CN102588012B - Method and device for predicting and monitoring high-cycle fatigue life of turbine welded rotor - Google Patents

Abstract

The invention relates to a method and device for predicting and monitoring the high-cycle fatigue life of a turbine welded rotor. The method for monitoring the high-cycle fatigue life of a turbine welded rotor consists of specific steps of: determining, through flaw detection, the crack size of a welding rotor of the turbine, determining a fatigue crack extensional stress strength factor threshold value delta KthR, distinguishing the possibility of the crack fatigue extension of the welded rotor of the turbine, calculating the maximum stress sigma max of the high cycle fatigue of welded rotor of the turbine, the critical size ac of the welded rotor of the turbine, the life circulation times of the high cycle fatigue of the turbine rotor, the average high cycle fatigue circulation times ey of the welded rotor of the turbine, the life year of the high cycle fatigue of the welded rotor of the turbine, and controlling the safety of the life of the high cycle fatigue of the welded rotor of the turbine. Through the invention, quantitative prediction and quantitative monitoring of the high-cycle fatigue life of a turbine welded rotor are realized.

Description

The prediction and control method of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction

Technical field

The prediction and control method and the device that the present invention relates to steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, belong to steam turbine technology field.

Background technique

In the stable state rated load operation of steam turbine, due to the effect of centrifugal force load and thermal force, in steam turbine welded disc turbine rotor, produce stable stress at rest and be called average stress.Static large span, the steam turbine welded disc turbine rotor of up to a hundred tons, under the effect of self gravitation load, the outer surface generation pressure stress in welded disc turbine rotor center of gravity with upper part, produces tensile stress at the following position of welded disc turbine rotor center of gravity outer surface.In service at steam turbine, welded disc turbine rotor outer surface a bit, except bearing the stable average stress that centrifugal force load and thermal force produce, when this point rotates to welded disc turbine rotor top (90 ° of positions), because rotor and the blade independent role of conducting oneself with dignity will produce pressure stress; When this point rotates to rotor bottom (270 ° of positions), because rotor and blade deadweight independent role is by the tensile stress producing.Under steam turbine band stable state rated loan condition, the alternating stress that rotates to diverse location is that the self gravitation load by welded disc turbine rotor and blade causes; Often circle, steam turbine welded disc turbine rotor bears deadweight independent role and produces fatigue and cyclic once.For half speed thermoelectricity or nuclear steam turbine, fatigue and cyclic per second 25 times, moves 7000 hours every year, circulation 1.89 * 10 in 30 years ¹⁰inferior; Circulation 3.78 * 10 in 60 years ¹⁰inferior.For full rotating speed thermoelectricity or nuclear steam turbine, circulation per second 50 times, year operation 7000 hours, circulation 3.78 * 10 in 30 years ¹⁰inferior, circulation 7.56 * 10 in 60 years ¹⁰inferior.The prediction and control method in existing turbine rotor life-span, provided the prediction and control method of steam turbine welded disc turbine rotor low-cycle fatigue life, for the prediction and control of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, also do not have suitable method and apparatus available.

Summary of the invention

The prediction and control method and the device that the object of this invention is to provide a kind of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, realize quantitative forecast and the quantitative monitoring of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction.

For realizing above object, technological scheme of the present invention is to provide a kind of prediction and control method of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, use the supervisory device of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, the supervisory device of described steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction is comprised of ultrasonic flaw detector and calculation server, ultrasonic flaw detector is connected with calculation server with turbine rotor, it is characterized in that, adopt the computer software of the steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction of C language compilation, operate on calculation server, be applied to the prediction and control of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, concrete steps are:

The first step: the crack size of steam turbine welded disc turbine rotor is determined in flaw detection:

In steam turbine welded disc turbine rotor manufacture process, adopt ultrasonic flaw detector to determine position, place and the crack size of Seam and heat effected zone crackle, position, crackle place refers to three coordinate values of the Ellipse crack central position of welded disc turbine rotor Seam and heat effected zone, and crack size refers to minor axis radius a and the major axis radius c of welded disc turbine rotor Seam and heat effected zone Ellipse crack:

Second step: the major principal stress of calculating position, steam turbine welded disc turbine rotor crackle place:

Crackle for steam turbine welded disc turbine rotor, adopt existing finite element method (fem) analysis method, the major principal stress of calculating Seam and heat effected zone under stable state rated loan condition is determined major principal stress σ when certain of steam turbine welded disc turbine rotor threedimensional model a bit rotates to rotor bottom (270 ° of positions) _{270 °}, at three direct stress and six shearing stress of the point of this welded disc turbine rotor top same radius and same axial position (90 ° of positions), forming three stress vectors, these three stress vectors project to bottom major principal stress σ _{270 °}direction draws the direct stress σ that the party makes progress _{90 °};

The 3rd step: the stress amplitude σ that calculates steam turbine welded disc turbine rotor _a:

Steam turbine welded disc turbine rotor under stable state rated loan condition, the alternating stress amplitude σ causing due to blade and rotor gravity _aformula be:

The 4th step: the average stress σ that calculates steam turbine welded disc turbine rotor _m:

The average stress σ of steam turbine welded disc turbine rotor under stable state rated load _mformula be:

In formula:

σ _r---the residual stress of welded disc turbine rotor;

The 5th step: the stress ratio R that calculates steam turbine welded disc turbine rotor:

The formula of the stress ratio R of steam turbine welded disc turbine rotor under stable state rated loan condition is:

$R=\frac{{\mathrm{\σ}}_m-{\mathrm{\σ}}_a}{{\mathrm{\σ}}_m+{\mathrm{\σ}}_a}$

In formula:

σ _m---average stress

σ _a---stress amplitude;

The 6th step: the stress intensity factor range Δ K that calculates steam turbine welded disc turbine rotor:

The formula of steam turbine welded disc turbine rotor stress intensity factor range Δ K is:

$\mathrm{\ΔK}=2{\mathrm{\σ}}_a\sqrt{\mathrm{Ma}}$

In formula:

σ _a---stress amplitude

A---elliptical crack minor axis radius

M---the constant relevant with crack shape parameter Q,

For underbead crack,

For surface crack,

$Q={\∫}_0^{\frac{\mathrm{\π}}{2}}(1-\frac{c^2-a^2}{c^2}{\sin }^2\mathrm{\θ})\mathrm{d\θ}={\∫}_0^{\frac{\mathrm{\π}}{2}}\{1-[1-{\left(\frac{a}{c}\right)}^2\left]s{\mathrm{in}}^2\mathrm{\θ}\right\}\mathrm{d\θ};$

C---elliptical crack major axis radius;

θ---the angle of any point radial line and transverse on mistake crackle contour;

The 7th step: the threshold stress intensity factor Δ K that determines crack Propagation _th ^r:

For the Seam and heat effected zone of steam turbine welded disc turbine rotor, the threshold stress intensity factor Δ K of the crack Propagation that stress ratio is R _th ^rformula be:

ΔK _th ^R＝ΔK _th ⁰(1-R) ^m

In formula:

Δ K _th ⁰---the threshold stress intensity factor of the crack Propagation that stress ratio is R=0;

R---stress ratio;

M---testing of materials constant;

The 8th step: the possibility of differentiating steam turbine welded disc turbine rotor Fatigue Propagation of Cracks:

If Δ K≤Δ K _th ^r, at the stress amplitude σ of stable state rated loan condition _aunder effect, can there is not high cycle fatigue expansion in the crackle that the flaw detection of steam turbine welded disc turbine rotor is found, steam turbine welded disc turbine rotor has infinite life, and its high-Cycle Fatigue Life Prediction is N _f>=4.0 * 10 ¹⁰, enter the 12 step;

If Δ K> Δ K _th ^r, at the stress amplitude σ of stable state rated loan condition _aunder effect, can there is high cycle fatigue expansion in the crackle that the flaw detection of steam turbine welded disc turbine rotor is found, enter the 9th step;

The 9th step: the maximum stress σ that calculates steam turbine welded disc turbine rotor high cycle fatigue _max:

