JP2006046226A - Excitation reducing structure for rotor and stator blade - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To increase resonance force reducing effect and estimate resonance force reducing effect. <P>SOLUTION: This structure is adopted to a rotary machine which consists of a stator blade train 1 and a rotor blade train 2. A rotor blade element of the rotor blade train 2 is indicated by an equation of motion: A-f(t)=0. A is expressed by a second degree differentiation term, a first degree differentiation term and a non-differentiation term (function of coordinates x) in relation to time of general coordinates x established in a rotary system. "f(t)" expresses external force received from the stator blade train element of the stator blade train. "x" is general coordinate especially is coordinate on a circle. A pitch of the stator blade train 1 is not constant and is expressed by a function P(t) in relation to time t of a rotation. Time variable t of the function P(t) is same as a variable t of the function f(t). The coordinate x is expressed by a function in relation to time as a solution of the equation of motion and pitch P(t) can be expressed by coordinates. Reduction of excitation can be optimized by expressing pitch by the function in relation to time without expressing as constant. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to an excitation reduction structure for a moving and stationary blade, and more particularly to an excitation reduction structure for a moving and stationary blade of a rotary machine.

  Multistage axial flow turbomachines such as steam turbines and gas turbines are required to develop advanced resonance avoidance techniques. In the turbomachine, rotating blades formed as a moving blade row are opposed to the annular surface of the stationary blade row. The stationary blade row is arranged at the front stage and the rear stage. A so-called cascade interference force acts due to the interference (potential interference) of the moving blade with the pressure field of the front stator vane or the latter blade. The fundamental frequency of cascade interference force acting on the moving blade is the product of the number of stationary blades and the number of rotations. If the fundamental frequency matches the natural frequency of the rotor blade, a large resonance stress is generated. Such generation of resonance stress is one of the important causes of high cycle fatigue.

ここで、上付（ｔ）は、ｘ_ｎがｔの関数であることを示し、式中の係数は下記の通りである。非対称配置静翼列のオフセット変更法の応答は、Ｎ＝２であれば、次式で計算することができる。下付添字ｎは、モードの字数を示す。

これらの式の定数記号と変数記号は、後述される。 In order to reduce the resonance stress with respect to the cascade interference force, a technique is known in which the stationary blades are arranged asymmetrically in the circumferential direction (rotation direction) to reduce the cascade interference force of a specific frequency component. Such a known technique is particularly effective for a variable speed machine in which it is difficult to avoid resonance, particularly in a turbo machine in which it is difficult to expand an axial span. The asymmetrical arrangement technique of the stationary blades divides the entire circumference into appropriate N segments. The number of divisions is usually two. The following two asymmetric arrangement methods are known.
(1) Change the number of stationary blades in the N segment (number change method)
(2) Changing the pitch between N segments (offset method)
The response of the method of changing the number of asymmetrically arranged stationary blade rows can be calculated by the following equation if N = 2.

Here, the superscript (t) indicates that _xn is a function of t, and the coefficients in the equation are as follows. The response of the offset changing method for the asymmetrically arranged stationary blade row can be calculated by the following equation if N = 2. The subscript n indicates the number of characters in the mode.

The constant symbols and variable symbols of these equations will be described later.

  The method of changing the number of sheets has a resonance force reduction effect of 30 to 40% with respect to the symmetrical arrangement structure. This level of effect is insufficient. The offset method requires an offset amount of an angle close to 180 degrees in order to obtain a response reduction effect comparable to that of the blade number change method over a realistic range of blade attenuation or number of stationary blades. This means that the vane pitch is forced to change significantly at the boundary between the upper half segment (upper half casing) and the lower half segment. For this reason, the offset method is not practical if the influence on the low-order harmonic excitation force or the influence on the flow stability such as surge is taken into consideration.

