Fatigue damage evaluation method and fatigue damage evaluation program

Abstract

To evaluate the fatigue of an apparatus / piping system more realistically than before.SOLUTION: A fatigue accumulation coefficient of an apparatus is evaluated by: obtaining an acceleration response waveform at an installation location of an evaluation target apparatus 2 through earthquake response analysis; inputting the obtained acceleration response waveform to perform a time history response analysis by varying a natural frequency of a one-mass system model; calculating a time history displacement response waveform for each vibration mode of the evaluation target apparatus 2 that is not modeled in the time history response analysis; assuming that the maximum stress generated during an earthquake occurs at the maximum value of the time history displacement response waveform of all vibration modes; obtaining a stress waveform so that a displacement amplitude ratio to the time history maximum displacement and a stress amplitude ratio to the maximum stress coincide with each other; obtaining the allowable number of cycles of each peak of the obtained stress waveform from a design fatigue diagram; and obtaining the equivalent number of cycles during an earthquake by summing up the ratios of the obtained maximum peak stress to the allowable number of cycles.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a fatigue damage evaluation method and a fatigue damage evaluation program. [Background technology]

[0002] Patent Document 1 describes how a mechanism is provided that can record the maximum relative displacement between the relatively deforming members of an elastic-plastic support device, and how fatigue is evaluated based on the maximum relative displacement obtained by this mechanism and the equivalent number of earthquake cycles calculated at the time of plant design, to determine whether maintenance is necessary.

[0003] Non-patent document 1 summarizes matters related to the establishment of standard earthquake motion, geological and ground surveys, stability evaluation of foundation ground and surrounding slopes, and the establishment of standard tsunami. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2001-83047 A [Non-patent literature]

[0005] [Non-Patent Document 1] "Technical Guidelines for Seismic Design of Nuclear Power Plants" (JEAG4601-2015) Summary of the Invention [Problem to be solved by the invention]

[0006] A large number of equipment and piping systems are installed inside the reactor building of a boiling water nuclear power plant, and their seismic design takes into account a wide range of conditions, including earthquake motion and variations in the physical properties of the structures.

[0007] This earthquake-resistant design also includes fatigue design of important equipment and piping systems against earthquakes, and an index called the equivalent number of cycles has been used to realize simple fatigue evaluation under many conditions.

[0008] This equivalent number of cycles is given as the number of cycles at which the total energy of vibrations of equipment, piping systems, etc. caused by an earthquake has the same energy as a sine wave whose amplitude is the maximum value of the vibration response. By using this index, fatigue evaluation against earthquake motion can be easily performed for the many equipment and piping systems that exist in nuclear power plants.

[0009] In Japan, the method for calculating the equivalent number of cycles is summarized in Non-Patent Document 1 (Nuclear Power Plant Seismic Design Technical Regulations JEAC4601-2015). In this Non-Patent Document 1, the peak stress method and its evaluation flow are presented as an effective method for calculating the equivalent number of cycles.

[0010] In this peak stress method, an earthquake response analysis model of the building and large equipment system is used. If the earthquake response analysis model is not used and the earthquake load is calculated from the response spectrum, the time history acceleration response waveform at the installation location of the equipment to be evaluated is calculated from the earthquake response analysis. The time history acceleration response waveform is used as input to perform a time history response analysis of a single mass system to calculate the time history displacement response waveform. At this time, it is assumed that the maximum peak stress occurs when the maximum displacement of the time history displacement response waveform occurs, and the allowable number of cycles for the maximum peak stress is calculated. Then, it is assumed that stress proportional to the amount of displacement occurs at each peak of the time history displacement response waveform, and the stress for each peak is calculated. The allowable number of cycles for the stress at each peak of this stress waveform is calculated, and the cumulative fatigue coefficient is calculated. Then, the allowable number of cycles for the maximum peak stress is multiplied by the cumulative fatigue coefficient to calculate the equivalent number of cycles for the earthquake input. Similarly, the natural frequency of the one-mass system is varied, and the equivalent number of repetitions is calculated for all of the frequency ranges in which the main vibration modes of all equipment exist, and the maximum equivalent number of repetitions within that target frequency range is set as the design equivalent number of repetitions.

[0011] This method assumes that the same maximum peak stress always occurs for the maximum displacement of all vibration modes in the target frequency range. Because of this, the relative deformation and strain are actually small in the high frequency range, so the smaller stress level is evaluated overly conservatively.

