to provide a method of calculating fatigue damage in a frequency domain for vibration testing of a mechanical system such as an automobile part, Existing methods of calculating fatigue damage by measuring the strain by attaching a strain gauge to measure fatigue damage in the time domain and then using a zero-crossing peak count method are accurate For a mechanical system acting as a circle with one irregular random signal, it is difficult to process vast amounts of data in the time domain. Conventional methods for calculating in the frequency domain to solve this difficulty are only for harmonic ones Solves the problem of the fatigue damage calculation methods of the prior art which had applicable limitations (Sine-on-random) conditions in which the linear system exhibits different frequency spectra in the frequency domain as well as the random and harmonic states, so that the fatigue damage degree can be calculated And a method of calculating fatigue damage in a frequency region capable of coping with various vibration spectrum patterns.

It is another object of the present invention to provide a method and apparatus for calculating randomness, harmonics, and fatigue damage in the SOR state as described above, random, and fatigue damage calculations in the presence of harmonics and ultimate control of fatigue damage in random, harmonic, and SOR states. And to provide a method of calculating a fatigue damage degree in a frequency region capable of coping with various vibration spectrum patterns configured to be capable of both.

In order to achieve the above object, according to the present invention, there is a disadvantage that the amount of data to be processed increases when calculating fatigue damage in the frequency domain for vibration testing of a mechanical system including an automotive part In order to solve the problems of the fatigue damage calculation method in the time domain of the technique and the fatigue damage calculation method in the frequency domain of the prior art, which has limitations applicable only to harmonic excitations, In addition, it is also possible to execute a process on the computer or dedicated hardware to calculate the fatigue damage degree under the condition that the linear system in the frequency domain is exposed to the sine-on-random (SOR) A method of calculating fatigue damage in a frequency region capable of coping with various vibration spectrum patterns On, the input condition setting step of setting a frequency input condition corresponding to the vibration of the process is to analyze; A data collecting step of applying vibration to an object according to a frequency input condition set in the input condition setting step and acquiring acceleration data as response data; And a fatigue damage degree calculating step of calculating a fatigue damage degree of the object by an acceleration based pseudo damage method based on the acceleration data obtained in the data collecting step There is provided a method of calculating a fatigue damage degree in a frequency region capable of coping with a vibration spectrum pattern.

Here, the input condition setting step sets a single frequency input condition, a random frequency input condition, and an SOR (single + random) input condition in which two conditions operate in combination according to need, And a process of applying various vibration spectrums different from each other to the object is performed.

The data acquisition step may include a step of attaching an acceleration measurement device to the object and measuring and collecting data on the acceleration of the object in real time in accordance with the vibration applied in accordance with the frequency input condition set in the input condition setting step Is performed.

 The fatigue damage degree calculating step may be configured to calculate the fatigue damage degree according to each of the single frequency input condition, the random frequency input condition, and the SOR input condition set in the input condition setting step. do.

That is, in the fatigue damage degree calculation step, when the input condition set in the input condition setting step is a single frequency input condition, the process of calculating the fatigue damage degree is performed using the following equation do.

(Where, N is the agreement of the components of the discrete frequency domain, the number, ω _i is the frequency, Ti is the time with the total, b, and S ₀ is SN curve associated slope and the joints (intercept) the stress of the object, a _i are each an acceleration )

, 파고율을

라 하고, 최대 크기의 기대값을 이하의 수학식으로 나타낼 때, Also, the fatigue damage degree calculation step may include calculating a root-mean-square value of the stress when the input condition set in the input condition setting step is a random frequency input condition

, Crest factor

And the expected value of the maximum size is expressed by the following equation,

The process of calculating the fatigue damage degree is performed using the following equation.

에 대해 각각 T_h,i, T_r,i 만큼 인가되는 것으로 할 때, 반복 횟수는 N_h,i, N_r,i (N_h,i < N_r,i)로 계산되고, N_h,i 횟수 동안 응력의 크기는 랜덤과 조화가진 크기가 중첩되며, 나머지 반복횟수 동안에는 랜덤 가진 크기만 영향을 주게 되는 것에 근거하여, 이하의 수학식을 이용하여 상기 주파수

에서 상기 피로 손상도를 계산하는 처리가 수행되도록 구성되는 것을 특징으로 한다. In addition, the fatigue damage degree calculation step may include calculating the fatigue damage degree based on at least one of a harmonic excitation and a random excitation frequency when the input condition set in the input condition setting step is the SOR input condition.

