JP6178251B2 - Turbomachine dynamic characteristic calculation method and turbomachine dynamic characteristic calculation apparatus - Google Patents

Description

  The present invention relates to a technique for calculating dynamic characteristics of each machine element constituting a rotor system of a turbomachine.

  In a turbomachine that compresses or pumps a fluid by rotating an impeller connected to a rotating shaft, a self-excited vibration occurs in the rotor due to the fluid destabilizing force of the high-pressure fluid, and the turbomachine must be stopped. May be. Whether or not self-excited vibration occurs in the rotor is determined by determining the dynamic characteristics of each machine element, such as the rigidity and mass of the rotating shaft, the rigidity and damping coefficient of the bearing, and the destabilizing force generated by the impeller and seal. Can be judged appropriately.

  Here, in Patent Document 1, in a rotating machine configured to be able to vibrate a rotating shaft, the load condition is changed while the rotation speed is constant, and the rotating machine's vibration response data for each load condition is used. The dynamic characteristics of the rotating machine are calculated by obtaining the damping ratio or the allowable excitation coefficient. In Patent Document 2, as in Patent Document 1, the dynamic characteristic of the rotating machine is calculated by obtaining the damping ratio or the allowable excitation coefficient of the rotating machine.

Japanese Patent Publication No. 3-65857 Japanese Examined Patent Publication No. 3-65858

  However, Patent Documents 1 and 2 merely calculate the dynamic characteristics of the rotating machine as a whole, and each machine element (for example, a rotating shaft, an impeller, a bearing, a seal member, etc.) constituting the rotor system of the rotating machine. The dynamic characteristics are not calculated. Therefore, when the techniques of Patent Documents 1 and 2 are adopted, the dynamic characteristics of each machine element are unknown, and it is determined whether or not self-excited vibration is generated in the rotor, or self-excited vibration is not generated in the rotor. Therefore, there is a possibility that the design for the purpose cannot be sufficiently examined.

  The present invention has been made in view of the above problems, and an object of the present invention is to provide a technique for calculating the dynamic characteristics of each machine element constituting a rotor system of a turbomachine.

  In order to achieve the above object, a turbo machine dynamic characteristic calculation method according to the present invention is a turbo machine dynamic characteristic calculation method for compressing or pumping fluid by rotating an impeller coupled to a rotating shaft, By expressing the characteristic matrix in the vibration equation of the rotor system of the turbomachine by a known parameter related to a machine element whose dynamic characteristics can be calculated in advance and an unknown parameter related to a machine element whose dynamic characteristics are difficult to calculate in advance, Based on the modeling process for modeling the rotor system with a vibration equation, the vibration detection process for detecting the vibration generated in the rotor system, and the signal data of the vibration detected in the vibration detection process, A mode analysis step for calculating an eigenvalue and a vibration mode, a vibration equation obtained in the modeling step, an eigenvalue calculated in the mode analysis step, and And a dynamic mode, characterized in that it comprises a dynamic characteristic calculation step of calculating the unknown parameter.

  In order to achieve the above object, a turbo machine dynamic characteristic calculation apparatus according to the present invention is a turbo machine dynamic characteristic calculation apparatus that compresses or pumps fluid by rotating an impeller coupled to a rotary shaft. The characteristic matrix in the vibration equation of the rotor system of the turbomachine is expressed by a known parameter related to a machine element whose dynamic characteristics can be calculated in advance and an unknown parameter related to a machine element whose dynamic characteristics are difficult to calculate in advance. Based on signal data output from a modeling unit that models the rotor system by a vibration equation and vibration detection means that detects vibration generated in the rotor system, eigenvalues and vibration modes of the rotor system are determined. From the mode analysis unit to be calculated, the vibration equation obtained by the modeling unit, and the eigenvalue and vibration mode calculated by the mode analysis unit, Characterized in that and a dynamic characteristic calculation unit for calculating a parameter.

  Generally, among the mechanical elements that make up the rotor system, the rigidity and mass of the rotating shaft can be calculated accurately from the dimensions and physical properties, while the mechanical elements other than the rotating shaft such as impellers, bearings, and seal members It is difficult to accurately predict dynamic characteristics. Therefore, in the present invention, the characteristic matrix in the vibration equation of the rotor system of the turbomachine is set to a known parameter related to a mechanical element (for example, a rotating shaft) whose dynamic characteristics can be calculated in advance, and a mechanical element whose dynamic characteristics are difficult to calculate in advance. The rotor system is modeled separately from unknown parameters (for example, impeller, bearing, seal member). Then, the unknown parameter is calculated from the vibration equation obtained by this modeling and the eigenvalue and vibration mode of the rotor system calculated from the signal data of the vibration generated in the rotor system. In other words, according to the present invention, by modeling as described above, it is possible to calculate unknown parameters relating to machine elements whose dynamic characteristics are difficult to predict, and for each machine element constituting the rotor system of the turbomachine Dynamic characteristics can be calculated.

