Impeller and manufacturing method of impeller

Abstract

To obtain an impeller of blading by intentional mistune suppressing an increase in AF at the time of harmonics resonance of a rotation order to be noticed without depending on a shape and a vibration mode of the impeller.SOLUTION: An impeller includes: a rotor core 12; and a plurality of blades (16, 18) arranged at equal intervals along the peripheral direction on a peripheral surface of the rotor core 12. Each blade is composed of a first blade 16 having a first vibration characteristic value and a second blade 18 having a second vibration characteristic value different from the first vibration characteristic value. The first blade and the second blade are alternately arranged with a prescribed regularity in the peripheral direction so as to form mistune distribution which does not include a mistune Fourier component having a wave number twice as large as a node diameter number ND determined by an expression (1). The expression (1): H+ND=nN (where, H is a rotation order of resonance by harmonics excitation, ND is a node diameter number in a traveling wave mode, n is an integer, and N is the number of blades).SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to an impeller for use in turbomachinery and the like, and a method for manufacturing the impeller, and more particularly to an intentionally mistuned impeller and a method for manufacturing the impeller. [Background technology]

[0002] In an impeller (rotor) with blades (moving blades) arranged at equal intervals along the circumferential direction of the rotor core, there is a small difference (hereafter referred to as mistune) in the eigenvalues ​​of each blade due to manufacturing errors and errors in actual operation. In a state where this unavoidable random difference (hereafter referred to as random mistune) exists (hereafter referred to as a mistuned system), the response of each individual blade is amplified or reduced during resonance due to harmonic excitation with a frequency that is an integer multiple of the impeller rotation speed, compared to a state where the eigenvalues ​​of each individual blade are all ideally the same (hereafter referred to as a tuned system). The resonant response amplification factor of this tuned system is called the Amplification Factor (hereafter referred to as AF).

[0003] In response to the demand for high efficiency, light weight, and high output of turbomachinery, impeller blades are often designed to be thin and under high load, which increases the risk of damage due to high cycle fatigue. Response amplification due to random mistuning further increases the risk of this high cycle fatigue and causes damage due to breakage, so if a method for controlling the resonance response amplification rate could be obtained, it would be a great advantage in product development. For this reason, research is being conducted into controlling the resonance response amplification rate by intentional mistuning distribution (hereinafter referred to as intentional mistuning).

[0004] On the other hand, in a development style called MBD (Model Based Development) and 1D CAE (1D Computer Aided Engineering), which is becoming more widespread these days, the design variables are determined in the early stages of development, prior to the detailed design of the blade's shape, with an eye on the feasibility of the product and its functions, allowing the quality of the impeller to be ascertained in advance, which is expected to reduce rework.

[0005] However, blade vibration response and intentional mistune are highly dependent on the blade shape and the aerodynamic conditions during operation of the impeller, and there are few examples of efforts from the perspective of 1DCAE, which aims to improve characteristics at an intangible stage. In particular, much of the research on intentional mistune aims to reduce the response to a lower level (resonant response amplification factor AF<1.0) than the response of the tuned system by utilizing the coupling of the traveling wave (sometimes referred to as TW in the following explanation) mode, which has large aerodynamic damping.

[0006] A known example of a conventional intentionally mistuned impeller (rotor) is a rotor in which the resonant frequency of the two-node diameter mode of the impeller is equal to or lower than the second rotational harmonic frequency of the rated rotational speed of the impeller, and in which the blades are arranged so that Nd≧5 and the ratio of the maximum mistuned component among the rotational order components of the circumferential mass distribution, stiffness distribution or natural frequency distribution of a plurality of blades is Nd≧5, and the impeller is composed of rotational order components whose ratio when divided by the magnitude of the rotational order Nd component is less than 1 / 2 (for example, Patent Document 1). [Prior art documents] [Patent documents]

[0007] [Patent Document 1] Patent No. 5519835 Summary of the Invention [Problem to be solved by the invention]

[0008] The above-mentioned conventional impeller is limited to the effect at the resonance point of the two-node diameter mode and the second rotation harmonic vibration. However, impellers used in turbo devices generally have many natural vibration modes of the blades, and in particular, harmonic resonance with respect to the stator blades has many harmonic resonance points in the normal operating range, so there is a possibility that harmonic resonance with unexpected response amplification will occur due to the influence of mistuning.

