Hereinafter, an embodiment of a rotating electrical machine according to the present invention will be described with reference to the drawings.
First, an analysis method related to vibration suppression of an embodiment of a rotating electrical machine according to the present invention will be described.
FIG. 1 is a schematic cross-sectional view perpendicular to the rotation axis of the rotating electrical machine according to the embodiment of the present invention. FIG. 2 is a diagram showing an example of the distribution in the circumferential direction in a cross-sectional view perpendicular to the axis of the rotating electrical machine, of the electromagnetic force applied to the fixed support member of the rotating electrical machine.
In a hammering test, it is known that a mode having nodes in the axial direction cannot be obtained in a frequency range of several thousand Hz or less where electromagnetic vibration is a problem. Therefore, for the sake of simplicity, the stationary support member 10 including the stator of the rotating electrical machine and the outer stator frame is approximated by a uniform ring as shown in FIG. 1 that does not consider the axial distribution of displacement. I decided to. Here, the name of the “fixed support member” is “fixed” in the sense that the rotor 50 is supported without rotating, and when considering the vibration of the fixed support member 10, It is not fixed and vibrates.
It is assumed that the fixed support member 10 is cylindrical and has a uniform thickness in the circumferential direction. Inside the fixed support member 10, a rotor 50 that rotates around an axis common to the axis of the fixed support member 10 is disposed. A gap 51 is formed between the fixed support member 10 and the rotor 50.
P non-uniform mass bodies 11 (mass: m _{Ip} ) are installed outside the fixed support member 10 at positions in the circumferential angle θ = α _{p} (p = 1,..., P). N food dampers (Houd Damper) 30 are installed at positions of the circumferential angle θ = θ _{j} (j = 1,..., N). In the example shown in FIG. 1, the number of non-uniform mass bodies 11 is P = 1, and the number of hood dampers 30 is N = 2. Further, it is assumed that the angular position coordinates are taken in the rotation direction of the rotor 50 indicated by the arrow A in FIG. Further, α _{1} = 0 degrees is set as the origin of the angular position coordinates of the non-uniform mass body 11.
The hood damper 30 generally refers to a vibration damping device including a resistance element 13 (damping coefficient: c _{Hj} ) and a damper mass body 14 (mass: m _{Hj} ) attached to the tip thereof. Here, since it is assumed that the fixed support member 10 performs an annular vibration, the damper mass body 14 is assumed to be movable at least in the radial direction. However, the structure of the hood damper 30 is not limited to the structure shown in FIG. 1. For example, a granular material or a viscous fluid that can move in a closed container as disclosed in Patent Document 2 is used. May have been.
The radial displacement u of the fixed support member 10 is expressed by the following equation (1) when considering M vibration modes.
here,
θ: Coordinates in the circumferential direction (rad) (counterclockwise is positive)
i: integer representing a vibration mode in the circumferential direction a _{i} : displacement of a cos type mode i having a belly at θ = 0 b _{i} : displacement of a sin type mode i having a belly at θ = π / (2i)
As a general external force acting on the electric motor, a force acting in the radial direction is an electromagnetic force distributed in the circumferential direction and rotating in the circumferential direction. Therefore, this is expressed by the following equation (2).
Where s: integer representing the mode of electromagnetic force Ω _{s} : angular frequency of electromagnetic force having mode s F _{s} : amplitude of electromagnetic force of mode s
The actual electromagnetic force contains many frequency components, only the component of _{F s cos (-Ω s t +} sθ) for simplicity assume that act. Also, assuming that the non-uniform mass is not so large, it is treated as an inertial force, and a viscous damping force acts on the stator. When only the i-th mode is adopted and the case of i = s is handled, the equation of motion is expressed by the following equation: (3) to (5).