Each for T _{h, i,} T _r, when being _i applied by, the number of iterations is N _{h, i,} N _{r, i} (N _{h, i} <N _{r, i)} is calculated to be, N _{h, i} On the basis of the fact that the magnitude of the stress during the number of times is superimposed on the random and harmonic magnitudes and only the magnitude of the random magnitude influences the remaining number of iterations,

And a process of calculating the fatigue damage degree is performed in the control unit.

Further, the calculation method may further include calculating a fatigue damage degree calculated in the fatigue damage degree calculation step according to a method of calculating a fatigue damage degree in the time domain and a method of calculating fatigue damage degree in the frequency domain And a verification step of verifying the error in comparison with the fatigue damage obtained by the verification step.

According to the present invention, there is also provided a computer-readable recording medium on which is recorded a program configured to perform a method of calculating fatigue damage in a frequency region capable of coping with various vibration spectrum patterns described above on a computer or dedicated hardware .

In addition, according to the present invention, in calculating fatigue damage in the frequency domain for vibration testing of a mechanical system including an automotive part, there is a disadvantage that the amount of data to be processed increases, In order to solve the problem of the fatigue damage calculation method in the frequency domain of the prior art, which has limitations applicable only to harmonic excitation methods, a linear system in the frequency domain as well as a random and harmonic excitation A fatigue damage calculation system configured to calculate fatigue damage degree in a state exposed to a sine-on-random (SOR) condition having different frequency spectra, the system comprising: An input unit for setting and inputting a condition; A vibration testing unit for applying a vibration environment to an object according to an input condition input through the input unit and collecting response data measured from the object; An analysis unit for calculating a fatigue damage degree of the object based on the response data collected by the vibration testing unit; And a display unit for visually displaying an analysis result analyzed by the analyzing unit, wherein the analyzing unit performs a calculation method of a fatigue damage degree in a frequency region corresponding to the various vibration spectrum patterns described above, And calculating and analyzing the fatigue damage degree of the fatigue damage calculation system.

As described above, according to the present invention, a method of calculating a fatigue damage degree in a random excitation state using acceleration data under a sine-on-random (SOR) excitation condition showing different frequency spectra is presented, And a method of calculating a fatigue damage degree in a frequency region capable of coping with various vibration spectrum patterns configured to be linked to a fatigue calculation method in a state of existing harmonic excitation, In the fatigue damage calculation method in the region, strain gauges are attached to measure the fatigue damage in the time domain, and then the fatigue damage is measured using a zero-crossing peak count method The existing methods for computing the error are accurate, but they act as a circle with an irregular random signal In the mechanical system, it is difficult to process vast amounts of data in the time domain. Conventional methods of calculating in the frequency domain to solve this difficulty have been limited by the prior art fatigue damage calculation method Can be solved.

Also, according to the present invention, as described above, the fatigue damage degree in a state where the linear system is exposed to the sine-on-random (SOR) excitation condition in which the linear system exhibits different frequency spectra in the frequency domain as well as the random and harmonic excitation state By using the acceleration data measured in the excitation state, it is possible to apply randomly, harmonically, and / or logically to any linear system in which the linearity between the response acceleration and the response strain generated in various excitation situations is guaranteed. It is possible to provide a method of calculating a fatigue damage in a frequency region that can cope with various vibration spectrum patterns having an advantage that all of them can be applied in the SOR state.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagram schematically showing the overall configuration of a method of calculating fatigue damage in a frequency region capable of coping with various vibration spectrum patterns according to an embodiment of the present invention; FIG.
2 is a view schematically showing the overall configuration of a notched simple specimen used in a vibration test for verifying the performance of a method of calculating fatigue damage in a frequency region capable of coping with various vibration spectrum patterns according to an embodiment of the present invention .
3 is a view schematically showing a specimen actually manufactured to perform a vibration test for verifying the performance of a method of calculating fatigue damage in a frequency region capable of coping with various vibration spectrum patterns according to an embodiment of the present invention.
FIG. 4 is a table showing specific contents of a vibration profile applied to a vibration test for verifying the performance of a method of calculating a fatigue damage degree in a frequency region that can cope with various vibration spectrum patterns according to an embodiment of the present invention.
FIG. 5 is a graph showing a result of calculating the number of repetitions of strain and acceleration data for each section by using a zero-crossing peak counting method using the measurement data in the time domain.
FIG. 6 is a table showing the degree of damage based on acceleration versus strain-based damage and three different slopes.
FIG. 7 is a table showing the fatigue damage calculated in the frequency domain using the strain and acceleration data.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, with reference to the accompanying drawings, a description will be given of a specific embodiment of a method of calculating fatigue damage in a frequency region that can cope with various vibration spectrum patterns according to the present invention.

