CN110569614A - fatigue prediction method for water turbine top cover bolt - Google Patents
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Abstract
The invention discloses a hydraulic turbine top cover bolt fatigue prediction method, which comprises the steps of solving the gradient of stress load to time history to the collected stress load-time history data in the time domain range to obtain the power density of a stress amplitude; carrying out power density conversion on the S-N curve of the top cover bolt material to obtain an S-N power density curve of the bolt material; in the frequency domain range, carrying out short-time Fourier transform on the power density of the stress amplitude of the acquired data to obtain a curve of the stress amplitude changing along with the frequency at a certain moment; predicting the fatigue life of the top cover bolt by using a linear fatigue accumulation method in combination with an S-N power density curve of a bolt material; the method integrates the time domain fatigue life method and the frequency domain fatigue life method, accurately represents the process that the loading frequency of the stress load generates tiny cracks on the bolt, and simultaneously the size of the loading frequency shows the limit degree of high cycle; the prediction method can accurately judge the damage degree of the bolt and predict the fatigue life of the top cover bolt.
Description
Technical Field
The invention relates to the technical field of bolt fatigue prediction, in particular to a method for predicting fatigue of a water turbine top cover bolt.
Background
The water turbine top cover is a main component for supporting the water guide mechanism and the guide bearing parts, is also one of main flow passage components of the water turbine, is of a welding structure, and is connected with a seat ring of the water turbine through key bolts of the top cover, and a main flange adopts a double-flat-plate upper flange structure.
The top cover bolt needs to bear loads under various different working conditions in the actual operation process, including low-cycle high-level loads such as starting, stopping and load shedding, high-cycle loads during normal operation of the unit and sudden-change loads borne during working condition change. The random alternating loads can cause cracks and defects to be formed inside the bolts, and the bolts are subjected to fatigue failure along with the change of working conditions and the accumulation of time, so that the fatigue life of the bolts of the top cover of the water turbine needs to be predicted, and the accidents of flooding plants are avoided.
The traditional bolt fatigue life prediction method is a fatigue life calculation method based on a rain flow method. The rain flow method is a method for counting in the time domain and converting random irregular time-load history into a series of complete cyclic load processes. The counted mean value and amplitude cycle times can comprehensively reflect the whole process of random load. In combination with the linear fatigue criterion, under the repeated action of stress, the damage and the stress cycle form a linear accumulation relationship, and when the damage accumulation reaches 1, the fatigue failure occurs.
The conventional bolt fatigue life prediction method based on the rain flow method cannot take out all full cycles in stress-strain, or even take out some full cycles with obvious closed rings; the rain flow counting method only considers the cumulative damage effect of the variable amplitude load in the time domain, does not consider the effect of the loading frequency, and meanwhile, the mean value obtained by the cycle counting ignores the influence of a plurality of low-cycle large-amplitude loads, so that the method has many defects and shortcomings, and causes the following problems:
1. The traditional rain flow method-based bolt fatigue prediction is not accurate enough;
2. And a large number of time series samples are needed for predicting the service life of the bolt, and the calculation amount is large.
In order to solve the problems, a hydraulic turbine roof bolt fatigue prediction method is developed by the inventor.
Disclosure of Invention
The invention aims to solve the problems and provide a method for predicting fatigue of a water turbine roof bolt.
the invention realizes the purpose through the following technical scheme:
a hydraulic turbine roof bolt fatigue prediction method comprises the following steps:
S1, calibrating the top cover bolts of the water turbine with the same specification in a laboratory to obtain characteristic parameters of the top cover bolts;
s2, introducing the calibrated specific attributes of the bolt into a real-time online monitoring system, and setting a certain initial value of the bolt object;
s3, under the normal operation state of the water turbine, acquiring data of a stress load-time history curve of the top cover bolt by using an online real-time monitoring system;
S4, in a time domain range, solving the gradient of the stress load to the time history to the collected stress load-time history data to obtain the power density of the stress amplitude; carrying out power density conversion on the S-N curve of the top cover bolt material to obtain an S-N power density curve of the bolt material;
S5, in a frequency domain range, carrying out short-time Fourier transform on the power density of the stress amplitude of the collected data to obtain a stress amplitude variation curve along with frequency at a certain moment;
And S6, based on the concept of the power density method, combining the S-N power density curve of the bolt material, and performing fatigue life prediction on the top cover bolt by using a linear fatigue accumulation method.