Where r: radius of the ring of the fixed support member E: longitudinal elastic modulus of the fixed support member A: cross-sectional area of the fixed support member (the product of the ring thickness H and the axial length L in the case of a rectangular cross section) )
I: moment of inertia of about primary vertical axis to the plane of the ring of the fixed support member (LH ^{3/12} in the case of rectangular cross-section)
ρ: Density of fixed support member c _{0i} : Viscous damping coefficient of main system (i = 1,..., M)
x _{j} : Displacement of the hood damper installed at θ = θ _{j} (j = 1,..., N)
C _{Hj} : Viscous damping coefficient of the hood damper installed at θ = θ _{j} (C _{Hj} = 2γ _{Hj} m _{Hj} ω _{0i} )
ω _{0i} : Natural angular frequency of i-th mode m _{Hj} : Mass of hood damper installed at θ = θ _{j} m _{Ip} : Mass of non-uniform mass installed at θ = α _{p} P: Number of non-uniform mass N : Number of food dampers
Here, the mode of i = 2 is taken as an example, and vibration suppression by a non-uniform mass body and a hood damper is considered. For example, with two hood dampers, the steady solutions of equations (3) to (5) are set as the following equations (6) to (9).
a _{2} = A _{1} cosΩ _{2} t + B _{1} sinΩ _{2} t (6)
b _{2} = A _{2} cosΩ _{2} t + B _{2} sinΩ _{2} t (7)
x _{1} = A _{3} cosΩ _{2} t + B _{3} sinΩ _{2} t (8)
x _{2} = A _{4} cosΩ _{2} t + B _{4} sinΩ _{2} t (9)
When i is 0, the vibration of the circular ring becomes larger or smaller as it is. When i is 1, the shape and size of the circular ring remains unchanged, and the vibration is alternately displaced to one circumferential position and the opposite side. In formulas (3) and (4), these are excluded.
When i is 2, the radial displacement is at an intermediate position between the belly where the amplitude is maximum and the belly and the belly every 90 degrees in the circumferential direction, similar to the distribution of force shown in FIG. A node having the smallest amplitude is formed. When i is 3 or more, belly and nodes are alternately formed at equal intervals in the circumferential direction.
In a vibration phenomenon in an actual rotating electrical machine, the case where i = s is 2 is usually most important. Therefore, in the following, the case of i = s = 2 will be studied. Therefore, each phenomenon at each angular position in the circumferential direction described below is the same at 180 degrees from the angle, and the displacement, speed, acceleration, etc. at each time are the same, and 90 degrees and 270 degrees are shifted from the angle. In terms of position, this means that a phenomenon occurs in which the absolute values of displacement, speed, acceleration, etc. at each time are the same and the signs are reversed.
[Numerical analysis results]
Here, there is only one non-uniform mass 11 at the angular coordinate position α _{1} = 0 ° (P = 1), and the first and second hood dampers 30 are angular coordinate positions θ _{1} , θ _{2} , respectively. The result of numerical analysis of the state of the ring vibration of the fixed support member 10 in the position (N = 2) will be described with reference to FIGS. Here, the angle coordinate position θ1 of the _{first} hood damper 30 is an opening angle between the non-uniform mass body 11 and the first hood damper 30, and in the following description, the non-uniform mass body / damper opening angle. Call it. In addition, the opening angle Δθ = θ _{2} −θ _{1} between the two hood dampers 30 is referred to as a damper opening angle.
The mode mass of i = 2 of the fixed support member 10 is m, and the mass ratio m _{I1} / m of the non-uniform mass 11 is μ _{I.} The i = 2 mode mass m of the fixed support member 10 is represented by m = (5/4) πrρA. Further, the hood damper mass ratio m _{Hj} / m of the j-th (j = 1, 2) hood damper 30 is μ _{Hj} , and the hood damper damping ratio C _{Hj} / (2m _{Hj} ω _{02} ) is γ _{Hj} . However, ω _{02} ^{2} = 36EI / (5ρAr ^{4} ).
For comparison, the calculation results (Without imperfect mass and Houde damper) when there is no non-uniform mass 11 and no hood damper 30 are also displayed in FIGS.
The embodiment of the present invention satisfies the condition that the amplitude obtained by the analysis is as small as possible.
