Energy and Power Engineering, 2013, 5, 1484-1489
doi:10.4236/epe.2013.54B281 Published Online July 2013 (
Calculation of Thermal Stress and Fatigue Life of
1000 MW Steam Turbine Rotor
Shuang Bian, Wenyao Li
Energy Power and Mechanical Engineering Institute, North China Electric Power University, Beijing, China
Received 2013
The paper calculated the temperature and stress fields of 1000 MW ultra-supercritical steam turbine rotors which start in
cold condition using the finite element calculation program (ANSYS). After getting rotor stress field, the paper use the
general slope method to estimate the low cycle fatigue life loss, the rest of the conditions can be calculated in this
Keywords: Component; Steam Turbine; Thermal Stress; Finite Element Method; Fatigue Life
1. Introduction
When power plant stat up and shut down or change load,
the internal of rotor metal will produce the temperature
gradient, due to the presence of the temperature gradient,
rotor will produce thermal stress in the unstable condi-
tions. When steam turbine starts up, temperature of rotor
surface gradually raise with the steam temperature rais-
ing, temperature of central part change lag behind the
rotor surface, so rotor surface endure pressure stress, on
the contrary rotor surface endure tension stress in the
shutdown process, after a certain number of circulation,
the surface of rotor may produce fatigue crack [1]. Ul-
tra-supercritical unit woks under the high pressure and
temperatureworking environment of rotor is worse, so
the analysis of thermal stress and fatigue damage about
rotor has the important practical significance.
Using FEM, this paper analyzes the startup and shut-
down process of a 1000MW steam turbine. Analysis gets
the temperature field and stress field of the tutorthus we
can determine the dangerous position of the rotorand
calculate the maximum stress. According to local stress
and strain method, this paper calculates the fatigue life
loss of the dangerous position.
2. Thermal Stress Calculation
2.1. Calculating Object
The calculating object of this paper is the rotor of a
1000MW ultra-supercritical steam turbine. The unit is
N1000-25.0/600/600 with a intermediate reheat, single
shaft, four overcastting, four condenser in the plant. The
unit startup mode is high casing start-up. Due to the
steam enters high pressure cylinder firstly, and the steam
parameters such as temperature and pressure are higher
in the high pressure cylinder, the thermal stress of rotor is
larger than the stress in the ip-lp cylinders. The calcu-
lated object of this paper is hp cylinder rotor. The mate-
rial of rotor is improved 12Cr.mat”.
2.2. Model Establishment and Grid Partition
Rotor is regarded as a column object, which has no inner
heat source, and is homogeneous and is tropical. Calcu-
lating rotor temperature field belongs to solve rotational
symmetry unsteady temperature function [2]. Differential
equation is expressed in the following form:
Cz rrr
 
 
λ —— thermal conductivity;
ρ —— density of material;
C—— heat capacity;
Initical condition:
r (2)
Boundary condition:
tat t
Transient analysis of the heat balance equation is ex-
pressed in the following form [3]:
 