  A technique for making the pitch non-constant using a plurality of pitch nozzles is known from Patent Document 1 described later. A technique for making the nozzle pitch different between the upper half and the lower half is known from Patent Document 2 described later. A technique for dividing nozzle blocks and changing the pitch between adjacent blocks is known from Patent Document 3 listed later. The wake inflow position with respect to the second stage stationary blade is L.P. E. A clocking technique which is arranged so as to be close is known from Patent Document 4 described later. A technique for varying the pitch of the variable nozzles is known from Patent Document 5 described later.

  In a known asymmetrically arranged stationary blade row of the number changing method or the offset method, the stationary blades are arranged at equal pitches within each segment. In such a stationary blade row, the moving blades that pass through each segment are vibrated at the same frequency and resonance grows, so that it is difficult to obtain a sufficient resonance force reduction effect. is there.

  It is required to further increase the effect of reducing the resonance force. Furthermore, it is desirable that it is easy to predict the resonance force reduction effect.

Japanese Patent Laid-Open No. 8-61002 JP-A-11-200808 JP-A-9-256802 Special table hei 9-512320 JP 2000-204907 A

An object of the present invention is to provide an excitation reduction structure for a moving and stationary blade that further increases a resonance force reduction effect.
Another object of the present invention is to provide an excitation reduction structure for a moving and static blade that can easily predict a resonance force reduction effect.

The structure for reducing excitation and movement of moving blades and stator blades according to the present invention is applied to a rotating machine including a stationary blade row (1) and a moving blade row (2). The moving blade row element of the moving blade row (2) has the following equation of motion:
A−f (t) = 0
It is represented by A is expressed by a second-order differential term, a first-order differential term, and a non-differential term (function of the coordinate x) with respect to time of the general coordinate x set in the rotating system. f (t) represents the external force received from the stationary blade row elements of the stationary blade row. Here, x is a general coordinate, in particular, a coordinate on one circumference. The pitch of the stationary blade row (1) is not constant and is expressed by a function P (t) of time t for one rotation. The time variable t of the function P (t) is the same as the variable t of the function f (t). As a solution to the equation of motion, the coordinate x can be expressed as a function of time, and the pitch P (t) can be expressed in coordinates.

  By expressing the pitch as a function of time without making the pitch constant, the reduction in excitation can be optimized.

f (t) is the following formula:
f (t) = Fbsin [fk (t) · t]
Fb: Exciting force fk (t) received by the moving blades: Expressed by the angular frequency of the exciting force. This expression is the most generalized expression.

The formula is in particular:
fk (t) = N _T · Ω + α · t + β · t · t
α, β: Coefficient N _T : Number of stationary blade row elements Ω: Number of rotations (dimension is reciprocal of time)
It is represented by The coefficient is obtained in the optimization process. Specifically, β = 0.

  The stationary blade row is configured in multiple stages from a first stationary blade row (1F) and a second stationary blade row (1FF) facing the first stationary blade row. When the number of first stator blade row elements is the same as the number of second stator blade row elements, it is effective to give a phase difference in the rotational direction between the first stator blade row and the second stator blade row. is there.

  The pitch between adjacent first stationary blade row elements of the first stationary blade row is represented by an arithmetic sequence on the coordinate x in the rotation direction, and the second stationary blade row element adjacent to the second stationary blade row. The pitch between them is represented by an arithmetic sequence on the coordinate x in the rotation direction.

  The moving blade row is formed of a first moving blade row and a second moving blade row, the first moving blade row is arranged to face the first stationary blade row, and the second moving blade row is the second moving blade row. It is arranged facing the stationary blade row.

The stationary blade row is formed of an upper half stationary blade row in which N1 stationary blade row elements are arranged and a lower half stationary blade row in which N2 stationary blade row elements are arranged, and N1−N2 = ± 2. Such a small number difference effectively shows an excitation reduction effect. In this case, the number of moving blade row elements of the moving blade row is represented by Nb, and the following formula:
Nb = α · (N1 + N2), α = 2 · (2n−1), n: It is theoretically and empirically preferable to be represented by a natural number.