Hereinafter, it is to be noted that the following description is only an embodiment for carrying out the present invention, and the present invention is not limited to the contents of the embodiments described below.

In the following description of the embodiments of the present invention, parts that are the same as or similar to those of the prior art, or which can be easily understood and practiced by a person skilled in the art, It is important to bear in mind that we omit.

That is, the present invention relates to a method of calculating a fatigue damage degree in a frequency domain for vibration testing of a mechanical system such as, for example, an automobile part, as described later. In order to measure the degree of fatigue damage in the time domain, The conventional methods of calculating the fatigue damage using the zero-crossing peak count method after measuring the strain by attaching the strain gauges are accurate, but in a mechanical system acting as a circle with an irregular random signal It is difficult to process a large amount of data in the time domain. Conventional methods of calculating in the frequency domain in order to solve such a difficulty include the conventional method of calculating the fatigue damage by the harmonic method In order to solve the problem of random and harmonic oscillations, Calculation of fatigue damage in the frequency domain that can cope with various vibration spectrum patterns that can be calculated to calculate the fatigue damage degree under the condition that the linear system is exposed to the sine-on-random (SOR) &Lt; / RTI &gt;

In order to calculate the fatigue damage degree in the random, harmonic, and SOR states as described later, the present invention uses random data obtained by using the acceleration data under the SOR condition having different frequency spectra, In this paper, we propose a method to calculate fatigue damage in an excited state, and it is possible to calculate fatigue damage in random, harmonic and SOR states by connecting it with the existing method of calculating fatigue with harmonic excitation. To a method of calculating a fatigue damage in a frequency region that can cope with various vibration spectrum patterns constituted by a plurality of vibration spectrum patterns.

That is, the sine-on-random (SOR) test, in which random and harmonic excitations are applied at the same time, not only shortens the vibration test period, but is also similar to the actual vibration environment of the moving machine system, And it is necessary to calculate the fatigue damage degree in order to calculate the degree of severity of the test or to calculate what operating conditions the actual conditions have in practice.

However, in the case of the existing random or harmonic excitation, the frequency domain fatigue damage calculation method suitable for the corresponding conditions has been developed. However, since the SOR condition is not suitable for the conventional methods, a new frequency domain fatigue damage calculation method It is necessary.

Therefore, in the embodiment of the present invention described below, in order to calculate the fatigue damage degree when the linear system is exposed to the sine-on-random (SOR) condition in the frequency domain using the acceleration data, In this paper, we propose a new fatigue damage method which can be computed in a frequency domain with a random state, and at the same time, a fatigue damage calculation method which can be calculated in the SOR state in conjunction with the previously known fatigue damage method In order to confirm the reliability, vibration test is carried out using simple notched specimen and compared with the conventional method calculated in the time domain through strain gauge, Fatigue damage degree is sufficiently reliable.

More specifically, the embodiment of the present invention described below compares and evaluates to what extent the fatigue damage degree based on the vibration test acceleration data shows a certain degree of reliability as compared with the strain-based fatigue damage degree in the vibration test environment. , One-way excitation test was performed using a simple linear specimen with a notch. The excitation profile spectral pattern was selected as random, harmonic function and SOR, and an acceleration sensor and a strain gauge were attached to the vibration specimen. The measured fatigue damage was calculated by using the measured response data.

In addition, the degree of damage was calculated in the time domain using the strain data measured at the weak portion of the specimen, and then compared with the fatigue damage based on the acceleration. In the embodiment of the present invention, the fatigue damage degree (R = -1), the cracks are generated by the accumulation of fatigue in the elastic region in the weak region of the material due to the small strain amount and high frequency value. Therefore, the calculation method of the fatigue damage degree Is limited to the method of calculating from the stress-based SN diagram by the Minor's law.

Therefore, the present invention can be applied to any linear system that guarantees linearity between response acceleration and response strain occurring in various excitation situations, and it can be applied in random, harmonic and SOR states using only acceleration data measured in the excited state All of which can be applied.

Next, with reference to the drawings, the details of the fatigue damage degree calculation method in the frequency domain that can be applied to various vibration spectrum patterns according to the embodiment of the present invention constructed as described above will be described.

Hereinafter, a method of calculating the fatigue damage degree in the time domain and the frequency domain will be described before explaining the specific contents of the frequency domain fatigue damage degree calculation method capable of coping with various vibration spectrum patterns according to the embodiment of the present invention. Respectively.

