A system identification method for mechanical damping of a compressor blade

Abstract

The application discloses a system identification method for mechanical damping of a compressor blade, and the method is as follows: a working condition is determined through steady CFD calculation of a multistage compressor, and is used as an initial field to carry out unsteady CFD calculation; blade modal force amplitude f and phase θ are calculated based on the results of the aerodynamic unsteady calculation and strength finite element analysis; aerodynamic damping under different pitch diameters is calculated by combining the influence coefficient method, and average aerodynamic damping coefficients of aerodynamic damping under all different pitch diameters are calculated; vibration response values of the blade under typical states in the test are measured, and are converted into blade generalized displacement q; the modal force amplitude f, the phase θ, the blade generalized displacement q and the average aerodynamic damping coefficients are brought into a formula to obtain mechanical damping of the blade. Advantageous effects: the real mechanical damping of the blade in a multistage environment is obtained, and based on the obtained mechanical damping, the prediction accuracy and reliability of forced response of the blade in subsequent blade type optimization and blade modification design of derivative types can be effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of compressor blades, in particular to a system identification method for mechanical damping of compressor blades. BACKGROUND

[0002] In order to improve the performance of an aero-engine, three-dimensional swept blade shaping technology is used in modern compressor design, and lightweight alloys or composite materials are widely used in production and processing, which has the characteristics of light weight, high pressure ratio and high aerodynamic load. The axial gap between the rotor and stator blade rows of the compressor is also becoming smaller, and the unsteady disturbance between the rotor and stator blade rows is increasing. Among them, the vibration problem of the rotor and stator blades caused by the unsteady aerodynamic excitation such as wake, potential interference and shock has become one of the problems that must be overcome in engine design and testing. At present, the reliability problems such as high-cycle fatigue failure and fracture failure of blades have significantly affected the design and testing cycle, maintenance cost and service life of the engine.

[0003] Forced response is the vibration response of the blade after being subjected to periodic aerodynamic excitation (wake, potential interference, inlet distortion and shock) of the upstream and downstream blade rows. When the external excitation frequency is the same as the natural frequency of the blade, resonance occurs, which may lead to high-cycle fatigue failure. The designer of turbomachinery can predict the dangerous rotating speed at which resonance may occur by the intersection of the blade natural frequency and the aerodynamic excitation on the Campbell diagram, and avoid the dangerous point at which resonance may occur within the working rotating speed by adjusting the natural frequency of the blade (such as changing the maximum thickness of the blade and the position of the maximum thickness). However, in engineering practice, it is difficult for the designer to avoid the resonance point at low rotating speed and the vibration mode corresponding to the high-order mode. The prediction of forced response of compressor blades not only needs to consider the unsteady excitation force, but also needs to consider the damping ratio. Under the 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, the method of directly giving the mechanical damping equal to the aerodynamic damping or simplifying the method by giving a constant according to experience is mostly used, so it is difficult to accurately predict the forced vibration. SUMMARY

[0004] In order to solve the above problems, especially in view of the shortcomings of the prior art, the present application provides a system identification method for mechanical damping of compressor blades, which can solve the above problems.

[0005] In order to achieve the above purpose, the following technical means are adopted in the present application:

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

[0007] Step one, determine the working condition through multi-stage compressor steady CFD calculation, 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 two, based on the aerodynamic unsteady calculation results and strength finite element analysis of step one, the blade modal force amplitude f and phase θ are calculated;

[0009] Step three, under the excitation condition of blade vibration in the form of traveling wave, the aerodynamic damping under different pitch radii is calculated by combining influence coefficient method, and the average aerodynamic damping coefficient of aerodynamic damping under all different pitch radii is calculated

[0010] Step four, the dynamic stress measuring points of the blades of each stage are arranged on the compressor test piece, the vibration response values of the blades under typical states are measured in the test, and the vibration response values are converted into blade generalized displacements q;

[0011] Step five, finally, the modal force amplitude f, the phase θ, the blade generalized displacement q and the average aerodynamic damping coefficient are brought into the following formula to obtain the mechanical damping of the blade:

[0012]

[0013] Further scheme of the application is that in step two, the calculation of the modal force amplitude f is 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] Wherein, the integral domain s is the surface of the blade, p(t) is the unsteady pressure suffered by the surface of the blade, Φ x , Φ y , Φ z are projections of the modal displacement Φ in x, y and z directions respectively, n x , n y , n z are three direction normal vectors of the blade surface element ds.

