Method for analysis of 3D features using a 2D probabilistic analysis
View Patent ↗A method for analyzing a three-dimensional stress concentrating feature of a component ( 60 ), such as a borehole ( 62 ), using a two-dimensional probabilistic technique. A circumferentially-dependent stress concentration profile around the stress concentrating feature is determined, and then a probability of failure of the component is calculated using a 2D probabilistic failure analysis of the stress concentration profile. The probabilistic failure analysis may include a Monte Carlo theta integration approach.
1. A method for analysis of 3D features of a curved component, subject to cyclical stresses, in a gas or combustion turbine, using a 2D probabilistic analysis, the method comprising:
operating a system for evaluating the curved component subjected to a stress field, the system comprising a processor and an output device, the system being operated for:
modeling the curved component comprising a stress concentrating feature;
determining a circumferentially-dependent stress concentration profile around the stress concentrating feature;
calculating a probability of failure of the curved component using a 2D probabilistic failure analysis of the stress concentration profile;
performing a 2D probabilistic failure analysis for each of multiple angles around a circumference of the stress concentration profile;
averaging results of the analyses to obtain a single probability of failure value of the curved component;
outputting the probability of failure;
controlling a downtime of the curved component based on an output generated by the system; and
extending the service interval of the curved component,
wherein a 3D stress field distribution of a 3d feature of the curved component or the curved component is mapped onto a 2D stress field.
2. The method of claim 1 , further comprising performing the 2D probabilistic failure analysis using only a maximum stress concentration factor determined in the stress concentration profile.
3. The method of claim 1 , further comprising calculating the probability of failure of the curved component using a Monte-Carlo theta integration approach.
4. The method of claim 1 wherein the stress concentrating feature comprises a borehole, and the probability of failure of the curved component is represented in a Monte-Carlos theta integration approach by a plurality of voxels V i for i=1, 2, . . . n, and a stress increase for each voxel near the borehole is determined by a uniformly distributed random variable angle θi=U (0,360) using the equation
σ
i
=
σ
2
[
1
+
(
a
r
)
2
-
(
1
+
3
(
a
r
)
4
)
cos
2
θ
i
]
where
θ
i
=
U
(
0
,
360
)
where σ is a stress value along an x axis according to a 2D axis-symmetric model, σ i is an increased stress at a distance r from the borehole, a is a borehole diameter, and θ is an angle measured from the x axis.
5. The method of claim 1 , further comprising:
identifying a plurality of voxels surrounding the stress concentrating feature;
randomly assigning a circumferential position value θ for each voxel, where θ is equally distributed over the range 0 to 360 degrees;
determining a stress field value for each voxel based on its respective circumferential position value θ;
aggregating all determined stress fields; and
determining a probability of failure of the curved component responsive to the aggregated stress fields.
6. A method for analysis of 3D features of a curved component, subject to cyclical stresses, in a gas or combustion turbine, using a 2D probabilistic analysis, the method comprising:
operating a system for evaluating the curved component subjected to a stress field, the system comprising a processor and an output device, the system being operated for:
modeling the curved component comprising a stress concentrating feature;
determining a circumferentially-dependent stress concentration profile around the stress concentrating feature;
calculating a probability of failure of the curved component using a 2D probabilistic failure analysis of the stress concentration profile;
performing a 2D probabilistic failure analysis for each of a plurality of sectors around a circumference of the stress concentration profile; and
averaging results obtained for the plurality of sectors to obtain a single probability of failure value of the curved component;
outputting the single probability of failure; and
extending the service interval of the curved component,
wherein a 3D stress field distribution of a 3d feature of the curved component or the curved component is mapped onto a 2D stress field.
7. The method of claim 6 , wherein each sector circumscribes an angular arc, and wherein a single stress field value for use in a 2D probabilistic failure analysis for a respective sector is determined from the stress concentration profile at a midpoint of the angular arc of the respective sector.
8. The method of claim 6 , wherein each sector circumscribes an angular arc, and wherein a single stress field value for use in a 2D probabilistic failure analysis for a respective sector is a maximum stress concentration factor of the stress concentration profile within the angular arc of the respective sector.
9. A method of analysis of 3D features of a curved component, subject to cyclical stresses, in a gas or combustion turbine, using a 2D probabilistic analysis, the method comprising:
operating a system for evaluating the component subjected to a stress field, the system comprising a processor and an output device, the system being operated for:
modeling the component including removing borehole material from a component model to represent a borehole;
determining a stress field in a region proximate the borehole; and
executing a probability determining program to determine a probability of failure of the component after N cycles using stress field values as determined at the determining step;
outputting a probability of failure;
controlling a downtime of the component based on an output generated by the system,
wherein the stress field is determined for a plurality of different values of θ according to
σ
θ
=
σ
2
[
1
+
(
a
r
)
2
-
(
1
+
3
(
a
r
)
4
)
cos
2
θ
]
where σ is the stress value according to a 2D axis-symmetric model, σ θ is an increased stress at a distance r from a borehole center, a is a borehole diameter, and θ is an angle measured from an X axis, wherein the step of executing determines a probability of failure for the plurality of different θ values, and the probability of failure values are averaged for determining a probability of failure for the component,
extending the service interval of the curved component,
wherein a 3D stress field distribution of a 3d feature of the curved component or the curved component is mapped onto a 2D stress field.
10. The method of claim 9 wherein the stress field is determined for all values of θ according to
σ
θ
=
σ
2
[
1
+
(
a
r
)
2
-
(
1
+
3
(
a
r
)
4
)
cos
2
θ
]
where σ is a stress value according to a 2D axis-symmetric model, σ θ is an increased stress at a distance r from a center of the borehole, a is a diameter of the borehole, and θ is an angle measured from an X axis and lies in the range from 0° to 360°.
11. The method of claim 10 wherein for calculated stress field values where σ θ is less than the stress field values for σ, the stress field value for σ is used in the step of executing.
12. The method of claim 9 wherein the stress field is represented at all angular locations by a value obtained from
σ
90
=
σ
[
1
+
1
2
(
a
r
)
2
+
3
2
(
a
r
)
4
]
where σ is the stress value according to a 2D axis-symmetric model, σ 90 is an increased stress at a distance r from a borehole center, a is a borehole diameter.
13. The method of claim 9 further comprising a step of including correction values to a determined stress field.
14. The method of claim 9 wherein all stress field values within a region proximate the borehole are represented by a single stress field value.
15. The method of claim 9 wherein the borehole is represented by a plurality of pie-shaped sectors and the stress field values within each pie-shaped sector are represented by a single stress field value for that sector.
16. The method of claim 15 wherein each sector circumscribes a number of degrees and the single stress field value is determined at a θ value of one half an angular arc between two opposing edges of the pie-shaped sector.