JPS6357725B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method and apparatus for coupling a plurality of rotors, and more particularly to a method and apparatus for coupling multi-span rotors in a chain, such as a coupled shaft system between a turbine and a generator.

Generally, when a plurality of rotors are combined, each rotor is balanced individually as a preliminary step. Balancing is performed by adding a correction weight (hereinafter sometimes referred to as a balance weight) to the rotor so that the unbalanced vibration of the single rotor is minimized. In this method, the correction weights are determined by trial and error, which requires considerable effort and expense, although this will vary depending on the experience of the balance measurement engineer. In addition, in most rotors such as turbines, it is impossible to arbitrarily select the number and position of correction surfaces, so it is naturally impossible to completely reduce the amount of unbalance remaining in each individual rotor to zero. Therefore, the multi-span rotor as described above is composed of a plurality of rotors having a large amount of residual unbalance.

By the way, one interesting phenomenon is that depending on the relative angle between each rotor when they are combined,
It has been experienced that the vibrations as a multi-span rotor system vary. That is, for a certain relative angle, the vibration is large, and for another certain relative angle, the vibration is small. This means that by appropriately selecting the relative angle of each rotor, it is possible to reduce vibration as a multi-span rotor system. However, determining the optimal angle through trial and error many times requires a huge amount of time and expense, and is not practical. Therefore, it was desired to find the optimal angular conditions for vibration suppression without requiring many trials and errors.

SUMMARY OF THE INVENTION Accordingly, an object of the present invention is to provide a method and apparatus for coupling multiple rotors that can realize a multi-span rotor with low vibration by rationally determining the optimum phase angle between the rotors.

The present invention uses the optimum phase angle between adjacent rotors as an unknown quantity to determine this relative angle by calculation under the condition that the vibration of the multi-span rotor is minimized, and connects multiple rotors based on this determination. It is something.

DESCRIPTION OF THE PREFERRED EMBODIMENTS The rotor coupling method and apparatus of the present invention will be explained below with reference to the drawings.

FIG. 1 is a block diagram of a rotor coupling device showing one embodiment of the present invention, and FIG. 2 is a flowchart showing the operation of this embodiment.

The device of this embodiment includes a storage device, an arithmetic unit, a determiner,
and a display device. A storage device 1 for determining and storing the residual unbalance vibration after single rotor balance for each single rotor, and a storage device for storing the influence coefficient of each single rotor and the influence coefficient after rotor combination are provided in the computing unit 3. Connecting. Arithmetic unit 3
The equivalent residual unbalance amount is determined based on the information from the two storage devices using the influence coefficient method described later. Here, the influence coefficient is expressed as α ^(r) _noi , and represents the vibration that appears at point m under the condition of speed (r) when there is an unbalance of unit mass at the nth position in the axial direction of single rotor i. (See Figure 3 for the functions of m and n.) In addition, the equivalent residual unbalance amount refers to the amount of residual unbalance that exists distributed in the axial direction of each single rotor at several locations in the axial direction, as a step before combining multiple single rotors to form a multi-span rotor. This is a limited representation. The computing unit 3 is connected to the next computing unit 4. The calculator 4 calculates the combination influence coefficient of the same distribution as the axial distribution of the equivalent residual unbalance determined by the calculator 3. Arithmetic unit 4 is the next arithmetic unit 5
Connect to. The calculator 5 calculates the coupling angle between the rotors from the combined influence coefficients determined by the calculator 4. Next, the computing unit 5 is connected to a computing unit 6 which predicts and calculates the vibration after the rotor is coupled in accordance with the coupling angle determined here. The calculator 6 is connected to a determiner 7 that compares the predicted vibration obtained here with an allowable vibration value, and the determiner 7 is connected to a display device 8 and a calculator 9, and the output terminal of the calculator 9 is also displayed. Connect to device 8. The calculator 9 performs balance calculation when the vibration does not meet the allowable value and calculates the residual vibration after adding the balance weight, and the display device 8 displays the relationship between the coupling angles of the rotors and predicted vibration values. , the size, angle, axial position, etc. of the balance weight to be added are displayed.
Further, another display device 10 is connected to the arithmetic unit 3. The display device 10 is a monitoring device that displays the magnitude, angle, and axial position of the equivalent residual unbalance determined by the calculator 3, as well as the accuracy of these values.