The stationary blade row is formed of an upper half stationary blade row in which N1 stationary blade row elements are arranged and a lower half stationary blade row in which N2 stationary blade row elements are arranged. In this case, the following conditions:
N1-N2 = ± 1, and 40 <(N1 + N2) <80
Is theoretically and empirically preferred.

The stationary blade row is formed of an upper half stationary blade row in which N1 stationary blade row elements are arranged and a lower half stationary blade row in which N2 stationary blade row elements are arranged. In this case, the following conditions:
N1-N2 = ± 1
Is given. In this case, it is theoretically and empirically preferable that the upper half stator blade row and the lower half stator blade row have a deviation of 0.11 pitch.

The stationary blade row is formed of an upper half stationary blade row in which N1 stationary blade row elements are arranged and a lower half stationary blade row in which N2 stationary blade row elements are arranged. In this case, the following conditions:
N1-N2 = 0
Is given. In this case, it is theoretically and empirically preferable that the upper half stator blade row and the lower half stator blade row have a deviation of 0.16 pitch.

  The excitation-reduction structure for a moving blade and stationary blade according to the present invention enables a mathematical analysis and optimally reduces excitation.

A preferred embodiment of the structure for reducing vibration of a moving blade and stationary blade according to the present invention will be described in detail with reference to the drawings. As shown in FIG. 1 represented as a development view, the front (front stage) stationary blade row is formed by _NT stationary blade elements 1. A large number of moving blades 2 rotate along the side surface (rotating surface) formed by the stationary blade row 1 at a rotational speed Ω (1 / t: t is a unit time). The _NT stationary blades 1 are preferably congruent with each other from the viewpoint of simplifying the calculation described later.

The circumferential distance (pitch) between the center positions between the first stator blade element 1 and the second stator blade element 1 is set to 2π / _NT by design. The circumferential distance (pitch) between the center positions between the second stator blade element 1 and the third stator blade element 1 is designed to be 2π / (N _T + ΔN / N _T ). Here, ΔN indicates an equal difference pitch between two adjacent stationary blades. A circumferential distance (stator blade pitch) Pi _-1 between the center positions between the i-th stator blade element 1 and the (i + 1) -th stator blade element 1 is expressed by the following equation.
P _i-1 = 2π / {N _T + ΔN (i-1) / N _T )}
N _T : Number of stator blades (number)
ΔN: pitch change amount (angle)
P _i-1 is an arithmetic sequence, and the difference is ΔN / N _T.

式中の（ｔ）は、一般座標ｘが時間ｔの関数であることを示す。右辺に現れるＦｂは、動翼が前置静翼から受ける加振力の振幅を示す。 As described above, the frequency of the nozzle wake excitation force that the moving blade 2 receives from the front stationary blade changes continuously (equal difference pitch) during one rotation of the moving blade. It is important to know the excitation force that the moving blade 2 receives in order not to cause the moving blade to resonate with the nozzle wake frequency due to this change. The excitation force f (t) is expressed by the following equation.
f (t) = Fbsin [(N _T Ω + ΔN · Ω · t / T) t] (3)
(N-1) T <t <nT
T: Rotational period of the rotor This excitation force f (t) is replaced with the right side of the already-known equation (1), and the equation of motion representing the vibration of the moving blade is expressed by the following equation (4). .

(T) in the equation indicates that the general coordinate x is a function of time t. Fb appearing on the right side indicates the amplitude of the excitation force that the moving blade receives from the front stationary blade.

