System identification method for mechanical damping of compressor blade

Abstract

The invention discloses a system identification method for mechanical damping of a compressor blade, which comprises the following steps of: determining a working condition through steady CFD (Computational Fluid Dynamics) calculation of a multi-stage compressor, taking the working condition as an initial field, and carrying out unsteady CFD calculation; based on a pneumatic unsteady calculation result and strength finite element analysis, blade modal force amplitude f and phase theta calculation is carried out; calculating aerodynamic damping under different pitch diameters in combination with an influence coefficient method, calculating an average aerodynamic damping coefficient # imgabs0 # test for the aerodynamic damping under all different pitch diameters, measuring a vibration response value of the blade in a typical state, and converting the vibration response value into a generalized displacement q of the blade; and substituting the modal force amplitude f, the phase theta, the blade generalized displacement q and the average aerodynamic damping coefficient # imgabs 1 # into a formula to obtain the mechanical damping of the blade. The method has the beneficial effects that the real mechanical damping of the blade in the multi-stage environment is obtained, and based on the obtained mechanical damping, the blade forced response prediction precision and credibility in subsequent blade profile optimization and derivative type blade modification design can be effectively improved.

Description

Technical Field

[0001] The invention relates to the technical field of compressor blades, and in particular to a system identification method for mechanical damping of compressor blades. Background Art

[0002] In order to improve the performance of aircraft engines, modern compressor designs often use three-dimensional swept blade shaping technology, and a large number of lightweight alloys or composite materials are used in production and processing, which have the characteristics of light weight, high pressure ratio, and high aerodynamic load. The axial clearance between the moving and stationary blade rows of the compressor is also getting smaller and smaller, and the unsteady interference between the moving and stationary blade rows is intensifying. Among them, the vibration problem caused by the unsteady aerodynamic excitation of the rotor and stator blades such as wake, potential interference, and shock waves has become one of the difficult problems that must be overcome in engine design and testing. At present, reliability issues such as high-cycle fatigue failure and fracture failure of blades have significantly affected the design and finalization cycle, maintenance cost and service life of the engine.

[0003] Forced response is the study of the blade vibration response after being subjected to periodic aerodynamic excitation (wake, potential interference, inlet distortion, shock wave, etc.) from upstream and downstream blade rows. When the external excitation frequency is the same as a certain natural frequency of the blade, resonance is generated, which may lead to high-cycle fatigue failure. The impeller machinery designer can predict the dangerous speed where resonance may occur by the intersection of the blade natural frequency and aerodynamic excitation on the Campbell diagram, and avoid the dangerous point where resonance may occur within the working speed by adjusting the blade natural frequency (such as changing the maximum thickness of the blade and the maximum thickness position, etc.). However, in engineering practice, it is difficult for designers to avoid the resonance point in the low speed zone and the vibration mode corresponding to the high-order mode. The prediction of the forced response of the compressor blade needs to consider not only the unsteady exciting force, but also the damping ratio. Under current conditions, the aerodynamic damping of the compressor blade can be obtained by numerical calculation, but the mechanical damping of the blade cannot be accurately given. At present, most of them adopt the method of directly giving the mechanical damping equal to the aerodynamic damping or simplifying it based on empirical constants. Therefore, it is difficult to accurately predict forced vibration. Summary of the invention

[0004] In order to solve the above problems, especially to address the deficiencies in the prior art, the present invention provides a method for systematically identifying the mechanical damping of compressor blades that can solve the above problems.

[0005] To achieve the above purpose, the present invention adopts the following technical means:

[0006] A system identification method for mechanical damping of compressor blades is as follows:

[0007] Step 1: Determine the operating conditions through steady CFD calculation of multi-stage compressor, and use it as the initial field to carry out unsteady CFD calculation, so as to obtain the time domain signal of the aerodynamic excitation force of each blade;

[0008] Step 2: Calculate the blade modal force amplitude f and phase θ based on the aerodynamic unsteady calculation results and strength finite element analysis of step 1;

[0009] Step 3: Under the excitation condition of the blade vibrating in the traveling wave mode, the aerodynamic damping under different node diameters is calculated by combining the influence coefficient method, and the average aerodynamic damping coefficient of all aerodynamic damping under different node diameters is calculated.