[0012] According to the above evaluation procedure shown in Non-Patent Document 1, a safe design equivalent number of cycles can be set for a large number of equipment and piping systems, but since the magnitude relationship of the displacement in the target frequency range is ignored, an equivalent number of cycles with a margin in the high frequency range is calculated. In particular, when the high frequency range is dominant and the design equivalent number of cycles is calculated, this index has an excessive margin.

[0013] Furthermore, Patent Document 1 discloses an elastic-plastic support device and a fatigue evaluation method and a maintenance method using the same, and, as in Non-Patent Document 1, calculates the equivalent number of cycles.

[0014] In the techniques of Non-Patent Document 1 and Patent Document 1, the magnitude relationship of the relative maximum displacement over time in the target frequency range, i.e., the magnitude relationship of the stress, is omitted, and the same maximum peak stress is assumed in all frequency bands. Therefore, for high frequency components where the displacement and stress are expected to be small, the maximum peak stress is set to be large, and an equivalent number of cycles with sufficient conservativeness is set.

[0015] In particular, when performing seismic evaluations that take into account vibration modes excited in the high-frequency range, such as out-of-plane vibrations of the building floors and walls, such as when using an earthquake response analysis model in which the building is modeled using the three-dimensional finite element method, it is expected that this conservatism will become excessive.

[0016] In light of this situation, an object of the present invention is to provide a fatigue damage evaluation method and a fatigue damage evaluation program that can perform more realistic fatigue evaluation of equipment and piping systems than has been conventionally possible. [Means for solving the problem]

[0017] The present invention includes a plurality of means for solving the above-mentioned problems. Examples of the present invention include an acceleration response waveform calculation procedure for determining an acceleration response waveform at an installation position of a target device by earthquake response analysis, a time history response analysis procedure for performing a time history response analysis by varying the natural frequency of a one-mass system model using the acceleration response waveform determined in the acceleration response waveform calculation procedure as an input, a time history displacement response waveform calculation procedure for calculating a time history displacement response waveform for each vibration mode of the target device that is not modeled in the time history response analysis, an assumption procedure for assuming that the maximum stress generated during an earthquake occurs at the maximum value of the time history displacement response waveform of all vibration modes, a stress waveform calculation procedure for determining a stress waveform such that the displacement amplitude ratio to the time history maximum displacement and the stress amplitude ratio to the maximum stress match, an allowable number of repetitions calculation procedure for determining the allowable number of repetitions of each peak of the stress waveform determined in the stress waveform calculation procedure from a design fatigue diagram, and a fatigue accumulation coefficient evaluation procedure for determining an equivalent number of repetitions during an earthquake by summing up the ratio of the allowable number of repetitions to the maximum peak stress determined in the allowable number of repetitions calculation procedure, and evaluating the fatigue accumulation coefficient of the device. Effect of the Invention

[0018] According to the present invention, it is possible to perform a more realistic fatigue evaluation of equipment and piping systems than in the past. Problems, configurations and effects other than those described above will become apparent from the following description of the embodiments. [Brief description of the drawings]

[0019] [Figure 1] 4 is a flowchart for explaining a method for calculating an equivalent number of cycles in the fatigue damage evaluation method for nuclear equipment according to the first embodiment. [Diagram 2] Cross-section of the reactor building. [Diagram 3] Schematic diagram of the reactor building floor where the equipment will be installed. [Figure 4] Schematic diagram of a one-mass system model. [Diagram 5]Schematic diagram of the time history displacement response waveform calculated using a single mass model. [Figure 6] Schematic diagram of maximum displacement data (displacement response spectrum). [Figure 7] FIG. 4 is a diagram showing the relationship between a displacement waveform and a stress waveform. [Figure 8] 1 is a graph showing the relationship between stress and allowable number of cycles based on a design fatigue diagram. [Figure 9] FIG. 4 is a diagram showing the relationship between natural frequency and equivalent number of repetitions. [Figure 10] 6 is a flowchart for explaining a method for calculating an equivalent number of cycles in the fatigue damage assessment method for nuclear equipment according to the second embodiment. [Figure 11] Schematic diagram of the floor of a reactor building on which equipment and piping systems with multiple support points are installed. [Figure 12] Schematic diagram of maximum displacement data (displacement response spectrum) when there are multiple equipment installation positions. [Figure 13] 13 is a flowchart for explaining a method for calculating an equivalent number of cycles in the fatigue damage assessment method for nuclear equipment according to the third embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] The following describes an embodiment of the fatigue damage evaluation method and fatigue damage evaluation program of the present invention with reference to the drawings. The present invention is a method for evaluating the fatigue of equipment and piping systems by eliminating the excessive margin included in the equivalent number of cycles calculated when the high frequency region is dominant, and calculating the equivalent number of cycles during an earthquake according to the relative displacement level for each vibration mode.