First, a method for calculating the stress-based physical damage degree in the time domain fatigue damage calculation method will be described. This is a method for calculating the fatigue damage degree from the measurement data in the time domain using a conventional counting method. To use Minor's law.

More specifically, in the case of response data measured in a vibration environment, since there is no average stress and the stress value does not deviate from the elastic region of the material, the same result can be obtained by various methods other than the widely used rain- In the present invention, the number of stress repetitions is calculated for each stress section using a zero-crossing peak counting method.

That is, if the sorted i-th stress is s _i and the counted number is N _i , the fatigue damage can be calculated by the following equation (1) by the Minor's law .

[Equation 1]

In Equation (1), N _si is the limit excitation frequency that can be tolerated until the material _undergoes cracking due to the magnitude s _i strain, and the number of counts is calculated for all the classified stress magnitudes The fatigue damage degree is derived as shown in the following equation (2).

&Quot; (2) &quot;

Next, a description will be given of a method for calculating the similar-damage based on the acceleration. The method of calculating the fatigue damage in the time domain includes pseudo-damage using data of other physical quantities other than strain (stress) In particular, in the vibration test, it is common to measure only the acceleration in the test profile, response data, etc. Therefore, it is possible to apply the similar damage method suitable for relative comparison of severity between tests by using the physical quantity For example, details of ISO-16750-3 have been provided as test methods for automotive parts.

More specifically, as in the case of stress, the damage calculation method utilizes a zero-crossing peak hold and introduces a virtual AN diagram composed of an acceleration magnitude and a repetition frequency similar to the SN curve .

That is, if it is assumed that the acceleration of the sorted i-th magnitude is a _i and the counted number of times, the degree of damage can be derived using the following equation (3).

&Quot; (3) &quot;

In Equation (3), N _ai is the number of limit excursions assuming that breakage will occur due to ai acceleration.

In addition, by expanding and counting the number of counts for all the classified acceleration magnitudes and superimposing them, the similar damage value is derived as in Equation (4) below.

&Quot; (4) &quot;

Here, the pseudo impairment degree is not related to the physical fatigue damage of the test subject, but is only valid from the viewpoint of relatively evaluating the acceleration of two or more test results.

Next, the fatigue damage degree analysis method in the frequency domain will be described.

First, in the present invention, a method of analyzing the fatigue damage degree by utilizing only the acceleration data measured in the actual vibration environment after acquiring the relationship between the response acceleration and the strain rate in advance is utilized. To apply the analytical method, an energy contour containing the frequency response condition between acceleration and strain should be introduced.

Here, in order to apply the above method, in the present invention, the acceleration obtained at an arbitrary node of the target specimen under the single input spectrum condition is given by Equation (5) below, and the relationship between the acceleration and the stress The linear assumption given by the following equation (6) is applied.

&Quot; (5) &quot;

&Quot; (6) &quot;

와

는 각각 진폭 및 주파수를 나타내고,

는 시간 지연이며,

는 해당 응력의 크기 값을 나타낸다. here,

Wow

Respectively represent amplitude and frequency,

Is a time delay,

Represents the magnitude value of the stress.

)은, Miner 법칙에 의해 대상 재료의 S-N 선도 관련 기울기와 절점(intercept) 응력이 각각 b와 S₀라고 가정하면 이하의 [수학식 7]과 같이 나타낼 수 있다. Also, stress (

) Can be expressed by the following Equation (7), assuming that the SN curve related slope and the intercept stress of the material of interest are b and S ₀ , respectively, according to the Miner's law.

&Quot; (7) &quot;

Here, Ti represents the total excitation time in which the acceleration of (1) is applied to the system.

In addition, the vibration energy can be represented by the following equation (8) using the PSD function expressing the energy value in the frequency domain.

&Quot; (8) &quot;

The fatigue damage of Equation (7) and the vibration energy of Equation (8) can be expressed as Equation (9) below under a single input spectrum condition using an energy contour. The detailed equations (10). &Quot; (10) &quot;

&Quot; (9) &quot;

&Quot; (10) &quot;

Here, the energy contour line of Equation (10) is a value obtained by normalizing the input size of Equation (5) and then calculating fatigue damage due to stress.

In addition, the above relational expression is a representation for a single spectrum, which can be superimposed on all feasible frequency bands from a machine under the assumption that the target system is linear.

Therefore, the extended fatigue damage degree for all the frequency bands can be expressed by the following Equation (11).

&Quot; (11) &quot;

Where N is the number of the sum of the components in the discretized frequency domain.