In FIGS 17, the vertical axis A ^{2,} as shown in the following equation (10), an average of the square of the radial displacement u of the formula (1) in space and time (F _{2} π / k _{02} ) This is defined as being dimensionless by dividing by ^{2} .
However, k _{02} = 9EIπ / r ^{3} and T = 2π / Ω _{2} .
Further, the horizontal axis ν of the resonance curves shown in FIGS. 5 and 6 is ν = Ω _{2} / ω _{02 and} the angular frequency of the electromagnetic force is made non-dimensional with the natural angular frequency of the secondary mode. Therefore, ν = 1 on the horizontal axis in FIGS. 5 and 6 is the dimensionless natural angular frequency of the secondary mode of the main system, that is, the resonance point. Furthermore, the maximum dimensionless amplitude value of the resonance curve obtained from the calculation using the set parameter values is adopted as the dimensionless amplitude value on the vertical axis of FIGS. .
(When the mass ratio and damping ratio of the two hood dampers are equal)
First, with reference to FIG. 3 to FIG. 9, an analysis result in the case where the mass ratio and the damping ratio of the two hood dampers 30 are equal, that is, μ _{H1} = μ _{H2} and γ _{H1} = γ _{H2} will be described. .
FIG. 3 is a graph showing the influence of the nonuniform mass / damper opening angle θ _{1} and the damper opening angle Δθ = θ _{2} −θ _{1} on the amplitude in the rotating electric machine according to the embodiment of the present invention. It is a graph which shows the case where uniform mass body and damper opening angle (theta) _{1} are 10-30 degree | times. FIG. 4 is a graph showing the effects of the non-uniform mass body / damper opening angle θ _{1} and the damper opening angle Δθ on the amplitude in the rotating electrical machine according to the embodiment of the present invention. It is a graph which shows the case where angle (theta) _{1} is 40-90 degree | times (0 degree | times). 3 and 4, the mass ratio μ _{I} = 0.1 of the non-uniform mass 11, the mass ratio μ _{H1} = μ _{H2} = 0.05 of the hood damper 30, and the damping ratio γ _{H1} = γ _{H2 of the} hood damper 30. = 0.5. The damper opening angle Δθ was analyzed in various ways in the range of 0 to 90 degrees.
3 and 4, the dimensionless amplitude A ^{2} is greater when the non-uniform mass body 11 and the two hood dampers 30 are present than when the non-uniform mass body 11 and the hood damper 30 are absent. It turns out that it falls remarkably.
When the non-uniform mass / damper opening angle θ _{1} shown in FIG. 3 is 10 to 30 degrees, the dimensionless amplitude A ^{2} is less dependent on the damper opening angle Δθ. On the other hand, when the non-uniform mass / damper opening angle θ _{1} shown in FIG. 4 is 50 to 90 degrees, the dimensionless amplitude A ^{2} depends on the damper opening angle Δθ, and the damper opening angle Δθ is 20 to 20 degrees. It can be seen that the minimum value is obtained in the range of 60 degrees.
In Figure 4, when non-uniform mass damper opening angle theta _{1} is 40 degrees, the damper opening angle Δθ assumes a minimum value in the range of 40 to 80 degrees. The non-uniform mass / damper opening angle θ _{1} is 30 degrees (FIG. 3) and 50 degrees (FIG. 4), and the non-uniform mass / damper opening angle θ _{1} is 35 to 45 degrees. Can be estimated that the damper opening angle Δθ takes a minimum value in the range of 40 to 80 degrees.
FIG. 5 is a graph showing an example of a resonance curve in which the dimensionless frequency is plotted on the horizontal axis and the dimensionless amplitude is plotted on the vertical axis in the rotating electric machine according to the embodiment of the present invention. It is a graph which shows the case where the angle θ _{1} = 30 degrees and the damper opening angle Δθ = 50 degrees. FIG. 6 is a graph showing an example of a resonance curve in which the dimensionless frequency is plotted on the horizontal axis and the dimensionless amplitude is plotted on the vertical axis in the rotating electrical machine according to the embodiment of the present invention. It is a graph which shows a case where angle θ _{1} = 70 degrees and damper opening angle Δθ = 41 degrees. 5 and 6 correspond to the cases where the amplitude is relatively small in the analysis condition ranges shown in FIGS. 3 and 4, respectively.