F where is the conductivity matrix, whch includes
thermal conductivity,convection coefficient,radiance and
shape factor. is heat capacity matrix, in view of the
increase of the system internal energy. is the temperature
Copyright © 2013 SciRes. EPE
S. BIAN, W. Y. LI 1485
vector of node. is the time derivative of temperature. is
heat flow rate vector of node.
The calculation can be completed by a integration
method, which is called Crank-Nichalson/Enther θ [4].
The geometry shape of hp cylinder rotor calculated in
this paper is irregular, boundary conditions has a large
change, the governing stage has double flow stages, rotor
has eight pressure stages. To simulate the temperature
and stress field of 12Cr in the process of operation more
accurately, we should build a geometric model which
conforms to reality. This paper builds an ax symmetrical
two-dimensional calculation model. The initial tempera-
ture of rotor distribute homogeneous, and is equal to the
steam temperature. Model which be meshed is showed in
the following Figure 1.
2.3. Initial Conditions and Boundary Conditions
The physical properties of rotor are regarded as variable
Boundary conditions include the first and the third
kind of boundary condition. Calculating heat transfer
coefficient is a difficult point in the third kind of bound-
ary condition. Generally, we use two kinds of formula to
calculate the heat transfer coefficient, the Westinghouse
formula and Nagong-Haqi formula [5]. This paper calcu-
lated the heat transfer coefficient through the Westing-
house formula.
2.4. Analysis of Temperature and Stress Field
The stress field of the rotor is influenced by the tempera-
ture field, when temperature gradient is biggest between
rotor center and surface, the thermal stress is max. The
time is about 24000 s, at which thermal stress is max,
when unit closes to quasi steady state. Figure 2 is the
distribution of temperature field at the time that stress is
max, when unit starts up according to the actual cold
start-up curve. The nominal parameter of main steam in
the hp cylinder is 25 MPa, 600.
Figure 1. Mesh dividing model of steam turbine rotor.
the thermal stress caculation for steam rotor
342.664 365.364 388.064 410.764 433.464 456.164 478.864 501.564 524.264 546.964
NOV 27 2012
SUB =200
DMX =.036519
SMN =342.664
SMX =546.964
Figure 2. Temperature field of rotor at 24000s.
Copyright © 2013 SciRes. EPE
S. BIAN, W. Y. LI.
Figure 3 is the distribution of stress field at the time
that stress is max, when unit starts up according to the
actual cold start-up curve. As can be seen from the grapy,
the stress concentration is large near the impeller root of
governing stage, whose thermal stress is largest.
According to the analysis of the temperature and stress
field of rotor, when unit starts up in the cold state, we can
see the position whose thermal stress is largest is the im-
peller root of governing stage. Analyzing this position,
this paper get the temperature-time and stress-time
curves of impeller root of governing stage, shown in the
following Figure 4 and Figure 5.
Figure 5 shows that thermal stress has been on the rise
in the startup process. When starting time reaches to
200min, the rotation rate of rotor ascend to 3000r/min,
steam temperature changes faster, and stress increases
speedly. Up to rated load, the stress trend tends to be
gentle. When the steam temperature is kept constant,
rotor temperature gradient decreases gradually, rotor
stress begins to decline.
Figure 3. Stress distribution of rotor at 24000s.
Figure 4. Temperature curve varying with time in the cold start-up condition.
Copyright © 2013 SciRes. EPE
S. BIAN, W. Y. LI 1487
Figure 5. Stress curve varying with time in the cold start-up condition.
Figure 6. Temperature curve varying with time during shut-down period.
2.5. Condition of Shut-down
The pulling stress and mechanical stress of the rotor have
the same direction when the unit is shutdown, thus stress
is easy be large. We should control the change rate of
temperature in the shutdown process.
Figure 6 is the temperature curve varying with time
Copyright © 2013 SciRes. EPE
S. BIAN, W. Y. LI.
during shut-down period. Figure 7 is the stress curve
varying with time during shut-down period. From the
Figure 7 we can say that the maximum stress is 135MPa
in the shutdown process.
3. Calculation of Fatigue Life
his paper calculates the fatigue life loss of rotor using
Figure 7. Stress curve varying with time during shut-down period.
local stress and strain method. The local stress and strain
method can consider the influence of plastic strain and
loading sequence. According to the local stress and strain
method, we can get the fatigue life loss by the stress stain
curve and stain life curve.
3.1. Calculation of Stain
There are many models which describe the stress strain
curve, because the engineering material is commonly
hardening material, we can use the model called Ramger-
Osgood, the model can be expressed as:
K is cycle strength factor, n is circulating strain
hardening index.
Through the calculation of the stress field of the rotor,
this paper get that the maximum stress of rotor is
171MPa. By referring to data, we determinate that K is
375.5[6], and the cyclic strain hardening index n is
0.086[7], when the maximum stress is 171 MPa, the
strain is 0.002.
3.2. Calculation of Fatigue Life
Manson-Coffin formula is widely used in all the formu-
las which describe the strain-life curve, Manson-Coffin
expressed as:
 
aeapa f
 c
N (6)
is fatigue strength coefficient, f
is fatigue con-
tinue coefficient, b is fatigue strength index, c is a
continuation index.
The rotor material of 1000 MW ultra-supercritical unit
is new 12Cr, this paper estimate the fatigue life loss of
rotor with the general slope method [8] .
The best way to get the strain life curve is the fatigue
test under the control of strain. But sometimes because of
conditions, we can’t use the experimental method, so we
can approximately estimate the fatigue performance
curve by some static tensile performance parameters,
such as strength of extension, Young’s modulus, fatigue
resistance coefficient and true fracture strength. Estima-
tion methods that we commonly use are general slope
method , four correlation method an improved four cor-
Copyright © 2013 SciRes. EPE
S. BIAN, W. Y. LI 1489
relation method, this paper select the general slope
method to calculate the fatigue life.
General slope method is created by a variety of mate-
rial performance date fitting. In this method, b = -0.12, c
= -0.6, f
= 1.75
, f
= 0.50.6
, so Manson- Cof-
fin can be expressed as:
 
0.12 0.6
1.75 20.52
aeapa f
 
Through the formula, this paper get that N is 5601, the
fatigue life loss is 0.0095, when unit starts up in cold
condition everytime.
There are many fatigue cumulative damage models at
present, in the actual operation, linear damage accumula-
tion theory used more widely. Although linear damage
accumulation theory has some shortcomings, it needs
relatively few data, and is simple and easy in calculation.
When we get the loss of fatigue life under different con-
ditions, this paper suggests using the linear damage ac-
cumulation theory.
4. Conclusions
Because 1000 MW ultra-supercritical units have the high
steam parameters, and rotors work in severe conditions,
we should pay more attention to the fatigue life of rotor.
In this 1000 MW ultra-supercritical unit, the position
which own the maximum stress of the rotor appear in the
impeller root of regulation stage.
General slope method can estimate the fatigue life loss
of rotor.
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