Systems and methods for monitoring material fatigue

Abstract

A system for monitoring the fatigue of a mechanical structure includes a memory (101) that stores response values, each response value being associated with one of a plurality of predetermined stress ranges and one of a plurality of predetermined mean stresses. Each response value represents an upper limit of the number of stress cycles at a predetermined observation point of the mechanical structure in the case where a cycle has a stress range and a mean stress associated with the response value. The system includes a processing device (103) for updating a stress history value for each response value, the stress history value representing the number of cycles that have occurred in the time trend of the stress and having a stress range and a mean stress associated with the response value. Based on the response value and the stress history value, a fatigue damage sum is updated. The fatigue damage sum represents the cumulative fatigue damage of the mechanical structure and can be used for real-time fatigue monitoring.

Description

Technical Field

[0001] The present disclosure generally relates to monitoring material fatigue. More specifically, the present disclosure relates to a system and method for monitoring fatigue of a mechanical structure. In addition, the present disclosure relates to a computer program for monitoring fatigue of a mechanical structure. Background Art

[0002] In many cases, mechanical structures are subjected to cyclic mechanical loads, which may cause fatigue in the materials of the mechanical structures. The mechanical structure can be, for example, part of a working machine (such as a crane), part of a vehicle, or part of some other equipment, or the entire equipment. If the above cyclic mechanical load is higher than a certain threshold, microcracks will begin to form at stress concentration points, such as the surface, persistent slip bands "PSB", component interfaces in the case of composite materials, and grain interfaces in the case of metals. After crack initiation, the cracks will propagate, and finally, the mechanical structure will eventually fail due to fatigue. The shape of the mechanical structure can significantly affect the fatigue strength. For example, square holes and sharp corners can cause local stress elevation, resulting in fatigue cracks. In contrast, round holes and smooth transitions and fillets will increase the fatigue strength of the mechanical structure. In welded metal structures, the area adjacent to the weld joint is usually critical because, from the perspective of fatigue strength, the local geometry, high residual stress, and the presence of welding deformation in the weld joint are usually not ideal.

[0003] An inherent challenge associated with damage caused by fatigue is that during the use of the mechanical structure, it is generally impossible to identify the above microcracks. Another challenge is that crack propagation accelerates as the crack length increases, and thus the mechanical structure may fail due to fatigue even if the load remains unchanged. Therefore, in many cases, fatigue of the materials of the mechanical structure may lead to costly production stoppages. Therefore, there is a need for techniques for monitoring fatigue in mechanical structures during the life of the mechanical structure. Summary of the Invention

[0004] A simplified overview is given below in order to provide a basic understanding of some aspects of various inventive embodiments. This overview is not an extensive summary of the present invention. It is neither intended to identify the key or decisive elements of the present invention nor to depict the scope of the present invention. The following overview only presents some concepts of the present invention in a simplified form as a prelude to a more detailed description of the exemplary embodiments of the present invention.

[0005] According to the present invention, there is provided a new system for monitoring fatigue of a mechanical structure. For example, the mechanical structure can be part of a working machine (such as a crane), part of a vehicle, or part of some other equipment, or the entire equipment.

[0006] The system according to the present invention includes a storage device that stores a database containing predetermined response values, each response value being associated with one of a predetermined stress range (i.e., a stress change range) and one of a predetermined mean stress. In the case where a cycle has a predetermined stress range and a predetermined mean stress associated with the considered response value, each response value represents an upper limit of the number of stress cycles at a predetermined observation point of the mechanical structure, where the upper limit corresponds to a predetermined survival probability of the mechanical structure.

[0007] The system further includes a processing device configured to:

[0008] - For each of the above response values, repeatedly update a stress history value that represents the number of cycles that have occurred in the time trend of the stress and has a predetermined stress range and a predetermined mean stress associated with the considered response value, and

[0009] - Based on the response value and the stress history value associated with the response value, repeatedly update the total fatigue damage.

[0010] The total fatigue damage represents the cumulative fatigue damage of the mechanical structure, and thus the total fatigue damage can be used for real-time fatigue monitoring during the life of the mechanical structure. The system according to an advantageous embodiment of the present invention is suitable for real-time monitoring of the fatigue of a mechanical structure during its use.

[0011] It is noted that the calculations performed to update the above total fatigue damage do not necessarily have to be performed with stress values, but can also be performed with values of another quantity related to stress. For example, each response value can be associated with one of a predetermined strain range and one of a predetermined mean strain. However, since strain is related to stress via deterministic rules, the response value is indirectly related to one of a predetermined stress range and one of a predetermined mean stress.