[0010] Step 4: arrange blade dynamic stress measurement points at various levels on the compressor test piece, measure the vibration response value of the blade under a typical state in the test, and convert it into the blade generalized displacement q;

[0011] Step 5: Finally, the modal force amplitude f, phase θ, blade generalized displacement q, and average aerodynamic damping coefficient obtained in the above steps are Substitute the following formula to obtain the mechanical damping of the blade:

[0012]

[0013] A further solution of the present invention is that in step 2, the modal force amplitude f is calculated as follows:

[0014] f(t)=Φ T F a =∫∫ s p(t)(Φ x n x +Φ y n y +Φ z n z )ds

[0015] Where, the integration domain s is the blade surface, p(t) is the unsteady pressure on the blade surface, Φ x , Φ y , Φ z are the projections of the modal displacement Φ in the x, y, and z directions, respectively, n x 、n y 、n z They are the three direction normal vectors of the blade surface element ds.

[0016] A further solution of the present invention is that in step 2, the phase θ is calculated as follows:

[0017] Select the time domain modal force within a rotation period and perform fast Fourier transform on it;

[0018]

[0019] Where T is the rotor vibration period, j is the imaginary unit, k is the harmonic order, k∈Z, and ω is the excitation frequency;

[0020] According to F(kω), the frequency distribution of the modal force can be obtained, and the value of the Tyler-Sofrin modal expression can be determined;

[0021] The modal forces on each blade are linearly superimposed by different Tyler-Sofrin modes:

[0022]

[0023] Among them, [.] means rounding down, θ i is the circumferential angle of the i-th blade, and its value range is {θ i [0<θ i <2π,i=1,2,…,N]}, is the component of the Tyler-Sofrin mode at the i-th node diameter, is the modal force component of a certain natural frequency ω0 on the i-th blade, By solving the above linear equations, the modal forces at all node diameters can be obtained: Then the modal force amplitude f and phase θ can be obtained.

[0024] A further solution of the present invention is that in step 3, the average aerodynamic damping coefficient The calculation method is as follows:

[0025] Specify the middle blade No. 0 to perform a small amplitude simple harmonic vibration with its vibration mode and natural frequency ω0, and keep the other blades stationary. Calculate the modal force F on all blades i (ω0), the vibrations of adjacent blades differ by a fixed inter-blade phase angle:

[0026]

[0027] N is the number of blades, ND is the number of circumferential pitch diameters, and the value range is Then the modal force generated by the vibration of the adjacent blade No. i on the blade No. 0 is:

[0028]

[0029] Based on the principle of linear superposition, when the blade vibrates in a traveling wave with an inter-blade phase angle σ, the aerodynamic work performed on blade 0 is:

[0030]

[0031] The aerodynamic damping coefficient at different inter-blade phase angles is:

[0032]

[0033] The average aerodynamic damping coefficient is obtained by averaging it:

[0034]

[0035] Beneficial effects of the present invention:

[0036] The present invention proposes a system identification method for the mechanical vibration of a compressor blade, reduces the order of the structural dynamics equation of blade vibration, and uses the modal reduction method to simplify it into a single-degree-of-freedom mass-spring-damper oscillator equation. The modal force and aerodynamic damping of the blade are obtained through CFD numerical simulation, and the response values ​​of each mode of the blade are obtained through the blade dynamic stress response measurement test. The reduced-order structural dynamics equation is solved to finally obtain the true mechanical damping of the blade in a multi-stage environment. In actual engineering applications, dynamic stress measurement points of the blade are usually arranged on the compressor performance test piece or the core engine test piece. The mechanical damping obtained by back-calculation based on the measured data can effectively improve the prediction accuracy and reliability of the forced response of the blade in the subsequent blade optimization and the blade modification design of the derivative model, and plays a vital role in enhancing the fatigue life of the compressor blade, and ultimately achieves the purpose of reducing the development risk, shortening the cycle, and saving money. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a flow chart of the present invention;