Steam turbine welded disc turbine rotor is at the maximum stress σ of stable state rated loan condition _maxformula be:

σ _max＝σ _m+σ _a

The tenth step: the critical crack size a that calculates steam turbine welded disc turbine rotor _c:

Steam turbine welded disc turbine rotor critical crack size σ _cformula be

$a_c=\frac{{K_{1C}}^2}{M{{\mathrm{\σ}}_{\max }}^2}$

In formula:

K _1C---fracture toughness;

The 11 step: the high-Cycle Fatigue Life Prediction cycle-index of calculating turbine rotor:

At Δ K> Δ K _th ^rsituation under, steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction cycle-index N _fformula be:

$N_f=\frac{2}{(m_0-2)C_0{\mathrm{\σ}}_{\max }^{m_0}{M}^{\frac{m_0}{2}}}[\frac{1}{a^{\frac{(m_0-2)}{2}}}-\frac{1}{a_c^{\frac{(m_0-2)}{2}}}]$

In formula:

C ₀, m ₀---fatigue crack propagation test constant;

The 12 step: calculate the average annual high cycle fatigue cycle-index of steam turbine welded disc turbine rotor e _y:

For the welded disc turbine rotor of the power station steam turbine of full rotating speed, high cycle fatigue cycle-index per second is 50 times, and year hours run is e by the average annual high cycle fatigue cycle-index of calculating for 7000 hours _y=1.26 * 10 ⁹;

For the welded disc turbine rotor of the power station steam turbine of half speed, high cycle fatigue cycle-index per second is 25 times, and year hours run is e by the average annual high cycle fatigue cycle-index of calculating for 7000 hours _y=6.3 * 10 ⁸;

The 13 step: calculate steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction year number:

Steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction year is counted τ _cLformula be:

${\mathrm{\τ}}_{\mathrm{CL}}=\frac{N_f}{e_f}$

In formula:

E _f---average annual high-Cycle Fatigue Life Prediction cycle-index;

The 14 step: the Security of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction is controlled:

For thermal power steam turbine welded disc turbine rotor, if τ _cL>=30 years, the Security of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction reached requirement; If τ _cL<30, the Security of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction does not reach requirement, need to cut out the weld defects of steam turbine welded disc turbine rotor, again welds, detects a flaw, and re-starts high-cycle fatigue life and monitors its Security;

For nuclear steam turbine welded disc turbine rotor, if τ _cL>=60 years, the Security of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction reached requirement; If τ _cL<60, the Security of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction does not reach requirement, need to cut out the weld defects of steam turbine welded disc turbine rotor, again welds, detects a flaw, and re-starts high-cycle fatigue life and monitors its Security;

The 15 step: printout result:

Predicting the outcome and control measure of output steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, the Assessment For Welding Defects and the workmanship that are applied to steam turbine welded disc turbine rotor process are controlled.

The present invention has following characteristics: in the manufacture process of steam turbine welded disc turbine rotor, adopt ultrasonic flaw detector, flaw detection draws the surface crack of steam turbine welded disc turbine rotor weld seam and heat affected zone and position, place and the crack size of underbead crack, use monitoring method and the device of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction provided by the invention, the high-Cycle Fatigue Life Prediction year number of quantitative forecast steam turbine welded disc turbine rotor, for the long period safe operation of steam turbine welded disc turbine rotor provides foundation.

Advantage of the present invention is quantitative forecast and the quantitative monitoring that has realized steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction; If the high-Cycle Fatigue Life Prediction of steam turbine welded disc turbine rotor partially in short-term, by again welding to meet the security requirement of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, reached the technique effect of quantitative monitoring steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction.

Accompanying drawing explanation

Fig. 1 is the skeleton diagram of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction supervisory device of the present invention;

Fig. 2 is the flow process journey of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction monitoring method of the present invention;

Fig. 3 is the computer software block diagram that calculation server of the present invention adopts;

Fig. 4 is the schematic diagram of certain model 300MW steam turbine welding low pressure rotor structure.