[0012] According to the present invention, there is also provided a new method for monitoring the fatigue of a mechanical structure. The method includes:

[0013] - Maintaining a database containing predetermined response values, each response value being associated with one of a predetermined stress range and one of a predetermined mean stress. In the case where a cycle has a predetermined stress range and a predetermined mean stress associated with the considered response value, each response value represents an upper limit of the number of stress cycles at a predetermined observation point of the mechanical structure, and the upper limit corresponds to a predetermined survival probability of the mechanical structure,

[0014] - For each of the above response values, repeatedly update a stress history value that represents the number of cycles that have occurred in the time trend of the stress and has a predetermined stress range and a predetermined mean stress associated with the considered response value, and

[0015] - Repeatedly update the total fatigue damage based on the response value and the stress history value associated with the response value.

[0016] According to the present invention, there is also provided a new computer program for monitoring the fatigue of a mechanical structure. The computer program includes computer-executable instructions for controlling a programmable processing device to:

[0017] - Retrieve data from a database containing predetermined response values, each response value being associated with one of a predetermined stress range and one of a predetermined mean stress, and in the case of a cycle having the predetermined stress range and the predetermined mean stress associated with the considered response value, each response value represents an upper limit of the number of stress cycles at a predetermined observation point of the mechanical structure, the upper limit corresponding to a predetermined survival probability of the mechanical structure,

[0018] - For each response value, repeatedly update the stress history value, which represents the number of cycles occurring in the time trend of the stress and has the predetermined stress range and the predetermined mean stress associated with the considered response value, and

[0019] - Repeatedly update the total fatigue damage based on the response value and the stress history value associated with the response value.

[0020] According to the present invention, there is also provided a new computer program product. The computer program product includes a non-volatile computer-readable medium encoded with the computer program according to the present invention, for example, a compact disc "CD".

[0021] Various exemplary and non-limiting embodiments are described in the appended dependent claims.

[0022] When read in conjunction with the accompanying drawings, the exemplary and non-limiting embodiments regarding the construction and method of operation, together with their additional objects and advantages, will be best understood from the following description of specific exemplary embodiments.

[0023] The verbs "comprise" and "include" are used in this document as open limitations, neither excluding nor requiring the presence of unrecited features. Unless otherwise explicitly stated, the features recited in the appended dependent claims may be freely combined with each other. In addition, it should be understood that the use of "a" or "an" (i.e., the singular form) in this document does not exclude the plural. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The exemplary and non-limiting embodiments and their advantages are explained in more detail in the following examples and with reference to the drawings, in which:

[0025] Figure 1 A functional block diagram of a system for monitoring the fatigue of a mechanical structure according to an exemplary and non-limiting embodiment is shown,

[0026] Figure 2a and Figure 2b illustrates an exemplary manner of visualization results obtained by a system according to exemplary and non - limiting embodiments, and

[0027] Figure 3 illustrates a flowchart of a method for monitoring fatigue of a mechanical structure according to exemplary and non - limiting embodiments. DETAILED DESCRIPTION

[0028] The specific examples provided in the following description should not be construed as limiting the scope and / or applicability of the appended claims. Unless otherwise expressly stated, the lists and groups of examples provided in the specification are not exhaustive.

[0029] Figure 1 illustrates a functional block diagram of a system for monitoring fatigue of an exemplary mechanical structure 109 according to exemplary and non - limiting embodiments. In Figure 1 the exemplary case shown, the mechanical structure 109 includes a welded T - joint 110, and fatigue at an observation point 111 of the mechanical structure 109 is monitored. It should be noted that the mechanical structure 109 is shown for illustrative purposes only, and Figure 1 the system shown is applicable to many different mechanical structures to be monitored.

[0030] The system includes a storage device 101 that stores a database 102, and the database 102 contains predetermined response values N 1,1 ,…,N P,Q . Each predetermined response value N 1,1 ,…,N P,Q is associated with one of the predetermined stress ranges Δσ1,…,Δσ ，Q and one of the predetermined mean stresses σ 1,mean ,…,σ P,mean . In the case where a cycle has a predetermined stress range Δσ and a predetermined mean stress σ mean associated with the considered response value, each response value represents an upper limit of the number of stress cycles at the observation point 111 of the mechanical structure 109. This upper limit corresponds to a predetermined survival probability of the mechanical structure 109 in the above - mentioned case. Each predetermined response value N 1,1 ,…,N P,Q can be estimated based on the fatigue performance of the mechanical structure 109. Generally, on the positive side, the sum of the mean stress and the amplitude converted to the nominal stress level (i.e., stress range / 2) should not exceed the yield strength of the considered material. The maximum allowable compressive nominal membrane stress should not exceed the yield strength on the compressive side, respectively. In the exemplary case of monitoring thin and slender mechanical structures, the maximum allowable compressive stress related to the buckling capacity, such as plate buckling, bending, or lateral buckling of columns, should not be exceeded.

