Method of determining a maximum acceptable alternating stress for a part that is subjected to cyclic loading; a unit for determining such a stress

Abstract

A method of determining a maximum acceptable alternating stress at a point of a part subjected to cyclic loading: simulating that the part is subjected to constant loading equal to a threshold value during a level period, and assuming that the part has elasto-viscoplastic behavior; from the results of the simulation, determining a final static stress at the point at the end or after the end of the level period; and for the point under consideration, using a Goodman diagram to determine the maximum acceptable alternating stress, which is determined for a static stress equal to the final static stress; the duration of the level period being equal to the duration of the loading of the testpieces that were used to draw up the Goodman diagram.

Claims

1. A determination method for determining a maximum acceptable alternating stress at a point of a part that is to be subjected to substantially cyclic loading, the method comprising: digitally simulating that the part is subjected, during a level period, to constant loading equal to a threshold value; taking account during said simulating of an elasto-viscoplastic model of behavior for a material constituting the part at the point under consideration; from results of the simulating, determining a final static stress at said point at an end of the level period or after the end of the level period; and for the point under consideration, determining the maximum acceptable alternating stress, using a static stress equal to the final static stress as an input in a first Goodman diagram, the maximum acceptable alternating stress being output from the first Goodman diagram, wherein a duration of the level period is substantially equal to a duration of loading of testpieces that were used to draw up said first Goodman diagram.

2. The determination method according to claim 1, wherein the first Goodman diagram is obtained by interpolation between at least two Goodman diagrams.

3. The determination method according to claim 1, wherein the part is a part of a rotary machine.

4. The determination method according to claim 1, wherein the part is a part of an aeroengine for an aircraft, the threshold value for the loading applied during the level period is equal to a mean value of a loading to which the part is subjected during a takeoff of the aircraft.

5. The determination method according to claim 1, wherein: the method comprises simulating digitally that the part, after the level period, is subjected to varying loading during a final period after the level period; and the final static stress determined is an end-of-final-period stress at said point at the end of said final period.

6. The determination method according to claim 1, wherein: the method comprises simulating digitally that the part, prior to the level period, is subjected to loading varying from a zero value up to the threshold value during a period of rising load.

7. A method of verifying the suitability of a part for being subjected to substantially cyclic loading, the method comprising: determining a maximum acceptable alternating stress at at least one point of the part when the part is subjected to said loading, using the method according to claim 1; evaluating at said at least one point of the part, an alternating stress to which the part is subjected at said at least one point; and for said at least one point, verifying that the alternating stress is less than the maximum acceptable alternating stress at the point under consideration, and concluding that the part is not suitable for being subjected to said loading when the verification is negative for at least one point.

8. A non-transitory computer readable medium including program code instructions for executing the method according to claim 1 when executed on a computer.

9. A determination unit for determining a maximum acceptable alternating stress at a point of a part that is to be subjected to substantially cyclic loading, the unit comprising: a processor configured to simulate digitally that the part is subjected to constant loading equal to a threshold value during a level period; take account of an elasto-viscoplastic behavior model for a material constituting the part at the point under consideration; determine a final static stress at said point of the part at the end of the level period or after the end of the level period; and determine the maximum acceptable alternating stress using a static stress equal to the final static stress as an input in a first Goodman diagram, the maximum acceptable alternating stress being output from the first Goodman diagram, wherein a duration of the level period is substantially equal to a duration of loading of testpieces that were used to draw up said first Goodman diagram.