The expression (4) in which the value in the sin on the right side changes periodically in one rotation clearly shows that the frequency of the excitation force acting on the moving blade during one rotation is not constant. The natural frequency of the moving blade does not coincide with the moving blade frequency solved by Equation (4) over the entire period during one rotation of the moving blade (instantaneously matches at one point on the entire circumference). That is possible.) Therefore, the moving blade does not resonate during one rotation, or the resonance force is extremely attenuated. FIG. 2 shows the frequency of the excitation force that the moving blade receives based on the equation (4). The frequency changes periodically between (N _T + ΔN) · Ω and _NT · Ω, and in principle does not coincide with the natural frequency of the blade, and the resonance force that the blade receives is continuously Resonance is effectively avoided under the damping force.

ここで、Ｆｂは既述のＦｂに同じであり、Ｆａは動翼２が後置静翼列から受ける加振力の振幅を示している。図４に示されるように、前置静翼に対応する加振周波数と後置静翼に対応する加振周波数との間には、位相差φａが存在する。φａを適正に選択することにより、後置静翼列１Ｒは、更に、共振力を減衰させる。位相差φａは、前置静翼と後置静翼の回転方向の相対的位置を変更することにより容易に与えられ得る。 FIG. 3 shows another preferred form of implementation of the structure for reducing excitation of a stationary blade according to the present invention. In this embodiment, the stationary blade row 1 is formed of a front stationary blade row 1F and a rear stationary blade row 1R. The moving blade 2 rotates between both surfaces of the front stationary blade row 1F and the rear stationary blade row 1R. The number of the front stator blade rows 1F and the pitch structure of the arithmetic sequence are the same as those of the previously described stator vane row in FIG. The rear stationary blade row 1R is the same as the front stationary blade row 1F in terms of the number of the stationary blade rows 1R and the pitch structure of the equidistant number rows. The rotational direction phase of the rear stationary blade row 1R is shifted in the forward direction or the backward direction by φa with respect to the front stationary blade row 1F. In this embodiment, Expression (4) is changed to the following Expression (5).

Here, Fb is the same as Fb described above, and Fa indicates the amplitude of the excitation force that the moving blade 2 receives from the rear stationary blade row. As shown in FIG. 4, there is a phase difference φa between the excitation frequency corresponding to the front stator blade and the excitation frequency corresponding to the rear stator blade. By appropriately selecting φa, the rear stationary blade row 1R further attenuates the resonance force. The phase difference φa can be easily given by changing the relative positions of the front stator blade and the rear stator blade in the rotation direction.

ここで、Ｆｂは既述のＦｂに同じであり、Ｆｂ２は動翼２が２段前静翼列から受ける加振力の振幅を示している。図６に示されるように、前置静翼列１Ｆに対応するノズルウェーク励振力の加振周波数と２段前静翼列１ＦＦに対応するそれの加振周波数との間には、位相差φｂが存在する。動翼が受ける加振力が小さくなるようにφｂが適当に選択される。 FIG. 5 shows still another preferred form of implementation of the structure for reducing excitation of a stationary blade according to the present invention. In this embodiment, the stationary blade row 1 is formed of a front stationary blade row 1F and a two-stage front stationary blade row 1FF. The second stage moving blade 2F rotates on the downstream side of the front stationary blade row 1F. The front stator blade row 1F and the two-stage front stator blade row are the same in terms of the number and the pitch structure of the arithmetic sequence, and those of the front stator blade row described above in FIG. It is the same as the structure. The pitch of the front stator blade row 1F and the two-stage front stator blade row is similarly reduced or increased, and the frequency of the nozzle wake excitation force received from the front stator blade and the nozzle received from the second stage stator blade row The point that the resonance of the moving blade is suppressed by continuously changing the frequency of the wake excitation force is the same as the embodiment described above, but the two-stage front stator blade row 1FF and the front stator blade row 1F are the same. By providing the phase difference φb between the two nozzles to cancel both nozzle wake excitation forces, the response of the rotor blade can be reduced, and the resonance of the rotor blade can be further suppressed. As such φb, there is an appropriate value for reducing the excitation force applied to the moving blade, which is calculated by the following formula and verified by an actual machine.