  In the method for calculating the dynamic characteristics of the turbomachine according to the present invention, the modeling may be performed by including, in the unknown parameters, parameters relating to the dynamic characteristics of the base system that supports the rotor system. Similarly, in the turbo machine dynamic characteristic calculation apparatus according to the present invention, the unknown parameter may include the parameter related to the dynamic characteristic of the base system that supports the rotor system for the modeling.

  If the rigidity of the base system that supports the rotor system is sufficiently larger than that of the rotor system, there is no particular problem even if the influence of the dynamic characteristics of the base system is ignored. However, for example, when the turbomachine is large and it is necessary to increase the rigidity of a bearing that supports the rotor system, the rigidity of the base system is relatively decreased. In such a case, as described above, by calculating the dynamic characteristics by including the parameters related to the dynamic characteristics of the base system in the unknown parameters, the dynamic characteristics of each mechanical element constituting the rotor system can be accurately calculated. can do.

  Here, in the turbo machine dynamic characteristic calculation method according to the present invention, in the vibration detection step, vibration may be applied by a vibrator provided outside the turbo machine. In this way, if the rotor system can be vibrated by the vibrator, the vibration mode of the rotor system can be excited. As a result, it is possible to measure vibration data suitable for calculation of eigenvalues and vibration modes in the subsequent mode analysis process, and it is possible to preferably calculate the dynamic characteristics of each machine element.

  In the mode analysis step, the signal data may be frequency-analyzed to calculate the eigenvalue and vibration mode of the rotor system, and in the dynamic characteristic calculation step, the unknown parameter may be calculated by a least square method. Thus, by calculating an unknown parameter by the least square method, the calculated value is always a least square solution, and thus a stable and accurate value can be calculated. As a result, the dynamic characteristics of each machine element can be grasped more accurately.

It is a mimetic diagram showing the dynamic characteristic arithmetic unit concerning a 1st embodiment of the present invention, and the turbo compressor which is a measuring object. It is an AA arrow line view of FIG. It is a flowchart which shows the dynamic characteristic calculation method concerning 1st Embodiment. It is a flowchart which shows the dynamic characteristic calculation method concerning 2nd Embodiment. It is a schematic diagram which shows the dynamic characteristic calculating apparatus concerning 3rd Embodiment of this invention, and the turbo compressor which is a measuring object. It is a flowchart which shows the dynamic characteristic calculation method concerning 3rd Embodiment. It is a flowchart which shows the dynamic characteristic calculation method concerning 4th Embodiment.

  Hereinafter, embodiments of a dynamic characteristic calculation apparatus and dynamic characteristic calculation method for a turbomachine according to the present invention will be described with reference to the drawings. In the following embodiments, a centrifugal turbo compressor is a measurement target. However, the measurement target may be other as long as it is a turbo machine that compresses or pumps fluid by rotating an impeller. For example, an axial flow type turbo compressor, a turbo pump, a blower, a turbine, and the like can be measured.

[First Embodiment]
After describing the configuration of the dynamic characteristic calculation apparatus according to the first embodiment of the present invention with reference to FIGS. 1 and 2, the dynamic characteristic calculation method according to the first embodiment of the present invention will be described with reference to FIG. explain.

<Turbo compressor>
The centrifugal turbo compressor 1 shown in FIG. 1 is a measurement target of dynamic characteristics by the dynamic characteristic calculation apparatus 100. The turbo compressor 1 is configured by accommodating a rotor system 20 in an internal space of a housing 10. The rotor system 20 includes a rotating shaft 21, a pair of impellers 22 provided at both ends of the rotating shaft 21, two bearings 23 that rotatably support the rotating shaft 21, an impeller 22, and a bearing 23. And two seal members 24 provided therebetween. As the bearing 23, for example, a sliding bearing can be employed. It should be noted that the specific configuration of the rotor system 20, that is, what and how many mechanical elements are arranged can be changed as appropriate. Further, in the following description, a rotating body composed of the rotating shaft 21 and a pair of impellers 22 is simply referred to as a rotor 25 to be distinguished from the rotor system 20.

  A gear (pinion gear) 30 is provided at the center of the rotating shaft 21. The gear 30 is meshed with a large-diameter gear (not shown) having a larger diameter than the gear 30, and the rotor 25 is rotated via the gear 30. The gear 30 and the large-diameter gear constitute a speed increasing mechanism, and the rotor 25 can be rotated at a rotational speed of 20000 to 30000 rpm, for example.