Next, the random frequency input condition will be described. A typical method of calculating the fatigue damage degree for a mechanical system in which a random frequency component acts as an input source circle is a probability-based calculation method that utilizes a strain (stress) PSD diagram of stress This is mainly used for objects requiring a technique for analyzing fatigue damage probability probabilistically in a very irregular time.

Accordingly, the present invention proposes a method of expanding the damage calculation formula of Equation (11) to a random frequency using the energy contour technique.

주파수에 해당된 반복횟수는 이하의 [수학식 12]와 같다. That is, in the single input frequency component condition (see [Equation 7]),

The number of iterations corresponding to the frequency is expressed by Equation (12) below.

&Quot; (12) &quot;

주파수와 관련된 성분은 해당 주파수 및

보다 높은 주파수 성분들의 중첩에 의해 결정되며, 최대 크기 조건은 모든 조화 성분들이 모두 최대 크기를 가질 조건이 된다. Here, since the random frequency input condition is an assumption that all the frequency components exist at the same time,

The components associated with the frequency are

Is determined by superposition of higher frequency components, and the maximum size condition is a condition that all harmonics all have the maximum size.

주파수와 관련된 최대 크기는 이하의 [수학식 13]과 같이 나타낼 수 있다. therefore

The maximum size related to the frequency can be expressed by the following equation (13).

&Quot; (13) &quot;

However, in practice, the size of the random signal is less than the response type, the probability of occurrence of the maximum peak component is determined according to the crest factor value, and the root mean square (RMS) value of the random signal is constant Value.

이고, 파고율이

라고 가정하면, 최대 크기의 기대값은 이하의 [수학식 14] 및 [수학식 15]와 같이 나타낼 수 있다. The square root mean square value of the response stress

, And the crest factor

, The expected value of the maximum size can be expressed by the following equations (14) and (15).

&Quot; (14) &quot;

&Quot; (15) &quot;

Under such conditions, the degree of fatigue damage according to the frequency can be expressed by the following equation (16).

&Quot; (16) &quot;

Where N is the number of the sum of the components in the discretized frequency domain.

Next, in order to calculate the fatigue damage degree for the input condition in which the two frequency components operate in a complex manner, in the present invention, the damage degree for each input condition (11) and (15), which correspond to the method described above.

That is, the fatigue damage methods derived as described above can be calculated for the SOR state because the input patterns are different, but the damage degrees are also calculated in the same frequency and then superimposed.

에 대해 각각 T_h,i, T_r,i 만큼 인가된다고 가정하면, 상기한 [수학식 12]로부터 반복 횟수가 N_h,i, N_r,i (N_h,i < N_r,i)로 계산된다. If the harmonic oscillator and the random oscillator have frequencies

Each T _{h, i,} assuming that the applying as T _{r, i} for, in the above-described [Equation 12] repeated from the number of times N _{h, i,} N _{r, i} (N _{h, i} <N _{r, i)} .

Here, the frequency of the excitation frequency of the random excitation is generally large because the excitation probability that can be generated during the entire excitation time is high.

During the N _{h, i} times, the magnitude of the stress is superimposed on the random and harmonic magnitudes, and only the magnitude of the random magnitude influences the other iterations.

에서 계산되는 피로 손상도는 이하의 [수학식 17]과 같이 나타낼 수 있다. Therefore,

The fatigue damage degree calculated in Equation (17) can be expressed by Equation (17) below.

&Quot; (17) &quot;

Therefore, it is possible to implement a method of calculating fatigue damage in the frequency domain that can cope with various vibration spectrum patterns according to the embodiment of the present invention.

That is, referring to FIG. 1, FIG. 1 is a diagram schematically showing a general configuration of a method of calculating a fatigue damage in a frequency region capable of coping with various vibration spectrum patterns according to an embodiment of the present invention.

 As shown in FIG. 1, a method of calculating fatigue damage in a frequency region that can cope with various vibration spectrum patterns according to an embodiment of the present invention includes a step of setting a frequency input condition corresponding to a vibration environment to be analyzed (S20) of acquiring acceleration data as response data by applying vibration to an object according to a frequency input condition set in the step (S20); and calculating a similar impairment degree based on the acceleration based on the acceleration data obtained in the step and calculating a fatigue damage degree of the object by a pseudo damage method (S30).

Here, the step (S10) of setting the frequency input condition may include selectively setting a single frequency input condition, a random frequency input condition, and an SOR (single + random) input condition in which the two conditions operate in combination And to apply various vibration spectrums different from one another to the object according to the respective input conditions.