[0031] Each response value N k,q (where k = 1, 2, ..., P and q = 1, 2, ..., Q) can be calculated, for example, according to the following equations:

[0032]

[0033] where C ref is the fatigue performance specific to the mechanical structure under consideration and corresponds to the selected survival probability, Δσ q is the stress range at the observation point of the mechanical structure, and m ref is a model parameter (i.e., the slope of the S-N curve, e.g., 5.85). R local is the local stress ratio at the observation point (e.g., notch) of the mechanical structure:

[0034]

[0035] where σ mean and Δσ are the mean stress and stress range, respectively, at the observation point of the mechanical structure, taking into account the elastic-plastic behavior of the material.

[0036] The above local stress ratio R local and the subsequent response value N k,q depend particularly on the material strength, residual stresses within the mechanical structure (in both the welded and post-welded conditions), the geometry and dimensions of the mechanical structure, etc., and the weld joint and / or edge-cutting parameters, such as the toe or root side geometry of the weld joint and the surface quality of the edge cut.

[0037] The theoretical background related to the above Equations 1 and 2 can be found in the following publications: Timo and Timo 's "Assessment of fatigue strength of steel buttwelded joints in as-welded condition – Alternative approaches for curve fitting and mean stress effect analysis", Lappeenranta University of Technology, Steel Structures Laboratory, Marine Structures 44, pp. 288–310, 2015, Elsevier Ltd; and Timo and Timo "A new proposal for assessment of the fatigue strength of steel butt welded joints improved by peening under constant amplitude tensile loading", School of Energy Systems, Lappeenranta University of Technology, Wiley Publishing Ltd. Fatigue Fract Engng Mater Struct, 2016, 39, pp. 566 - 582. It should be noted that the above response values N 1,1 ,…,N P,Q can be obtained by any suitable method, and thus the present invention is not limited to any specific method for obtaining the response values N 1,1 ,…,N P,Q .

[0038] The above mean stress advantageously takes into account the mean stress level of the external stress range and the influence of the residual stress. The third - level stress (i.e., the third - order stress) of the residual stress as the notch stress level is advantageously considered at the notch stress, and the second - order stress as the structural - level stress is advantageously multiplied by the notch factor. Moreover, the relaxation of the residual stress can be considered, and the analysis can apply the relaxed stress values.

[0039] The system includes a processing device 103 configured to repeatedly update the corresponding stress - history values n 1,1 ,…,n P,Q for each of the above - mentioned response values N 1,1 (t),…,n P,Q (t), where the corresponding stress - history values n 1,1 (t),…,n P,Q (t) represent the number of cycles occurring in the time trend of the stress σ(t) and have a predetermined stress range and a predetermined mean stress related to the considered response value. The stress - history values n 1,1 (t),…,n P,Q (t) are represented as a function of time t since their values change with time. The update rate can be, for example, in the range of 0.01 Hz to 20 Hz. In other words, the time interval between successive updates of the stress - history values n 1,1 (t),…,n P,Q (t) can be from 50 milliseconds to 100 seconds. In the Figure 1 example system shown, the storage device 101 stores a database 107 that contains the stress - history values n 1,1(t), …, n P,Q (t).

[0040] In a system according to exemplary and non - limiting embodiments, the processing device 103 is configured to run a rain - flow counting algorithm to update the stress history value n based on the time trend of the stress σ(t) at the observation point 111 of the mechanical structure 109 1,1 (t), …, n P,Q (t). The rain - flow counting algorithm (also known as the "rain - flow counting method") is commonly used in fatigue analysis and monitoring to reduce a stress spectrum that varies over time into a set of cycle counts that correspond to a given set of mean values and a given set of ranges of variation. For example, more details of the relevant rain - flow counting algorithm can be found in the publication "M. Matsuishi and T. Endo: Metal Fatigue under Varying Stresses, Transactions of the Japanese Society of Mechanical Engineers 1968". It should be noted that there are many cycle - counting algorithms for fatigue analysis and monitoring, and thus the present invention is not limited to any particular cycle - counting algorithm.