10. A system for assisting in verifying the suitability of a part for being subjected to substantially cyclic loading, the system comprising: a determination unit according to claim 9 for determining a maximum acceptable alternating stress and configured to determine a maximum acceptable alternating stress at at least one point of the part when the part is subjected to said loading; and a processor configured to acquire an alternating stress at said at least one point; and verify for said at least one point that the alternating stress is less than the maximum acceptable alternating stress at the point under consideration and indicate that the part is not qualified when the verification is negative for at least one point.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention can be well understood and its advantages appear better on reading the following detailed description of embodiments given as non-limiting examples. The description refers to the accompanying drawings, in which:

(2) FIG. 1, described above, is a diagrammatic view based on a traditional Goodman diagram, having superposed thereon a curve of an effective Goodman diagram;

(3) FIG. 2 is a diagrammatic view of a turbine engine in which some of the blades have been verified using an implementation of the method of the invention for verifying the suitability of parts;

(4) FIG. 3 is a diagrammatic view showing the loading applied to a part, in particular cyclic loading, during a simulation;

(5) FIG. 4 is a diagrammatic view showing the variations of stress within the part when it is subjected to the loading shown in FIG. 3;

(6) FIG. 5 is a diagrammatic view showing the loading applied to a part, during a simulation performed in an implementation of the method of the invention, the curve including a level portion;

(7) FIG. 6 is a diagrammatic view showing the variations of stress in the part when it is subjected to the loading shown in FIG. 5;

(8) FIG. 7 is a flow chart of a method of the invention for determining the maximum acceptable alternating stress;

(9) FIG. 8 is an adapted Goodman diagram showing the final step of the FIG. 7 method;

(10) FIG. 9 is a flow chart of a method of the invention for verifying the suitability of a part;

(11) FIG. 10 is a diagrammatic representation of the hardware of a system of the invention for verifying the suitability of a part, the system including a unit for determining a maximum acceptable alternating stress in accordance with the invention; FIG. 11 is a diagrammatic functional representation of a unit of the invention for determining a maximum acceptable alternating stress; and FIG. 12 is a diagrammatic functional representation of a system of the invention for verifying the suitability of a part.

DETAILED DESCRIPTION OF THE INVENTION

(12) The invention is described below in the context of designing a blade 50 of a rotor wheel 60 of a high pressure turbine 65 in a turbine engine 70, as shown in FIG. 2.

(13) The loading to which the blade 50 is exposed while it is in use (i.e. throughout the entire lifetime of the engine 70) is shown in FIG. 3.

(14) This figure shows the variations in the mechanical loading F to which the blade is subjected as a function of time t (in seconds). This loading corresponds to a force F (in newtons) acting mainly, but not only, in the longitudinal direction of the blade. The force F is due in particular to the centrifugal force to which the blade is subjected as a result of the rotor wheel rotating; it represents the stresses to which the part is subjected during a “mission” or stage of operation during which the part is in use, which may for example, for an aeroengine part, be a stage of an airplane taking off, etc.

(15) As can be seen in FIG. 3, this loading, apart from a period P1 in which the loading rises, which period extends from an instant t0 to an instant t1, is in the form of loading that is cyclic, varying about a mean value F.sub.mean.

(16) FIG. 4 shows the stress variations at a point P of the blade when it is subjected to the loading shown in FIG. 3. FIG. 4 is shown with a time scale and with proportions that are quite different from those of FIG. 3.

(17) FIG. 4 comprise a first curve 20 representing variations in the stress (total stress) σ at the point P as a function of time t. It also has a second curve 22 that shows the variations as a function of time in the static stress σ.sub.stat. Curve 22 shows the variations of the mean value of the stress σ (and thus for each cycle, the curve 22 passes through the point having the value of the mean value of stress during that cycle). The curve 22 thus does not take account of high frequency variations in the stress σ.

(18) Two implementations of the method of the invention for determining the maximum acceptable alternating stress are described below with reference to FIGS. 5 to 8 and in particular with reference to FIG. 7.

(19) Whereas FIG. 3 shows values of loading F as used in conventional manner for determining the maximum acceptable alternating stress, in contrast, FIGS. 5 and 6 show the loading values and the stresses that are used in accordance with the invention.

(20) Preparing the Simulation

(21) The first step a) of the method, a simulation step, requires the following data to be prepared; a digital model of the blade 50; a model of the behavior of the material of the blade; parameters of the material of the blade; and the loading applied to the blade.

(22) The digital model of the blade is defined initially. This model is prepared in a format that makes it possible to perform the simulation step.