  A suction port 11 is formed in a portion of the housing 10 that faces the surface of each impeller 22 (the surface on the side opposite to the rotation shaft 21). Further, in the internal space defined by the inner wall of the housing 10, a portion radially outside the impeller 22 is configured as a discharge chamber 12 in which the impeller 22 can discharge gas in the centrifugal direction. With such a configuration, the turbo compressor 1 sucks the gas from the suction port 11 by the impeller 22 and compresses the sucked gas by the rotation of the impeller 22, as indicated by the one-dot chain line arrow in FIG. The compressed gas is discharged into the discharge chamber 12.

<Dynamic characteristic calculation device>
Next, the dynamic characteristic calculation apparatus 100 will be described. The dynamic characteristic calculation device 100 is a device for calculating the dynamic characteristics of each mechanical element (rotary shaft 21, impeller 22, bearing 23, seal member 24) constituting the rotor system 20 of the turbo compressor 1, and is a model. Each of the functional units of the conversion unit 101, the mode analysis unit 102, and the dynamic characteristic calculation unit 103 is configured. These functions will be described later. If the rotor system 20 includes other machine elements, it is of course possible to calculate the dynamic characteristics of the machine elements.

  Each of the functional units included in the dynamic characteristic calculation device 100 is realized by cooperation with software such as a program executed on the hardware with logical calculation hardware such as a microcomputer as a core. In other words, each functional unit shows a share as a function, and does not necessarily need to be configured physically independently. The program is stored in a memory (not shown), and the dynamic characteristic calculation apparatus 100 reads the program from the memory as necessary, thereby calculating the dynamic characteristic of each machine element.

<Input means and display means>
An input unit 111 and a display unit 112 are connected to the dynamic characteristic calculation apparatus 100. The input unit 111 is a unit for inputting data to the dynamic characteristic calculation apparatus 100, and includes a keyboard or the like. An operator can input, for example, a known parameter, which will be described later, to the dynamic characteristic calculation device 100 via the input unit 111.

  The display unit 112 is a unit for displaying the data output from the dynamic characteristic calculation device 100 so that the operator can recognize the data, and includes a monitor or the like. For example, it is possible to cause the display unit 112 to display a result of calculating an unknown parameter, which will be described later, by the dynamic characteristic calculation device 100.

<Vibration sensor>
A plurality of vibration sensors (vibration detecting means) 31 for detecting vibration of the rotating shaft 21 are disposed in the vicinity of the peripheral surface of the rotating shaft 21 of the turbo compressor 1. The vibration sensor 31 is provided at four locations as shown in FIG. 1 with respect to the axial direction of the rotary shaft 21, and is provided at two locations with respect to the circumferential direction of the rotary shaft 21 as shown in FIG. . 2 is a view taken in the direction of arrows AA in FIG.

  More specifically, in the axial direction, vibration sensors 31 are provided at a position between the impeller 22 and the seal member 24 and at a position between the bearing 23 and the seal member 24, respectively. Furthermore, at each position in the axial direction, as shown in FIG. 2, two symmetrically with respect to the vertical plane with a predetermined interval of 90 °, for example, along the upper peripheral surface of the rotating shaft 21. Has been placed. However, such an arrangement form of the vibration sensor 31 is merely an example, and the number and position of the vibration sensor 31 can be appropriately changed.

  For example, the vibration sensor 31 detects the displacement of the rotating shaft 21 to generate signal data related to the vibration of the rotating shaft 21, and outputs the signal data to the dynamic characteristic calculation device 100. The signal data relating to the vibration of the rotating shaft 21 output from the vibration sensor 31 is used as data relating to the vibration of the rotor system 20 in the calculation of the dynamic characteristics of the mechanical elements described later.

<Exciter>
In the present embodiment, a vibration exciter 32 for applying vibration to the turbo compressor 1 is provided. The vibration exciter 32 is, for example, an electromagnetic type, and is placed on the housing 10 of the turbo compressor 1. When the shaker 32 is operated, the vibration generated by the shaker 32 is indirectly transmitted to the rotary shaft 21 via the housing 10 and the bearing 23. The conditions of vibration that can be applied by the vibrator 32 can be changed as appropriate.