[0041] The processing device 103 is configured to update the fatigue damage sum D based on the response values N 1,1 , …, N P,Q and the stress history values n 1,1 (t), …, n P,Q (t) that are related to the response values. The fatigue damage sum D represents the cumulative fatigue damage of the mechanical structure 109 and can be used to estimate the remaining service life that can be generated by the mechanical structure. The update rate can be, for example, in the range of 0.01 Hz to 20 Hz. In other words, the time interval between successive updates of the fatigue damage sum D can be from 50 milliseconds to 100 seconds.

[0042] In a system according to exemplary and non - limiting embodiments, the processing device 103 is configured to calculate the fatigue damage sum D according to the Palmgren - Miner damage accumulation formula:

[0043]

[0044] A system according to exemplary and non - limiting embodiments includes a display element 106, and the processing device 103 is configured to control the display element 106 to show the growth of the fatigue damage sum D as a function of the cumulative service generated by the mechanical structure 109. The display element 106 can be, for example, a part of the user interface 108 of the system. The cumulative service generated by the mechanical structure 109 can be, for example, the cumulative service time, the cumulative distance traveled by a vehicle or another device including the mechanical structure, the cumulative load mass transferred or lifted by a device including the mechanical structure, the cumulative product of the transferred mass and the transferred distance (e.g., ton - kilometers), or some other quantity indicating the cumulative service generated by the device including the mechanical structure 109.

[0045] In a system according to exemplary and non - limiting embodiments, the processing device 103 is configured to calculate the average growth rate of the total fatigue damage D. In Figure 2a , the average growth rate of the total fatigue damage D is the slope of line 223. The processing device 103 is configured to estimate the remaining service life P res 1,1 (e.g., remaining useful time) that can be generated by the mechanical structure 109 based on: i) the current value D curr of the total fatigue damage D, ii) the above - mentioned average growth rate of the total fatigue damage, and iii) the value of the total fatigue damage corresponding to a predetermined damage probability. In Figure 2a , line 221 represents the total damage value D1 corresponding to the first damage probability, and line 222 represents the total damage value D2 corresponding to a second damage probability greater than the first damage probability. In other words, the total damage value D1 corresponds to a greater survival probability than the total damage value D2.

[0046] In a system according to exemplary and non - limiting embodiments, the processing device 103 is configured to calculate an estimated value of the instantaneous growth rate dD / dt of the total fatigue damage D. In Figure 2a , the instantaneous growth rate of the total fatigue damage D is the slope of line 224. The instantaneous growth rate can be estimated as, for example, (D(t0) – D(t -1 )) / (t0 – t -1 ), where t0 is the update time of the total fatigue damage D, and t -1 is an earlier update time of the total fatigue damage D. However, numerical derivations of the above type are vulnerable to interference, and thus it may be more advantageous to fit a polynomial or some other suitable curve to the time - discrete values of the total fatigue damage D and then estimate the instantaneous growth rate using the derivative of the polynomial or some other suitable curve. The processing device 103 is configured to estimate the remaining service life P res 1,2 that can be generated by the mechanical structure 109 based on: i) the current value D curr of the total fatigue damage D, ii) the estimate of the instantaneous growth rate of the total fatigue damage D, and iii) the value of the total fatigue damage corresponding to a predetermined damage probability (e.g., D1 or D2).

[0047] Figure 2b Shows a display dial that shows the instantaneous growth rate dD / dt of the total fatigue damage D. "Normal use / 100%" corresponds to the designed (i.e., nominal) instantaneous growth rate of the total fatigue damage D, such that if the instantaneous growth rate dD / dt were always "normal use / 100%", the mechanical structure would produce the designed cumulative service, e.g., designed service time.

[0048] In a system according to exemplary and non - limiting embodiments, Figure 1 the processing device 103 shown in is configured to repeatedly estimate a stress σ(t) at an observation point 111 of a mechanical structure 109 based on data indicating a mechanical load directed to the mechanical structure 109. The estimation rate can be, for example, in the range of 0.01 Hz to 20 Hz. In other words, the time interval between successive estimations of the stress σ(t) can be from 50 milliseconds to 100 seconds. The measurement rate is advantageously significantly greater than the above - mentioned estimation rate. For example, the measurement rate can be in the range from 1 Hz to 5 kHz. The system may also include a data interface for receiving data indicating the stress σ(t) at the observation point 111 of the mechanical structure 109 from an external device.

