Patent Application
20080206058
The present invention concerns the field of turbomachines and aims at a method for reducing the vibrations on the blades of a bladed wheel subject to a periodic excitation resulting from perturbations in the gas flow passing through the turbomachine, as produced by a bladed wheel or an obstacle close to said wheel, one wheel generally moving and the other being stationary.
A turbomachine comprises one or more rotors formed of bladed wheels, that is to say of blades mounted on a moving disk rotating about an axis, and one or more cascades formed of bladed wheels that are stationary, that is to say not moving in rotation with respect to the above axis. The blades of the stationary and moving wheels over which a gaseous fluid passes in a direction generally parallel to the axis. One of the principal sources of excitation of the stationary or moving blades is due to the wakes and the pressure fluctuations generated by obstacles adjacent the blading. These various obstacles, namely the blades of stages upstream and downstream, or even the arms of the casing, lead to perturbations in the flow of fluid through the blading. Movement of the blades in these perturbations creates a harmonic excitation synchronous with the rotor's rotation speed and generates an unsteady pressure field on the surface of the blade.
In the field of aeronautical turbomachines, the bladings are particularly sensitive parts because their design must meet the requirements of aerodynamic performance, of aeroacoustics and of mechanical resistance to rotation, to the temperature and to aerodynamic load. These aspects together mean that these structures are under quite a high static load and that, taking account of lifetime requirements, the amplitudes of vibrations they are subjected to must remain low. Moreover, the aeroelastic coupling, that is the coupling between the dynamics of the bladed wheels and the fluid flow, determines the vibration stability of the structure.
Within the context of the design of a turbomachine, and taking account of the multidisciplinarity of the contributors, the design process is iterative. The vibration design work is carried out to avoid the presence of critical resonances in the machine's operational range. The assembly is validated at the end of the design cycle using a test engine on which the vibration amplitudes are measured. Sometimes there are high vibration levels linked either to resonances or to vibrational instabilities. The rotor concerned must then be readjusted, which is particularly time-consuming and expensive.
The objective of the present invention is to control, already during the machine's design or development phase, the vibration response levels of the bladed wheels in a turbomachine structure comprising at least one moving bladed wheel and one stationary bladed wheel over which a gas flow passes.
The invention thus aims to deal with the vibrations produced by perturbations generated, for example, by one of the wheels in the gas flow on the other bladed wheel. In one particular case it targets the perturbations in the gas flow generated by the wake of a stationary bladed wheel or of an obstacle such as casing arms. These perturbations produce vibrations on the moving bladed wheel situated downstream.
The objective of the present invention is not limited to the control of vibration levels in a configuration where the bladed wheels are adjacent; it aims to control vibration responses on a bladed wheel for perturbations whose origin is upstream or downstream of the bladed wheel without being limited to the adjacent wheels.
The invention also targets excitations of the type distorting the aerodynamic flow path due to one or more bleeds in the gas stream or to distortion of the engine air inlet duct, when the engine is a turbojet, in the case of crosswind or incident wind. In the following, these distortions are included under the term “obstacle”.
Another objective of the invention is to implement a method allowing corrective measures to be taken as early or as far upstream as possible in the process of designing and adjusting the bladed wheels of turbomachines.
More particularly its objective is to reduce the vibration levels synchronous with the rotor's rotation speed on a moving or stationary bladed wheel, generated by the relative movement of the wakes or of the distortion resulting from a bladed wheel that is adjacent or at one or two stages remove upstream or downstream.
In accordance with the invention, the method for reducing vibration levels likely to occur in a turbomachine comprising at least a first bladed wheel and a second bladed wheel, where the two wheels are moving relative to one another about an axis of rotation and a gaseous fluid is passing over them, due to perturbations of an aerodynamic origin that are produced by the second bladed wheel or an obstacle on the first bladed wheel, is characterized in that the following steps are included in the design of said two bladed wheels:
Modification of the initial configuration preferably starts with the stationary wheel, whether this is the exciting bladed wheel or the wheel being subjected to the excitation.
More particularly, the invention allows various cases to be dealt with:
The invention results from the theoretical analysis of vibration phenomena. Assuming a unit norm for the eigenvectors with respect to the mass, it is shown that the forced response y(ω) of a linear structure subject to a harmonic excitation force f(ω) is linked to the latter by a relation that can be formulated using complex terms in the manner expressed below:
where:
the sign Σ means that the forced response y(ω) is the sum of the forced responses of each of the eigenmodes ν at the angular frequency ω. The forced response for a determined eigenmode is given by the relation in brackets. The sum takes account of all the n eigenmodes ν taken into consideration and which it is necessary to deal with, that is from the eigenmode ν=1 through to the eigenmode ν=n;
yν corresponds to the mode shape of the mode ν on the assumption of a unit norm for the eigenvectors with respect to the mass;
Tyν corresponds to the transpose of the preceding vector;
ων corresponds to the angular frequency of the eigenmode ν;
ω corresponds to the angular frequency of the excitation;
j
2=−1;
βν corresponds to the generalized modal damping for the eigenmode ν; and
f(ω) is the harmonic excitation force, itself being of the form fcos(ωt+φ) with time t and temporal phase shift φ.
