Method for operating a component that is cyclically loaded during operation

Abstract

A method for operating a component of predetermined geometry Ω that is cyclically loaded during operation, wherein a probability of failure P is determined for the component taking account of distributions of failure times, which are caused by deviations in material properties, the component is operated depending on the determined probability of failure P, wherein at least one maintenance time is set for the component, in particular depending on the determined probability of failure P.

Claims

1. A method for operating a component of predetermined geometry Ω that is cyclically loaded during operation, comprising: determining a probability of failure P for the component taking account of distributions of failure times, which are caused by deviations in material properties, operating the component depending on the determined probability of failure P, wherein at least one maintenance time is set for the component, depending on the determined probability of failure P, wherein the probability of failure P is determined taking additional account of distributions of failure times, which are caused by deviations of the component form from a standard geometry, wherein data that were obtained by determining the geometry of a predetermined number of representative components by metrology are resorted to for the purposes of taking account of the form deviation from the standard geometry, wherein the probability of failure P is determined according to the formula $P\left(t\right)\approx 1-\frac{e^{-t^m\left[J+\Delta J\right]+\frac{1}{2}{t}^{2m}{\sigma }^2}\left(1-\Phi \left(t^m\sigma -\frac{J+\Delta J}{\sigma }\right)\right)}{1-\Phi \left(-\frac{J+\Delta J}{\sigma }\right)},$ with the coordinate vector X of all nodes of the finite element model of the geometry Ω of the component, the discretized objective functional J(X)=J(X,U(X)) for LCF (low cycle fatigue) or for another fault mechanism, the number of load cycles t, a form parameter of the Weibull distribution m, the error function, which is the distribution function of the standard normal distribution Φ(t), and with J=J(X.sub.d) where Xd is the standard position of the nodes in the standard geometry, and with ΔJ=(dJ/DX)′ΔX with the mean process ΔX deviation and with σ.sub.2=(dJ/dX)′C(dJ/dX) with the process distribution C.

2. The method as claimed in claim 1, wherein each of the representative components was measured using a coordinate measuring machine or a white light interferometer, for the purposes of determining the geometry of the representative components by metrology.

3. The method as claimed in claim 2, wherein a set of coordinate points xij was obtained by determining the geometry of the representative components by metrology, where i specifies the respectively measured component and j specifies a respectively measured standard point, wherein the coordinates xj were obtained, from a CAD data record that represents the standard geometry of the components.

4. The method as claimed in claim 3, wherein the coordinates are chosen as surface mesh points of a finite element analysis mesh.

5. The method as claimed in claim 3, wherein the mean production process deviation at the point j is determined by
Δx.sub.j=(1/n)Σ.sub.i(x.sub.ij−x.sub.j)=(1/n)Σ.sub.iΔx.sub.ij and the covariance matrix of the deviations is determined by
c.sub.jk=(1/(n−1))(1/n)Σ.sub.i(Δx.sub.ij−Δx.sub.j)(Δx.sub.ik−Δx.sub.ik), where i specifies the respectively measured component.

6. The method as claimed in claim 1, wherein a limit is set for the probability of failure P, said limit determining the time at which the probability of failure will reach the limit and this time being set as maintenance time.

7. The method as claimed in claim 1, wherein a decision as to whether the production process of the component satisfies sufficiently stringent quality requirements for a specified application of the component is made on the basis of the determined probability of failure P.

8. The method as claimed in claim 1, wherein the component is a component of a gas turbine or a steam turbine or of a generator or of a jet engine or of a shaft or of an aircraft wing.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Further features and advantages of the present invention are elucidated on the basis of the following description of a method for operating a component according to an embodiment of the present invention, with reference being made to the attached drawing. In the drawing:

(2) FIG. 1 is an exemplary embodiment of the method according to the invention as a flowchart,

(3) FIG. 2 is a graph, in which the probability of failure P is plotted over the number t of load cycles for a standard geometry and for a distributed geometry, and

(4) FIG. 3 is a graph, in which the probability of failure P is plotted over the number t of load cycles for a standard geometry and for a distributed geometry with a systematic displacement in J as a consequence of ΔJ≠0;

(5) FIG. 4 is flow chart illustrating the operation of a method substantially as recited in claim 1.

DETAILED DESCRIPTION OF INVENTION

(6) The method according to the invention for operating a component according to the illustrated exemplary embodiment starts in a first step S1 with the provision of a component of predetermined geometry Ω that is cyclically loaded during operation, said component in the present case being a rotor blade, not illustrated in the figures, of a gas turbine that is likewise not illustrated.

(7) Geometry data that were obtained by determining the geometry Ω of a predetermined number of in this case 100 representative components by metrology are provided in a second step S2. The representative components, which are likewise rotor blades, are distinguished by the same geometry as the component provided in step S1—with the exception of production tolerances—and were produced by the same producer and in the same production method.

(8) The data provided for the representative components are, specifically, a set of coordinate points x.sub.ij, said set having been created by virtue of each of the representative 100 components having been measured by means of a coordinate measuring machine, a white light interferometer in the present case, at a predetermined number of standard points. Here, i denotes the respectively measured component and j denotes the respective standard point. Consequently, x.sub.ij represents a vector in three-dimensional space. The corresponding coordinates x.sub.i of the standard or intended geometry of the representative components were obtained by a CAD program, specifically in the form of a CAD data record of the component geometry provided for the production. Here, the coordinates were chosen as surface grid points of a finite element analysis (FEA) mesh. The geometry data for the representative components, captured by metrology, were captured by the producer of the provided component immediately after the production of the representative components using the white light interferometer.