Embodiment

Below in conjunction with embodiment, illustrate the present invention.

Embodiment

As shown in Figure 1, the skeleton diagram of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction supervisory device of the present invention, steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction device of the present invention is comprised of ultrasonic flaw detector 1 and calculation server 2, and ultrasonic flaw detector 1 is connected with calculation server 2 with steam turbine welded disc turbine rotor.

As shown in Figure 2, the flow chart of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction monitoring method of the present invention, as shown in Figure 3, the computer software block diagram that calculation server of the present invention adopts, this software adopts C language compilation, be arranged on the calculation server of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, be applied to the calculation and control of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction.

For certain model 300MW thermal power steam turbine, the structure of low pressure rotor employing welded disc turbine rotor as shown in Figure 4, rotor material is 25Cr2NiMoV, manufacture process at the welding low pressure rotor of this 300MW thermal power steam turbine, adopt the computer software shown in device, the flow chart shown in Fig. 2 and the Fig. 3 shown in Fig. 1, the result of calculation that calculates this welding low pressure rotor high-Cycle Fatigue Life Prediction, concrete steps are:

The first step: the crack size of steam turbine welding low pressure rotor is determined in flaw detection: in this steam turbine welding low pressure rotor manufacture process, the weld seam position A that adopts ultrasonic flaw detector to record this 300MW thermal power steam turbine welding low pressure rotor has inner Ellipse crack, its minor axis radius is a=2mm, and major axis radius is c=5mm; Position, heat affected zone B has surperficial half elliptic crackle, and its minor axis radius is a=18mm, and major axis radius is c=45mm;

Second step: the major principal stress of calculating position, steam turbine welded disc turbine rotor crackle place:

Crackle for steam turbine welded disc turbine rotor, adopt existing finite element method (fem) analysis method, the major principal stress of calculating Seam and heat effected zone under stable state rated loan condition is determined major principal stress σ when certain of steam turbine welded disc turbine rotor threedimensional model a bit rotates to rotor bottom (270 ° of positions) _{270 °}, at three direct stress and six shearing stress of the point of this welded disc turbine rotor top same radius and same axial position (90 ° of positions), forming three stress vectors, these three stress vectors project to bottom major principal stress σ _{270 °}direction draws the direct stress σ that the party makes progress _{90 °};

The 3rd step: the stress amplitude σ that calculates steam turbine welded disc turbine rotor _a:

Steam turbine welded disc turbine rotor under stable state rated loan condition, the alternating stress amplitude σ causing due to blade and rotor gravity _aformula be:

The 4th step: the average stress σ that calculates steam turbine welded disc turbine rotor _m:

The average stress σ of steam turbine welded disc turbine rotor under stable state rated load _mformula be:

In formula:

σ _r---the residual stress of welded disc turbine rotor, is taken as 5% of yield limit under operating temperature;

The 5th step: the stress ratio R that calculates steam turbine welded disc turbine rotor:

The formula of the stress ratio R of steam turbine welded disc turbine rotor under stable state rated loan condition is:

$R=\frac{{\mathrm{\&sigma;}}_m-{\mathrm{\&sigma;}}_a}{{\mathrm{\&sigma;}}_m+{\mathrm{\&sigma;}}_a}$

In formula:

σ _m---average stress

σ _a---stress amplitude;

The 6th step: the stress intensity factor range Δ K that calculates steam turbine welded disc turbine rotor:

The formula of steam turbine welded disc turbine rotor stress intensity factor range Δ K is:

$\mathrm{\&Delta;K}=2{\mathrm{\&sigma;}}_a\sqrt{\mathrm{Ma}}$

In formula:

σ _a---stress amplitude

A---elliptical crack minor axis radius

M---the constant relevant with crack shape parameter Q,

For underbead crack,

For surface crack,

$Q={\&Integral;}_0^{\frac{\mathrm{\&pi;}}{2}}(1-\frac{c^2-a^2}{c^2}{\sin }^2\mathrm{\&theta;})\mathrm{d\&theta;}={\&Integral;}_0^{\frac{\mathrm{\&pi;}}{2}}\{1-[1-{\left(\frac{a}{c}\right)}^2\left]s{\mathrm{in}}^2\mathrm{\&theta;}\right\}\mathrm{d\&theta;};$