(23) The digital model of the blade is generally a three-dimensional model defined by finite elements. In the context of the invention, it is possible to use any kind of modeling for the part for example points connected together by springs, or more generally any digital modeling method capable of simulating the static, quasi-static, and vibratory or dynamic behavior of the part by means of a computer.

(24) Thereafter, the parameters relating to the blade material are determined:

(25) The model for the behavior of the blade material is determined and the parameters of the material of the blade are determined.

(26) In the context of the invention, the behavior model of the material of the blade is an elasto-viscoplastic (EVP) behavior.

(27) For example, the behavior model of the material of the blade may be a viscoplastic flow in the form of a Norton potential.

(28) The loading applied to the blade s also determined.

(29) In the two implementations described herein, the loading to be applied to the blade is initially defined during simulation step a) by means of a diagram such as the diagram shown in FIG. 5.

(30) This diagram shows the variations in the mechanical loading F to which the blade (as an example of a part) is subjected as a function of time t.

(31) This diagram has a period P1 in which the loading rises between an instant t0 and an instant t1, a level period P2 from the instant t1 to an instant t2, and a final period from the instant t2 to an instant t3.

(32) At the instant t0, the loading (or applied force) F is zero, as is the deformation or movement of the blade.

(33) As from the instant t1 and throughout the level period P2, the loading is constant and equal to a threshold value. The threshold value is generally selected to be equal to the mean value F.sub.mean of the loading applied to the blade; this is what FIG. 5 shows. This mean value represents the mean value of the loading during the critical stage of the mission carried out by the part; this mean value is obtained by filtering out or excluding the (vibratory) loading at high frequency

(34) The value of the loading during the level period P2 may likewise be selected to be equal to the value of the maximum loading applied to the blade, or it may be selected to be equal to some other value.

(35) The duration of the period P1 during which the loading rises is generally negligible, e.g. being less than 1/10th of the duration of the level period P2. For a blade such as the blade 50, the duration of the period P1 is nevertheless preferably not less than one second. The duration of the level period P2 is discussed below.

(36) The final period P3 is a period representing a final stage of using the blade, e.g. a stage of descending flight.

(37) Although in the example shown, the loading F applied to the blade is mechanical loading, the invention is equally applicable to loading of some other kind, e.g. thermal, etc.

(38) a) Simulating the Operation of the Blade

(39) After preparing all of the elements necessary for simulation, the behavior of the blade is simulated.

(40) The simulation consists in simulating the above-defined loading that is applied to the blade, the blade being made of a specified material, the material of the blade responding in compliance with the selected behavior model.

(41) Advantageously, since the variation in the loading is quite simple, in particular during the level period, the time selected for the simulation may be made discrete using a very small number of time steps.

(42) For example, it is possible to use time steps of increasing durations:

(43) A first time step that is very short, corresponding to the period of increasing load, having a duration t1=2 seconds (s);

(44) followed by five time steps during the level period, of durations that increase exponentially, e.g. successive durations equal respectively to 10 s, 100 s, 1000 s, 10,000 s, and 100,000 s.

(45) The duration of the level period t2 is selected follows:

(46) The frequency f of the loading cycles of the machine used for making the Goodman diagram is generally known in advance.

(47) Also known is the number N of loading cycles during which the blade needs to be capable of being used (this number is usually the number of cycles used for making the Goodman diagrams that are drawn up for the part).

(48) The duration D of the loading on the parts used to draw up the Goodman diagrams for the blade material is thus given by:
D=N/f

(49) In accordance with the invention, during the simulation, the duration t2 of the level period is said to be equal to the above-defined value D. The level period thus has the same duration as the duration of loading for the parts that were used for drawing up the Goodman diagrams(s) for the material.

(50) Furthermore, as mentioned above, FIGS. 5 and 6 correspond to two different implementations.

(51) In the first implementation, the simulation may be interrupted at the end of the level period P2, whereas in the second implementation, the simulation of all three periods P1, P2, and P3 is necessary.

(52) The reason for this difference is explained below.