<Calculation of dynamic characteristics>
A method of calculating the dynamic characteristics of each mechanical element of the rotor system 20 by the dynamic characteristic calculation apparatus 100 will be described with reference to FIG. Here, as an example, the rotating shaft 21 is taken up as a mechanical element whose dynamic characteristics can be calculated in advance, and the bearing 23 is taken up as a mechanical element whose dynamic characteristics are difficult to calculate in advance. The case where the stiffness matrix K _br and the damping matrix C _br of the bearing 23 are obtained as dynamic characteristics of the bearing 23 will be described. In the following equations, the matrix is shown in bold capital letters and the vector is shown in bold small letters. However, since bold letters cannot be used in the text of the specification, they are written in normal fonts.

(Modeling process)
Here, assuming that λ _i is the i-th order eigenvalue of the rotor system 20 and φ _i is the vibration mode corresponding to the i-th order eigenvalue, the vibration equation of the rotor system 20 including the bearing 23 is the characteristic matrix (mass of the rotor system 20 It can be expressed by equation (1) using a matrix M, a damping matrix C, and a stiffness matrix K).

  In the dynamic characteristic calculation method according to the present embodiment, first, the rotor system 20 is modeled (step S201). Modeling here refers to expressing the characteristic matrices M, C, and K in the vibration equation (1) of the rotor system 20 with known parameters for the rotating shaft 21 and unknown parameters for the bearing 23.

Specifically, based on information on dimensions and physical properties obtained from a design drawing or the like, known parameters that can be calculated in advance, that is, the mass matrix M _rt , the damping matrix C _rt, and the stiffness matrix K _rt of the rotating shaft 21 are described. The operator calculates these values in advance and inputs the values to the dynamic characteristic calculation device 100 via the input unit 111. On the other hand, unknown parameters that are difficult to calculate in advance, that is, the stiffness matrix K _br and the damping matrix C _br of the bearing 23 are set as unknowns.

When formula (1) is rewritten using known parameters and unknown parameters, formula (2) is obtained. Then, when the term including the unknown parameter in Equation (2) is moved to the left side and the known parameter is moved to the right side to rearrange the equation, Equation (3) is obtained.

  As described above, the modeling process in which the characteristic matrix in the vibration equation of the rotor system 20 is expressed by the known parameter and the unknown parameter is executed by the modeling unit 101 of the dynamic characteristic calculation device 100.

(Vibration detection process)
Next, the operation of the turbo compressor 1 is started (step S202), and then the vibrator 32 is operated to vibrate the turbo compressor 1 (step S203). At this time, the rotating shaft 21 is indirectly excited by the shaker 32. Then, the vibration generated in the rotor system 20 is detected by the plurality of vibration sensors 31 (step S204). In addition, although various forms can be employ | adopted as a vibration form by the shaker 32, a sweep vibration shall be performed here.

(Mode analysis process)
Based on the signal data output from the vibration sensor 31, the mode analysis unit 102 of the dynamic characteristic calculation device 100 executes mode analysis for calculating the natural frequency, the damping ratio, and the vibration mode of the rotor system 20 (step S205). . Specifically, the above-described values can be calculated by measuring the frequency response function of the rotor system 20 subjected to the sweep excitation and using, for example, the MDOF method. Thus, the natural value λ _i (calculated from the natural frequency and damping ratio) and the vibration mode φ _i of the rotor system 20 in the equation (3) are obtained.

ここで、行列成分Ｃ、Ｋおよび振動モードφの添え字のうち、「１」は１つ目の軸受２３に関するものであること、「２」は２つ目の軸受２３に関するものであることを示す。また、行列成分Ｃ、Ｋの添え字のうち、「ｘｘ」は水平方向に変位した場合に生じる水平方向の減衰力または弾性力に関するものであること、「ｘｙ」は水平方向に変位した場合に生じる垂直方向の減衰力または弾性力に関するものであること、「ｙｘ」は垂直方向に変位した場合に生じる水平方向の減衰力または弾性力に関するものであること、「ｙｙ」は垂直方向に変位した場合に生じる垂直方向の減衰力または弾性力に関するものであることを示す。また、振動モードφの添え字のうち、「ｘ」は水平方向に関する振動モード、「ｙ」は垂直方向に関する振動モードであることを示す。なお、軸受２３に関する振動モードφは、振動センサー３１から出力された信号データに基づいて求められる。 (Dynamic characteristics calculation process)
When the eigenvalue λ _i and the vibration mode φ _i of the rotor system 20 are obtained in the mode analysis step, the right side of Equation (3) is a known value. Therefore, when the right side of Equation (3) is a known vector b and the left side is expanded into each component, Equation (4) is obtained.