[0009] The effect of reducing the blade vibration response due to the distribution of intentional mistune in conventional impellers is limited to specific harmonic resonance conditions where the blade mode shape is dependent on the blade shape and the aerodynamic conditions during operation are clear. Therefore, it cannot be considered to be constant for applications such as aircraft engines, which have a wide operating range, many blades are subjected to the same harmonic excitation, and various changes in aerodynamic conditions during operation are possible.

[0010] It is believed that the optimal intentional mistune design becomes possible at the detailed design stage in the later stages of development, when the resonance points of the impeller that require attention in operation (resonance points that are the target of suppression) become clear. Changes in the impeller design caused by these resonance points will affect shape changes in the early stages of development. For this reason, there is a demand for the development of technology that can determine the quality of an impeller's characteristics as much as possible, regardless of the shape or vibration mode of the impeller, in the early stages of impeller development.

[0011] In view of the above background, an objective of the present invention is to obtain an impeller with an intentionally mistuned blade arrangement that suppresses an increase in AF during harmonic resonance of a notable rotational order, regardless of the shape or vibration mode of the impeller. [Means for solving the problem]

[0012] In order to solve the above problems, one embodiment of the present invention is an impeller comprising a rotor core (12) and a plurality of blades (16, 18) arranged at equal intervals along the circumferential direction of the rotor core, wherein the blades comprise a first blade (16) having a first vibration eigenvalue and a second blade (18) having a second vibration eigenvalue different from the first vibration eigenvalue, and the first blade and the second blade are arranged alternately in the circumferential direction with a predetermined regularity so as to result in a mistuned chain distribution that does not include a mistuned Fourier component having a wave number twice the nodal diameter number ND determined by equation (1). H + N D = n N (1) (where H is the rotational order of resonance due to harmonic excitation, ND is the number of nodal diameters in the traveling wave mode, n is an integer, and N is the number of blades.)

[0013] According to this configuration, an impeller with an intentionally mistuned blade arrangement can be obtained that suppresses the increase in AF during harmonic resonance of a notable rotational order, regardless of the shape or vibration mode of the impeller.

[0014] In the above embodiment, the arrangement of the first blades and the second blades that requires regularity may be such that every third blade is alternated with respect to each other, or every fourth blade is alternated with respect to each other.

[0015] According to this configuration, the first blade and the second blade are arranged symmetrically in the circumferential direction of the rotor core with the rotation center of the impeller as the point of symmetry, so that no unbalanced load acts on the impeller when the impeller rotates.

[0016] In order to solve the above problems, one aspect of the present invention is a method for manufacturing an impeller, comprising the steps of preparing a rotor core, preparing a plurality of first blades having a first vibration eigenvalue and a plurality of second blades having a second vibration eigenvalue different from the first vibration eigenvalue, and arranging the first blades and the second blades alternately in the circumferential direction with a predetermined regularity on the peripheral surface of the rotor core at equal intervals along the circumferential direction and so as to obtain a mistuned chain distribution that does not include a mistuned Fourier component having a wave number twice the nodal diameter number ND defined by equation (1). H + N D = n N (1) (where H is the rotational order of resonance due to harmonic excitation, ND is the number of nodal diameters in the traveling wave mode, n is an integer, and N is the number of blades.)

[0017] According to this manufacturing method, an impeller with an intentionally mistuned blade arrangement can be manufactured that suppresses the increase in AF during harmonic resonance of a notable rotational order, regardless of the shape or vibration mode of the impeller. Effect of the Invention

[0018] According to the above aspect, an impeller with an intentionally mistuned blade arrangement can be obtained that suppresses the increase in AF during harmonic resonance at a noteworthy resonance point, regardless of the shape or vibration mode of the impeller. [Brief description of the drawings]

[0019] [Figure 1] FIG. 1 is a perspective view showing one embodiment of an impeller according to the present invention; [Diagram 2] FIG. 1 is a vibration model diagram of an impeller according to a first embodiment in which first blades and second blades are arranged alternately every third blade. [Diagram 3] An explanatory diagram showing the traveling wave mode [Figure 4] Graph showing the natural frequency characteristics in the traveling wave mode [Diagram 5] FIG. 13 is a vibration model diagram of an impeller according to a second embodiment in which the first blades and the second blades are arranged alternately every four blades. [Figure 6] A graph showing the natural frequency characteristics in the traveling wave mode of two different types of impellers. [Figure 7] A graph showing the ratio of natural frequencies of each blade [Figure 8] Graph showing mistuned Fourier components [Figure 9] Graph showing the distribution of natural frequencies (upper part) and the corresponding mistuned Fourier component vibration characteristics (lower part) of the first embodiment [Figure 10] Graph showing the distribution of natural frequencies (upper part) and the corresponding mistuned Fourier component vibration characteristics (lower part) of the second embodiment DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] Hereinafter, one embodiment of an impeller according to the present invention will be described with reference to Figs.