A is elliptical crack minor axis radius, and c is elliptical crack major axis radius, gets

This 300MW thermal power steam turbine welding weld seam position A of low pressure rotor and the major principal stress σ of position, heat affected zone B _{270 °}, stress amplitude σ _a, average stress σ _m, stress ratio R and stress intensity factor range Δ K result of calculation list in table 1;

[table 1]

The 7th step: the threshold stress intensity factor Δ K that determines crack Propagation _th ^r:

For the Seam and heat effected zone of steam turbine welded disc turbine rotor, the threshold stress intensity factor Δ K of the crack Propagation that stress ratio is R _th ^rformula be:

ΔK _th ^R＝ΔK _th ⁰(1-R) ^m

In formula:

Δ K _th ⁰---the threshold stress intensity factor of the crack Propagation that stress ratio is R=0;

R---stress ratio;

M---testing of materials constant;

The material trademark of the Seam and heat effected zone of this 300MW thermal power steam turbine welding low pressure rotor is 25Cr2NiMoV, the threshold value Δ K of the stress intensity factor of the crack Propagation that its stress ratio is R _th ^rresult of calculation list in table 2;

[table 2]

The 8th step to the 11 steps:

For the position A of this 300MW thermal power steam turbine welding low pressure rotor, due to Δ K=0.0586< Δ K _th ^r=0.3803, at the stress amplitude σ of stable state rated loan condition _aunder effect, can there is not Fatigue in the crackle that the flaw detection of steam turbine welded disc turbine rotor is found, steam turbine welded disc turbine rotor has infinite life, and its high-Cycle Fatigue Life Prediction is N _f>=4.0 * 10 ¹⁰;

For the position B of this welding low pressure rotor, at the stress amplitude σ of stable state rated loan condition _aunder effect, can there is Fatigue in the crackle that the flaw detection of steam turbine welded disc turbine rotor is found;

Steam turbine welded disc turbine rotor is at the maximum stress σ of stable state rated loan condition _max=σ _m+ σ _a=290.78+1.42=292.20MPa

Steam turbine welded disc turbine rotor critical crack size this position 25Cr2NiMoV material $K_{1C}=118.81\mathrm{MPA}\sqrt{m},$ a _c＝131.4mm；

Steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction cycle-index $N_f=\frac{2}{(m_0-2)C_0{\mathrm{\&sigma;}}_{\max }^{m_0}{M}^{\frac{m_0}{2}}}[\frac{1}{a^{\frac{(m_0-2)}{2}}}-\frac{1}{a_c^{\frac{(m_0-2)}{2}}}],$ C ₀=1.23 * 10 ^-11, m ₀=3.31, the high-Cycle Fatigue Life Prediction N at this position _f=6.7875 * 10 ⁹;

The 12 step to the 15 steps: for this 300MW thermal power steam turbine welding low pressure rotor, full rotating speed unit, moves 7000 hours every year, and average annual high cycle fatigue cycle-index is e _y=1.26 * 10 ⁹, the high-Cycle Fatigue Life Prediction year number of this welding low pressure rotor position A is year, reach 30 years of designing requirement; The high-Cycle Fatigue Life Prediction year number of this welding low pressure rotor position B is year, because the high-Cycle Fatigue Life Prediction year number of this welding low pressure rotor position B is less than 30 years, the control measure of recommending are: the weld defects that cuts out this steam turbine welding low pressure rotor position B, again weld, detect a flaw, re-start high-cycle fatigue life and monitor its Security, printout result: predicting the outcome and control measure of output steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, is applied to Assessment For Welding Defects and the workmanship control of steam turbine welded disc turbine rotor process.

Adopt prediction and control method and the device of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction provided by the invention, quantitative forecast goes out the high-Cycle Fatigue Life Prediction year number the control measure of recommending out position B again to weld of the weld seam position A of this 300MW thermal power steam turbine welding low pressure rotor and position, heat affected zone B, and has reached this 300MW thermal power steam turbine of quantitative forecast and quantitative monitoring and has welded the technique effect of low pressure rotor high-Cycle Fatigue Life Prediction.