Here, among the subscripts of the matrix components C and K and the vibration mode φ, “1” is related to the first bearing 23 and “2” is related to the second bearing 23. Show. Of the subscripts of the matrix components C and K, “xx” relates to the horizontal damping force or elastic force generated when the horizontal displacement occurs, and “xy” corresponds to the horizontal displacement. "Yx" relates to the vertical damping force or elastic force generated, "yx" relates to the horizontal damping force or elastic force generated when displaced in the vertical direction, "yy" is displaced vertically This indicates that the vertical damping force or elastic force is generated. Of the subscripts of the vibration mode φ, “x” indicates a vibration mode in the horizontal direction, and “y” indicates a vibration mode in the vertical direction. The vibration mode φ related to the bearing 23 is obtained based on the signal data output from the vibration sensor 31.

ただし、

である。 When the left side of Expression (4) is arranged into a known coefficient matrix and an unknown vector, Expression (5) is obtained.

However,

It is.

式（７）は各モードに対してそれぞれ成り立つので、式（８）に示すように１次〜ｍ次モードまで使用する。

Furthermore, when the coefficient matrix of Expression (5) is A and separated into a real part and an imaginary part, Expression (7) is obtained.

Since Equation (7) holds for each mode, the first to m-th order modes are used as shown in Equation (8).

If the number of rows in the coefficient matrix of equation (8) is greater than the number of columns, that is, if the number of equations is greater than the number of unknown parameters, the equation can be solved by the least square method. The solution at this time is shown in Formula (9). However, the subscript “T” represents a transposed matrix, and “−1” represents an inverse matrix.

Thus, from the vibration equation (3) obtained in the modeling process, the eigenvalue λ _i and the vibration mode φ _i calculated in the mode analysis process, unknown parameters, that is, the stiffness matrix K _br and the damping matrix C of the bearing 23 are obtained. _The process of calculating _br is executed by the dynamic characteristic calculation unit 103 of the dynamic characteristic calculation apparatus 100 (step S206).

  Finally, the dynamic characteristic calculation apparatus 100 determines whether or not to end the measurement (step S207), ends the operation when the measurement is ended, and returns to step S203 when the measurement is not ended. Repeat the above steps.

Information on the stiffness matrix K _br and the damping matrix C _br of the bearing 23 calculated by the dynamic characteristic calculation unit 103 is displayed on the display unit 112 at the end of the measurement or at an appropriate timing during the measurement. Then, by referring to the result displayed on the display unit 112, the operator determines whether or not self-excited vibration is generated in the rotor 25, or the rotor system 20 so that the self-excited vibration is not generated in the rotor 25. It is possible to appropriately examine the design of each machine element.

As described above, in the present embodiment, the characteristic matrices M, C, and K in the vibration equation (1) of the rotor system 20 of the turbo compressor 1 are related to the rotating shaft 21 that is a mechanical element that can calculate the dynamic characteristics in advance. Known parameters (mass matrix M _rt , damping matrix C _rt, and stiffness matrix K _{rt of the} rotating shaft 21) and unknown parameters related to the bearing 23 that is a mechanical element whose dynamic characteristics are difficult to calculate in advance (the stiffness matrix K of the bearing 23 _br and damping matrix C _br ), the rotor system 20 is modeled. Then, from the vibration equation (3) obtained by this modeling, the eigenvalue λ _i of the rotor system 20 and the vibration mode φ _i calculated from the signal data of the vibration generated in the rotor system 20, the unknown The parameter is calculated. In other words, according to the present embodiment, by modeling as described above, it is also possible to calculate parameters relating to mechanical elements (such as the bearing 21) whose dynamic characteristics are difficult to predict, and the rotor system 20 of the turbo compressor 1 can be calculated. It is possible to calculate the dynamic characteristics of each machine element constituting the.

  In the present embodiment, in the vibration detection step, vibration is applied by the vibration exciter 32 provided outside the turbo compressor 1. In this way, if the rotor system 20 can be vibrated by the vibrator 32, the vibration mode of the rotor system 20 can be excited. As a result, it is possible to measure vibration data suitable for calculation of eigenvalues and vibration modes in the subsequent mode analysis process, and it is possible to preferably calculate the dynamic characteristics of each machine element.

  In the present embodiment, in the mode analysis step, the signal data output from the vibration sensor 31 is subjected to frequency analysis (measuring the frequency response function), the eigenvalue and vibration mode of the rotor system 20 are calculated, and dynamic characteristics are calculated. In the process, unknown parameters are calculated by the least square method. Thus, by calculating an unknown parameter by the least square method, the calculated value is always a least square solution, and thus a stable and accurate value can be calculated. As a result, the dynamic characteristics of each machine element can be grasped more accurately.