[0021] In the following, various devices and piping operating in a nuclear power plant will be described as examples of the subject of evaluation, but the devices to be evaluated are not limited to devices and piping in a nuclear power plant.

[0022] In the drawings used in this specification, the same or corresponding components are denoted by the same or similar reference numerals, and repeated description of these components may be omitted.

[0023] <First Example> A first embodiment of the fatigue damage evaluation method and the fatigue damage evaluation program of the present invention will be described with reference to FIGS. 1 to 9. FIG.

[0024] Fig. 1 is a flow chart for explaining a method for calculating the equivalent number of cycles according to the first embodiment of the present invention. Fig. 2 is a cross-sectional view of a reactor building, Fig. 3 is a schematic diagram of a floor 1 of the reactor building on which the equipment to be evaluated is installed, Fig. 4 is a schematic diagram of a one-mass system model, Fig. 5 is a schematic diagram of a time history displacement response waveform calculated by the one-mass system model, Fig. 6 is a schematic diagram of a maximum displacement data group (displacement response spectrum), Fig. 7 is a diagram showing the relationship between a displacement waveform and a stress waveform, Fig. 8 is a diagram showing the relationship between stress based on a design fatigue diagram and the allowable number of cycles, and Fig. 9 is a diagram showing the relationship between the natural frequency and the equivalent number of cycles.

[0025] First, a procedure for determining the equivalent number of cycles required for fatigue damage evaluation will be described with reference to FIG.

[0026] As shown in FIG. 1, first, in step S1, an earthquake response analysis is performed using a seismic model of a building and large equipment system that can simulate the vibration behavior of buildings and large equipment such as reactor pressure vessels as shown in FIG. 2 and FIG. 3.

[0027] Then, in step S2, a time history acceleration response waveform at the installation position of the evaluation target device 2 is acquired.

[0028] Next, in step S3, the natural frequency f i Using the one-mass system model, a time history acceleration response waveform is input as ground motion and a time history response analysis is performed. This step S3 and the above-mentioned step S2 correspond to an acceleration response waveform calculation procedure (step) for obtaining an acceleration response waveform at the installation position of the evaluation target device 2 by earthquake response analysis.

[0029] Next, in step S4, the time history displacement response waveform of the single mass system model obtained by time history response analysis is obtained, and in step S5, the time history displacement response waveform is preferably stored in a database in a processing device that executes the fatigue damage assessment method and fatigue damage table program of the present invention.

[0030] Of these steps S4 and S5, step S4 corresponds to a time history response analysis procedure (step) that uses the acceleration response waveform obtained in the acceleration response waveform calculation procedure (step) as input and performs a time history response analysis by varying the natural frequency of the single-mass system model, and step S5 corresponds to a time history displacement response waveform calculation procedure (step) that calculates the time history displacement response waveform for each vibration mode of the evaluation target equipment 2 that is not modeled in the time history response analysis.

[0031] Next, in step S6, it is determined whether the current mode number i is equal to or greater than the mode number M of the maximum frequency in the target frequency range. If it is determined to be less than M, the process proceeds to step S7, where the mode number i in the one-mass system model is changed to i+1, and the natural frequency f i+1 Then, the above steps S3 to S6 are repeated.

[0032] When it is determined in step S6 that the mode number i is equal to or greater than M, the data set of the time history displacement response waveform is stored in the database. In step S8, as shown in FIG. 5, the displacement amplitude X ki Get the.

[0033] Next, in step S9, a data set of maximum amplitudes of the time history displacement response waveforms at each natural frequency is created as shown in FIG. 6, and the maximum displacements X max Request.

[0034] Furthermore, in step S10, the maximum peak stress σ max is the maximum displacement X of the time history response waveform within the target frequency range of all vibration modes. maxThis step S10 corresponds to the assumption step of assuming that the maximum stress generated during an earthquake occurs at the maximum value of the time history displacement response waveform of all vibration modes.