The step of acquiring acceleration data (S20) may be configured such that an acceleration measuring device is attached to an object, and the acceleration of the object according to the vibration applied according to the frequency input condition set in the step is measured and collected in real time.

In addition, the step S30 of calculating the fatigue damage degree described above may be performed by using the single frequency input condition, the random frequency input condition, and the SOR (S21), as described above with reference to the above- And a process of calculating the fatigue damage degree according to the input condition, respectively, can be performed.

That is, the step (S30) of calculating the fatigue damage degree calculates the fatigue damage degree using Equation (11) for a single frequency input condition, and calculates the fatigue damage degree using Equation (16) And the fatigue damage degree may be calculated using Equation (17) for the SOR input condition, respectively.

Furthermore, the fatigue damage degree calculation method in the frequency domain that can cope with various vibration spectrum patterns according to the embodiment of the present invention can be applied to a method of calculating the fatigue damage degree calculated as described above, for example, And a verification step of verifying the error in comparison with the fatigue damage obtained by the existing method.

Therefore, according to the present invention, a method of calculating a fatigue damage degree in a frequency region capable of coping with various vibration spectrum patterns according to an embodiment of the present invention constructed as described above is executed by a computer or dedicated hardware, (Sine-on-random) conditions in which the linear system exhibits different frequency spectra in the frequency domain as well as the random and harmonic states using both the acceleration data .

Subsequently, in order to verify the performance of the frequency domain fatigue damage calculation method capable of coping with various vibration spectrum patterns according to the embodiment of the present invention as described above, a vibration test using a simple specimen was carried out, The results of comparison with the methods of Fig.

In other words, the present inventors constructed a uniaxial environment for comparing and evaluating different fatigue damage based on the response data measured in the vibration test process, and prepared a simple specimen having a notch. At this time, The sensors were constructed in the same way as the previous studies.

2 and 3, FIG. 2 is a block diagram of a vibration test method for verifying the performance of a method for calculating a fatigue damage degree in a frequency region that can cope with various vibration spectrum patterns according to an embodiment of the present invention FIG. 3 is a view schematically showing the overall configuration of a simple specimen having a notch, and FIG. 3 is a view schematically showing a state of a specimen actually produced.

As shown in Fig. 2, in the embodiment of the present invention, a simple specimen with a notch was S45C, and the physical quantity of the SN diagram thus obtained was -0.0806 in slope and 664.5 MPa in stress section, It is designed to have at least one resonance point within 5,000Hz which is the maximum frequency band (MODAL 110 Exciter / MB dynamics).

In addition, the dynamic characteristics of the specimen were checked through a separate modal test (Test.Lab / LMS) using the simple specimen as described above. As a result, the first resonance point was 1162.7 Hz and the attenuation value was 0.55% It was found that the resonance of the specimen was included within the frequency range.

As described above, since the acceleration acceleration and strain (stress) signals are required to calculate the fatigue damage degree of the specimen generated in the vibration process, the acceleration sensor 1A is provided on one side of the specimen, And the strain value was measured by attaching a strain gage (1S) to the center of the notch on the other surface.

Here, since the exciter is excited in the direction of the short axis of the Z axis, the measured acceleration and strain data corresponds to a response value in the out-of-plane direction, and the attached sensor signals are as shown in FIG.

In addition, the excitation profile generally used for performing the uniaxial vibration test using the simple specimen constructed as described above can be divided into a random component for simultaneously applying all frequency bands, and a harmonic component for applying one frequency component.

Therefore, in the embodiment of the present invention, a representative excitation profile corresponding to random and harmonic components is constructed, and in addition to each excitation test consisting of random and harmonic components to analyze fatigue damage according to various excitation spectrum patterns An additional SOR vibration test was performed to apply two patterns at the same time.

That is, referring to FIG. 4, FIG. 4 is a table showing specific contents of the vibration profile applied to the vibration test for verifying the performance of the method of calculating the fatigue damage degree in the frequency domain capable of coping with various vibration spectrum patterns according to the embodiment of the present invention Fig.

Therefore, as shown in FIG. 3, the vibration test is sequentially performed in the order of the random vibration, the harmonic vibration, and the SOR test using two vibration profiles. During the vibration test, as shown in FIG. 3, 1A and the strain gage 1S to measure acceleration and strain response data.

Here, all the tests were conducted at least three times to reflect the errors that occurred during the test process.

Next, calculation of the fatigue damage degree through the vibration test as described above will be described.