[Second Embodiment]
Next, a dynamic characteristic calculation method according to the second embodiment of the present invention will be described with reference to FIG. The dynamic characteristic calculation method according to the present embodiment is different from the dynamic characteristic calculation method according to the first embodiment in that the step of exciting the turbo compressor 1 with the shaker 32 is omitted. The other points are the same as in the first embodiment, and steps S301 to S306 shown in FIG. 4 are the same steps as steps S201, S202, and S204 to S207 shown in FIG. Is omitted.

  As in the present embodiment, even if vibration is not performed by the vibration generator 32, the rotor 25 is vibrated due to the operation of the turbo compressor 1, so that dynamic characteristics can be measured. Therefore, by omitting the step of vibrating by the vibrator 32, the cost and labor of installing the vibrator 32 can be saved, so that the dynamic characteristics of each mechanical element of the rotor system 20 can be measured more easily. .

[Third Embodiment]
Next, a dynamic characteristic calculation method according to the third embodiment of the present invention will be described with reference to FIGS. 5 and 6. The dynamic characteristic calculation method in the present embodiment is different from the dynamic characteristic calculation method in the first embodiment in that the equation of motion related to the rotor system 20 is solved in consideration of the dynamic characteristics related to the base system 40 that supports the rotor system 20. There is a point. In addition, the same code | symbol is attached | subjected to the same component as 1st Embodiment, and description is abbreviate | omitted. Hereinafter, a description will be given focusing on differences from the first embodiment.

  As shown in FIG. 5, in the turbo compressor 1, the housing 10 that houses the rotor system 20 is fixedly supported with respect to the fixed surface G via a support member 41. Hereinafter, the housing 10 and the support member 41 are collectively referred to as a base system 40. Here, when the rigidity of the base system 40 is sufficiently larger than that of the rotor system 20, the dynamic characteristics of the rotor system 20 are calculated ignoring the influence of the dynamic characteristics of the base system 40 as in the first embodiment. But there is no particular problem.

  However, for example, when the turbo compressor 1 is large, it is necessary to increase the rigidity of the bearing 23 that supports the rotor system 20, and as a result, the rigidity of the base system 40 may be relatively decreased. Then, the influence of the dynamic characteristics of the base system 40 cannot be ignored, and it is necessary to consider the dynamic characteristics of the base system 40 in order to accurately calculate the dynamic characteristics of the rotor system 20. In the present embodiment, assuming such a case, the dynamic characteristics of the rotor system 20 are calculated in consideration of the dynamic characteristics of the base system 40.

  In the turbo compressor 1 shown in FIG. 5, a speed increasing mechanism is configured by meshing a gear 30 provided at the center of the rotating shaft 21 with a large-diameter gear 33 having a larger diameter than the gear 30. Yes. And in order to ensure the space which accommodates the large diameter gear 33, the center part of the housing 10 protrudes partially outside, and the protrusion part 10a is formed. The support member 41 is provided on both the left and right sides of the protruding portion 10a. In other words, the base system 40 including the housing 10 and the support member 41 is configured to be approximately bilaterally symmetrical about the protruding portion 10a. In addition, the vibration exciter 32 is arrange | positioned on the protrusion part 10a.

  In the calculation of dynamic characteristics to be described later, the base system 40 is divided into a system comprising a portion of the housing 10 on the left side of the protruding portion 10a and a support member 41 on the left side, and a portion of the housing 10 on the right side of the protruding portion 10a. The model is divided into two parts, a system composed of the right support member 41. However, the modeling method of the base system 40 is not limited to this, and can be appropriately changed so as to conform to the actual configuration.

  In this embodiment, in addition to the vibration sensor 31 for detecting the vibration of the rotating shaft 21, a plurality of vibration sensors 34 for detecting the vibration of the base system 40 are provided. Specifically, the vibration sensor 34 is provided on the outer side of the housing 10 and at a position facing the bearing 23, and detects the displacement of the housing 10 to generate signal data related to the vibration of the base system 40, It outputs to the characteristic calculation apparatus 100. As described above, by providing the vibration sensor 34 in the vicinity of the bearing 23, it is possible to accurately detect vibration propagated from the base system 40 to the rotor system 20 via the bearing 23. However, the position and number of the vibration sensors 34 can be changed as appropriate.

<Calculation of dynamic characteristics>
Next, a method for calculating the dynamic characteristics of each mechanical element of the rotor system 20 by the dynamic characteristic calculation apparatus 100 will be described with reference to FIG. Here, as an example, the rotating shaft 21 is taken up as a mechanical element whose dynamic characteristics can be calculated in advance, the bearing 23 is taken up as a mechanical element whose dynamic characteristics are difficult to calculate in advance, and the foundation system 40 that is difficult to calculate in advance is used. Consider dynamic characteristics. In addition, the stiffness matrix K _br and the damping matrix C _br of the bearing 23 are obtained as the dynamic characteristics of the bearing 23, and the mass matrix M _bs and the stiffness matrix K _bs of the foundation system 40 are obtained as the dynamic characteristics of the foundation system 40. explain. In the following equations, the matrix is shown in bold capital letters and the vector is shown in bold small letters. However, since bold letters cannot be used in the text of the specification, they are written in normal fonts.