Here, Fb is the same as Fb described above, and Fb2 indicates the amplitude of the excitation force that the moving blade 2 receives from the two-stage front stationary blade row. As shown in FIG. 6, there is a phase difference φb between the excitation frequency of the nozzle wake excitation force corresponding to the front stationary blade row 1F and the excitation frequency corresponding to the two-stage front stationary blade row 1FF. Exists. Φb is appropriately selected so that the vibration force applied to the moving blade is reduced.

FIG. 7 shows still another preferred form of implementation of the structure for reducing excitation of a stationary blade according to the present invention. In this embodiment, the stationary blade row 1 is formed of an upper half stationary blade row 1U and a lower half stationary blade row 1D. The upper half stator blade row 1U and the lower half stator blade row 1D are arranged on the same circumference. The number of upper half stator blade rows 1U and the pitch structure of the difference number sequence are the same as the number of lower half stator blade rows 1D and the pitch structure of the difference number sequence. The excitation force f (t) that the moving blade 2 receives is expressed by the following equation.
f (t) = Fbsin [(N _T Ω + ΔN · Ω · t / T) t] (7)
(N-1) T / 2 <t <nT / 2

The pitch Pu of the upper half stator blade row 1U and the pitch Pd of the lower half stator blade row 1D are respectively expressed by the following equations.
Pu = 2π / {N _T + ΔN (i−1) / N _T )}, i = 1 to N _T / 2.
Pd = 2π / [N _T + ΔN {i− (N _T / 2 + 1) / N _T }], i = N _T / 2 + 1 to N _T
The moving blade 2 receives the nozzle wake excitation force during one rotation, and the resonance force attenuation suppression effect every half cycle (half of one rotation cycle). As shown in FIG. The effect of suppressing the generation of resonance force is fast and halved during one rotation cycle.

In the above-described form, the pitch change is represented by an even number sequence during one rotation or half rotation. By expressing the pitch change in a continuous function, it is possible to realize more precise resonance suppression.
f (t) = Fbsin {fb (t) t}, (n−1) <T <nT (8)
Here, the excitation force f (t) received by the moving blade 2 is given as a function of time t. When the pitch of the stationary blade is changed linearly with time, the frequency fb (t) of the excitation force is defined by the following equation.
fb (t) = N _T Ω + αt (8-1)
When the pitch of the stationary blade is changed nonlinearly with time, fb (t) is defined by the following equation.
fb (t) = N _T Ω + α · t + β · t · t (8-2)

過渡応答Ｘの最適値は、式（９）から求めることができる。過渡応答Ｘｍａｘが最小化されるように式（９）の係数α，βが求められる。 More generally, the function fb (t) is defined by a multi-order function of time, but a sufficiently good resonance damping characteristic can be obtained by a quadratic function. In order to optimize the resonance damping characteristics, it is preferable to optimize the coefficients α and β by various known optimization problem solving methods. In that case, constraints such as flow stability or performance are taken into account. As a constraint condition, appropriately setting the pitch difference between adjacent stationary blades to be equal to or less than a specified value is exemplified. The equation of motion of the moving blade 2 when the equation (8-2) is applied is represented by the following equation (9).

The optimum value of the transient response X can be obtained from Equation (9). The coefficients α and β in Equation (9) are obtained so that the transient response Xmax is minimized.