(53) b) Determining the Final Static Stress

(54) In the first implementation, the final static stress (σ.sub.stat_fin) is selected for each point P as being the stress at the end of the level, i.e. the stress at the instant t2, at the end of the level period. It is written herein σ.sub.stat_fin_1.

(55) In contrast, in the second implementation, the final static stress (σ.sub.stat_fin) is selected for each point P as being the stress at the instant t3, at the end of the final period P3. It is written herein σ.sub.stat_fin_2.

(56) c) Determining the Maximum Acceptable Alternating Stress

(57) In parallel, independently of simulating the behavior of the blade and determining the final static stress σ.sub.stat_fin, as performed in steps a) and b), a Goodman diagram is drawn up or at least obtained for the material of the part when taken to the temperature T to which the point of the part is taken during the expected operating conditions (i.e. loading conditions).

(58) When a Goodman diagram is not available for the temperature T, a Goodman diagram for the temperature T can be made by interpolating Goodman diagrams that have been made for other temperatures.

(59) The Goodman diagram is made for a certain number of loading cycles to be expected for the part, specifically in the present example 10.sup.7.

(60) The maximum acceptable alternating stress σ.sub.alt_max for the point P under consideration of the blade is then determined merely by selecting the ordinate value of the point of the curve for which the abscissa value is the static stress at the end of the level period.

(61) Depending on the, selected implementation, two distinct values are naturally obtained for the maximum acceptable alternating stress, i.e. σ.sub.alt_max_1 and σ.sub.alt_max_2 (FIG. 8).

(62) Specifically, in this example, and as can be seen in FIG. 6, the stress to which the blade is subjected at instant t2 is greater than the stress to which it is subjected at the instant t3; this therefore gives rise to the following inequality:
σ.sub.stat_fin_1>σ.sub.stat_fin_2

(63) Since the curve in the Goodman diagram slopes downwards (FIG. 8), it follows, conversely:
σ.sub.alt_max_1<σ.sub.alt_max_2

(64) This result represents the fact that the maximum acceptable alternating stress obtained by the method is the maximum acceptable alternating stress at the moment selected for the final static stress: since during the final step P3 the static stress decreases, then conversely the maximum acceptable alternating stress σ.sub.alt_ max increases.

(65) The method of determining the maximum acceptable alternating stress σ.sub.alt_max serves to design parts that are subjected to cyclic loading.

(66) An example of the method for verifying the suitability of parts for being subjected to such loading is described below with reference to FIG. 9.

(67) In this method, the suitability of the part for use is verified by verifying that during use of the part, the stress to which all points of the part (or in reality a certain number of verification points) remains at a value or within a range that is acceptable.

(68) For this purpose, the method of verifying the suitability of parts comprises the following steps:

(69) Firstly the shape of the part is designed or selected (step 0, FIG. 9), which shape is defined in the form of a digital model. The digital model is defined in particular by a certain number of points P, which are the vertices of blocks (or polyhedra) defining the three-dimensional shape of the part.

(70) The material of the part is specified, and a behavior model is selected that is considered as being representative for this material.

(71) Finally, the utilization or working conditions of the part are specified. These conditions include in particular defining all of the loading that is to be applied to the part, whether that loading is mechanical, thermal, conditions at geometrical limits, etc.

(72) The loading is defined as a function of time, and at least during the level period, it presents cyclic variations.

(73) The purpose of the method is to determine whether, for the specified material, and with the specified shape for the part, at various selected points in the part (referred to as “verification points”), the stresses to which the part is subjected during expected operation (while being subjected to the specified loading) will remain within values that are acceptable. For this purpose, the procedure is as follows: A. At each of the verification points P, the maximum acceptable alternating stress σ.sub.alt_max is determined while the part is being subjected to the expected loading, by using the above-described method. B. The alternating stress to which each of the points P is, in fact, subjected is then evaluated. This evaluation is generally performed by subjecting the part to real tests, and by measuring the alternating stress to which the part is subjected by means of strain gauges or the equivalent. It is thus written σ.sub.alt_test. This test alternating stress σ.sub.alt_test may in particular be the alternating stress at the point P under stabilized operating conditions for the part. It may also be a maximum value for the alternating stress, e.g. the alternating stress at the point P during a takeoff stage, for engine blades in an airplane or a helicopter. C. For each of the verification points, it is verified that the test alternating stress σ.sub.alt_test is less than the maximum acceptable alternating stress σ.sub.alt_max at the point in question.