[0035] Then, in step S11, the displacement amplitude ratio to the maximum displacement in the time history and the maximum peak stress σ max The stress amplitude ratio at the k-th peak of the time history stress waveform is equivalent to that at the k-th peak of the time history stress waveform. ki is calculated according to formula (1). This step S11 corresponds to a stress waveform calculation procedure (step) for obtaining a stress waveform so that the displacement amplitude ratio to the maximum displacement in the time history and the stress amplitude ratio to the maximum stress coincide with each other.

[0036]

number

[0037] This makes it possible to generate a stress waveform that takes into account the relative magnitude relationship of each vibration mode while maintaining the waveform shapes of the displacement and stress as shown in Figure 7.

[0038] Then, in step S12, the maximum peak stress σ 1 , which is each peak of the stress waveform, is calculated using the design fatigue diagram of FIG. 8 obtained in the previous step S11. max The allowable number of repetitions of 0 Calculate the following.

[0039] Then, in step S13, the stress amplitude σ of each of the stress wave fatigue cumulative coefficient shapes is ki Similarly, the allowable number of cycles N is calculated from the design fatigue diagram shown in Fig. 8 for the peak of ki =f(σ ki ) is calculated.

[0040] This step S13 and the above-mentioned step S12 correspond to an allowable number of repetitions calculation procedure (step) for determining, from a design fatigue diagram, the allowable number of repetitions of each peak of the stress waveform determined in the stress waveform calculation procedure (step).

[0041] Next, in step S14, the natural frequency f i Fatigue accumulation factor F i is calculated based on formula (2), where L is the number of peaks of stress.

[0042]

number

[0043] Then, in step S15, the equivalent number of repetitions N ei is calculated based on equation (3).

[0044]

number

[0045] This step S15 and the above-mentioned step S14 correspond to a fatigue accumulation coefficient evaluation procedure (step) in which the equivalent number of cycles during an earthquake is calculated by summing up the ratio of the maximum peak stress calculated in the allowable number of cycles calculation procedure (step) to the allowable number of cycles, and the fatigue accumulation coefficient of the equipment is evaluated.

[0046] Then, in step S16, the equivalent number of repetitions N obtained for each natural frequency as shown in FIG. ei The equivalent number of design cycles N is set as the maximum value of the target frequency range. e When the vibration mode of the target equipment is specified, the natural frequency f i The time history analysis of the single mass system model can be limited to only the target vibration mode.

[0047] The equivalent number of iterations for design N is calculated by the procedure shown in Figure 1. e After calculating the equivalent number of cycles for design N e The maximum stress σ caused by the maximum response acceleration of the equipment during an earthquake α Furthermore, this maximum stress σ α The allowable number of repetitions forα and obtain the equivalent number of cycles for design N e The number of allowed repetitions is N α Calculate the fatigue accumulation factor by dividing by this and confirm that it is below the allowable limit (1.0).

[0048] Each of the above steps can be realized by a processing device such as a PC (PERSONAL COMPUTER) equipped with hardware such as a calculation device such as a CPU, a main storage device such as a semiconductor memory and an auxiliary storage device such as a hard disk, input devices such as a keyboard and a USB port, and an output device such as a display unit composed of a monitor, and the control of the operation of each device and various calculation processes described below are executed based on various programs.

[0049] The programs may be stored in an internal storage unit, an external recording medium, a data server (all not shown), etc., and may be read and executed by the CPU. The control processes may be integrated into one program, or may be separated into multiple programs, or may be a combination of these. Some or all of the programs may be realized by dedicated hardware, or may be modularized. Furthermore, the various programs may be installed from a program distribution server, an internal storage medium, or an external recording medium.

[0050] Next, the effects of this embodiment will be described.