[0016] Further scheme of the application is that in step two, the calculation of the phase θ is as follows:

[0017] A time domain modal force in a rotation period is selected, and fast Fourier transform is performed on the time domain modal force;

[0018]

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

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

[0021] The modal force on each blade is linearly superimposed by different Tyler-Sofrin modal lines:

[0022]

[0023] where [.] represents the floor function, θ i is the circumferential angle of the i-th blade, and the value range is {θ i [0<θ i <2π,i=1,2,…,N]}. is the component of the i-th pitch Tyler-Sofrin modal, is the modal force component of the i-th blade under a certain natural frequency ω0, By solving the linear equation set, the modal force under all pitches can be obtained, and the modal force amplitude f and the phase θ can be obtained.

[0024] Further schemes of the present application are that in step three, the calculation method of the average aerodynamic damping coefficient is as follows:

[0025] The middle 0-th blade is designated to make small amplitude harmonic vibration with its vibration mode and natural frequency ω0, and other blades remain in a static state, and the modal force F i (ω0) on all blades is calculated, and the vibration between adjacent blades is different by a fixed inter-blade phase angle:

[0026]

[0027] N is the number of blades, ND is the number of circumferential pitches, and the value range is Then the modal force generated by the vibration of the adjacent i-th blade on the 0-th blade is:

[0028]

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

[0030]

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

[0032]

[0033] The average aerodynamic damping coefficient is obtained by calculating the arithmetic mean:

[0034]

[0035] Advantages of the present application:

[0036] The present application provides a system identification method for mechanical ni of a compressor blade. The structural dynamics equation of blade vibration is reduced, and a modal reduction method is used to simplify it into a single degree of freedom mass-spring-damping oscillator equation. The modal force and aerodynamic damping of the blade are obtained by CFD numerical simulation. The response values of each mode of the blade are obtained by blade dynamic stress response measurement test. The reduced structural dynamics equation is solved to finally obtain the real mechanical damping of the blade in a multi-stage environment. In actual engineering application, dynamic stress measurement points of the blade are usually arranged on a compressor performance test piece or a 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 blade forced response in subsequent blade optimization and blade modification design of derivative models, and plays a crucial role in enhancing the fatigue life of the compressor blade, and finally achieves the purpose of reducing the development risk, shortening the cycle and saving funds. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 Flowchart of the present application;

[0038] Figure 2 The influence coefficient method calculation domain diagram in the embodiment of the present application is shown. DETAILED DESCRIPTION

[0039] The technical solutions of the present application will be described in detail below with reference to the drawings. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0040] Embodiment

[0041] As shown in Figure 1 A system identification method for mechanical damping of a compressor blade, the specific method is as follows:

[0042] Step one, determine the working condition by 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 aerodynamic excitation force of each blade;

[0043] Step two, based on the aerodynamic unsteady calculation results and strength finite element analysis of step one, carry out blade modal force calculation. The modal force is the projection of unsteady aerodynamic force on the blade vibration mode.

[0044] The calculation of modal force amplitude f is 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] Wherein, the integral 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 modal displacement Φ in x, y, z directions respectively, n x , n y , n z are the three direction normal vectors of blade surface element ds;

[0047] The calculation of phase θ is as follows:

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

[0049]

[0050] Wherein, T is the rotor vibration period, j is the imaginary unit, k is the harmonic order, k∈Z, ω is the excitation frequency, the frequency distribution of modal force can be obtained according to F(kω), that is, the value of Tyler-Sofrin modal expression can be determined, and it is assumed that the modal force on each blade is linearly superimposed by different Tyler-Sofrin modal lines:

[0051]

[0052] Wherein, [.] represents rounding down, θ i is the circumferential angle of the i-th blade, and the value range is {θ i [0<θ i <2π,i=1,2,…,N]}. is the component of Tyler-Sofrin modal of i pitch, is the modal force component of the i-th blade under a certain natural frequency ω0, By solving the linear equation set, the modal force under all pitches can be obtained, And then the modal force amplitude f and phase θ can be obtained;