In the device configured as above, the operation is as follows. Note that the following symbols are used to simplify the explanation.

m: Number indicating the vibration detection position in the axial direction of the computing unit (m = 1, 2, ..., M. See Figure 3.) n, n': Unbalance that equivalently or actually exists in the single rotor A number indicating the position in the axial direction (n = 1, 2, ..., N. n' = 1, 2, ...
…, N′. See Figure 3. ) i; Number of single rotor (i=1, 2,..., I.) l; Number indicating the vibration detection position in the axial direction of the combined rotor (l=1, 2,..., L, L=M× I.) r; Number representing the rotational speed of a single rotor (r=
1, 2, ..., R. ) V ^(r) _ni ; Residual unbalance vibration at point m in single rotor i at post-balance speed (r) α ^(r) _noi ; Unbalance of unit mass exists at the nth position in the axial direction of single rotor i _In the _{case of} Unbalance amount W _i that actually exists at the n'th position in the axial direction of i; Set vector of equivalent residual unbalance amounts of single rotor i (W _i = {W ₁ , W ₂ , ..., W _N } _i ) V ^(r) _l ; m at speed (r) in coupled rotor
Point residual unbalance vibration A ^(r) _li ; represents the unbalance vibration that appears at point m of the combined rotor under the condition of speed (r) when there is unbalance of the unit combined mass in the i-th single rotor. Combination influence coefficients _JW , Jθ of coupled rotors: Evaluation function First, residual unbalanced vibration of the balanced single rotor is determined at each vibration detection point. Then, this residual vibration is stored in the storage device 1. Separately, calculate or actually measure the influence coefficient of a single rotor, and also calculate the influence coefficient when each rotor is combined (or use data from past measurements of rotors of the same type if available). These are determined and stored in the storage device 2. Next, based on these stored data, the computing unit 3 determines the equivalent residual unbalance amount of each single rotor. The equivalent residual unbalance amount is determined as follows.

Although the single rotor is sufficiently balanced by known means before the rotors are coupled, residual unbalance vibrations exist in the rotor as described above because the balance is within the tolerance range. This residual unbalance amount exists in many axial positions as shown in FIG. 4a. The single rotor shown in the figure is composed of a rotor 101, a bearing 102 that supports the rotor 101, and couplings 103 and 104 for connecting a plurality of rotors 101. Now, _the deviation ΔV ni between the residual unbalance vibration V ^(r) _ni when the single rotor with rotor number i is balanced and the residual unbalance vibration V _ni ^(r) when the equivalent residual unbalance amount W _oi is added Calculating ^(r) gives the following equation (1).

ΔV ^(r) _ni = V ^(r) _ni −Σα ^(r) _noi・W _oi ...(1) As ΔV ^(r) _ni in equation (1) becomes smaller, W _oi becomes smaller than the actually existing residual defect. The balance amount U _o ′ _i will be modeled. Therefore, in order to satisfy this condition, the following evaluation function is defined.

J _W = _R 〓 ^r=1 _M 〓 ^m=1 ｜ΔV ^(r) _ni ｜ ² ……(2) In other words, since it is sufficient to find W _oi that minimizes equation (2), the following equation (3) Once the solution is obtained, the equivalent residual unbalance amount is determined.

∂J _W /∂W _oi =0 (n=1, 2, ..., N) ...(3) Figure 4 b and c show the equivalent distribution of the unbalance existing in the rotor in figure a. Here is an example. b is
For W ₁ , c is for W ₃ . The equivalent residual unbalance is expressed as follows as if only one existed in each rotor.

W _i {W ₁ , W ₂ , ..., W _N } _i ...(4) Regarding the equivalent residual unbalance distribution of each rotor obtained in this way, the combination influence when the rotors are connected with one point in a certain axial direction as a reference The coefficient is calculated by the following operator 4
Find it at Specifically, the combination influence coefficient is determined as follows.