[0051] The fatigue damage evaluation method of the first embodiment of the present invention described above includes an acceleration response waveform calculation procedure for determining an acceleration response waveform at the installation position of the evaluation target equipment 2 by earthquake response analysis, a time history response analysis procedure for performing a time history response analysis by varying the natural frequency of a one-mass system model using the acceleration response waveform determined in the acceleration response waveform calculation procedure as input, a time history displacement response waveform calculation procedure for calculating a time history displacement response waveform for each vibration mode of the evaluation target equipment 2 that is not modeled in the time history response analysis, an assumption procedure for assuming that the maximum stress generated during an earthquake occurs at the maximum value of the time history displacement response waveform of all vibration modes, a stress waveform calculation procedure for determining a stress waveform so that the displacement amplitude ratio to the time history maximum displacement and the stress amplitude ratio to the maximum stress match, an allowable number of repetitions calculation procedure for determining the allowable number of repetitions of each peak of the stress waveform determined in the stress waveform calculation procedure from a design fatigue diagram, and a fatigue accumulation coefficient evaluation procedure for determining an equivalent number of repetitions during an earthquake by summing up the ratio of the allowable number of repetitions to the maximum peak stress determined in the allowable number of repetitions calculation procedure, and evaluating the fatigue accumulation coefficient of the equipment.

[0052] This makes it possible to eliminate the excessive margin included in the equivalent number of cycles calculated when the high-frequency region is dominant, and to calculate a realistic equivalent number of cycles during an earthquake that corresponds to the relative displacement level for each frequency, thereby enabling fatigue evaluation of equipment and piping systems that is more realistic than before and does not overestimate maintainability.

[0053] <Second Example> A fatigue damage assessment method and a fatigue damage assessment program according to a second embodiment of the present invention will be described with reference to Fig. 10 to Fig. 12. Fig. 10 is a flowchart explaining a method for calculating the equivalent number of cycles in the fatigue damage assessment method for nuclear equipment according to the second embodiment, Fig. 11 is a schematic diagram of the floor of a reactor building on which equipment and piping systems having multiple support points are installed, and Fig. 12 is a schematic diagram of a group of maximum displacement data (displacement response spectrum) when there are multiple equipment installation positions.

[0054] As shown in Figure 10, the fatigue damage assessment method and fatigue damage assessment program of the second embodiment are characterized by assuming a case where there are multiple support points, i.e., multiple installation positions 3A, 3B, 3C of the evaluation target equipment 2, as shown in Figure 11, and calculating a stress waveform taking into account the relative magnitude relationship of the installation positions 3A, 3B, 3C of the evaluation target equipment 2 and the vibration mode.

[0055] As shown in FIG. 10, first, in step S1, an earthquake response analysis is performed.

[0056] Next, instead of step S2 shown in FIG. 1, in step S22, as shown in FIG. 11, multiple equipment installation positions j (installation positions 3A, 3B, 3C of the evaluation target equipment 2) are assumed and a time history acceleration response waveform is obtained at each installation position, and then in step S3, a time history response analysis of a one-mass system is performed on the time history acceleration response waveform at each installation position obtained in step S22, and a time history displacement response waveform is obtained in step S4 and stored in a database in step S5.

[0057] The above-mentioned step S22 is an acceleration response waveform calculation procedure (step) for determining acceleration response waveforms for all device installation positions, for devices having multiple installation positions.

[0058] This series of processes is performed by varying the natural frequency of the one-mass system, and is repeated up to the mode order of the maximum frequency in the target frequency range (Yes in steps S3 to S6). Then, in step S8, the displacement amplitude X ki (Extreme values ​​of time history displacement response waveform) are calculated.

[0059] These processes are repeated to calculate the displacement amplitude for the equipment installation position j (steps S62, S72). When the equipment installation position j has the maximum number of support points or more (Yes in step S62), the maximum displacement X max is extracted (step S92).

[0060] Here, Fig. 12 is a schematic diagram of a group of maximum displacement data (displacement response spectrum) when there are multiple equipment installation positions. As shown in Fig. 12, the magnitude relationship of the displacement is determined based on the group of maximum displacement data for each installation position.

[0061] Next, in step S102, the maximum displacement X max Maximum peak stress σ max This step S102 is an assumption procedure (step) for assuming that the maximum stress generated during an earthquake occurs at the maximum value of the time history displacement response waveforms of all vibration modes at all equipment installation positions.

[0062] Then, in step S11, the displacement amplitude ratio to the maximum displacement and the maximum peak stress σ max so that the stress amplitude ratio to σ is equivalent ki = σ max ×(X ki / X max ) is calculated, and then, in the same manner as in the first embodiment, the maximum peak stress is calculated based on the allowable number of cycles N 0 Calculate the allowable number of repetitions of each peak of the stress waveform, N kij is calculated (steps S12 and S13).