The invention has the beneficial effects that:
The fatigue prediction method for the water turbine top cover bolt overcomes the defects that the conventional method can only carry out statistics and counting in a time domain and combines a linear fatigue accumulation theory to carry out fatigue life analysis, and the influence of loading frequency and alternating load on the fatigue life is not considered in a frequency domain;
The concept of power density is introduced, not only is the derivative of the stress load considered in the time domain, but also short-time Fourier transform is carried out in the frequency domain to obtain the loading frequency and the stress amplitude, and the influence of the loading main frequency in a tiny time period is researched;
The fatigue life method of time domain and frequency domain is fused, the process that the loading frequency of the stress load generates tiny cracks on the bolt is accurately represented, and meanwhile, the size of the loading frequency shows the limit degree of high cycle;
Compared with the traditional method, the prediction method can accurately judge the damage degree of the bolt and objectively predict the fatigue life of the top cover bolt.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a stress-fatigue life (S-N) curve of the bolt material in the example.
Detailed Description
The invention will be further described with reference to the accompanying drawings in which:
As shown in fig. 1, the stress-fatigue life (S-N) curve S ═ f (N) of the materialf) The derivative of the stress load with respect to time can be found by experiment as follows:
rdS/dt＝f1(Nf) (1)
In formula 1, dS/dt is the power density of stress versus time, NfThe limit cycle times when the material is broken and damaged, and r is a reliability coefficient;
Performing an inverse function transformation on equation 1 can result in:
Nf＝f2(rdS/dt) (2)
And monitoring real-time data of the bolt according to an ultrasonic measurement online real-time monitoring system to obtain a stress-time history curve.
According to the concept of power density: the gradient of the stress load spectrum born by the bolt in a certain time to the time is defined as power density, and the power generated by applying work to the material load in unit volume is represented, namely:
In the formula 3, P is power density, and the unit in dimension is N.Pa/s ≡ N/(m)2·s)≡N·m/(m3·s)≡W/m3S is the axial load borne by the bolt, and t is the time history.
short-time Fourier transform (STFT) is a transformation form for windowing an actually measured signal z (t) on the basis of traditional Fourier transform, a proper window function g (t) is selected for windowing the signal, Fourier transform of local signals is carried out on the signal in a window to obtain a local frequency spectrum, and the two-dimensional time frequency spectrum of the whole signal can be realized by moving the window function along a time axis. STFT is basically defined as:
In equation 4, z (t) is a time domain signal, and g (t- τ) is a time window centered around time t τ. The short-time fourier transform (STFT) is therefore understood to be the fourier transform performed by multiplying the measured signal z (t) by a window function g (t- τ) at time τ, called the "local spectrum".
The window function width delta t is selected, and according to the inaccuracy measuring principle, for the STFT, the time resolution and the frequency resolution are always contradictory, so that the analysis progress of a time domain and a frequency domain cannot be improved infinitely at the same time. One of which narrows and the other necessarily widens. Therefore, it is necessary to select a proper window function to reduce the leakage of the spectrum and to comprehensively consider the width of the window function to obtain the optimal time resolution and frequency resolution. According to the characteristics of the actual measurement load of the key bolt of the hydropower station, a Kaiser (Kaiser) window is selected, the width of a main lobe and the width of a side lobe can be adjusted simultaneously, and the Kaiser window has the advantages that other window functions do not have, and is defined as follows
in formula 5, N is the length of the sequence, I0Is a first class of modified Bessel function of zero order, beta is any non-negative real number, used to adjust the appearance of the Kaiser window.
The power density (dS/dt) -time t curve obtained in equation 3 is subjected to a short-time fourier transform (STFT). According to the Fourier transform, any continuous random signal can be decomposed into an infinite number of sine functions Sigma A of different amplitudes and different frequenciesisin(2πfit) or cosine function ∑ Aicos(2πfit) are added. Thus, any time t is chosen as t0Power densityCan be decomposed into a superposition of multiple cosine signals. Power density at a certain moment of time of
In equation 6, the power density curve of the stress load is calculated from equation 3, and t is read as t0Power density value of timeFiis t ═ t0Main frequency of time short-time Fourier transform, Ai＝(dS/dt)iIs mainly composed ofFrequency Ficorresponding to the power density, Δ t is the width of the window function.
according to the time interval delta t and the main frequency Fithe number of cycles in a certain time delta t can be calculated
Ni＝FiΔt (7)
In formula 7, NiThe number of cycles in a certain time Deltat, FiIs t ═ t0The main frequency of the time short-time Fourier transform.