(9) In a next step S3, the mean geometry deviation at the point j is calculated from the set of coordinates provided for the representative components by
Δx.sub.j=(1/n)Σ.sub.i(x.sub.ij−x.sub.j)=(1/n)Σ.sub.iΔx.sub.ij

(10) and the covariance matrix of the deviations is calculated by
c.sub.jk=(1/(n−1))(1/n)Σ.sub.i(Δx.sub.ij−Δx.sub.j)(Δx.sub.ik−Δx.sub.ik).

(11) A single random deviation vector ΔX=(Δx.sub.i) is considered. A normal distribution) ΔX˜N(ϕx,C) can be assumed for this deviation.

(12) Subsequently, a probability of failure P for the provided component is determined in step S4 using the formula

(13) $P\left(t\right)\approx 1-\frac{e^{-t^m\left[J+\Delta J\right]+\frac{1}{2}{t}^{2m}{\sigma }^2}\left(1-\Phi \left(t^m\sigma -\frac{J+\Delta J}{\sigma }\right)\right)}{1-\Phi \left(-\frac{J+\Delta J}{\sigma }\right)}$

(14) according to the invention, with ΔJ=(dJ/dX)′ΔX and
σ.sup.2=(dJ/dX)′C(dJ/dX).

(15) Here, m=1.5 is chosen within the scope of the present exemplary embodiment, which lies in the range of the Weibull form parameters of the probabilistic low cycle fatigue (LCF). Furthermore, J=(1/3000).sup.m is formulated for the present example, which corresponds to 3000 cycles as the

(16) $1-\frac{1}{e}\approx 0.63$
guanine of the Weibull distribution of the probability of failure of the standard geometry. Further, the assumption is initially made that ΔJ=0, meaning that the production process is centered about the standard geometry, that is to say X.sub.d=X.sub.0, i.e., the geometry deviations of the 100 representative components from the CAD standard geometry have a mean of zero.

(17) Finally, σ=0.6*J is assumed, meaning that the 1σ distribution in J(X) is 60% of the absolute J=J(X.sub.d) value, which factors in approximately 5% of the cases with the negative approximation for J(X).

(18) FIG. 2 illustrates, by way of the full line, the resultant probability of failure P(t) over the number of cycles t. The probability of failure P(t), which arises without the consideration of the geometry distribution according to the invention, is likewise plotted, specifically using the dashed line. This probability of failure P has been calculated according to the formula known in advance from the prior art, which only takes account of the distribution as a consequence of material properties but not that as a consequence of geometry deviations (cf. EP 2 835 706 A1).

(19) At first sight, taking account of the geometry distribution according to the invention appears to lead to moderate deviations. However, if the assumption is made that the maximum acceptable risk for LCF crack initiation lies at a probability of failure of 10%, a cycle number of t=670 is obtained when only taking account of the distribution as a consequence of material properties. By contrast, in the case of the additional consideration of the geometric distribution according to the invention, a cycle number of t=648 arises. The maximum acceptable probability of failure according to the exemplary embodiment is therefore already reached 22 cycles earlier. The fact that 22 cycles represent a significant economic value highlights the importance of the apparently moderate change as a consequence of the procedure according to the invention.

(20) In a last step S5, the provided component is operated depending on the determined probability of failure. Specifically, maintenance of the component being carried out when the maximum tolerable probability of failure of 10% has been reached, i.e., after 648 cycles, is specified.

(21) Since, according to the invention, the geometry distribution that leads to the maximum tolerable probability of failure being reached earlier is additionally taken into account when determining the probability of failure P, it is possible to ensure a particularly safe and particularly economic operation of the gas turbine comprising the considered rotor blade. This is because maintenance (planning) is implemented on the basis of calculated risk values, in which the distribution of the failure times as a consequence of the geometry distribution was also taken into account. Misjudgments of the component failure are reliably avoided.

(22) It should be noted that the influence of the presence of a systematic deviation of the production process, which results in a systematic geometry deviation, on the probability of failure was found to be substantially more significant.

(23) In order to elucidate this effect, the exemplary embodiment described above is modified in such a way that ΔJ=0.2*J is assumed instead of ΔJ=0. This corresponds to a change of 10% in the J-value as a consequence of a difference of X.sub.0−X.sub.d. The result can be gathered from FIG. 3, which once again illustrates the probability of failure P, once with additionally taking account, according to the invention, of the geometry distribution by way of the full line and once according to the prior art by way of the dashed line. It is possible to identify that the maximum acceptable probability of failure of 10% is now already reached at 568 cycles when the geometry distribution is additionally taken into account according to the invention and when there is a systematic deviation, i.e., for ΔJ=0.2*J. Compared to the cycle number of 670 when the geometry distribution is not taken into account like in the present invention, the maximum acceptable probability of failure is already obtained 102 cycles earlier. This elucidates that the procedure according to the invention is of particular importance in the case where a systematic deviation in the component production process is present since only this allows significant misjudgments of the component failure to be avoided.

(24) Even though the invention was illustrated more closely and described in detail by the preferred exemplary embodiment, the invention is not restricted by the disclosed examples and other variations can be derived therefrom by a person skilled in the art without departing from the scope of protection of the invention.