Method for introducing a deliberate mismatch on a turbomachine bladed wheel and bladed wheel with a deliberate mismatch

1. A method for introducing a deliberate mismatch into a turbomachine bladed wheel so as to reduce vibration amplitudes of the wheel in forced response, the method comprising the steps of:

determining an optimum value of the standard deviation for the mismatch as a function of operating conditions of the wheel inside the turbomachine, with respect to the maximum vibration amplitude response required on the wheel, and

at least partly placing blades with different natural frequencies on said wheel such that the standard deviation of the frequency distribution of all blades is equal to at least said mismatch value,

wherein said mismatch value is determined statistically including the following steps:

defining a first value of the mismatch standard deviation σ j ,

generating a statistically significant number R of random mismatch distributions within said standard deviation σ j ,

for each of the R random distributions, calculating the forced mismatched response as a function of the operating conditions of the wheel inside the turbomachine,

extracting from the forced mismatched response a maximum value,

choosing another value of σ j , and

repeating said calculating and extracting steps a sufficient number of iterations to obtain response values as a function of the values σ j .

2. The method according to claim 1 , wherein the number of different blade natural frequencies outside manufacturing tolerances is limited to three.

3. The method according to claim 2 , comprising distributing blades according to patterns with blades with natural frequency f1 and blades with natural frequency f2, f2 being different from f1.

4. The method according to claim 3 , wherein subsequent patterns are similar or vary slightly from one pattern to the next.

5. The method according to claim 4 , wherein each pattern includes (s1+s2) blades, s1 blades with frequency f1 and s2 blades with frequency f2.

6. The method according to claim 5 , wherein s1=s2 and s1 is not greater than the total number N of blades in the wheel divided by 4.

7. The method according to claim 4 , wherein each pattern comprises (s1+s2+/−2) blades, including (s1+/−1) blades with frequency f1 and (s2+/−1) blades with frequency f2.

8. The method according to claim 2 , further comprising subjecting the bladed wheel to a harmonic excitation of n disturbances per revolution, wherein n is less than the number N of blades in the bladed wheel divided by two (n<N/2), and distributing the blades in n identical patterns or with a slight variation from one pattern to the next.

9. The method according to claim 1 , further comprising subjecting the bladed wheel to a harmonic excitation of n disturbances per revolution, wherein n is greater than a number N of blades in the wheel divided by two (n>N/2), and wherein a number of patterns is equal to a number of diameters in the mode concerned.

10. The method according to claim 2 , further comprising modifying the resonant frequency of the blades by geometrically modifying the blades.

11. The method according to claim 2 , further comprising modifying the resonant frequency of the blades by geometrically modifying blade roots, the blades not being modified, so as to modify the stiffness.

12. The method according to claim 2 , further comprising modifying the resonant frequency of the blades by adding mass or varying the material from which the blades are made.

13. The method according to claim 12 , wherein the blades are hollow or recessed, and said modifying is induced by filling in part of cavities with a material of an appropriate density.

14. The method according to claim 3 , wherein a fillet between the blade and a hub varies from one blade to the next.

15. A method for introducing a deliberate mismatch into a turbomachine bladed wheel so as to reduce vibration amplitudes of the wheel in forced response, the method comprising the steps of:

statistically determining an optimum value of the standard deviation for the mismatch as a function of operating conditions of the wheel inside the turbomachine, with respect to the maximum vibration amplitude response required on the wheel, and

at least partly placing blades with different natural frequencies on said wheel such that the standard deviation of the frequency distribution of all blades is equal to at least said mismatch value,

calculating an average of damping coefficients corresponding to each possible phase angle between the blades, and

checking that an aeroelastic damping of a mode concerned by floating is less than said average, to firstly determine if introducing a deliberate mismatch improves the aeroelastic stability.