[0021] 1, the impeller 10 of this embodiment has a frusto-conical rotor core 12. The rotor core 12 has a central hole 14 extending along its central axis Xt.

[0022] A plurality of first blades 16 and a plurality of second blades 18 are arranged at equal intervals along the circumferential direction on the outer circumferential surface of the rotor core 12. In other words, the impeller 10 includes a plurality of first blades 16 and a plurality of second blades 18 arranged at equal intervals along the circumferential direction of the rotor core 12 on the outer circumferential surface of the rotor core 12.

[0023] The first blade 16 has a first vibration eigenvalue. The second blade 18 has a second vibration eigenvalue that is purposefully different from the first vibration eigenvalue.

[0024] 2 shows a vibration model of the impeller 10 having a first blade 16 and a second blade 18. The first blade 16 is a vibrating body with a mass M1 and a spring constant K1 (rigidity), and the second blade 18 is a vibrating body with a mass M2 and a spring constant K2 (rigidity). The masses M1 and M2 are different from each other, or the spring constants K1 and K2 are different from each other, or both are different from each other, so that the first blade 16 has a first vibration eigenvalue and the second blade 18 has a second vibration eigenvalue that is intentionally different from the first vibration eigenvalue. The first blade 16 and the second blade 18 that are adjacent to each other are connected to each other by the rotor core 12 with a spring constant Kc.

[0025] The impeller 10 has a total of 16 blades, including eight first blades 16 and eight second blades 18, and constitutes an intentionally mistuned impeller. For convenience of explanation, hereafter, as shown in FIG. 2, the first blades 16 and the second blades 18 may be sequentially numbered as blade numbers #1 to #16, which increase in the counterclockwise direction.

[0026] The impeller 10 is a periodically symmetrical structure, and when we look at the vibration form of the entire system, as shown in the lower part of Figures 3(B) to (E), the entire structure is treated as a virtual disk D, which elastically deforms and undulates in the direction of rotation, generating TW mode vibration in which nodal circles Cn and a series of nodal diameters Dn appear. Note that Figure 3(A) shows a state in which all the blades of the impeller 10 vibrate in the same phase and no nodal diameters appear (nodal state).

[0027] The upper figures of Figures 3(A) to (E) are plan views of disk D seen from above, and the lower figures of Figures 3(A) to (E) are perspective views showing elastic deformation due to vibration of disk D. Figure 3(A) shows a state in which nodal diameter Dn appears and the nodal diameter number ND=0.

[0028] FIG. 3(B) shows a TW mode with nodal diameter number ND=1 and wave number κ=1, in which one nodal diameter Dn appears, dividing the nodal circle Cn in half.

[0029] FIG. 3(C) shows a TW mode with nodal diameter number ND=2 and wave number κ=2, in which two nodal diameters Dn appear that divide the nodal circle Cn into four equal parts.

[0030] FIG. 3(D) shows a TW mode with nodal diameter number ND=3 and wave number κ=3, in which three nodal diameters Dn appear that divide the nodal circle Cn into six equal parts.

[0031] FIG. 3(E) shows a TW mode with nodal diameter number ND=4 and wave number κ=4, in which four nodal diameters Dn appear, dividing the nodal circle Cn into eight equal parts.

[0032] The (+) in the upper row of Figures 3(B) to (E) indicates areas that are deformed upward from the knot-free state shown in Figure 3(A), and the (-) indicates areas that are deformed downward from the knot-free state.

[0033] 4 shows the natural frequency (frequency) of the impeller 10 in each TW mode of the impeller 10 with the number of blades N=16. In this impeller 10, for example, when it is excited by harmonics 20 or the like and ND=4 in formula (1) is in a resonant state, the TW of ND=4 and the TW of ND=(-4) are likely to be coupled because their vibration natural values ​​(natural frequencies) are close to each other. Therefore, |(-4)-4|=|(-4)×2|=2×ND=8, and it is necessary to aim not to include 8 in the Fourier components.