[0038] Figure 2 Schematic diagram of the calculation domain of the influence coefficient method in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] Example

[0041] like Figure 1 As shown in FIG. 1 , a system identification method for mechanical damping of compressor blades is shown in FIG. 1 . The specific method is as follows:

[0042] Step 1: Determine the operating conditions through steady CFD calculation of multi-stage compressor, and use it as the initial field to carry out unsteady CFD calculation, so as to obtain the time domain signal of the aerodynamic excitation force of each blade;

[0043] Step 2: Based on the aerodynamic unsteady calculation results of step 1 and the strength finite element analysis, the blade modal force is calculated. The modal force is the projection of the unsteady aerodynamic force on the blade vibration mode.

[0044] The modal force amplitude f is calculated as follows:

[0045] f(t)=Φ T F a =∫∫ s p(t)(Φ x n x +Φ y n y +Φ z n z )ds

[0046] Where, the integration domain s is the blade surface, p(t) is the unsteady pressure on the blade surface, φ x ,φ y ,φ z are the projections of the modal displacement Φ in the x, y, and z directions, respectively, n x 、n y 、n z They are the three direction normal vectors of the blade surface microelement ds;

[0047] The phase θ is calculated as follows:

[0048] Select the time domain modal force within a rotation period and perform fast Fourier transform on it;

[0049]

[0050] Where T is the rotor vibration period, j is the imaginary unit, k is the harmonic order, k∈Z, ω is the excitation frequency, and the frequency distribution of the modal force can be obtained according to F(kω), which can determine the value of the Tyler-Sofrin modal expression. It is assumed that the modal force on each blade is composed of different Tyler-Sofrin modes linearly superposed:

[0051]

[0052] Among them, [.] means rounding down, θ i is the circumferential angle of the i-th blade, and its value range is {θ i [0<θ i <2π,i=1,2,…,N]}, is the component of the Tyler-Sofrin mode at the i-th node diameter, is the modal force component of a certain natural frequency ω0 on the i-th blade, By solving the above linear equations, the modal forces at all node diameters can be obtained: Then the modal force amplitude f and phase θ can be obtained;

[0053] Step 3: Under the excitation condition of the blade vibrating in the traveling wave mode, the aerodynamic damping under different node diameters is calculated by combining the influence coefficient method, such as Figure 2 As shown in the figure, the unsteady aerodynamic force on the middle blade No. 0 is equal to the sum of the unsteady aerodynamic forces generated on blade No. 0 when all other blades vibrate individually. Due to the rotational symmetry of the geometry, the force generated on blade No. 0 when blade No. 1 vibrates is equal to the force generated on blade No. -1 when blade No. 0 vibrates. Therefore, the middle blade No. 0 is specified to vibrate with a small amplitude simple harmonic vibration at its vibration mode and natural frequency ω0, and the other blades remain stationary. The modal force F on all blades is calculated. i (ω0), assuming that the vibrations of adjacent blades differ by a fixed inter-blade phase angle:

[0054]

[0055] N is the number of blades, ND is the number of circumferential pitch diameters, and the value range is Then the modal force generated by the vibration of blade No. 1 on blade No. 0 is:

[0056] F -i (ω0)e jiσ

[0057] Based on the principle of linear superposition, when the blade vibrates in a traveling wave with an inter-blade phase angle σ, the aerodynamic work performed on blade 0 is:

[0058]

[0059] The aerodynamic damping coefficient at different inter-blade phase angles is:

[0060]

[0061] The average aerodynamic damping coefficient is obtained by averaging it:

[0062]

[0063] Step 4: arrange blade dynamic stress measurement points at various levels on the compressor test piece, measure the vibration response value of the blade under a typical state in the test, and convert it into the blade generalized displacement q;

[0064] Step 5: Finally, the modal force amplitude f, phase θ, blade generalized displacement q, and average aerodynamic damping coefficient obtained in the above steps are Substitute the following formula to obtain the mechanical damping of the blade:

[0065]

[0066] The examples given in the present invention are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here, and the obvious changes or modifications derived therefrom are still within the protection scope of the present invention.