[0049] In a system according to exemplary and non - limiting embodiments, the processing device 103 is configured to calculate the stress σ(t) at the observation point 111 as a weighted sum of i) a membrane stress σ m (t) and ii) a bending stress σ b (t) acting on a region of the mechanical structure 109 at a distance from the observation point 111 of the mechanical structure 109. The weight factors of the weighted sum are predetermined local stress concentration factors K m for the membrane stress σ b (t) and K t,m for the bending stress σ t,b . Thus, in this exemplary case, the processing device 103 is configured to calculate the following stress σ k (t) according to the following equation:

[0050] σ k (t)=K t,m σ m (t)+K t,b σ b (t). (4)

[0051] An exemplary method for determining local stress concentration factors based on finite element analysis "FEA" is presented in the following publication: A. Ahola, T. and T. "Effect of loading type on the fatigue strength of asymmetric and symmetric transverse non-load carrying attachments", School of Energy Systems, Lappeenranta University of Technology, Wiley Publishing Ltd. Fatigue Fract Engng Mater Struct, 2017, 40, pp. 670-682. An exemplary method for determining the local stress concentration factor based on an artificial neural network "ANN" is presented in the following publication: M. Dabiri, M. Ghafouri, H. R. Rohani Raftar and T. "Neural network-based assessment of the stress concentration factor in a T-welded joint", Steel Structures Laboratory, Lappeenranta University of Technology, Journal of Constructional Steel Research 128, pp. 567-578, 2017. An exemplary method for determining the local stress concentration factor based on an analytical equation is presented in the following publication: "Stress concentration factor formulae widely used in Japan" by K. Iida and T. Uemura, University of Tokyo, Fatigue Fract. Engng Mater. Struct. Vol. 19, No. 6, pp. 779-786, 1996.

[0052] In a system according to an exemplary and non-limiting embodiment, the processing device 103 is configured to calculate the above-mentioned membrane stress σ m (t) and bending stress σ b (t) based on the outputs s1(t) and s2(t) of the strain gauges 104 and 105 attached to the mechanical structure 109. The membrane stress σ m (t) is proportional to the average value (s1(t)+s2(t)) / 2 of the outputs of the strain gauges 104 and 105, and the bending stress σ b (t) is proportional to the difference s1(t)–s2(t) of the outputs of the strain gauges 104 and 105. In many cases, there may be more than two strain gauges.

[0053] In a system according to exemplary and non-limiting embodiments, a processing device 103 is configured to calculate a stress σ k (t) at an observation point 111 of a mechanical structure 109 based on a force directed to the mechanical structure 109, an inverse matrix of a stiffness matrix of a finite element model of at least a portion of the mechanical structure 109, and an element-level force-displacement equation of the finite element model indicating that stress σ k (t) varies with a nodal displacement of a suitable node of the finite element model. In an exemplary case where the mechanical structure 109 operates in a linear region such that Hooke's law is valid, a storage device 101 is advantageously configured to store the inverse matrix of the stiffness matrix of the finite element model, and the processing device 103 is advantageously configured to use the stored inverse matrix of the stiffness matrix when repeatedly calculating stress σ k (t). Thus, it is not necessary to calculate the inverse matrix of the stiffness matrix every time stress σ k (t) is calculated.

[0054] In a system according to exemplary and non-limiting embodiments, in addition to a predetermined stress range and a predetermined mean stress, each value in a set of response values N 1,1 , …, N P,Q is related to one or more quantities that describe the operating condition of the mechanical structure 109. The one or more quantities may include, for example, the temperature of the mechanical structure 109, since the strength capacity of the mechanical structure 109 may depend on temperature. In this exemplary case, the processing device 103 is configured to update each stress history value n 1,1 (t), …, n P,Q (t) to represent the number of cycles that occur in the time trend of the stress such that 1) the cycles that occur have a predetermined stress range and a predetermined mean stress related to the response value being considered, and 2) the operating condition of the mechanical structure 109 corresponds to one or more quantities related to the response value being considered. For example, the temperature of the mechanical structure belongs to a temperature range related to the response value being considered, and / or the effect of a corrosive environment on the fatigue performance of the material corresponds to the same effect of the corrosive environment related to the response value being considered. In this exemplary embodiment, one or more values in the set of response values N 1,1 , …, N P,Q may be related to the same stress range and the same mean stress, and the one or more quantities that describe the operating condition differ between these response values.

[0055] The implementation of the processing device 103 may be based on one or more analog circuits, one or more digital processing circuits, or a combination thereof. Each digital processing circuit may be a programmable processor circuit provided with appropriate software, a dedicated hardware processor (such as an application specific integrated circuit "ASIC"), or a configurable hardware processor (such as a field programmable gate array "FPGA"). The memory device 101 may include one or more memory circuits, and each memory circuit may be, for example, a random access memory "RAM" circuit.