Calculating the limit cycle number of the material when the material fails according to the S-N curve obtained by the formula 2;
In formula 8, Nf,iis the limit cycle number when the material fails,is t ═ t0Time dominant frequency FiThe corresponding power density.
Over a given time interval Δ t, the cumulative fatigue damage caused is
AD＝∑Ni/Nf,i (9)
in the formula 9, D is the amount of damage caused within Δ t time, NiIs the dominant frequency F within the time delta tiCorresponding cumulative cycle number, Nf,iIs the power density A of the material at failurei＝(dS/dt)icorresponding limit cycle times.
For the entire stress-time signal measured, the sampling period T is discretized into m time steps, and the damage quantity accumulated in the entire time steps is
In the formula 10, LADThe total cumulative damage amount for a given signal.
According to equation 10, the estimated fatigue life hours for the cap bolt is
In formula 11, HL is the fatigue life hours estimated for the head cover bolt, T is the time for collecting the stress load of the bolt, LADThe total cumulative damage amount for a given signal.
examples
1. The bolt material used in the application is 8.8-grade alloy steel, and the allowable stress [ sigma ] of the alloy steel is determined according to a mechanical design manual]640MPa, strength limit σb893MPa, yield limit 770 MPa. As shown in FIG. 1, the stress-fatigue life (S-N) curve of the material was determined as
S＝860.6764-63.8162log Nf
In the formula, S is stress fatigue limit, MPa; n is a radical offFatigue life, second time;
According to the above formula, the gradient of stress versus time, i.e. the power density is obtained
r(dS/dt)i＝Zi(860.6764-63.8162log Nf,i)×106
in the formula, ZiTo select the time t ═ t0Absolute value of the ratio of power density to stress (dS/dt)iPower density of stress versus time, Nf,iThe limit cycle number of the material in fracture and damage, and r is the reliability coefficient
2. And (3) performing inverse function transformation on the step 1, and taking the limit cycle total times when the failure damage of the material occurs, which is expressed by the power density, as r-99.9 percent
In the formula, C is t ═ t0Time of day power density and ZiI.e. C ═ dS/dt)i/Zi。
3. and monitoring real-time data of the bolt according to an ultrasonic measurement online real-time monitoring system to obtain a stress-time history curve.
4. according to the concept of power density: the gradient of the stress load spectrum born by the bolt in a certain time to the time is defined as power density, and the power generated by applying work to the material load in unit volume is represented, namely
In the formula, P is power density, and the unit in dimension is N.Pa/s ≡ N/(m)2·s)≡N·m/(m3·s)≡W/m3S is the axial load borne by the bolt, and t is the time history.
5. Short-time Fourier transform (STFT) is a transformation form for windowing an actually measured signal z (t) on the basis of traditional Fourier transform, a proper window function g (t) is selected for windowing the signal, Fourier transform of local signals is carried out on the signal in a window to obtain a local frequency spectrum, and the two-dimensional time frequency spectrum of the whole signal can be realized by moving the window function along a time axis. STFT is defined basically as
In this equation, z (t) is a time domain signal, and g (t- τ) is a time window centered around time t τ. The short-time fourier transform (STFT) is therefore understood to be the fourier transform performed by multiplying the measured signal z (t) by a window function g (t- τ) at time τ, called the "local spectrum".