[0063] And the natural frequency f i Fatigue accumulation factor F ij The equivalent number of repetitions N for all natural frequencies at the equipment installation position j is calculated by multiplying the number of reciprocals of the permissible number of repetitions by two (step S14). eij (Step S15), and the equivalent number of cycles for design N is calculated as the maximum value of the target frequency range at all installation positions. e is set (step S162).

[0064] The other configurations and operations are substantially the same as those of the fatigue damage evaluation method and fatigue damage evaluation program of the first embodiment described above, and details thereof will be omitted.

[0065] The fatigue damage evaluation method and fatigue damage evaluation program of the second embodiment of the present invention also provide substantially the same effects as those of the fatigue damage evaluation method and fatigue damage evaluation program of the first embodiment described above.

[0066] Furthermore, in the second embodiment, when there are multiple equipment installation positions, fatigue evaluation can be performed taking into consideration the magnitude relationship of displacement between the equipment installation positions.

[0067] <Third Example> A fatigue damage assessment method and a fatigue damage assessment program according to a third embodiment of the present invention will be described with reference to Fig. 13. Fig. 13 is a flow chart for explaining a method of calculating an equivalent number of cycles in the fatigue damage assessment method for nuclear equipment according to the third embodiment.

[0068] As shown in Figure 13, the fatigue damage assessment method and fatigue damage assessment program of the third embodiment are characterized by obtaining eigenvalue information such as the mode vector, stimulation coefficient, and natural frequency of the target equipment in advance, and estimating the actual displacement response waveform generated in the equipment based on this to determine the stress waveform.

[0069] 13, first, in step S1, an earthquake response analysis is performed. Then, in step S2, a time history acceleration response waveform at the installation position of the evaluation target device 2 is obtained.

[0070] Next, immediately before step S3, in step S301, eigenvalue information of the target device is separately acquired, and in step S3, the one-mass system (natural frequency f i ) is subjected to a time history response analysis, and a time history displacement response waveform is obtained in step S4 and stored in a database in step S5.

[0071] Next, in step S6, it is determined whether the current mode number i is equal to or greater than the mode number M of the maximum frequency in the target frequency range. If it is determined to be less than M, the process proceeds to step S7, where the mode number i in the one-mass system model is changed to i+1, and the natural frequency fi+1 Then, the above steps S3 to S6 are repeated.

[0072] Then, in step S302, the time history displacement response waveforms corresponding to each vibration mode of the evaluation target equipment 2 are multiplied by a stimulus function expressed as the product of the eigenmode vector and the stimulus coefficient as shown in equation (4) and added together to estimate the actual displacement response waveform.

[0073]

number

[0074] This step S302 is an assumption procedure (step) for assuming a maximum peak stress at a maximum displacement of a displacement time history response waveform obtained by multiplying the displacement time history response waveforms for each vibration mode of the evaluation target device 2 by a stimulus function and adding them together.

[0075] Then, in step S8, the displacement amplitude X for the k-th extreme value of the time history displacement response waveform is calculated. ki After obtaining the actual displacement response waveform, in step S309, the displacement amplitude Y k Calculate the maximum value Y max Extract.

[0076] Then, instead of step S10, in step S310, the maximum value Y max Maximum peak stress σ max In step S11, the stress amplitude σ is set so that the displacement amplitude ratio to the maximum displacement is equivalent to the stress amplitude ratio to the maximum stress. ki σ ki = σ max ×(X ki / X max ) is calculated using the formula:

[0077] Hereafter, as in the first embodiment, the allowable number of cycles of the maximum peak stress in the design fatigue diagram N 0 (Step S12), and the allowable number of repetitions N ki =f(σ ki) is calculated (step S13).

[0078] Then, in step S314, the fatigue accumulation factor F is calculated using the following formula (5): In formula (5), L is the number of peaks of stress.

[0079]

number

[0080] Furthermore, in step S315, the allowable number of repetitions N 0 Multiply this by the fatigue accumulation factor F to get the equivalent number of cycles for design N e Request.

[0081] These steps S310 to S315 constitute a fatigue accumulation coefficient evaluation procedure (steps) for determining the equivalent number of repetitions during an earthquake from the stress waveform and evaluating the fatigue accumulation coefficient of the evaluation target equipment 2.

[0082] The other configurations and operations are substantially the same as those of the fatigue damage evaluation method and fatigue damage evaluation program of the first embodiment described above, and details thereof will be omitted.

[0083] The fatigue damage evaluation method and fatigue damage evaluation program of the third embodiment of the present invention also provide substantially the same effects as those of the fatigue damage evaluation method and fatigue damage evaluation program of the first embodiment described above.