[0056] Figure 3 A flowchart of a method for monitoring fatigue of a mechanical structure according to an exemplary and non - limiting embodiment is shown. The method includes the following actions:

[0057] - Action 301: Maintain a database containing predetermined response values, each response value being associated with one of a predetermined stress range and one of a predetermined mean stress. In the case where a cycle has the predetermined stress range and the predetermined mean stress associated with the considered response value, each response value represents an upper limit of the number of stress cycles at a predetermined observation point of the mechanical structure, and this upper limit corresponds to a predetermined survival probability of the mechanical structure.

[0058] - Action 302: For each response value, repeatedly update the stress history value, which represents the number of cycles that have occurred in the time trend of the stress and has the predetermined stress range and the predetermined mean stress associated with the considered response value, and

[0059] - Action 303: Based on the response value and the stress history value associated with the response value, repeatedly update the total fatigue damage, which represents the cumulative fatigue damage of the mechanical structure.

[0060] The method according to an exemplary and non - limiting embodiment includes: repeatedly estimating the stress at a predetermined observation point of the mechanical structure based on data indicating the mechanical load applied to the mechanical structure.

[0061] The method according to an exemplary and non - limiting embodiment includes: calculating the stress as a weighted sum of i) the membrane stress and ii) the bending stress acting on a region of the mechanical structure at a certain distance from the predetermined observation point of the mechanical structure. The weighting factors of the weighted sum are predetermined local stress concentration factors defined for the membrane stress and the bending stress, respectively.

[0062] The method according to an exemplary and non - limiting embodiment includes: calculating the membrane stress and the bending stress based on the output of a strain gauge attached to the mechanical structure. The membrane stress is proportional to the average value of the output of the strain gauge, and the bending stress is proportional to the difference of the output of the strain gauge.

[0063] The method according to exemplary and non - limiting embodiments includes calculating stress based on a force directed at a mechanical structure, an inverse matrix of a stiffness matrix of a finite - element model of at least a portion of the mechanical structure, and an element - level force - displacement equation of the finite - element model representing stress as a function of nodal displacements of the finite - element model.

[0064] The method according to exemplary and non - limiting embodiments includes storing an inverse matrix of the stiffness matrix of the finite - element model in a storage device and using the stored inverse matrix of the stiffness matrix in repeated stress calculations.

[0065] The method according to exemplary and non - limiting embodiments includes calculating a fatigue damage sum D according to the following equation:

[0066]

[0067] where n i,j (t) is a stress - history value that represents the number of cycles that occur in a time trend of stress and has a ith predetermined stress range and a jth predetermined mean stress, and N i,j is a response value associated with the ith predetermined stress range and the jth predetermined mean stress.

[0068] In the method according to exemplary and non - limiting embodiments, in addition to the predetermined stress range and the predetermined mean stress, each response value is related to one or more quantities that describe the operating condition of the mechanical structure, such as the temperature of the mechanical structure. In the method according to this exemplary and non - limiting embodiment, each stress - history value is updated to represent the number of cycles that occur in a time trend of stress such that 1) the cycles that occur have a predetermined stress range and a predetermined mean stress associated with the considered response value, and 2) the operating condition of the mechanical structure corresponds to one or more quantities associated with the considered response value.

[0069] The method according to exemplary and non - limiting embodiments includes controlling a display element to show the growth of the fatigue damage sum as a function of the cumulative service produced by the mechanical structure.

[0070] The method according to exemplary and non - limiting embodiments includes calculating an average growth rate of the fatigue damage sum and estimating the remaining service that the mechanical structure can produce based on: i) the current value of the fatigue damage sum, ii) the average growth rate of the fatigue damage sum, and iii) the value of the fatigue damage sum corresponding to a predetermined damage probability.

[0071] The method according to an exemplary and non - limiting embodiment includes calculating an estimate of the instantaneous growth rate of the total fatigue damage and estimating the remaining service that a mechanical structure can provide based on: i) the current value of the total fatigue damage, ii) the estimate of the instantaneous growth rate of the total fatigue damage, and iii) the value of the total fatigue damage corresponding to a predetermined damage probability.

[0072] A computer program according to an exemplary and non - limiting embodiment includes computer - executable instructions for controlling a programmable processing device to perform actions related to the method according to any of the above - mentioned exemplary and non - limiting embodiments.