6. The window function width delta t is selected, and according to the inaccuracy measuring principle, for the STFT, the time resolution and the frequency resolution are always contradictory, so that the analysis progress of a time domain and a frequency domain cannot be improved infinitely at the same time. One of which narrows and the other necessarily widens. Therefore, it is necessary to select a proper window function to reduce the leakage of the spectrum and to comprehensively consider the width of the window function to obtain the optimal time resolution and frequency resolution. According to the characteristics of the actual measurement load of the key bolt of the hydropower station, a Kaiser (Kaiser) window is selected, the width of a main lobe and the width of a side lobe can be adjusted simultaneously, and the Kaiser window has the advantages that other window functions do not have, and is defined as follows
in this formula, N is the length of the sequence, I0is a first class of modified Bessel function of zero order, beta is any non-negative real number, used to adjust the appearance of the Kaiser window. Aiming at the actually measured load signal characteristics and the power density processing method, the width of a Kaiser (Kaiser) window is selected to be 30, parameters influencing the side lobe of the window function are taken to be 18, and the window frame shift is 0.01 s.
7. According to the introduction of the steps 5 and 6, the power density (dS/dt) -time t curve obtained by the step 4 is subjected to short-time Fourier transform (STFT). According to the Fourier transform, any continuous random signal can be decomposed into an infinite number of sine functions Sigma A of different amplitudes and different frequenciesi sin(2πfit) or cosine function ∑ Aicos(2πfit) are added. Thus, any time t is chosen as t0power densityCan be decomposed into a superposition of multiple cosine signals. Power density at a certain moment of time of
In the formula, the first step is carried out,For calculating the power density curve of the stress load according to step 4, t is read out0Power density value at time, FiIs t ═ t0Main frequency of time short-time Fourier transform, Ai＝(dS/dt)iIs a dominant frequency FiCorresponding to the power density, Δ t is the width of the window function. Taking the time t equal to 9s as an example, the power density dS/dt of the stress curve is 372.6333W/m3. There are 4 dominant frequencies, respectively F1＝16.97Hz、F2＝24.55Hz、F3＝37.23Hz、F443.20Hz, corresponding short-time Fourier transform coefficient0.5817, 0.4477, 0.0793 and 0.0751 respectively.
8. According to the time interval delta t and the main frequency FiThe number of cycles in a certain time delta t can be calculated
Ni＝FiΔt
In the formula, NiThe number of cycles in a certain time Deltat, Fiis t ═ t0The main frequency of the time short-time Fourier transform. The four main frequencies respectively correspond to the calculation result N1＝0.1697，N2＝0.2455，N3＝0.3723，N4＝0.4320。
9. Calculating the limit cycle number of the material when the material fails according to the S-N curve obtained in the step 2
In the formula, Nf,iis the limit cycle number when the material fails,Is t ═ t0Time dominant frequency FiThe corresponding power density.
10. Over a given time interval Δ t, the cumulative fatigue damage caused is
AD＝∑Ni/Nf,i
In the formula, D is the amount of damage caused within Δ t time, NiIs the dominant frequency F within the time delta tiCorresponding cumulative cycle number, Nf,iIs the power density A of the material at failurei＝(dS/dt)iCorresponding limit cycle times.
the calculation results corresponding to steps 8, 9 and 10 are shown in the following table
Accumulated damage of bolt in time Δ t of 0.01s at time t of 9s
11. for the entire stress-time signal measured, the sampling period T is discretized into m time steps, and the damage quantity accumulated in the entire time steps is
In the formula, LADThe total cumulative damage amount for a given signal. The calculation result is LAD＝2.8208×10-7
12. According to step 11, the estimated fatigue life hours of the cap bolt is
In this formula, HL is the estimated fatigue life hours of the head cover bolt, T is the time for collecting the stress load of the bolt, LADThe total cumulative damage amount for a given signal. The calculated result is HL-2.9542 multiplied by 105h
The present invention is not limited to the above preferred embodiments, and any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. A hydraulic turbine roof bolt fatigue prediction method is characterized by comprising the following steps:
S1, calibrating the top cover bolts of the water turbine with the same specification in a laboratory to obtain characteristic parameters of the top cover bolts;
S2, introducing the calibrated specific attributes of the bolt into a real-time online monitoring system, and setting a certain initial value of the bolt object;
S3, under the normal operation state of the water turbine, acquiring data of a stress load-time history curve of the top cover bolt by using an online real-time monitoring system;
S4, in a time domain range, solving the gradient of the stress load to the time history to the collected stress load-time history data to obtain the power density of the stress amplitude; carrying out power density conversion on the S-N curve of the top cover bolt material to obtain an S-N power density curve of the bolt material;
S5, in a frequency domain range, carrying out short-time Fourier transform on the power density of the stress amplitude of the collected data to obtain a stress amplitude variation curve along with frequency at a certain moment;
And S6, based on the concept of the power density method, combining the S-N power density curve of the bolt material, and performing fatigue life prediction on the top cover bolt by using a linear fatigue accumulation method.