(Modeling process)
Here, when λ _i is an i-th order eigenvalue of the rotor system 20 and φ _i is a vibration mode corresponding to the i-th order eigenvalue, the vibration equation of the rotor system 20 including the bearing 23 and the base system 40 is Using the characteristic matrix (mass matrix M, damping matrix C, and stiffness matrix K), it can be expressed by equation (10).

  In the dynamic characteristic calculation method according to this embodiment, first, the rotor system 20 including the base system 40 is modeled (step S401). Modeling here refers to expressing the characteristic matrices M, C, K in the vibration equation (10) of the rotor system 20 with known parameters relating to the rotating shaft 21 and unknown parameters relating to the bearing 23 and the base system 40. Point to.

Specifically, based on information on dimensions and physical properties obtained from a design drawing or the like, known parameters that can be calculated in advance, that is, the mass matrix M _rt , the damping matrix C _rt, and the stiffness matrix K _rt of the rotating shaft 21 are described. The operator calculates these values in advance and inputs the values to the dynamic characteristic calculation device 100 via the input unit 111. On the other hand, unknown parameters that are difficult to calculate in advance, that is, the stiffness matrix K _br and the damping matrix C _{br of} the bearing 23 and the mass matrix M _bs and the stiffness matrix K _bs of the base system 40 are set as unknowns. . Here, the damping of the base system 40 is not considered as being sufficiently smaller than that of the rotor system 20.

When equation (10) is rewritten using the known parameter and the unknown parameter, equation (11) is obtained. Then, when the term including the unknown parameter in Expression (11) is moved to the left side and the known parameter is transferred to the right side to rearrange the expression, Expression (12) is obtained.

  As described above, the modeling process in which the characteristic matrix in the vibration equation of the rotor system 20 in consideration of the dynamic characteristics of the base system 40 is expressed by the known parameters and the unknown parameters is performed by the modeling unit 101 of the dynamic characteristic calculation apparatus 100. Is executed.

(Vibration detection process)
Next, the operation of the turbo compressor 1 is started (step S402), and then the vibrator 32 is operated to vibrate the turbo compressor 1 (step S403). At this time, the rotating shaft 21 is indirectly excited by the shaker 32. Then, the vibration generated in the rotor system 20 is detected by the plurality of vibration sensors 31, and the vibration generated in the base system 40 is detected by the plurality of vibration sensors 34 (step S404). In addition, although various forms can be employ | adopted as a vibration form by the shaker 32, a sweep vibration shall be performed here.

(Mode analysis process)
Based on the signal data output from the vibration sensor 31, the mode analysis unit 102 of the dynamic characteristic calculation device 100 performs mode analysis for calculating the natural frequency, the damping ratio, and the vibration mode of the rotor system 20 (step S405). . Specifically, the above-described values can be calculated by measuring the frequency response function of the rotor system 20 subjected to the sweep excitation and using, for example, the MDOF method. Thus, the natural value λ _i (calculated from the natural frequency and damping ratio) and the vibration mode φ _i of the rotor system 20 in the equation (12) are obtained.

(Dynamic characteristics calculation process)
When the eigenvalue λ _i and the vibration mode φ _i of the rotor system 20 are obtained in the mode analysis step, the right side of the equation (12) is a known value. Therefore, when the right side of equation (12) is a known vector b and the left side is expanded into each component, equation (13) is obtained.

  Here, of the subscripts of the matrix components M, C, K and the vibration mode φ, “br1” relates to the left bearing 23 in FIG. 5, and “br2” relates to the right bearing 23 in FIG. That is, “bs1” relates to the left half base system 40 in FIG. 5, and “bs2” relates to the right half base system 40 in FIG. 5. Of the subscripts of the matrix components M, C, and K, “xx” relates to the horizontal inertial force, damping force, or elastic force that occurs when displaced in the horizontal direction, and “xy” denotes the horizontal direction. "Yx" relates to the horizontal inertial force, damping force or elastic force generated when displaced in the vertical direction. In other words, “yy” indicates that it relates to the inertial force, damping force or elastic force in the vertical direction that occurs when displaced in the vertical direction. Of the subscripts of the vibration mode φ, “x” indicates a vibration mode in the horizontal direction, and “y” indicates a vibration mode in the vertical direction. The vibration mode φ related to the bearing 23 is obtained based on the signal data output from the vibration sensor 31, and the vibration mode φ related to the base system 40 is obtained based on the signal data output from the vibration sensor 34.