Claims

1. A method for systematic identification of mechanical damping of compressor blades, characterized in that: The specific method is as follows: Step 1: Determine the operating conditions through steady CFD calculation of multi-stage compressor, and use it as the initial field to carry out unsteady CFD calculation, so as to obtain the time domain signal of the aerodynamic excitation force of each blade; Step 2: Calculate the blade modal force amplitude f and phase θ based on the aerodynamic unsteady calculation results and strength finite element analysis of step 1; Step 3: Under the excitation condition of the blade vibrating in the traveling wave mode, the aerodynamic damping under different node diameters is calculated by combining the influence coefficient method, and the average aerodynamic damping coefficient of all aerodynamic damping under different node diameters is calculated. Step 4: arrange blade dynamic stress measurement points at various levels on the compressor test piece, measure the vibration response value of the blade under a typical state in the test, and convert it into the blade generalized displacement q; Step 5: Finally, the modal force amplitude f, phase θ, blade generalized displacement q, and average aerodynamic damping coefficient obtained in the above steps are Substitute the following formula to obtain the mechanical damping of the blade:

2. A method for systematic identification of mechanical damping of compressor blades according to claim 1, characterized in that: In step 2, the modal force amplitude f is calculated as follows: Where, the integration domain s is the blade surface, p(t) is the unsteady pressure on the blade surface, Φ x , Φ y , Φ z are the projections of the modal displacement Φ in the x, y, and z directions, respectively, n x 、n y 、n z They are the three direction normal vectors of the blade surface element ds.

3. A method for systematic identification of mechanical damping of compressor blades according to claim 1, characterized in that: In step 2, the phase θ is calculated as follows: Select the time domain modal force within a rotation period and perform fast Fourier transform on it; Where T is the rotor vibration period, j is the imaginary unit, k is the harmonic order, k∈Z, and ω is the excitation frequency; According to F(kω), the frequency distribution of the modal force can be obtained, and the value of the Tyler-Sofrin modal expression can be determined; The modal forces on each blade are linearly superimposed by different Tyler-Sofrin modes: Where [.] means round down, θ i is the circumferential angle of the i-th blade, and its value range is {θ i [0<θ i <2π,i=1,2,…,N]}, is the component of the Tyler-Sofrin mode at the i-th node diameter, is the modal force component of a certain natural frequency ω0 on the i-th blade, By solving the above linear equations, the modal forces at all node diameters can be obtained: Then the modal force amplitude f and phase θ can be obtained.

4. A method for systematic identification of mechanical damping of compressor blades according to claim 1, characterized in that: In step 3, the average aerodynamic damping coefficient The calculation method is as follows: Specify the middle blade No. 0 to perform a small amplitude simple harmonic vibration with its vibration mode and natural frequency ω0, and keep the other blades stationary. Calculate the modal force F on all blades i (ω0), the vibrations of adjacent blades differ by a fixed inter-blade phase angle: N is the number of blades, ND is the number of circumferential pitch diameters, and the value range is Then the modal force generated by the vibration of the adjacent blade No. i on the blade No. 0 is: F -i (ω0)e jiσ Based on the principle of linear superposition, when the blade vibrates in a traveling wave with an inter-blade phase angle σ, the aerodynamic work performed on blade 0 is: The aerodynamic damping coefficient at different inter-blade phase angles is: The average aerodynamic damping coefficient is obtained by averaging it:

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