Claims (1)

1. the prediction and control method of a steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, use a kind of supervisory device of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, the supervisory device of described steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction is comprised of ultrasonic flaw detector and calculation server, ultrasonic flaw detector is connected with calculation server with turbine rotor, it is characterized in that, adopt the computer software of the steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction of C language compilation, operate on calculation server, be applied to the prediction and control of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, concrete steps are:

The first step: the crack size of steam turbine welded disc turbine rotor is determined in flaw detection:

In steam turbine welded disc turbine rotor manufacture process, adopt ultrasonic flaw detector to determine position, place and the crack size of Seam and heat effected zone crackle, position, crackle place refers to three coordinate values of the Ellipse crack central position of welded disc turbine rotor Seam and heat effected zone, and crack size refers to minor axis radius a and the major axis radius c of welded disc turbine rotor Seam and heat effected zone Ellipse crack:

Second step: the major principal stress of calculating position, steam turbine welded disc turbine rotor crackle place:

Crackle for steam turbine welded disc turbine rotor, adopt existing finite element method (fem) analysis method, the major principal stress of calculating Seam and heat effected zone under stable state rated loan condition is determined major principal stress σ when certain of steam turbine welded disc turbine rotor threedimensional model a bit rotates to rotor bottom _{270 °}, at three direct stress and six shearing stress of the point of this welded disc turbine rotor top same radius and same axial position, forming three stress vectors, these three stress vectors project to bottom major principal stress σ _{270 °}direction draws the direct stress σ that the party makes progress _{90 °};

The 3rd step: the stress amplitude σ that calculates steam turbine welded disc turbine rotor _a:

Steam turbine welded disc turbine rotor under stable state rated loan condition, the alternating stress amplitude σ causing due to blade and rotor gravity _aformula be:

The 4th step: the average stress σ that calculates steam turbine welded disc turbine rotor _m:

The average stress σ of steam turbine welded disc turbine rotor under stable state rated load _mformula be:

In formula:

σ _r---the residual stress of welded disc turbine rotor;

The 5th step: the stress ratio R that calculates steam turbine welded disc turbine rotor:

The formula of the stress ratio R of steam turbine welded disc turbine rotor under stable state rated loan condition is:

$R=\frac{{\mathrm{\&sigma;}}_m-{\mathrm{\&sigma;}}_a}{{\mathrm{\&sigma;}}_m+{\mathrm{\&sigma;}}_a}$

In formula:

σ _m---average stress

σ _a---stress amplitude;

The 6th step: the stress intensity factor range Δ K that calculates steam turbine welded disc turbine rotor:

The formula of steam turbine welded disc turbine rotor stress intensity factor range Δ K is:

$\mathrm{\&Delta;K}=2{\mathrm{\&sigma;}}_a\sqrt{\mathrm{Ma}}$

In formula:

σ _a---stress amplitude

A---elliptical crack minor axis radius

M---the constant relevant with crack shape parameter Q,

For underbead crack,

For surface crack,

$Q={\&Integral;}_0^{\frac{\mathrm{\&pi;}}{2}}(1-\frac{c^2-a^2}{c^2}{\sin }^2\mathrm{\&theta;})\mathrm{d\&theta;}={\&Integral;}_0^{\frac{\mathrm{\&pi;}}{2}}\{1-[1-{\left(\frac{a}{c}\right)}^2\left]s{\mathrm{in}}^2\mathrm{\&theta;}\right\}\mathrm{d\&theta;};$

C---elliptical crack major axis radius;

θ---the angle of any point radial line and transverse on mistake crackle contour;

The 7th step: the threshold stress intensity factor Δ K that determines crack Propagation _th ^r:

For the Seam and heat effected zone of steam turbine welded disc turbine rotor, the threshold stress intensity factor Δ K of the crack Propagation that stress ratio is R _th ^rformula be:

ΔK _th ^R＝ΔK _th ⁰(1-R) ^m

In formula:

Δ K _th ⁰---the threshold stress intensity factor of the crack Propagation that stress ratio is R=0;

R---stress ratio;

M---testing of materials constant;

The 8th step: the possibility of differentiating steam turbine welded disc turbine rotor Fatigue Propagation of Cracks:

If Δ K≤Δ K _th ^r, at the stress amplitude σ of stable state rated loan condition _aunder effect, can there is not high cycle fatigue expansion in the crackle that the flaw detection of steam turbine welded disc turbine rotor is found, steam turbine welded disc turbine rotor has infinite life, and its high-Cycle Fatigue Life Prediction is N _f>=4.0 * 10 ¹⁰, enter the 12 step;

If Δ K> Δ K _th ^r, at the stress amplitude σ of stable state rated loan condition _aunder effect, can there is high cycle fatigue expansion in the crackle that the flaw detection of steam turbine welded disc turbine rotor is found, enter the 9th step;

The 9th step: the maximum stress σ that calculates steam turbine welded disc turbine rotor high cycle fatigue _max:

Steam turbine welded disc turbine rotor is at the maximum stress σ of stable state rated loan condition _maxformula be:

σ _max＝σ _m+σ _a

The tenth step: the critical crack size a that calculates steam turbine welded disc turbine rotor _c:

Steam turbine welded disc turbine rotor critical crack size a _cformula be

$a_c=\frac{{K_{1C}}^2}{M{{\mathrm{\&sigma;}}_{\max }}^2}$

In formula:

K _1C---fracture toughness;

The 11 step: the high-Cycle Fatigue Life Prediction cycle-index of calculating turbine rotor:

At Δ K> Δ K _th ^rsituation under, steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction cycle-index N _fformula be:

$N_f=\frac{2}{(m_0-2)C_0{\mathrm{\&sigma;}}_{\max }^{m_0}{M}^{\frac{m_0}{2}}}[\frac{1}{a^{\frac{(m_0-2)}{2}}}-\frac{1}{a_c^{\frac{(m_0-2)}{2}}}]$

In formula:

C ₀, m ₀---fatigue crack propagation test constant;

The 12 step: calculate the average annual high cycle fatigue cycle-index of steam turbine welded disc turbine rotor e _y:

For the welded disc turbine rotor of the power station steam turbine of full rotating speed, high cycle fatigue cycle-index per second is 50 times, and year hours run is e by the average annual high cycle fatigue cycle-index of calculating for 7000 hours _y=1.26 * 10 ⁹;

For the welded disc turbine rotor of the power station steam turbine of half speed, high cycle fatigue cycle-index per second is 25 times, and year hours run is e by the average annual high cycle fatigue cycle-index of calculating for 7000 hours _y=6.3 * 10 ⁸;

The 13 step: calculate steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction year number:

Steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction year is counted τ _cLformula be:

${\mathrm{\&tau;}}_{\mathrm{CL}}=\frac{N_f}{e_f}$

In formula:

E _f---average annual high-Cycle Fatigue Life Prediction cycle-index;

The 14 step: the Security of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction is controlled:

For thermal power steam turbine welded disc turbine rotor, if τ _cL>=30 years, the Security of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction reached requirement; If τ _cL<30, the Security of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction does not reach requirement, need to cut out the weld defects of steam turbine welded disc turbine rotor, again welds, detects a flaw, and re-starts high-cycle fatigue life and monitors its Security;

For nuclear steam turbine welded disc turbine rotor, if τ _cL>=60 years, the Security of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction reached requirement; If τ _cL<60, the Security of steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction does not reach requirement, need to cut out the weld defects of steam turbine welded disc turbine rotor, again welds, detects a flaw, and re-starts high-cycle fatigue life and monitors its Security;

The 15 step: printout result:

Predicting the outcome and control measure of output steam turbine welded disc turbine rotor high-Cycle Fatigue Life Prediction, the Assessment For Welding Defects and the workmanship that are applied to steam turbine welded disc turbine rotor process are controlled.