In FIGS. 5 and 6, as in FIGS. 3 and 4, the mass ratio μ _{I} = 0.1 of the non-uniform mass 11, the mass ratio μ _{H1} = μ _{H2} = 0.05 of the hood damper 30, and the hood The damping ratio γ _{H1} = γ _{H2} = 0.5 of the damper 30 is set.
According to the analysis results of FIG. 5 and FIG. 6, the dimensionless frequencies that take the peak of the sine mode and the cosine mode are shifted from each other, and the maximum dimensionless amplitude as the sum of the sine mode and the cosine mode Compared with the case where neither the non-uniform mass body 11 nor the hood damper 30 is provided, it is greatly reduced.
Figure 7 is a rotary electric machine according to an embodiment of the present invention, the value of the mass ratio mu _{I} of heterogeneous mass body 11 and the damper opening angle Δθ is a graph showing the effect on the amplitude, uneven mass- It is a graph which shows the case where damper opening angle (theta) _{1} is 70 degrees. The mass ratio of the hood damper 30 is set to μ _{H1} = μ _{H2} = 0.05, and the damping ratio of the hood damper 30 is set to γ _{H1} = γ _{H2} = 0.5. The value of the mass ratio mu _{I} of heterogeneous mass 11, instead of the three different 0.05,0.1,0.15, damper opening angle Δθ was analyzed variously changed in a range of 0 to 90 degrees.
From the analysis results of FIG. 7, the optimum range of the damper open angle Δθ in the case of a heterogeneous mass damper opening angle theta _{1} is 50 to 90 degrees in FIG. 4 described above is a mass ratio mu _{I} of heterogeneous mass 11 It can be seen that it is 20 to 60 degrees regardless of the value.
FIG. 8 is a graph showing the influence of the value of the mass ratio μ _{H1} = μ _{H2} of the hood damper 30 and the damper opening angle Δθ on the amplitude in the rotating electric machine according to the embodiment of the present invention. -It is a graph which shows the case where damper opening angle (theta) _{1} is 70 degree | times. The mass ratio mu _{I} of heterogeneous mass body 11 and 0.1, the damping ratio γ _{H1} = γ _{H2} = 0.5 hood damper 30. The value of the mass ratio μ _{H1} = μ _{H2} of the hood damper 30 is changed to four values of 0.025, 0.0375, 0.05, and 0.075, and the damper opening angle Δθ is variously in the range of 0 to 90 degrees. Changed and analyzed.
From the analysis result of FIG. 8, the optimum range of the damper opening angle Δθ when the non-uniform mass / damper opening angle θ _{1} of FIG. 4 is 50 to 90 degrees is the mass ratio μ _{H1} = μ _{H2 of the} hood damper 30. It can be seen that it is 20 to 60 degrees regardless of the value of.
FIG. 9 is a graph showing the influence of the value of the damping ratio γ _{H1} = γ _{H2} of the hood damper 30 and the damper opening angle Δθ on the amplitude in the rotating electric machine according to the embodiment of the present invention. -It is a graph which shows the case where damper opening angle (theta) _{1} is 70 degree | times. The mass ratio μ _{I} of the non-uniform mass 11 is 0.1, the mass ratio μ _{H1} = μ _{H2} of the hood damper 30 is 0.05, and the value of the damping ratio γ _{H1} = γ _{H2} of the hood damper 30 is 0. The damper opening angle [Delta] [theta] was varied in the range of 0 to 90 [deg.], And the analysis was performed in various ways: .1, 0.2, 0.3, and 0.5.