The equivalent residual unbalance shown in equation (4) can be expressed in terms of size and installation angle as shown in equation (5) below.

｜W _i ｜e ^j 〓 ⁱ = {｜W ₁ ｜・e ^j 〓 ¹ , ｜W ₂ ｜・e ^j 〓
² ... |W _N |・e ^j 〓 ^N } _i ...(5) In formula (5), θ _i is the coupling angle between each rotor. (Five)
In order to obtain the combination influence coefficient for the equivalent residual unbalance distribution in the equation, consider the following unbalance distribution using W ₁ with n=1 as a reference.

{1, |W ₂ |/|W ₁ |e ^j( 〓 ² 〓 ¹⁾ ,..., |W ₂ |/|W
₁ ｜e ^j( 〓 ^N- 〓 ¹⁾ _} iHere, the vibration detection position number in the rotor axial direction after direct connection to the rotor is l (l = 1, 2, ..., L;, L = M
×I). From this, the combination influence coefficient A ^(r) _li at the rotational speed (r) at the vibration detection position l for the unbalance distribution of the rotor number i can be determined by the following equation (6). That is, A ^(r) _li = {K ^(r) _l1・1+K ^(r) _l1 |W ₂ |/|W ₁ |e ^j( 〓 ^2-
〓 ¹⁾ ＋……＋K ^(r) _lN 1W _N ｜／｜W ₁ ｜e ^j( 〓 ^N- 〓 ¹⁾ ｝ _i ……(
6) Here, {K ^(r) _lo } _i is when each single rotor is combined,
This is an influence coefficient representing the vibration that appears at point l under the condition of speed (r) when there is an unbalance of unit mass at the n-th position in the axial direction of rotor i.
Although n=1 was used as the standard in equation (6), there is no need to limit the number to n. This is done for all rotors with rotor number i.

A ^(r) _ni =α _n1・1+α _n2 ｜W ₂ ｜／｜W ₁ ｜e ^j( 〓 ^2- 〓 ¹⁾ ＋
……＋α _ni ｜W _N ｜／｜W ₁ ｜e ^j( 〓 ^N- 〓 ¹⁾ ……(6) Unbalanced vibration occurs when the rotors are connected due to the amount of residual balance that exists in each single rotor. However, the next computing unit 5 uses the output from the computing unit 4 to determine the mutual angular relationship of the plurality of rotors by using the least squares method that minimizes the sum of squares of the unbalanced vibrations of the rotor main part. . Specifically, the bond angle is determined as follows.

The angle θ _i of each rotor shown in equation (5) above is the value to be determined, but this value can be considered to be an angle based on a specific rotor among the i rotors. The vibration V ^(r) _l after rotor coupling is expressed by the following equation (7) from the combination influence coefficient A ^(r) _li and the residual unbalance amount W _i .

V ^(r) _l = _I 〓 ⁱ⁼¹ A ^(r) _li・W _i ...(7) Next, define the evaluation function J〓 as the sum of squares of the rotor's unbalanced vibration V ^(r) _l .

J〓= _R 〓 ^r=1 _L 〓 ^l=1 ｜V ^(r) _l ｜ ² ...(8) In equation (7), the magnitude of the unbalance amount W _i |W _i | is (5)
A standard n is determined for each rotor i from each unbalance element in the equation, and its size is represented by |W _o | _i .

｜W _i ｜=｜W _o ｜ _i ...(9) If we find θ _i that minimizes equation (8) under equations (7) and (9), we can calculate the unbalanced vibration after rotor coupling. can be made as small as possible. In other words, we obtain the following simultaneous equations.

∂J/∂θ _i =0 (i=1, 2, ..., I) ...(10) Therefore, the angular relationship between the rotors after mutual connection is {θ _o1 , θ _o2 +θ ₂ −
θ ₁ , ..., θ _NI + θ _I − θ _I } (θ _o1 is rotor 1
θ _o2 +θ ₂ −θ ₁ represents the angle of rotor 2, and θ _NI +θ _I −θ _I represents the angle of rotor I. ). Therefore, if the parts are coupled so as to maintain this angular relationship, the unbalanced vibration after coupling will be minimized.