First, the calculation of the fatigue damage in the time domain is performed by using the zero-crossing peak counting method, which is a conventional counting method, using the measurement data in the time domain, and the number of iterations for the strain and acceleration data is calculated At this time, the number of times for each of the three excitation spectral patterns was calculated, and the results for the three tests were averaged for the same mode.

Referring to FIG. 5, FIG. 5 illustrates the result of calculating the number of repetitions of the strain and acceleration data for each section using the zero-crossing peak counting method using the measurement data in the time domain as a graph Fig.

More specifically, as shown in FIG. 5, the number of times of calculation for the acceleration and the strain is analyzed. As a result, the SOR condition and the random case have a similar distribution, but the harmonic function has a different distribution pattern .

This result shows similar tendency both in acceleration and strain. In case of random excitation, the repetition frequency decreases sharply in the high magnitude interval, while in the case of harmonic excitation and SOR, it has many repetition frequency in the relatively high magnitude interval can confirm.

Especially, in case of SOR, it is confirmed that the harmonic component and the random component overlap each other, and the repetition frequency is larger than the other excitation conditions in the maximum size band.

Here, in case of strain-based fatigue damage diagram, the fatigue damage value is only used because the SN curve determined by the material characteristics is used as it is. However, since the fatigue damage degree based on acceleration is a virtual SN curve, what kind of slope value is used The value of the damage can be varied accordingly.

That is, referring to FIG. 6, FIG. 6 is a table showing acceleration-based damage degrees for strain-based damage degrees and three different slopes.

As shown in FIG. 6, in the case of the strain (or stress), the SOR test mode was more severe in the fatigue damage degree than in the case of the random or harmonic type, but in the case of the acceleration based severity, It can be seen that there is a very different pattern.

The reason for this is that as the absolute value of the slope is increased, the sum of the degree of damage is relatively decreased because the main frequency of harmonic components is concentrated at a relatively low frequency in FIG. 5. In the case of relatively random excitation, This is due to the fact that the value of the graph is relatively increased.

Therefore, it can be seen that the acceleration-based fatigue damage is very sensitive to the determined slope.

Next, the analysis of the fatigue damage in the frequency domain will be described. In the calculation process of the fatigue damage in the frequency domain, the same data of the SN curve is used. The data of the equations (11), The fatigue damage is calculated according to different input spectrum patterns using Eq. (16).

The difference from the analysis method in the time domain is that the process of calculating the repetition frequency is in the frequency domain, and in the case of acceleration data, the frequency response function between two physical quantities is used to convert the data into stress data .

That is, referring to FIG. 7, FIG. 7 is a table showing fatigue damage calculated in the frequency domain using strain and acceleration data.

As shown in FIG. 7, indirect fatigue damage using fatigue damage and acceleration data directly using the strain gauge is 103.0% for random excitation, 81.5% for harmonic excitation and 81.5% for SOR And the relative error (based on time domain data) of 52.6% in the condition.

Of course, it can be seen that the error range is reduced by 72.7%, 81.1% with harmonics, and 42.1% with SOR, which are directly compared with the same strain data in the time domain and frequency domain, Is an exponential function.

The reason for the relatively large error in the random excitation is that since the crest factor of the time domain data is precisely controlled by the vibrator, the amplitude of the averaged spectrum in the frequency domain occurs in the real time domain This is because there is a limit to the irregular size component corresponding to one component.

From the above results, it can be seen that although the fatigue damage according to the random excitation shows the smallest value, the contribution increases in the SOR test mode acting as the excitation source at the same time as the harmonic excitation component. In Equation (16), the response magnitudes are overlapped and increased because the harmonic excitation and the random excitation occur at the same time.

That is, in the process of obtaining the frequency component of the acceleration to obtain only the random component in the SOR condition, the main components of the harmonic excitation generated in the specific interval are removed by superimposing and averaging 90% at the window size of 4096, When the major components were to be obtained, the maximum size components were extracted by overlapping using the peak hold option instead of the average at the same window size.

As described above, in the embodiment of the present invention, in order to compare fatigue damage calculation methods for a composite spectrum vibration environment, a simple test piece having a notch is used to perform vibration tests on random, The fatigue damage is calculated by using the strain and acceleration data in the time domain, and the same data is transformed into the frequency domain in the frequency domain and a similar calculation method is applied.

As a result, it was found that the fatigue damage degree calculated in the frequency domain for the three excitation conditions is generally derived from a similar value. Therefore, according to the present invention, the fatigue damage degree The calculation method is expected to be able to replace the conventional time domain calculation method with the advantage of the calculation efficiency and various excitation spectrum conditions as compared with other methods of the prior art.