[0034] In the impeller 10, the first blades 16 and the second blades 18 are arranged alternately with a predetermined regularity in the circumferential direction of the rotor core 12 so as to obtain a mischain distribution that does not contain mistuned Fourier components having a wave number twice the nodal diameter number ND determined by equation (1), where H is the rotational order (excitation rotational order) of resonance due to harmonic excitation, ND is the nodal diameter number in TW mode, and N is the total number of the first blades 16 and the second blades 18. H + N D = n N (1) (where n is an integer, N is an even number when ND≦N / 2, and N is an odd number when ND≦(N-1) / 2)

[0035] Once the number of blades N and the rotation order H of interest are determined by equation (1), the nodal diameter number ND can be derived.

[0036] By alternating the first blades 16 and the second blades 18 with a predetermined regularity in the circumferential direction of the rotor core 12, the coupling between traveling waves is broken, and the mistuned chain distribution does not include the 2×ND mistuned Fourier component, which suppresses the increase in AF at the time of harmonic resonance of the rotation order H, which is noteworthy. This reduces the vibration of the impeller 10 during rotation and improves the durability of the impeller 10.

[0037] 2 shows an example (embodiment 1) of an arrangement of the first blades 16 and the second blades 18 when the notable rotation order H is 4. In embodiment 1, the first blades 16 and the second blades 18 are arranged alternately every third blade in the circumferential direction of the rotor core 12.

[0038] In the first embodiment, when the number of blades N is 16, in the rotation order H=4, ND=(-4) in the formula (1) is obtained, and ND×2=|(-4)×2|=8, whereas the arrangement of every third blade does not include the Fourier component 8. This suppresses the increase in AF during harmonic resonance of the rotation order H=4.

[0039] 5 shows a second embodiment of the impeller 10. In the second embodiment, the first blades 16 and the second blades 18 are arranged alternately every four blades in the circumferential direction of the rotor core 12.

[0040] In the second embodiment, when the number of blades N=16, in the rotation order H=4, ND=(-4) in formula (1) and ND×2=|(-4)×2|=8, whereas an arrangement of every fourth blade does not include Fourier component 8. As a result, the increase in AF during harmonic resonance of the rotation order H=4 is suppressed in the second embodiment as well.

[0041] In both of the first and second embodiments, even if the first blades 16 and the second blades 18 have different vibration eigenvalues, the first blades 16 and the second blades 18 are arranged symmetrically in the circumferential direction of the rotor core 12 with the center of rotation of the impeller 10 as the point of symmetry, and therefore, in addition to obtaining the above-mentioned effects, an unbalanced load is not applied to the impeller 10 when the impeller 10 rotates. This improves the durability and quietness of the bearing portion of the impeller 10.

[0042] The inventor devised a simple method of forming intentional mistune, aiming to cut off the coupling between TW modes and maintain the resonance response amplification factor AF at approximately 1.0 at the initial design stage when the number of blades is still in an unformed state, and confirmed the effect of this method using a 1D CAE tool. Note that "1D" here is not limited to one physical dimension, but refers to investigating the behavior and function of the system by setting physical equations and variables in an unformed state.

[0043] The mechanism of response amplification is explained below. The symbols used in the following description are defined as follows. [M]: Mass matrix [K]: Stiffness matrix f(t): excitation force vector N: Number of sectors (number of blades) Na: Number of active modes Kc: Inter-sector (inter-blade) coupling stiffness matrix Mb: Sector (wing) mass matrix Mc: Inter-sector (inter-blade) coupled mass matrix F: Excitation force amplitude ω: Excitation angular frequency Z: mode vector of the sector m: Degree of freedom within the sector X: Modal vibration vector in space coordinate system ΔK: Mistuned stiffness matrix ΔM: Mistuned mass matrix A: TW mode amplitude vector P: TW mode matrix Ω: Natural angular frequency matrix of the traveling wave j,κ,l,r:TW mode index

[0044] First, the harmonic excitation response of the tuned system will be described.

[0045] In a cyclically symmetric structure such as an impeller, each blade that can be divided into identical structural elements that form the periodicity is called a sector. The vector whose components are the displacements at the representative positions of each sector (blade) is defined as χ, and is considered to include the degrees of freedom within the sector. The equation of motion in spatial coordinates for vector χ is given by equation (2).