[0084] In addition, in the third embodiment, the contribution rate of each vibration mode of equipment excited during an earthquake is taken into account, and the stress waveform is calculated using the superimposed displacement waveform, making it possible to perform fatigue evaluation that takes into account in more detail the relationship in magnitude of the stress generated between each vibration mode and the effect of high-frequency components on fatigue.

[0085] <Other> The present invention is not limited to the above-mentioned embodiment, but includes various modified examples. The above-mentioned embodiment has been described in detail to explain the present invention in an easily understandable manner, and the present invention is not necessarily limited to the embodiment having all of the described configurations.

[0086] It is also possible to replace a part of the configuration of one embodiment with the configuration of another embodiment, or to add the configuration of another embodiment to the configuration of one embodiment. It is also possible to add, delete, or replace part of the configuration of each embodiment with the configuration of another embodiment. [Explanation of symbols]

[0087] 1...Floor of the reactor building where the equipment to be evaluated is installed 2. Equipment to be evaluated 3. Equipment installation location on the reactor building floor 3A…Equipment installation position 1 3B…Equipment installation position j 3C…Equipment installation position j max 4…Displacement amplitude 5. Equipment and piping systems with multiple support points f i …Natural frequency of a one-mass system model corresponding to the i-th mode m i …Mass of a one-mass system model corresponding to the i-th mode c i …Damping coefficient of a one-mass system model corresponding to the i-th mode k i …Stiffness of a one-mass system model corresponding to the i-th mode M: Mode number with the maximum frequency in the target frequency range X ki …Natural frequency f i The displacement amplitude that is the k-th extreme value of the time history displacement response waveform at X max …Maximum displacement of time history displacement response waveform σ max …Maximum peak stress assumed in the peak stress method σ ki …Natural frequency f i The stress amplitude of the kth peak in the time history stress waveform of N 0 …Maximum peak stress σ max Allowable number of repetitions of N ki …Natural frequency f iThe kth peak in the time history stress waveform (stress amplitude σ ki ) allowed repetition count L…Number of stress peaks F i …Natural frequency f i Fatigue accumulation factor in N ei …Natural frequency f i Equivalent number of repetitions in N e …Equivalent number of cycles for design σ α …Maximum stress on equipment caused by maximum acceleration response during earthquake N α …The allowable number of repetitions of maximum stress on equipment caused by maximum acceleration response during an earthquake F ij …Natural frequency f at equipment installation position j i Fatigue accumulation factor in j max …Maximum number of equipment locations k max …The amplitude number when the displacement and stress amplitude are maximum i max …The order of the vibration mode in which the maximum displacement occurs in the target frequency range X kij …Natural frequency f at equipment installation position j i The displacement amplitude that is the k-th extreme value of the time history displacement response waveform of a single mass system of σ kij …The kth peak in the time history stress waveform of natural frequency fi at the equipment installation position j Stress amplitude that becomes the target N eij …Natural frequency f at equipment installation position j i Equivalent number of repetitions in x i (t)…Time history displacement response waveform of the i-th vibration mode β i …Stimulation coefficient of the i-th vibration mode u ij …Eigenmode vector value at point j of the equipment in the i-th vibration mode B ij …Stimulus function value at point j of the equipment in the i-th vibration mode yj (t)…Actual displacement response waveform at point j of the equipment Y k …The displacement amplitude that is the k-th extreme value of the actual displacement response waveform Y max …Maximum displacement of actual displacement response waveform N k …Allowable number of repetitions of the k-th peak in the time history stress waveform obtained from the actual displacement response waveform σ k …The stress amplitude of the kth peak in the time history stress waveform obtained from the actual displacement response waveform F: Fatigue accumulation coefficient based on the stress waveform obtained from the actual displacement response waveform