Therefore, the method of calculating the fatigue damage in the frequency domain that can cope with various vibration spectrum patterns according to the present invention can be implemented as described above.

Also, by implementing the method of calculating the fatigue damage in the frequency domain capable of coping with various vibration spectrum patterns according to the present invention as described above, according to the present invention, the SOR (Sine-on-random In this paper, we propose a method to calculate the fatigue damage in a random excitation state using acceleration data under the excitation condition and to apply it to various vibration spectrum patterns The present invention provides a method of calculating a fatigue damage degree in a frequency domain for a vibration test of a mechanical system such as an automobile part by measuring a fatigue damage degree in a time domain, After the strain was measured, a zero-crossing peak count eak count) method, it is difficult to process vast amount of data in the time domain for a mechanical system that operates as a circle with an irregular random signal. However, Conventional methods of calculating in the frequency domain to solve this difficulty can overcome the problems of the prior art fatigue damage calculation methods which have limitations applicable only to harmonic oscillators.

In addition, according to the present invention, as described above, the fatigue damage degree in a state in which the linear system is exposed to the sine-on-random (SOR) condition in which the linear system exhibits different frequency spectrums in the frequency domain as well as the random and harmonic states By using the acceleration data measured in the excitation state, it is possible to apply randomly, harmonically, and / or logically to any linear system in which the linearity between the response acceleration and the response strain generated in various excitation situations is guaranteed. It is possible to provide a method of calculating a fatigue damage in a frequency region that can cope with various vibration spectrum patterns having an advantage that all of them can be applied in the SOR state.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present invention as defined by the appended claims. It is a matter of course.

Claims (9)

A method of calculating a fatigue damage degree in a frequency domain capable of coping with various vibration spectrum patterns configured to be executed on a computer or dedicated hardware,
An input condition setting step of setting a frequency input condition corresponding to a vibration environment to be analyzed;
A data collecting step of applying vibration to an object according to a frequency input condition set in the input condition setting step and acquiring acceleration data as response data; And
Calculating a fatigue damage degree of the object by an acceleration based pseudo damage method based on the acceleration data obtained in the data collection step;
The input condition setting step includes:
(Sine-on-random, single + random) input conditions in which a single frequency input condition, a random frequency input condition, and a combination of two conditions are selectively set as needed, A process of applying various vibration spectrum patterns, each being different from each other, is performed,
The fatigue damage degree calculation step may include:
A process of calculating a fatigue damage degree according to each of the single frequency input condition, the random frequency input condition, and the SOR input condition set in the input condition setting step,
Wherein when the input condition set in the input condition setting step is a single frequency input condition, processing for calculating the fatigue damage degree is performed using the following equation 1,
[Equation 1]

(Where, N is the agreement of the components of the discrete frequency domain, the number, ω _i is the frequency, Ti is the time with the total, b, and S ₀ is SN curve associated slope and the joints (intercept) the stress of the object, a _i are each an acceleration )

When the input condition set in the input condition setting step is the random frequency input condition, the square root mean square value of the stress

, And the crest factor

, And when the expected value of the maximum size is represented by [Expression 2] below,
[Equation 2]

The processing for calculating the fatigue damage degree is performed using the following equation (3)
[Equation 3]

If the input condition set in the input condition setting step is the SOR input condition,

Each for T _{h, i,} T _r, when being _i applied by, the number of iterations is N _{h, i,} N _{r, i} (N _{h, i} <N _{r, i)} is calculated to be, N _{h, i} Based on the fact that the magnitude of the stress during the number of times is superimposed on the random and harmonic magnitudes and only the magnitude of the random magnitude influences the rest of the number of iterations,
Using Equation (4) below,

Wherein the calculation of the fatigue damage degree is performed in the frequency domain.
[Equation 4]

The method according to claim 1,
Wherein the data collection step comprises:
A process of attaching an acceleration measuring device to the object and measuring and collecting data on the acceleration of the object in real time according to the vibration applied according to the frequency input condition set in the input condition setting step, A method of calculating fatigue damage in a frequency region capable of coping with various vibration spectrum patterns.
delete delete delete delete 3. The method of claim 2,
In the calculation method,
The fatigue damage degree calculated in the fatigue damage degree calculation step is compared with the fatigue damage degree obtained by the calculation method of the prior art including the method of calculating the fatigue damage degree in the time domain and the method of calculating the fatigue damage degree in the frequency domain, And a verification step of verifying the vibration spectrum pattern in the frequency domain.
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