[0046]

number

[0047] The TW mode with wave number κ is denoted as TW[κ], and κ is called the TW mode index. If the number of sectors, i.e., the number of impeller blades, is N, the equation of motion (2) in spatial coordinates for the impeller excited with rotation order H=r can be rearranged into equation (3).

[0048]

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[0049] The sector mode vector Z has intra-sector degrees of freedom (m) in the sector modes (including the wing modes). The subscript κ represents the TW index. Using the TW mode matrix P expressed by equation (4) and the amplitude vector A of each TW mode expressed by equation (5), the amplitude X of the TW mode in spatial coordinates is expressed by equation (6), and the equation of motion in spatial coordinates of equation (3) is replaced by the equation of motion in modal coordinates of the TW mode (7).

[0050]

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[0051]

number

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[0052] For excitation of H=r, the balance of forces for the TWr mode, i.e., the rth line of equation (7) becomes equation (8), and for the other TW modes, it becomes equation (9). Therefore, the response amplitude (amplitude vector) A for excitation of H=r becomes equation (10), and it can be seen that only the TWr mode responds to excitation of H=r in the tuned system.

[0053]

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number

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[0054] In a mistuned system, there are differences in stiffness and mass for each blade. The equation of motion (3) in spatial coordinates for a tuned periodically symmetric structure, taking into account harmonic excitation forces, can be rewritten as equation (11) for a mistuned system.

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[0055] Here, the mistuned stiffness matrix ΔK and the mistuned mass matrix ΔM are matrices composed of the differences from the average values ​​for the stiffness and mass of each blade shown in equation (12), and will be referred to as mistune matrices hereinafter.

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[0056] Similar to the tuned system, the equation of motion for the mistuned system expressed in the modal coordinate system for the TW mode can be rearranged to equation (13).

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[0057] Here, Δ has the form of equation (14) and can be said to be a modal parameter newly generated by the mistuned matrix of equation (12).

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[0058] Looking closely at the (κ, j) components (Δκj) of this matrix, by expanding the first half of equation (14), we can see that the term (Δκj_ΔK) derived from the mistuned stiffness matrix ΔK and the term (Δκj_ΔM) derived from the mistuned mass matrix ΔM have the forms of equations (15) and (16), respectively. In other words, these terms Δκj can be understood as modal parameters generated by the association of the TWκ mode and the TWj mode. The mediator between these two TW modes can be understood as the Fourier component corresponding to the wave of wave number (κ-j) in the mistuned distribution over one revolution.

[0059]

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[0060]

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[0061] The balance of forces in the TWr mode against the excitation of H=r, i.e., the rth line of equation (13) is given by equation (17). From equation (17), it can be seen that in addition to the TWr mode, the TWr mode and all other TWs (κ=1,2...,N,κ≠r) also participate in the balance of forces by coupling via the mistuned Fourier components corresponding to waves with a wave number equal to the difference (r-κ) of the TW mode index. In addition to the deflection corresponding to the amplitude vector Ar on each of the first blade 16 and the second blade 18, the response amplitude A of the TW mode drawn into these couplings is 1 ~A N The vibrations corresponding to the above are superimposed on the same blade, and amplification or reduction from the tuning system occurs in the response of each of the first blade 16 and the second blade 18.

[0062]

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[0063] In general, when the number of blades in a tuned impeller is N, the TW mode with the nodal diameter number ND in the previously explained formula (1) as an exponent responds to the rotation order H. This will be called the original TW mode. H + N D = n N (1) However, ND≦N / 2, where N is an even number. ND≦(N-1) / 2, where N is an odd number

[0064] Regarding the AF in the harmonic resonance response of the blade, it can be said that the resonance response amplification factor AF is generated by the coupling between the originally responding TW mode and other TW modes, which is induced by the mistuned Fourier component contained in the mistune distribution over one revolution of the impeller. In addition, the induced mistuned Fourier component can be said to be a mistuned Fourier component with a wave number equivalent to the difference in the TW mode index of the two TW modes drawn into the coupling. The overlapping of the responses of these TW modes on the same blade causes response amplification or reduction from the tuning system for each blade, which can be said to lead to a change in the resonance response amplification factor AF.