Next, the calculator 6 predicts and calculates the unbalanced vibration after the rotors are coupled according to the coupling determined by the calculator 5, and the determiner 7 compares and determines the unbalanced vibration with the allowable vibration value.
The prediction calculation is performed by substituting θ _i obtained by the calculator 5 into equation (5) to obtain a combined influence coefficient A ^(r) _l , and then substituting this into equation (7).

As a result of the determination by the determiner 7, if the allowable vibration value is satisfied, the relationship between the coupling angles of the rotors and the predicted vibration value are displayed on the display device 8. On the other hand, if the vibration does not satisfy the allowable value as a result of the determination by the determiner 7,
A balance calculation is performed by the calculator 9, and residual vibration after adding the balance weight is calculated. After that, the display device 8 shows the relationship between the coupling angles of the rotors and the size of the balance weight to be added.
Displays angle, axial position, and predicted vibration values.

As a result of the determination by the determiner 7, if the unbalanced vibration exceeds the allowable value, the accuracy of the equivalent residual unbalance amount of each unit rotor determined by the calculator 3 is examined.
If the accuracy of the equivalent residual unbalance amount is not necessarily sufficient, the equivalent residual unbalance distribution is changed again and the operation of the calculator 3 is returned to. Since the unbalance distribution that exists in the rotor differs depending on the rotor,
In many cases, the equivalent residual unbalance distribution is also different. Therefore, vibration after coupling cannot be improved unless the equivalent residual unbalance distribution is appropriately selected.
As a criterion for this judgment, from the equivalent residual unbalance amount in equation (4), using equation (1), we use the evaluation function J _W of equations (2) and (3).
Find the relationship between the magnitudes of and use this. On the other hand, if the predicted vibration value during coupling exceeds the allowable value even though the accuracy of the equivalent residual unbalance amount is sufficiently good, perform balance simulation to determine the balance weight to be added to the rotor. axial position,
Calculate the angle and size. Here, the balance simulation can be sufficiently performed by known means (for example, Shiohata, Fujisawa, Transactions of the Japan Society of Mechanical Engineers, vol. 45, No. 391, ``Balancing of a multi-bearing rotating shaft system'') ). After that, the calculated balance weight is added to the rotor.

In this manner, the rotor is coupled when the unbalance vibration predicted value is within the allowable value and when the balance weight addition work is completed. After that, the rotor starts operating.

By employing the present embodiment described above, it becomes possible to quickly determine the optimal angle between the rotors that minimizes the shaft vibration of the multi-span rotor system. This makes it possible to eliminate the process of determining the angle between each single rotor by trial and error, which was conventionally performed at the time of coupling. In the conventional method,
If the multi-span rotor is the smallest two-span rotor, repeat trials of sequentially shifting the angle of one rotor with respect to the other.
After performing all trials it is possible to determine the optimal angle. But after setting it to some relative angle,
It is necessary to operate the two-span rotor each time to measure vibrations, which consumes a great deal of time and expense. If the multi-span rotor becomes a large-scale system with three or more span rotors, the number of combinations of relative angles will increase at once, and a huge number of trials will have to be repeated. In other words, the time and expense required to find the optimal angle are of an unfeasible order. On the other hand, if this embodiment is adopted, it is possible to find the optimum combination of angles without performing a trial run, and it is possible to provide a multi-span rotor with reasonably low vibration.

By the way, in the above-mentioned optimum coupling angle method, even if the optimum angle for rotor coupling is determined, it may not actually be possible to take an arbitrary angle due to the structure. for example,
Since the coupling ring has bolt holes along its circumferential direction, adjustment of the coupling angle between the rotors is limited to the range of the pitch angle of the bolt holes. In such a case, the rotors may be coupled under conditions closest to the calculated optimal angle. When coupling deviates from the optimum coupling angle conditions, unbalanced vibration will inevitably increase, but
If the vibration exceeds the allowable value, a balance simulation can be performed to correct the balance, thereby making it possible to provide a rotor with low vibration.