When the number of the front stator blade row 1F and the number of the rear stator blade row 1R are the same, the pitch change function of the front stator blade row 1F and the pitch change function of the rear stator blade row 1R are respectively defined. This further improves the resonance damping characteristics. Changing the frequency of the nozzle wake excitation force received by the moving blade from the front stationary blade row 1F and the frequency of the potential interference force received by the moving blade from the rear stationary blade row 1R continuously (stepwise) Can be more effectively suppressed. Further, by appropriately changing the phases of the front stationary blade row 1F and the rear stationary blade row 1R, the nozzle wake excitation force and the potential interference force are offset, and the blade response is further reduced. The resonance attenuation characteristics can be improved. The excitation force f (t) in this case is expressed by the following equation.
f (t) = Fbsin (fb (t) · t) + Fasin (fa (t) · t) (10)
(N-1) T <t <nT, n = 1, 2, 3,...
As described above, the minimization of the maximum transient response obtained by the equation of motion is executed, and the optimized resonance damping effect can be obtained. Here, as shown in FIG. 10, fb (t) indicates the angular frequency of the exciting force that the moving blade receives from the front stationary blade 1F, and fa (t) indicates that the moving blade is moved from the rear stationary blade 1R. Indicates the angular frequency of the excitation force received.

  FIG. 11 shows still another preferred form of implementation of the structure for reducing excitation of a moving blade and stationary blade according to the present invention. In this embodiment, the stationary blade row 1R is divided into four segments, and is divided into stationary blade rows 1Ra, 1Rb, 1Rc, and 1Rd. In the stator blade rows 1Ra and 1Rc, the pitch between adjacent stator blades is continuously shifted by ½ pitch. The pitch between adjacent stationary blades of the stationary blade row 1Rb is the same as the pitch between adjacent stationary blades of the stationary blade row 1Rd, and there is a 1/2 pitch deviation between the stationary blade row 1Rb and the stationary blade row 1Rd. . Such pitch distribution does not cause a large (extremely large) pitch difference (a large offset amount such as 180 degrees in the known offset method) in the region transition section (adjacent section of adjacent regions). Thus, by avoiding a sudden change in pitch, the influence on the flow stability such as surge can be reduced.

FIG. 12 shows a method of reducing the response reduction ratio (resonance damping effect degree), and this reduction method is applied to the above-described embodiment. In each form of FIGS. 1 to 11, the relationship between the number N1 of the stationary blades in the lower half segment and the number N2 of the stationary blades in the upper half segment is adopted as follows.
N1-N2 = 2 or N1-N2 = -2
As shown in FIG. 12, when the total number of stationary blades is 160, the response reduction ratio reaches 70%.

In a turbomachine adopting an infinite blade structure in which adjacent blades are connected to each other to form an annular blade row that is closed annularly, the number Nb of blades is given by the following formula:
Nb = α · (N1 + N2), α = 2 / (2n−1) (11)
, The nodal diameter mode generally satisfies the reverse phase condition, and a more stable response reduction effect can be obtained.

  FIG. 13 shows another reduction method of the response reduction rate, and this reduction method is applied to the above-described embodiment. N1-N2 = 1 or N1-N2 = -1 is set. N1 + N2 = 40 to 80, and the response reduction rate of the vibration response due to the nozzle wake excitation force is approximately 68%. The goal of reducing the response reduction rate, which is the subject of the present invention, to 70% or less can be generally achieved. Also in this case, conditional expression (11) is effective.

  FIG. 14 shows another reduction method of the response reduction rate using the offset method, and this reduction method is applied to the above-described embodiment. FIG. 15 shows the pitch shift between the upper half segment and the lower half segment. The horizontal axis in FIG. 14 indicates the common pitch shift amount for the upper half segment and the lower half segment. The response ratio curve of (N1 + N2) [H] ([H]: harmonic number) intersects the response ratio straight line of (N1 + N1) [H] at a point where the offset pitch is 0.11. By defining the pitch shift amount to be 0.11 pitch, an optimum response reduction ratio can be obtained. Conditional expression (11) is also effectively applied to this embodiment.