[0065] The maximum value of the resonance response amplification factor AF is shown to be (1+√N) / 2, but the TW modes that respond in a coupled manner are limited to those close to the excitation frequency, which are called active modes, and the maximum value of the resonance response amplification factor AF is shown to be (1+√Na) / 2 (where Na is the number of active modes). The maximum number of nodal diameters ND that an impeller can have is, for example, N / 2 when the number of blades N is an even number, so there are N TW modes that can become active modes, from -N / 2 to N / 2. In other words, it can be said that the maximum number of active modes is the number N of blades.

[0066] Intentional mistuning, which aims to suppress response amplification from a tuned system to a mistuned system, can be achieved by identifying the TW mode (TW_ND) that originally responds to the rotational order H of resonance, as well as TW modes that exist at frequencies close to this (i.e., modes that can become active modes), in addition to the TW mode (TW_ND) that originally responds to the rotational order H of resonance, with the aim of severing the coupling between TW modes, and by aiming to form a mistune distribution that does not contain or has only a small number of mistuned Fourier components for the wavenumber equivalent to the difference between their indexes.

[0067] This can be considered by eigenvalue analysis at the pre-machining stage of development. In particular, the eigenvalues ​​of the original response TW_ND mode and its conjugate TW_(ND) mode are generally close to each other (they are the same in a tuned system), and in a mistuned system, regardless of the impeller characteristics (strength or weakness of coupling between blades), it is the TW mode that is most likely to become the active mode for each other. Therefore, as for intentional mistune, as shown in equation (18), it is considered that eliminating the 2×ND component from the mistuned Fourier component will suppress the increase in the resonance response amplification factor AF regardless of the impeller characteristics. This can be considered at the early development stage when the number of blades is still to be determined, when there is no shape to it. ND-(-ND)=2×ND (18)

[0068] Here is a specific example of active mode coupling. If H=4, N=16, and n=0, then ND=(-)4 means that the TW(-)4 mode is the TW mode that originally responds in the tuned system. In the mistuned system, the TW4 mode, which is in a conjugate relationship, is thought to exist at a close frequency, and this can become an active mode and cause coupling (see Figure 4). Since the difference between the two TW indices is 4-(-)4=8, if the mistuned distribution has a mistuned Fourier component of 8, it may induce coupling between these two TW modes, resulting in response amplification from the tuned system. Therefore, for intentional mistune, it is thought that by forming a distribution that does not include the mistuned Fourier component of 8, it is possible to break the coupling between TW modes and suppress response amplification from the tuned system.

[0069] However, forming a distribution that includes the magnitude of mistune as a variable involves a huge number of possible combinations, and is unrealistic in terms of both processing control and quality control. Therefore, in this embodiment, two types of blades are used: the designed blade and a blade with a manageable eigenvalue difference at a portion where the influence of shape differences, etc. is tolerable, and the 2×ND mistune Fourier component is eliminated under the arrangement control of these.

[0070] Next, we will explain the evaluation of the change in the resonance response amplification factor during harmonic excitation due to the difference in the mistuned Fourier components that arise depending on the concept of intentional mistune.

[0071] In this evaluation, first the response of the tuned system to the harmonic excitation to be evaluated is obtained, then as an unavoidable random mistune, a random mistune of any size is reflected and the response at the time of the harmonic excitation is obtained in the same manner as for the tuned system. At this time, the maximum value of the amplitude is read and the resonant response amplification factor AF due to the random mistune is calculated from the ratio with the tuned system response.

[0072] The change in the resonant response amplification factor AF with respect to the magnitude of random mistune was investigated, the magnitude of random mistune, which is thought to have a small contribution to the change in the resonant response amplification factor AF, was confirmed, and this was taken as the magnitude of the eigenvalue difference of the intentional mistune. Multiple intentional mistune patterns were set with two types of blade arrangements with the eigenvalue difference, and the excitation response of noteworthy rotation orders was obtained by adding intentional mistune to the random mistune, and the resonant response amplification factor AF was calculated for each intentional mistune pattern. In addition, the mistune Fourier components for each mistune distribution were investigated, and the correlation with the resonant response amplification factor AF was considered.

[0073] In a series of evaluations, two types of impellers with different characteristics were assumed to investigate the difference in the resonance response amplification factor AF depending on the number of active modes. In addition, three types of random mistuning were considered as unavoidable random mistuning to eliminate chance.