In the case of an excitation of aerodynamic origin applied to a bladed wheel, the term τyνf(ω) represents the generalized aerodynamic force for the eigenmode ν.
Within the context of the invention, dealing with vibration phenomena comprises the implemention of means for reducing the modulus |y(ω)|.
Whereas to minimize the modulus |y(ω)| of the forced response subject to the excitation force f(ω) it is usual to seek to increase the factor βν linked with the damping for the eigenmode ν, in accordance with the present invention effort has been concentrated on reducing the modulus by a term corresponding to the generalized aerodynamic force of each of the eigenmodes ν.
A procedure for achieving this consists in modifying the stacking axis of the blades studied in the direction tangential to the axis of rotation. The profile of the airfoil of a blade is geometrically defined from the profiles of each of the mutually parallel cross sections made between the root of the blade and its tip. The cross sections thus form a stack along a curve which is designated the stacking axis. The profiles are aeromechanically determined.
The starting assumption was that for a determined cross section a modification in the tangential direction leaves the unsteady pressure modules unchanged for small variations (for example, of the order of one degree for a wheel made up of 150 sectors, cf.
This allows the temporal phase φ of the pressures to be linked directly to the tangential distance θ relative to the stacking axis through a cross section of the blade. The equivalence between the temporal phase shift on the pressures and the geometric phase shift, that is the tangential displacement to be applied to the blade, is established with the following relation:
φ=θNexcit
where
The procedure according to the invention is described further in detail below with reference to the figures in which:
As can be seen in
As mentioned above, movement of one wheel relative to the other within an axial gas flow, represented by the arrow F, is a source of perturbations. For example, with reference to
Other cases are possible in the context of the invention. In
In the case of
In the case of
Other cases are targeted by the present invention, but this is not limited to adjacent wheels.
The profile of a blade, and of its airfoil in particular, is generally determined by a number of cross sections carried out in the radial direction between the root and the tip.
In accordance with the invention the modulus of the forced response y(ω) of the blades of a first bladed wheel is reduced by searching for a distribution of pressure components suitable to minimize the modulus of the generalized aerodynamic force associated with each of the eigenmodes ν.
In fact, as results from the abovementioned formula (1), the generalized aerodynamic force associated with an eigenmode is a multiplying factor that appears in each of the terms of the sum Σ.
It is to be noted that the excited blade is not necessarily modified. It suffices to act on one of the blades, either forming the excitation source or being excited by the excitation source.
The procedure is elaborated below in relation to the flowchart of
The first two steps consist in defining the specifications in terms of the aerodynamic performance of the structure comprising two bladed wheels, then of calculating the initial configuration of the bladed wheels. This configuration includes the profiles of the cross sections c1, . . . cp and their stacking. Generally the procedure performs aerodynamic iterations, as is known to the person skilled in the art.
Step 3: The forced aeroelastic response y(ω) on the blading in the initial configuration is calculated when excited by a synchronous aerodynamic excitation f(ω):
If the vibration levels predicted (or measured in a test) are large in relation to experience, a target α|y(ω)| (with 0<α<1) in terms of the maximum vibration level is defined.
This must be done such that the value of α is as low as possible, taking account of manufacturing tolerances.
Step 4: The procedure according to the invention is applied with the above maximum vibration level as target.
The modulus of the forced aeroelastic response is minimized for a given mode, knowing that it could be extended to any mode.
The method consists in determining the geometric shift θ, illustrated in
To do this, spline/pole techniques, or techniques based on any discrete form or one chosen to project the stacking law are used for example.
Any optimization method may be used. By way of example, we cite some conventional methods: gradient method, the method called “simulated annealing”, genetic method, etc. (The quantity to be minimized is the modulus |Tyνf(ω)| or the sum of the moduli in the case of multimodal optimization.)
Step 5: Calculation of the forced aeroelastic response y′(ω) on the modified blading is carried out to verify that the target in terms of maximum vibration level has indeed been attained. If this is not the case a new definition of the profile is defined.
Step 6: Once the target is attained, it is verified that aerodynamic performance has been maintained by modifying the stacking axis of the blade concerned.
Step 7: The new definition of the blading is retained. It satisfies the aerodynamic criteria in terms of performance and the mechanical criteria in terms of vibration levels.
To the extent that the correction values are greater than the manufacturing tolerances for the blades, one has a means of reducing the vibration levels without adding mass or at the same time modifying aerodynamic performance of the turbomachine and of the technological interfaces of the blading.
The levels generated by wakes are reduced: namely, the wake of the stator/distributor or the wake of the moving bladed wheel. As specified above, the levels generated by distortions of the aerodynamic flow path, generated by one or more bleeds in the gas stream or by distortion of the engine's air inlet duct, are reduced. Other types of excitation are not taken into account. Although it addresses stator/distributor wheels and moving wheels, it is preferred to act on the excitation source which is a bladed stator/distributor wheel.
| Number | Date | Country | Kind |
|---|---|---|---|
| 07 01408 | Feb 2007 | FR | national |