(74) If during step C, at least one point P is found to have a test alternating stress that is greater than the maximum acceptable alternating stress, it is concluded that with the expected shape for the part and with the expected material, it is not possible to obtain a blade suitable for the expected use: it is then necessary to return to step 0 of the method and to modify one of the parameters of the blade, such as its shape, the choice of material, etc.

(75) The method of determining the maximum acceptable alternating stress described with reference to FIG. 7 is performed by a unit 80 for determining the maximum acceptable alternating stress.

(76) In order to perform the method, the unit 80 comprises various modules (FIG. 10): a simulation module 82 for performing the simulation step a); a determination module 84 for determining the final static stress, which module receives the results of the simulation from the module 82; and on the basis of these results, the module 84 serves to determine the final static stress by using the step b) for the verification points P selected for the part; and a determination module 86 for determining the maximum acceptable alternating stress, which module receives the final static stress from the module 84. The module 86 then serves to perform the step c) and to determine the maximum acceptable alternating stress for the various verification points P.

(77) The unit 80 for determining the maximum acceptable alternating stress itself forms a portion of a broader functional assembly constituting a system 100 for verifying the suitability of a part to be subjected to cyclic loading.

(78) The system 100 serves to perform the method of the invention for verifying the suitability of a part to be subjected to substantially cyclic loading.

(79) In order to perform the method, the system 100 comprises various units (FIG. 11) The above-described unit 80. It serves to determine the maximum acceptable alternating stress for each of the verification points P. An alternating stress acquisition unit 90. The unit 90 is configured to acquire the alternating stress σ.sub.alt_test at the various verification points P. The value of the alternating stress may either be produced by calculation, or else it acquired by the unit 90, which value is produced outside the system 100. A verification unit 95. From the maximum acceptable alternating stress received from the unit 80 and the alternating stress σ.sub.alt_max received from the unit 95, the unit 95 verifies for each of the verification points P that the alternating stress σ.sub.alt_test at that point is less than the maximum acceptable alternating stress σ.sub.alt_max. If for at least one of the inspection points P the result of this verification is negative, the verification unit 95 sends information indicating that the part is not suitable for being subjected to the expected loading.

(80) The above-described modules 82, 84, and 86 for simulation, for static stress determination, and for maximum acceptable alternating stress determination in the unit for determining the maximum acceptable alternating stress are software modules implemented within a computer 100.

(81) The computer 100 thus constitutes a unit in the meaning of the invention for determining the maximum acceptable alternating stress.

(82) Furthermore, the evaluation unit 90 and the verification unit 95 as described above are software modules, likewise implemented within the computer 100.

(83) The computer 100 thus constitutes a system in the meaning of the invention for assisting in verifying the suitability of a part to be subjected to loading.

(84) The computer 100 presents the hardware architecture shown diagrammatically in FIG. 12.

(85) It comprises in particular a processor 4, a random access memory (RAM) 5, a ROM 6, a non-volatile flash memory 7, together with communication means 8 enabling the user to communicate with the computer. These hardware elements may possibly be shared with other functional units.

(86) The ROM 6 of the unit 100 constitutes a data medium in accordance with the invention that is readable by the processor 4 and that stores a computer program in accordance with the invention including instructions for executing steps of a method in accordance with the invention for designing a part. The program includes in particular instructions for executing steps of a method in accordance with the invention for determining the maximum acceptable alternating stress.

(87) Although the present invention is described with reference to specific implementations, it is clear that various modifications and changes may be undertaken thereon without going beyond the general ambit of the invention as defined by the claims. By way of example, the invention may be implemented equally well for designing aviation turbine engines or terrestrial turbines or fuel-burning engines, . . . Consequently, the description and the drawings should be considered in a sense that is illustrative rather than restrictive.