From the analysis result of FIG. 9, the optimum range of the damper opening angle Δθ when the non-uniform mass / damper opening angle θ _{1} of FIG. 4 is 50 to 90 degrees is the damping ratio γ _{H1} = γ _{H2 of the} hood damper 30. It can be seen that it is 20 to 60 degrees regardless of the value of.
(When the mass ratio or damping ratio of the two hood dampers 30 is different)
In the above analysis results, the mass ratio and damping ratio of the two hood dampers 30 are equal, that is, μ _{H1} = μ _{H2} and γ _{H1} = γ _{H2} . Here, the analysis results when the mass ratios or the damping ratios of the two hood dampers 30 are different will be described with reference to FIGS.
10 to 13 are graphs showing the influence of the damper opening angle Δθ on the amplitude in the rotating electrical machine according to the embodiment of the present invention. The damping ratios γ _{H1} and γ _{H2 of the} two hood dampers 30 are It is a graph which shows a different case. 10 to 13, the mass ratio μ _{I} = 0.1 of the non-uniform mass 11 and the mass ratio μ _{H1} = μ _{H2} = 0.05 of the hood damper 30 are assumed. These analysis conditions are the same as those in FIGS.
10 and 11, the damping ratio γ _{H1} = 0.5 of the first hood damper 30 and the damping ratio γ _{H2} = 0.25 of the second hood damper 30 (ratio of damping ratios γ _{H1} / γ _{H2} = 2). ). FIG. 10 shows a case where the non-uniform mass body / damper opening angle θ _{1} is 10 to 30 degrees. This is a case where the influence of the damper opening angle Δθ on the amplitude is relatively small.
FIG. 11 shows a case where the non-uniform mass body / damper opening angle θ _{1} is 40 degrees to 90 degrees (0 degrees). In this range, the amplitude depends on the damper opening angle Δθ. Except for the case of θ _{1} = 40 degrees in the range, that is, the non-uniform mass / damper opening angle θ _{1} is in the range of 50 degrees to 90 degrees (0 degrees), and the damper opening angle Δθ is 20 to 60 degrees. The amplitude is minimal in degrees. This is the same as the tendency shown in FIGS. 4 and 7 to 9.
Further, in FIG. 11, if heterogeneous mass damper opening angle theta _{1} is 40 degrees, the damper opening angle Δθ amplitude is minimum in 40 to 80 degrees. This is the same as the tendency shown in FIG.
12 and 13, the damping ratio γ _{H1} = 0.25 of the first hood damper 30 and the damping ratio γ _{H2} = 0.5 of the second hood damper 30 (ramp ratio γ _{H1} / γ _{H2} = 1). / 2).
FIG. 12 shows a case where the non-uniform mass / damper opening angle θ _{1} is 10 to 30 degrees. This is a case where the influence of the damper opening angle Δθ on the amplitude is relatively small.
FIG. 13 shows a case where the non-uniform mass / damper opening angle θ _{1} is 40 degrees to 90 degrees (0 degrees). In this range, the amplitude depends on the damper opening angle Δθ. Within that range, except when θ _{1} = 40 degrees, that is, when the non-uniform mass / damper opening angle θ _{1} is 50 degrees to 90 degrees (0 degrees), the damper opening angle Δθ is 20 to 60 degrees. The amplitude is minimized at. This is the same as the tendency shown in FIGS. 4, 7 to 9, and 11.
Further, in FIG. 13, if heterogeneous mass damper opening angle theta _{1} is 40 degrees, the damper opening angle Δθ amplitude is minimum in 40 to 80 degrees. This is the same as the tendency shown in FIG.
14 to 17 are graphs showing the influence of the damper opening angle Δθ on the amplitude in the rotating electric machine according to the embodiment of the present invention, and the mass ratios μ _{H1} and μ _{H2 of the} two hood dampers 30 are mutually different. It is a graph which shows a different case. 14 to 17, the mass ratio μ _{I} = 0.1 of the non-uniform mass 11 and the damping ratio γ _{H1} = γ _{H2} = 0.5 of the hood damper 30 are set. These analysis conditions are the same as those in FIGS.