When all-around blades are coupled via a flexible disk with an all-round spelled blade structure (infinite blade structure) connected by a shroud of a turbomachine or a single blade structure, the vibration mode of the entire blade is a series. It is differentiated into a family of vibration modes with a nodal diameter. The resonance response of a coupled vibration having a nodal diameter responds only when the following resonance condition formula is satisfied simultaneously.
ΩH = ω, H ± ND = λNb
Ω: Shaft rotation speed H: Excitation harmonic number ω: Coupled natural frequency ND: Nodal diameter λ: Arbitrary integer Nb: Number of blades

In the vibration having such a node diameter, as shown in FIG. 16, the relationship between the frequency and the node diameter is folded back at the boundary of the (Nb / 2) node diameter, and there is a symmetrical relationship.
ω (Nb / 2 + i) = ω (Nb / 2−i)
There is no great difference in the vibration characteristics at the two points P and Q in the vicinity of the symmetrical reference axis (reverse phase condition line), but there is a large difference in the vibration characteristics at the two points P ′ and Q ′ far from the symmetrical reference axis. When changing the number of stationary blades in the upper and lower segments, the nodal diameters that respond when the moving blade passes through the upper and lower segments are different, and modes having different vibration characteristics are excited. In such a case, it is difficult to predict the response reduction effect by changing the number of stationary blades in the upper and lower segments. In contrast, by changing the number of stationary blades in the upper and lower segments near the nodal diameter that satisfies the antiphase condition, the influence on the vibration characteristics is small, and the response reduction effect can be easily predicted. Such a reverse phase condition is obtained when the number of nodal diameters is Nb / 2 when the number of excitation harmonics matches the total number of stator blades (N1 + N2). When the number of moving blades satisfies the following formula (12), the nodal diameter mode is almost in an anti-phase condition, the above-described prediction is easy, and a stable response reduction effect can be obtained.
Nb = α · (N1 = N2), α = 2 / (2n−1) (12)

  FIG. 17 shows the response reduction ratio by shifting the upper half segment and the lower half segment by 0.16 pitch in the circumferential direction when the difference in the number of stationary blades in the upper and lower segments is 0 (N1-N2 = 0). Yes. The response reduction rate curve corresponding to (N1 + N2) [H] crosses the response reduction rate curve corresponding to (N1 + N2 ± 1) [H] at a position of 0.16 pitch. A shift of 0.16 pitch indicates an optimum response reduction effect.

  The cascade is manufactured by dividing it into an upper half and a lower half in order to facilitate assembly. Usually, the upper half is placed on and coupled to a horizontal plane that is the upper surface of the lower half.

FIG. 1 is a developed view showing a preferred embodiment of an excitation reducing structure for a moving and stationary blade according to the present invention. FIG. 2 is a graph showing the frequency. FIG. 3 is a developed view showing another preferred embodiment of the structure for reducing the excitation of a moving blade according to the present invention. FIG. 4 is a graph showing other frequencies. FIG. 5 is a development view showing still another preferred embodiment of the implementation of the structure for reducing excitation of moving blades according to the present invention. FIG. 6 is a graph showing yet another frequency. FIG. 7 is a development view showing still another preferred embodiment of the implementation of the structure for reducing excitation of moving blades according to the present invention. FIG. 8 is a graph showing yet another frequency. FIG. 9 is a graph showing yet another frequency. FIG. 10 is a graph showing yet another frequency. FIG. 11 is a front view showing still another preferred embodiment of the implementation of the structure for reducing excitation of a moving blade and stationary blade according to the present invention. FIG. 12 is a graph showing response reduction. FIG. 13 is a graph showing another response reduction. FIG. 14 is a graph showing still another response reduction. FIG. 15 is a front view showing still another preferred embodiment of the implementation of the structure for reducing excitation of moving blades according to the present invention. FIG. 16 is a graph showing reverse phase conditions. FIG. 17 is a graph showing offset and response reduction.