If the unbalance distribution remaining in each individual rotor is appropriately concentrated in the axial position and furthermore, each individual rotor is appropriately coupled, balance simulation may not require the addition of balance weights. many. Further, depending on the rotor, such balancing work is required, but in this case, the work of adding a balance weight is performed when the rotor is a single rotor, so the work content is extremely easy.

As described above, according to the present invention, by rationally determining the optimum phase angle between the rotors, it is possible to realize a multi-span rotor with low vibration without performing a trial operation.

[Brief explanation of drawings]

Fig. 1 is a configuration diagram showing an embodiment of a coupling device for multiple rotors of the present invention, Fig. 2 is a flow diagram of this embodiment, and Fig. 3 is a vibration detection position and an axial position of an unbalance point in a single rotor. FIG. 4 is an explanatory diagram showing an example of the residual unbalance distribution and the equivalent residual unbalance distribution of a single rotor. 1, 2... Storage device, 3, 4, 5, 6, 9...
Arithmetic unit, 7...determiner, 8, 10...display device,
101...Rotor, 102...Bearing, 103,1
04...Katsupring.

Claims (1)

[Scope of Claims] 1. In a method of connecting multiple rotors in which single rotors are connected in the axial direction, an equivalent value for each single rotor before combination is determined from the amount of unbalance and influence coefficient existing in each single rotor before combination. Calculate the amount of residual unbalance, and calculate the phase angle at which the sum of squares of the product of the combined influence coefficient when the rotors are coupled, which is expressed as a function of the phase angle between each single rotor, and the equivalent amount of unbalance is the minimum. A method for coupling a plurality of rotors, characterized in that each rotor is coupled according to this phase angle. 2. In the method for coupling a plurality of rotors as set forth in claim 1, after calculating and determining the optimum phase angle between each single rotor, the unbalanced vibration assuming the state after coupling is calculated and determined. The predicted value is compared with the allowable value, and if it is less than the allowable value, the above-mentioned joining work is started immediately. If it is above the allowable value, a balance simulation is performed to calculate the corrected weight for the joint shaft system, and this corrected weight is applied to the single unit. A method for joining a plurality of rotors, characterized in that the joining operation begins after the rotors are attached. 3. In the method for coupling multiple rotors according to claim 1 or 2, the residual unbalance distributed in the axial direction of each single rotor is limited to several locations in the axial direction, and equivalent unbalance is achieved. define,
A method for coupling multiple rotors, characterized in that an equivalent residual unbalance amount is determined using this value as a representative value. 4. In the method for coupling a plurality of rotors according to claim 3, a combination influence coefficient of the coupled shaft system is calculated and determined from the representative value, and this value is used to calculate the angle. Features a method for connecting multiple rotors. 5 A first storage device that stores the residual unbalance vibration after single rotor balance, a second storage device that stores at least the influence coefficient of the single rotor, and a first storage device that stores the residual unbalance vibration after single rotor balance, and a second storage device that stores at least the influence coefficient of the single rotor. a first calculator for calculating the equivalent residual unbalance of the rotor; a second calculator for calculating a combined influence coefficient from the phase angle between the single rotors and the influence coefficient of the single rotor; A multi-rotor system comprising: a third calculating unit that calculates the optimum phase angle between the rotors at which residual vibration of the combined rotors is minimized based on the amount of balance; and a display device that displays the results of these calculations. Coupling device. 6. In the multiple rotor coupling device according to claim 5, the rotors are coupled between the third arithmetic unit and the display device according to the result obtained by the third arithmetic unit. A fourth calculator is provided to predict and calculate the vibration at the time of the vibration, and a determiner to compare this predicted value with an allowable value, and this determiner further performs a balance calculation when the predicted value does not satisfy the allowable value. A coupling device for a plurality of rotors, characterized in that a fifth arithmetic unit for calculating a correction weight is attached thereto.