14 and 15, the mass ratio μ _{H1} = 0.07 of the first hood damper 30 and the mass ratio μ _{H2} = 0.035 of the second hood damper 30 (ratio of mass ratios μ _{H1} / μ _{H2} = 2). ).
Figure 14 is a non-uniform mass damper opening angle theta _{1} indicates a case of 10 to 30 degrees. This is a case where the influence of the damper opening angle Δθ on the amplitude is relatively small.
FIG. 15 shows a case where the non-uniform mass / damper opening angle θ _{1} is 40 degrees to 90 degrees (0 degrees). In this range, the amplitude depends on the damper opening angle Δθ. Within that range, except when θ _{1} = 40 degrees, that is, when the non-uniform mass / damper opening angle θ _{1} is 50 degrees to 90 degrees (0 degrees), the damper opening angle Δθ is 20 to 60 degrees. The amplitude is minimized at. This is the same as the tendency shown in FIGS. 4, 7 to 9, 11, and 13.
Further, in FIG. 15, if heterogeneous mass damper opening angle theta _{1} is 40 degrees, the damper opening angle Δθ amplitude is minimum in 40 to 80 degrees. This is the same as the tendency shown in FIG.
16 and 17, the mass ratio μ _{H1} = 0.035 of the first hood damper 30 and the mass ratio μ _{H2} = 0.07 of the second hood damper 30 (ratio of mass ratios μ _{H1} / μ _{H2} = 1). / 2).
FIG. 16 shows a case where the non-uniform mass body / damper opening angle θ _{1} is 10 to 30 degrees and 80 to 90 degrees (0 degrees). This is a case where the influence of the damper opening angle Δθ on the amplitude is relatively small.
FIG. 17 shows a case where the non-uniform mass body / damper opening angle θ _{1} is 40 degrees to 70 degrees. In this range, the amplitude depends on the damper opening angle Δθ. Within that range, except when θ _{1} = 40 degrees, that is, when the non-uniform mass / damper opening angle θ _{1} is 50 degrees to 70 degrees, the amplitude is minimum when the damper opening angle Δθ is 20 to 60 degrees. It becomes. This is the same as the tendency shown in FIGS. 4, 7 to 9, 11, 13, and 15. However, as shown in FIG. 16, when the mass ratio ratio μ _{H1} / μ _{H2} = 1/2, when the non-uniform mass body / damper opening angle θ _{1} is 80 to 90 degrees (0 degrees), When the damper opening angle Δθ is 20 to 60 degrees, the amplitude does not tend to take the minimum value.
Further, in FIG. 17, if heterogeneous mass damper opening angle theta _{1} is 40 degrees, the damper opening angle Δθ amplitude is minimum in 40 to 80 degrees. This is the same as the tendency shown in FIG.
From the analysis results shown above, when one non-uniform mass body 11 and two hood dampers 30 are installed, the non-uniform mass body / damper opening angle θ _{1} is within the range of 50 to 90 degrees, and the damper opening is set. It can be seen that the amplitude can be kept low by setting the angle Δθ within the range of 20 to 60 degrees. When the mass ratios of the two hood dampers 30 are different, the amplitude suppression effect is large when the mass ratio ratio μ _{H1} / μ _{H2} is 1 or more.
Further, when the angular coordinate position of at least one of the first and second hood dampers 30 is in the range of 10 to 30 degrees, the effect of suppressing the amplitude is great regardless of the damper opening angle Δθ.
Further, in these cases, the frequency of the resonance point is not simply shifted, but the maximum amplitude is reduced, which is particularly effective for a rotating electrical machine that performs variable speed operation such as an inverter-driven electric motor.
As described above, the case where i = s = 2 was examined here. That is, each phenomenon at each angular position in the circumferential direction is a position shifted by 180 degrees from the angle, and the displacement, speed, acceleration, etc. at each time are the same, and a position shifted by 90 degrees or 270 degrees from the angle Then, a phenomenon occurs in which the absolute values of displacement, speed, acceleration, etc. at each time are the same and the signs are reversed.