2. The method for predicting fatigue of roof bolts of water turbine as claimed in claim 1, wherein in S4, a stress-fatigue life (S-N) curve S ═ f (N) of the material is obtained through testingf) The derivative of the stress load with respect to time is given by:
rdS/dt＝f1(Nf)
Where dS/dt is the power density of stress versus time, Nfthe limit cycle times when the material is broken and damaged, and r is a reliability coefficient;
Performing an inverse function transformation on the above equation can result in:
Nf＝f2(rdS/dt)。
3. The method for predicting the fatigue of the water turbine roof bolt as claimed in claim 2, wherein in S3, the stress load-time history curve is obtained by monitoring the real-time data of the bolt according to an ultrasonic measurement online real-time monitoring system.
4. The method for predicting fatigue of roof bolts of water turbine as set forth in claim 3, wherein the power density is obtained by a method of obtaining the power density in S4
wherein P is the power density and the unit in dimension is N.Pa/s.ident.N/(m)2·s)≡N·m/(m3·s)≡W/m3S is the axial load borne by the bolt, and t is the time history.
5. The method for predicting fatigue of hydraulic turbine head bolt according to claim 4, wherein in S5, the obtained power density (dS/dt) -time t curve is subjected to short-time Fourier transform (STFT), and any time t-t is selected0power densitycan be decomposed into a superposition of multiple cosine signals; power density at a certain moment of time of
in the formula, a power density curve of a stress load is calculated, and t is read out0Power density value of timeFiIs t ═ t0Main frequency of time short-time Fourier transform, Ai＝(dS/dt)iIs a dominant frequency FiCorresponding to the power density, Δ t is the width of the window function.
6. The method for predicting fatigue of roof bolts of water turbine as claimed in claim 5, wherein in S6, the time interval Δ t and the dominant frequency F are used as the basisiThe number of cycles in a certain time Δ t can be calculated:
Ni＝FiΔt
In the formula, Nithe number of cycles in a certain time Deltat, FiIs t ═ t0The main frequency of the time short-time Fourier transform;
And according to the S-N curve, calculating the limit cycle times when the material fails as follows:
In the formula, Nf,iIs made of woodthe limit cycle times when the material fails,is t ═ t0time dominant frequency FiThe corresponding power density.
7. The method for predicting fatigue of a roof bolt of a water turbine according to claim 6, wherein in S6, the cumulative fatigue damage caused during a given time interval Δ t is:
AD＝∑Ni/Nf,i
Wherein D is the amount of damage caused within Δ t time, NiIs the dominant frequency F within the time delta tiCorresponding cumulative cycle number, Nf,iIs the power density A of the material at failurei＝(dS/dt)icorresponding limit cycle times.
8. The method for predicting fatigue of a hydraulic turbine head bolt according to claim 7, wherein in S6, the measured entire stress-time signal is discretized into m time steps with a sampling period T, and the amount of damage accumulated in the entire time steps is:
In the formula, LADThe total cumulative damage amount for a given signal.
9. The method of claim 8, wherein in S6, the estimated fatigue life hours of the roof bolts are:
wherein HL is the fatigue life hours estimated by the top cover bolt, T is the time for collecting the stress load of the bolt, LADFor the total accumulated loss of a given signalAnd (4) injury amount.
10. the method for predicting fatigue of the water turbine roof bolt according to claim 5, wherein: selecting a proper window function g (t) to window the signal, performing Fourier transform on the signal in the window to obtain a local frequency spectrum, and moving the window function along a time axis to realize a two-dimensional time frequency spectrum of the whole signal; STFT is basically defined as:
Wherein z (t) is a time domain signal, and g (t- τ) is a time window centered around time t ═ τ;
The window function width Δ t is chosen as defined below
Wherein N is the length of the sequence, I0Is a first class of modified Bessel function of zero order, beta is any non-negative real number, used to adjust the appearance of the Kaiser window.
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