[0074] In evaluations of the blade vibration of an impeller, which behaves as a continuum, focusing on the properties of the structure as a cyclic symmetry structure, many literatures deal with models in which the symmetrical structural parts are replaced with lumped masses and springs, and the degrees of freedom are reduced in dimension. In this embodiment, a model as shown in FIG. 2, in which each sector is represented by one lumped mass and spring, was considered. In other words, the degree of freedom within one sector was considered to be one degree of freedom (m=1). The number of sectors (number of blades) N was set to 16.

[0075] In this evaluation, Amesim Version 2021.2 was used as a 1D simulation tool to simulate harmonic excitation. In the actual 1D simulation model, the blade mass was replaced with the moment of inertia, and the stiffness was determined by the direct stiffness Kd determined by the spring constants K1 and K2, the inter-blade coupling stiffness (spring constant) Kc, and the rotational stiffness. For mistune, the moment of inertia of each blade was adjusted and eigenvalue differences were given. The damping coefficient was given so that Qfactor ≒ 500 (half-width ≒ 0.1%) in the TW mode "4" of the tuned impeller. As with the stiffness, it was divided into a direct damping coefficient Cd and an inter-blade coupling damping coefficient Cc, and their ratio (Cc / Cd) was given in the form of a rotational damping coefficient, with the ratio (Kc / Kd) between the inter-blade coupling stiffness Kc and the direct stiffness Kd being the same. In the response evaluation, the amplitude of the excitation force was fixed at unit torque, and a frequency sweep was performed with a phase difference equivalent to an arbitrary harmonic excitation. The frequency sweep speed was 5 [Hz / s] for the resonance pass near 1345 [Hz]. The maximum value of the response angle amplitude of the 16 blades was read, and the resonance response amplification factor AF was calculated from the ratio to the tuned system angle amplitude.

[0076] In order to investigate the difference in the resonant response amplification factor AF depending on the number of active modes, two types of impellers with different characteristics were assumed as evaluation targets. Both of these two types of impellers have 16 blades N, but two types of impellers with different ratios (Kc / Kd) between the inter-blade coupling stiffness Kc and the direct stiffness Kd supporting from the center were prepared. The one with a larger ratio (Kc / Kd) is called "strong" and the one with a smaller ratio (Kc / Kd) is called "light." The "strong" impeller has a Kc / Kd of 1.887, and the "light" impeller has a Kc / Kd of 0.038. The characteristics of the two types of impellers are shown in Table 1. The types of mistunes given to the two types of impellers are shown in Table 2. In Table 2, the label IM2 indicates the one with the arrangement of every two blades in the first embodiment, and the label IM4 indicates the one with the arrangement of every four blades in the second embodiment.

[0077] [Table 1] [Table 2]

[0078] The relationship between the TW modes and eigenvalues ​​of these two types of impellers is shown in Figure 8. Here, the eigenvalue of TW mode "4" was adjusted so that it was the same for the two types of impellers. In the "light" impeller, all possible TW modes exist within a frequency range close to the eigenvalue of TW mode "4" of ±1.9%. This suggests that during harmonic excitation response as a mistuned system, more TW modes are drawn into coupling as active modes, and the resonant response amplification factor AF may be larger than that of the "strong" impeller.

[0079] Assuming that random mistunes are unavoidable in operation, the resonance response amplification factor AF was obtained by performing a harmonic excitation simulation with random mistunes. To eliminate chance, three types of random mistunes (RM1, RM2, RM3) were assumed. For the three types of random mistunes, three sets of 16 random numbers were generated, and the distribution of each set was scaled directly to the magnitude of an arbitrary random mistune. Here, the magnitude of the random mistune is calculated by multiplying the eigenvalue ωj of the jth blade by the average eigenvalue of all blades ω ave Due to the difference, it is defined as equation (19).

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[0080] Figure 7 shows the three types of random mistune distribution used in the evaluation. Figure 7 shows an example where the magnitude of random mistune is ±0.5%. Figures 8(A) to (C) show the Fourier components of the mistune (mistuned Fourier components) of random mistunes (RM1, RM2, RM3). This suggests that random mistunes contain many mistuned Fourier components, and may draw many TW modes into the coupling as active modes.

[0081] As a simple intentional mistune IM for the purpose of suppressing the resonant response amplification factor AF, we assumed the arrangement management of the two types of wing mentioned above, and evaluated the change in the resonant response amplification factor AF during harmonic excitation due to the difference in the mistuned Fourier components that arise depending on the arrangement of the two types of wing.