[0073] A computer program according to an exemplary and non - limiting embodiment includes a software module for monitoring the fatigue of a mechanical structure. The software module includes computer - executable instructions for controlling a programmable processing device to:

[0074] - retrieve data from a database containing predetermined response values, each response value being related to one of a predetermined stress range and one of a predetermined mean stress, and each response value representing an upper limit of the number of stress cycles at a predetermined observation point of the mechanical structure in the case where a cycle has the predetermined stress range and the predetermined mean stress related to the considered response value, the upper limit corresponding to a predetermined survival probability of the mechanical structure,

[0075] - for each response value, repeatedly update a stress history value, the stress history value representing the number of cycles that have occurred in the time trend of the stress and having the predetermined stress range and the predetermined mean stress related to the considered response value, and

[0076] - based on the response value and the stress history value related to the response value, repeatedly update a total fatigue damage, the total fatigue damage representing the cumulative fatigue damage of the mechanical structure.

[0077] The software module can be, for example, a sub - routine or a function implemented with programming tools suitable for a programmable processing device.

[0078] A computer program product according to an exemplary and non - limiting embodiment includes a computer - readable medium encoded with a computer program according to an exemplary and non - limiting embodiment, such as a compact disc "CD".

[0079] A signal according to an exemplary and non - limiting embodiment is encoded to carry information defining a computer program according to an exemplary and non - limiting embodiment.

[0080] The specific examples provided in the above description should not be construed as limiting the scope and / or applicability of the appended claims. The lists and groups of examples provided in the above description are not exhaustive unless otherwise expressly stated.

Claims

1. A system for monitoring the fatigue of a mechanical structure, characterized in that, The system includes a storage device (101) that stores a database (102) containing predetermined response values (N 1,1, …, N P,Q ), each response value being associated with one of a plurality of predetermined stress ranges and one of a plurality of predetermined mean stresses, and each response value representing an upper limit of the number of stress cycles at a predetermined observation point of the mechanical structure in the case where a cycle has a predetermined stress range and a predetermined mean stress associated with the considered response value, the upper limit corresponding to a predetermined survival probability of the mechanical structure, wherein the system includes a processing device (103) configured to: - For each response value, repeat the update of the stress history values (n 1,1 (t), …, n P,Q (t)), where the stress history values (n 1,1 (t), …, n P,Q (t)) represent the number of cycles occurring in the time trend of the stress and have a predetermined stress range and a predetermined mean stress associated with the response value being considered, and - Repeatedly update the total fatigue damage (D) based on the response value and the stress history value associated with the response value, where the total fatigue damage represents the cumulative fatigue damage of the mechanical structure. where, for k = 1, 2, ..., P and q = 1, 2, ..., Q, each response value N k,q is given by: where C ref is the fatigue property specific to the mechanical structure and corresponds to a predetermined survival probability, Δσ q is the predetermined stress range at a predetermined observation point of the mechanical structure and is related to the response value N k,q and m ref is a model parameter, which is the slope of the S-N curve, and R local is the local stress ratio at a predetermined observation point of the mechanical structure: where σ mean and Δσ are the mean stress and stress range at the observation point of the mechanical structure.

2. The system according to claim 1, wherein The processing device (103) is configured to repeatedly estimate the stress at a predetermined observation point of the mechanical structure based on data indicating the mechanical load applied to the mechanical structure.

3. The system according to claim 2, wherein, The processing device is configured to calculate the stress as a weighted sum of i) the membrane stress (σ m (t)) and ii) the bending stress (σ b (t)) acting on a region of the mechanical structure at a distance from a predetermined observation point of the mechanical structure, the weight factors of the weighted sum being predetermined local stress concentration factors (K t,m , K t,b ) defined for the membrane stress and the bending stress, respectively.

4. The system according to claim 3, wherein, The processing device is configured to calculate the membrane stress and the bending stress based on the outputs (s1(t), s2(t)) of strain gauges attached to the mechanical structure, where the membrane stress is proportional to the average value of the outputs of the strain gauges, and the bending stress is proportional to the difference between the outputs of the strain gauges.

5. The system according to claim 4, wherein The system includes the strain gauges (104, 105).

6. The system according to claim 2, wherein, The processing device is configured to calculate the stress based on: the force applied to the mechanical structure; the inverse matrix of the stiffness matrix of a finite element model of at least a part of the mechanical structure; and the element equations of the finite element model representing the stress as a function of the nodal displacements of the finite element model.

7. The system according to claim 6, wherein, The storage device is configured to store the inverse matrix of the stiffness matrix of the finite element model, and the processing device is configured to use the stored inverse matrix of the stiffness matrix when repeatedly calculating the stress.

8. The system according to any one of claims 1 to 7, wherein The processing device is configured to calculate the total fatigue damage D according to the following formula: where n i,j (t) is the stress history value, the stress history value represents the number of cycles occurring in the time trend of stress and has the i-th predetermined stress range and the j-th predetermined mean stress, and N i,j is the response value associated with the i-th predetermined stress range and the j-th predetermined mean stress.