Therefore, for example, in the above description, one non-uniform mass body 11 that is arranged at the position of the angular coordinate position α _{1} = 0 degree is set to any position of 0 degree, 90 degrees, 180 degrees, and 270 degrees. Even if the arrangement is changed or divided, the same vibration damping effect can be obtained.
Further, setting the angle coordinate position θ _{1} of the first hood damper 30 within the range of 50 to 90 degrees means that θ _{1} is any of 140 to 180 degrees, 230 to 270 degrees, and 320 to 360 degrees. It is equivalent to within the range and the vibration control effect. Similarly, setting θ _{1} to 35 to 45 degrees is equivalent to setting θ _{1} to any one of 125 to 135 degrees, 215 to 225 degrees, and 305 to 315 degrees. Similarly, setting θ _{1} within the range of 10 to 30 degrees is equivalent to setting θ _{1} within the range of _{100} to 120 degrees, 190 to 210 degrees, and 280 to 300 degrees. .
Similarly, setting the damper opening angle Δθ within the range of 20 to 60 degrees is equivalent to setting Δθ within the range of 110 to 150 degrees, 200 to 240 degrees, and 290 to 330 degrees. is there. Similarly, setting Δθ to 40 to 80 degrees is equivalent to setting Δθ to any one of 130 to 170 degrees, 220 to 260 degrees, and 310 to 350 degrees. Similarly, setting Δθ within the range of 10 to 80 degrees is equivalent to setting Δθ within the range of 100 to 170 degrees, 190 to 260 degrees, and 280 to 350 degrees.
When the angle coordinate position of one non-uniform mass body 11 is 0 degree, the angle coordinate positions of the other non-uniform mass bodies 11 are 10 degrees before and after 90 degrees, 180 degrees, and 270 degrees. Even if the degree is different, a similar vibration control effect is expected. The width of the angular coordinate position is an analogy from the allowable range width of the angular coordinate position of the hood damper 30. Therefore, it is preferable that the angular coordinate positions of the other divided non-uniform mass bodies 11 are in the range of 80 to 100 degrees, 170 to 190 degrees, and 260 to 280 degrees.
In numerical analysis explained above, a range weight ratio mu _{I} of heterogeneous mass body 11, it is clear that there is a damping effect larger, the accuracy of the results obtained in numerical calculation is guaranteed to some extent high accuracy the mass ratio mu _{I} was 0.05 to 0.15 as a. It goes without saying that even if the mass ratio mu _{I} larger than 0.15 damping effect is obtained.
Obviously, the greater the mass ratio μ _{Hj} (j = 1, 2) of the hood damper 30, the greater the damping effect.
As for the damping ratio γ _{Hj} of the hood damper 30, it is known that γ _{Hj} = 1 / √ [2 (2 + μ _{Hj} ) (1 + μ _{Hj} )] is optimal in a normal vibration system. For example, when the mass ratio μ _{Hj} = 0.05 of the hood damper 30, the damping ratio γ _{Hj} = 0.482 is optimal, and when the mass ratio μ _{Hj} = 0.025, the damping ratio γ _{Hj} = 0.491 is Is optimal. If the mass ratio μ _{Hj} is small, the optimum case is when the damping ratio γ _{Hj} is about 0.5. Therefore, as a condition for the above numerical analysis, the case where γ _{Hj} = 0.5 is used as a standard.
In the above description, the non-uniform mass body 11 is not necessarily attached particularly for vibration suppression, and includes a terminal box and cooling fins attached to the outside of the stator frame of the rotating electrical machine.
As mentioned above, although several embodiment of this invention was described, these embodiment is shown as an example and is not intending limiting the range of invention. These embodiments can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the spirit of the invention. These embodiments and their modifications are included in the scope and gist of the invention, and are also included in the invention described in the claims and the equivalents thereof.