[0082] Here, the intentional mistune IM is given by changing the arrangement of two types of blades: the original blade and a blade with a high eigenvalue (+5%). The magnitude of the intentional mistune IM is defined by equation (20).

[0083]

number

[0084] Figures 9 and 10 show the mistune distribution and mistune Fourier components of an impeller with intentional mistune added to random mistune. In the mistune Fourier components in the lower parts of Figures 9 and 10, RM1 with intentional mistune IM added out of the three types of random mistune is shown as a representative example. Compared to the random mistune shown in Figure 8, the included mistune Fourier components have been greatly reduced, suggesting that the TW modes that are the target of attraction for coupling are reduced.

[0085] Next, a manufacturing method of the impeller 10 of this embodiment will be described. The manufacturing method of the impeller 10 includes the steps of preparing the rotor core 12 shown in Fig. 1, preparing a plurality of first blades 16 having a first vibration eigenvalue and a plurality of second blades 18 having a second vibration eigenvalue different from the first vibration eigenvalue, and arranging the first blades 16 and the second blades 18 alternately in the circumferential direction of the rotor core 12 at equal intervals on the circumferential surface of the rotor core 12 with the above-mentioned predetermined regularity so as to obtain a mistune chain distribution that does not include a mistuned Fourier component having a wave number twice the nodal diameter number ND determined by formula (1). H + N D = n N (1)

[0086] In the manufacturing process of this impeller 10, once the number of blades N and the notable rotation order H are determined, the nodal diameter number ND can be derived. Therefore, regardless of the shape or vibration mode of the impeller 10, it is easy to obtain an impeller 10 with an intentionally mistuned blade arrangement that suppresses the increase in AF during harmonic resonance of the notable rotation order.

[0087] The present invention has been described above in terms of preferred embodiments thereof. However, as will be easily understood by those skilled in the art, the present invention is not limited to such embodiments, and can be modified as appropriate within the scope of the present invention. For example, the total number of the first blades 16 and the second blades 18 is not limited to 16, and may be any other number. The arrangement of the first blades 16 and the second blades 18 may be alternately arranged, such as every other blade, every third blade, or every fifth blade, depending on the total number of the first blades 16 and the second blades 18. The first blades 16 and the second blades 18 may be integrally provided on the rotor core 12 by cutting or the like, or may be separate parts from the rotor core 12 and attached to the rotor core 12. The first blades 16 and the second blades 18 may be provided on the inner circumferential surface of a cylindrical portion formed on the rotor core 12. [Explanation of symbols]

[0088] 10: Impeller 12: Rotating core 16:1st wing 18: 2nd wing

Claims

1. A rotor core; In the impeller, a plurality of blades are disposed at equal intervals along the circumferential direction of the rotatable core on the circumferential surface of the rotatable core, The impeller comprises a first blade having a first vibration eigenvalue and a second blade having a second vibration eigenvalue different from the first vibration eigenvalue, and the first blade and the second blade are arranged alternately with a predetermined regularity in the circumferential direction so as to result in a mistuned chain distribution that does not include a mistuned Fourier component having a wave number twice the nodal diameter number ND determined by equation (1). H+ND=nN...(1) (where H is the rotation order of resonance due to harmonic excitation, ND is the number of nodal diameters in the TW mode, n is an integer, and N is the number of blades.)

2. The impeller according to claim 1 , wherein the first blades and the second blades are arranged so as to alternate every third blade with each other.

3. The impeller according to claim 1 , wherein the first blades and the second blades are arranged so as to alternate every fourth blade.

4. A method for manufacturing an impeller, comprising the steps of: Providing a rotor core; providing a plurality of first blades each having a first vibration eigenvalue and a plurality of second blades each having a second vibration eigenvalue different from the first vibration eigenvalue; and arranging the first blades and the second blades alternately with a predetermined regularity in the circumferential direction on the peripheral surface of the rotating core at equal intervals along the circumferential direction and so as to obtain a mistuned chain distribution that does not include a mistuned Fourier component having a wave number that is twice the nodal diameter number ND determined by equation (1). H+ND=nN...(1) (where H is the rotation order of resonance due to harmonic excitation, ND is the number of nodal diameters in the TW mode, n is an integer, and N is the number of blades.)

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