9. The system according to any one of claims 1 to 7, wherein: - In addition to the predetermined stress range and the predetermined mean stress, each response value is also related to one or more quantities describing the operating condition of the mechanical structure, and - The processing device is configured to update each stress history value to represent the number of cycles that occur in the time trend of the stress, such that the cycles that occur have a predetermined stress range and a predetermined mean stress related to the considered response value, and the operating condition of the mechanical structure corresponds to the one or more quantities related to the considered response value.

10. The system according to claim 9, wherein The one or more quantities describing the operating condition of the mechanical structure include the temperature of the mechanical structure.

11. The system according to any one of claims 1 to 7, wherein, The system includes a display element (106), and the processing device is configured to control the display element to show the growth of the total fatigue damage as a function of the cumulative service generated by the mechanical structure.

12. The system according to any one of claims 1 to 7, wherein, The processing device is configured to calculate an average growth rate (223) of the total fatigue damage and estimate a remaining service life (P res 1,1) that can be generated by the mechanical structure based on: i) a current value (D curr ) of the total fatigue damage, ii) the average growth rate of the total fatigue damage, and iii) a value of the total fatigue damage corresponding to a predetermined damage probability.

13. The system according to any one of claims 1 to 7, wherein, The processing device is configured to calculate an estimate of the instantaneous growth rate (224) of the total fatigue damage and estimate the remaining service life (P res 1, 2) that can be generated by the mechanical structure based on: i) the current value (D curr ) of the total fatigue damage, ii) the estimate of the instantaneous growth rate of the total fatigue damage, and iii) the value of the total fatigue damage corresponding to a predetermined damage probability.

14. A method for monitoring the fatigue of a mechanical structure, characterized in that, The method includes: - Maintaining (301) a database containing predetermined response values, each response value being related to a range in a predetermined stress range and a stress in a predetermined mean stress, where each response value represents an upper limit of the number of stress cycles at a predetermined observation point of the mechanical structure in the case where the cycle has a predetermined stress range and a predetermined mean stress related to the considered response value, and the upper limit corresponds to a predetermined survival probability of the mechanical structure. - For each response value, repeatedly updating (302) the stress history value, where the stress history value represents the number of cycles that occur in the time trend of the stress and has a predetermined stress range and a predetermined mean stress related to the considered response value. - Repeatedly update (303) the total fatigue damage based on the response value and the stress history value associated with the response value, where the total fatigue damage represents the cumulative fatigue damage of the mechanical structure. wherein, for k = 1, 2, ..., P and q = 1, 2, ..., Q, each response value N k,q is:[[-END]] where C ref is the fatigue property specific to the mechanical structure and corresponds to a predetermined survival probability, Δσ q is the predetermined stress range at a predetermined observation point of the mechanical structure and is related to the response value N k,q and m ref is a model parameter, which is the slope of the S-N curve, and R local is the local stress ratio at a predetermined observation point of the mechanical structure: where σ mean and Δσ are the mean stress and stress range at the observation point of the mechanical structure.

15. A non - volatile computer - readable medium encoded with a computer program for monitoring the fatigue of a mechanical structure, characterized in that, The computer program includes computer-executable instructions for controlling a programmable processing device to: - Retrieve data from a database containing predetermined response values, each response value being associated with one of a predetermined stress range and a predetermined mean stress. In the case where a cycle has a predetermined stress range and a predetermined mean stress associated with the considered response value, each response value represents an upper limit of the number of stress cycles at a predetermined observation point of the mechanical structure, and the upper limit corresponds to a predetermined survival probability of the mechanical structure. - For each response value, repeatedly update the stress history value, where the stress history value represents the number of cycles occurring in the time trend of the stress and has a predetermined stress range and a predetermined mean stress associated with the considered response value, and - Repeatedly update the total fatigue damage based on the response value and the stress history value associated with the response value, where the total fatigue damage represents the cumulative fatigue damage of the mechanical structure. wherein for k = 1, 2, ..., P and q = 1, 2, ..., Q, each response value N k,q is: where C ref is the fatigue performance specific to the mechanical structure and corresponds to a predetermined survival probability, Δσ q is the predetermined stress range at a predetermined observation point of the mechanical structure and is related to the response value N k,q and m ref is a model parameter, which is the slope of the S-N curve, and R local is the local stress ratio at a predetermined observation point of the mechanical structure: where σ mean and Δσ are the mean stress and stress range at the observation point of the mechanical structure.

Images