Claims

1. A procedure for calculating the acceleration response waveform at the installation position of the target equipment through earthquake response analysis; a time history response analysis step of performing a time history response analysis by varying the natural frequency of a one-mass-point system model using the acceleration response waveform obtained in the acceleration response waveform calculation step as an input; A time history displacement response waveform calculation procedure for calculating a time history displacement response waveform for each vibration mode of a target device that is not modeled in the time history response analysis; A procedure in which it is assumed that the maximum stress generated during an earthquake occurs at the maximum value of the time history displacement response waveform of all vibration modes; A stress waveform calculation procedure for obtaining a stress waveform so that the displacement amplitude ratio to the maximum displacement in the time history and the stress amplitude ratio to the maximum stress are equal; an allowable number of cycles calculation procedure for calculating an allowable number of cycles of each peak of the stress waveform obtained in the stress waveform calculation procedure from a design fatigue diagram; and a fatigue accumulation factor evaluation step for calculating an equivalent number of cycles during an earthquake by summing up the ratio of the maximum peak stress calculated in the allowable number of cycles calculation step to the allowable number of cycles, and evaluating the fatigue accumulation factor of the equipment. Fatigue damage assessment methods.

2. The fatigue damage evaluation method according to claim 1, In the acceleration response waveform calculation step, the acceleration response waveform is calculated for each of the equipment installation positions, the equipment having a plurality of installation positions being the target, In the time history response analysis procedure and the time history displacement response waveform calculation procedure, the acceleration response waveform is input as the time history response analysis, and a natural frequency of a one-mass system model is varied to calculate a time history displacement response waveform for each vibration mode of the target equipment, In the assumption procedure, it is assumed that the maximum stress generated during the earthquake occurs at the maximum value of the time history displacement response waveform of all vibration modes of all equipment installation positions. Fatigue damage assessment methods.

3. The fatigue damage evaluation method according to claim 1, In the assumption step, a maximum peak stress is assumed at a maximum displacement of a displacement time history response waveform obtained by multiplying a displacement time history response waveform for each vibration mode of the target equipment by a stimulus function and adding the results together; In the stress waveform calculation procedure, the displacement time history response waveform is calculated so that the displacement amplitude ratio to the maximum displacement is equivalent; In the fatigue accumulation factor evaluation step, an equivalent number of cycles during an earthquake is calculated from the stress waveform, and a fatigue accumulation factor of the target equipment is evaluated. Fatigue damage assessment methods.

4. A procedure for calculating the acceleration response waveform at the installation position of the target equipment through earthquake response analysis; a time history response analysis step of performing a time history response analysis by varying the natural frequency of a one-mass-point system model using the acceleration response waveform obtained in the acceleration response waveform calculation step as an input; A time history displacement response waveform calculation procedure for calculating a time history displacement response waveform for each vibration mode of a target device that is not modeled in the time history response analysis; A procedure in which it is assumed that the maximum stress generated during an earthquake occurs at the maximum value of the time history displacement response waveform of all vibration modes; A stress waveform calculation procedure for obtaining a stress waveform so that the displacement amplitude ratio to the maximum displacement in the time history and the stress amplitude ratio to the maximum stress are equal; an allowable number of cycles calculation procedure for calculating an allowable number of cycles of each peak of the stress waveform obtained in the stress waveform calculation procedure from a design fatigue diagram; a fatigue accumulation coefficient evaluation procedure for calculating an equivalent number of cycles during an earthquake by summing up the ratio of the maximum peak stress calculated in the allowable number of cycles calculation procedure to the allowable number of cycles, and evaluating the fatigue accumulation coefficient of the equipment. Fatigue damage assessment step.

5. In the fatigue damage evaluation step according to claim 4, In the acceleration response waveform calculation step, the acceleration response waveform is calculated for each of the equipment installation positions, the equipment having a plurality of installation positions being the target, In the time history response analysis procedure and the time history displacement response waveform calculation procedure, the acceleration response waveform is input as the time history response analysis, and a natural frequency of a one-mass system model is varied to calculate a time history displacement response waveform for each vibration mode of the target equipment, In the assumption procedure, it is assumed that the maximum stress generated during the earthquake occurs at the maximum value of the time history displacement response waveform of all vibration modes of all equipment installation positions. Fatigue damage assessment step.

6. In the fatigue damage evaluation step according to claim 4, In the assumption step, a maximum peak stress is assumed at a maximum displacement of a displacement time history response waveform obtained by multiplying a displacement time history response waveform for each vibration mode of the target equipment by a stimulus function and adding the results together; In the stress waveform calculation procedure, the displacement time history response waveform is calculated so that the displacement amplitude ratio to the maximum displacement is equivalent; In the fatigue accumulation factor evaluation step, an equivalent number of cycles during an earthquake is calculated from the stress waveform, and a fatigue accumulation factor of the target equipment is evaluated. Fatigue damage assessment step.

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