[0053] Step three, under the excitation condition of blade vibration in traveling wave mode, the aerodynamic damping under different pitch diameters is calculated by combining the influence coefficient method, as shown in the following formula: Figure 2 As shown in the figure, the unsteady aerodynamic force on the middle 0th blade is equal to the sum of the unsteady aerodynamic forces generated on the 0th blade when all other blades vibrate alone. Due to the geometric rotational symmetry, the force generated on the 0th blade when the 1st blade vibrates is equal to the force generated on the -1th blade when the 0th blade vibrates. Therefore, the middle 0th blade is designated to vibrate with its mode shape and natural frequency ω0, and other blades remain in a static state. The modal force F i (ω0) on all blades is calculated, assuming that the difference between adjacent blade vibrations is a fixed interblade phase angle σ:

[0054]

[0055] N is the number of blades, ND is the number of circumferential pitch diameters, and the value range is The modal force generated on the 0th blade when the 1st blade vibrates is:

[0056] F -i (ω0)e jiσ

[0057] Based on the linear superposition principle, when the blades vibrate in a traveling wave with an interblade phase angle σ, the aerodynamic work on the 0th blade is:

[0058]

[0059] The aerodynamic damping coefficient under different interblade phase angles is:

[0060]

[0061] The average aerodynamic damping coefficient is obtained by calculating the arithmetic mean:

[0062]

[0063] Step four, arrange the dynamic stress measuring points of each stage of blades on the compressor test piece. In the test, the vibration response value of the blade under typical conditions is measured, and it is converted into the generalized displacement q of the blade;

[0064] Step five, finally, the modal force amplitude f, phase θ, blade generalized displacement q, and average aerodynamic damping coefficient are brought into the following formula to obtain the mechanical damping of the blade:

[0065]

[0066] The above description is only examples of the present application, and is not intended to limit the embodiments. Based on the above description, other different forms of changes or variations can be made by those of ordinary skill in the art, and all the embodiments do not need to be exhausted here, and the obvious changes or variations derived therefrom are still within the protection scope of the present application.

Claims

1. A system identification method for mechanical damping of a compressor blade, characterized by, The specific method is as follows: Step one, determine the working condition through steady CFD calculation of multi-stage compressor, and take it as the initial field to carry out unsteady CFD calculation, so as to obtain the time domain signal of aerodynamic exciting force of each blade; Step two, carry out blade modal force amplitude f and phase θ calculation based on the aerodynamic unsteady calculation result of step one and strength finite element analysis; Step three, under the excitation condition of blade vibration in traveling wave mode, the aerodynamic damping of different diameters is calculated by combining influence coefficient method, and the average aerodynamic damping coefficient of aerodynamic damping of all different diameters is calculated Step four, arrange the blade dynamic stress measuring points on the compressor test piece, and measure the vibration response value of the blade under the typical state in the test, and convert it into the generalized displacement q of the blade; Step five, finally, the modal force amplitude f, phase θ, blade generalized displacement q, average aerodynamic damping coefficient Substituting the following equation, the mechanical damping of the blade is obtained:

2. A system identification method for mechanical damping of a compressor blade according to claim 1, characterized in that, In the step two, the calculation of the modal force amplitude f is as follows: Where 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, z directions, respectively, and n x , n y , n z are the three directional normal vectors of the blade surface element ds.

3. The method of claim 1, wherein In the step two, the calculation of the phase θ is as follows: Select the time domain modal force in a rotation period, and carry out fast Fourier transform on it; Wherein, 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, that is, the value of the Tyler-Sofrin modal expression can be determined; The modal force on each blade is linearly superimposed by different Tyler-Sofrin modal lines: where [.] denotes the floor function, 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 i-th nodal radius Tyler-Sofrin mode, is the component of the modal force of the i-th blade at a certain natural frequency ω0, By solving the linear equations above, the modal forces at all nodal radii can be obtained, and the modal force amplitude f and phase θ can be obtained.

4. The method of claim 1, wherein In step three, the average aerodynamic damping coefficient is calculated as follows: The middle 0th blade is specified to vibrate in small amplitude simple harmonic vibration with its mode shape and natural frequency ω0, and other blades are kept in static state. The modal forces F on all blades are calculated i (ω0), with a fixed inter-blade phase angle between the vibrations of adjacent blades: N is the number of blades, ND is the number of circumferential pitch diameter, the value range is The modal force generated by the adjacent i-th blade on the 0-th blade is: F -i (ω0)e jiσ Based on the linear superposition principle, when the blade vibrates in the form of traveling wave with the interblade phase angle σ, the aerodynamic work on the 0th blade is: The aerodynamic damping coefficient under different interblade phase angles is: The average aerodynamic damping coefficient is obtained by calculating the arithmetic mean:

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