Explanation of symbols

1,1F, 1FF ... Static blade row (Static blade row element)
2 ... Rotor blade row (Robot row element)

Claims (14)

A stationary blade row,
With a row of blades,
The moving blade row element of the moving blade row has the following equation of motion:
A−f (t) = 0
A is represented by a second-order differential term, a first-order differential term and a non-differential term with respect to time of the general coordinate x set in the rotating system, and f (t) is a stationary blade of the stationary blade row Indicates the external force received from the row element,
The pitch of the stationary blade row is not constant, and is expressed by a function P (t) of time t of one rotation. The f (t) is represented by the following formula:
f (t) = Fbsin [fk (t) · t]
Fb: Excitation force fk (t) received by the moving blades: Expressed by the angular frequency of the excitation force. Said formula is:
fk (t) = N _T · Ω + α · t + β · t · t
α, β: Coefficient N _T : Number of stationary blade row elements Ω: Number of rotations (dimension is reciprocal of time)
The excitation-reduction structure for a moving and static blade according to claim 2, represented by: The structure for reducing excitation of a stationary blade according to claim 3, wherein β = 0. The excitation-reduction structure of a moving blade according to claim 1, wherein the function P (t) is represented by P (x (t)) as a function of a coordinate x obtained by solving the equation of motion. The excitation-reduction structure for a moving and stationary blade according to claim 5, wherein a pitch between adjacent stationary blade row elements of the stationary blade row is represented by an arithmetic sequence on the coordinate x in the rotation direction. The stationary blade row is
A first stationary blade row;
A second stator blade row arranged in the axial direction in the first stator blade row;
A phase difference is provided in the rotational direction between the first stationary blade row element of the first stationary blade row and the second stationary blade row element of the second stationary blade row, and the second stationary blade row element The structure of claim 1, wherein the number of the first stationary blade row elements is equal to the number of the first stationary blade row elements. The pitch between adjacent first stationary blade row elements of the first stationary blade row is represented by an arithmetic sequence on the coordinate x in the rotation direction, and the second stationary blade adjacent to the second stationary blade row. The excitation-reduction structure for a moving blade and the stationary blade according to claim 7, wherein a pitch between the row elements is represented by the arithmetic sequence on the coordinate x in the rotation direction. The blade row is
A first blade row,
A second blade row,
The moving blades and stator blades according to claim 7 or 8, wherein the first moving blade row is disposed facing the first stationary blade row, and the second moving blade row is disposed facing the second stationary blade row. Excitation reduction structure. The stationary blade row is
An upper half vane row in which N1 vane row elements are continuously arranged;
A lower half stationary blade row in which N2 stationary blade row elements are continuously arranged,
N1-N2 = ± 2. The excitation-reduction structure for a moving and static blade according to claim 1, wherein the structure is reduced from N1 to N2. The number of moving blade row elements of the moving blade row is represented by Nb, and the following formula:
The vibration reduction structure for a moving blade according to claim 10, wherein Nb = α · (N1 + N2), α = 2 · (2n−1), and n: a natural number. The stationary blade row is
An upper half vane row in which N1 vane row elements are continuously arranged;
A lower half stationary blade row in which N2 stationary blade row elements are continuously arranged,
The following conditions:
N1-N2 = ± 1, and 40 <(N1 + N2) <80
(Here, the large and small comparison symbols include the equal sign.)
The structure for reducing excitation of a moving blade and a stationary blade according to claim 1, wherein the structure is reduced. The stationary blade row is
An upper half vane row in which N1 vane row elements are continuously arranged;
A lower half stationary blade row in which N2 stationary blade row elements are continuously arranged,
The following conditions:
N1-N2 = ± 1
The excitation-reduction structure for a moving and stationary blade according to claim 1, wherein the upper half stator blade row and the lower half stator blade row have a deviation of 0.11 pitch. The stationary blade row is
An upper half vane row in which N1 vane row elements are continuously arranged;
A lower half stationary blade row in which N2 stationary blade row elements are continuously arranged,
The following conditions:
N1-N2 = 0
The excitation-reduction structure for a moving and stationary blade according to claim 1, wherein the upper half stator blade row and the lower half stator blade row have a deviation of 0.16 pitch.

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