ここで、Φ_i,M、Φ_i,C、Φ_i,Kは、式（１３）の左辺から未知数であるＭ、Ｃ、Ｋをベクトルとしてまとめ、かつ、スカラー量であるλをくくり出して残った成分を示す。また、

である。なお、式（１５）において軸受２３と土台系４０とは同じ式であるので、添え字の「ｂｒ」と「ｂｓ」は省略している。 When the left side of Expression (13) is arranged into a known coefficient matrix and an unknown vector, Expression (14) is obtained.

Here, Φ _{i, M} , Φ _{i, C} , and Φ _{i, K} are obtained by collecting unknown numbers M, C, and K as vectors from the left side of the equation (13) and extracting λ that is a scalar quantity. The remaining ingredients are indicated. Also,

It is. Since the bearing 23 and the base system 40 are the same in the formula (15), the subscripts “br” and “bs” are omitted.

式（１６）は各モードに対してそれぞれ成り立つので、式（１７）に示すように１次〜ｍ次モードまで使用する。

Furthermore, when the coefficient matrix of Expression (14) is A and separated into a real part and an imaginary part, Expression (16) is obtained.

Since equation (16) holds for each mode, the first to m-th order modes are used as shown in equation (17).

If the number of rows in the coefficient matrix of equation (17) is greater than the number of columns, that is, if the number of equations is greater than the number of unknown parameters, the equation can be solved by the least square method. The solution at this time is shown in Formula (18). However, the subscript “T” represents a transposed matrix, and “−1” represents an inverse matrix.

Thus, from the vibration equation (12) obtained in the modeling process, the eigenvalue λ _i and the vibration mode φ _i calculated in the mode analysis process, unknown parameters, that is, the stiffness matrix K _br and the damping matrix C of the bearing 23 are obtained. _br and the process of calculating the mass matrix M _bs and the stiffness matrix K _bs of the base system 40 are executed by the dynamic characteristic calculator 103 of the dynamic characteristic calculator 100 (step S406).

  Finally, the dynamic characteristic calculation apparatus 100 determines whether or not to end the measurement (step S407). If the measurement is to be ended, the operation is ended, and if the measurement is not to be ended, the process returns to step S403. Repeat the above steps.

Information on the stiffness matrix K _br and the damping matrix C _{br of} the bearing 23 calculated by the dynamic characteristic calculation unit 103 and the mass matrix M _bs and the stiffness matrix K _bs of the base system 40 are obtained at the end of the measurement or during the measurement. It is displayed on the display means 112 at the timing. Then, by referring to the result displayed on the display unit 112, the operator determines whether or not self-excited vibration is generated in the rotor 25, or the rotor system 20 so that the self-excited vibration is not generated in the rotor 25. It is possible to appropriately study the design of each machine element and the base system 40.

As described above, in the present embodiment, the characteristic matrices M, C, and K in the vibration equation (10) of the rotor system 20 of the turbo compressor 1 are related to the rotating shaft 21 that is a mechanical element that can calculate the dynamic characteristics in advance. Known parameters (mass matrix M _rt , damping matrix C _rt and stiffness matrix K _{rt of} rotating shaft 21) and unknown parameters (bearing 23) related to bearing 23 and base system 40 that are mechanical elements whose dynamic characteristics are difficult to calculate in advance. The rotor system 20 including the base system 40 is modeled by dividing the stiffness matrix K _br and the damping matrix C _br , and the mass matrix M _bs and the stiffness matrix K _bs ) of the base system 40. Then, from the vibration equation (12) obtained by this modeling, the eigenvalue λ _i of the rotor system 20 and the vibration mode φ _i calculated from the signal data of the vibration generated in the rotor system 20, the unknown The parameter is calculated. In other words, according to the present embodiment, by modeling as described above, it is also possible to calculate parameters relating to mechanical elements (such as the bearing 21) whose dynamic characteristics are difficult to predict, and the rotor system 20 of the turbo compressor 1 can be calculated. It is possible to calculate the dynamic characteristics of each machine element constituting the. In addition, by calculating the dynamic characteristics by including the parameters related to the dynamic characteristics of the base system 40 in the unknown parameters, even if the dynamic characteristics of the base system 40 cannot be ignored, the dynamics of the machine elements constituting the rotor system 20 are not affected. The characteristics can be calculated with high accuracy.

[Fourth Embodiment]
Next, a dynamic characteristic calculation method according to the fourth embodiment of the present invention will be described with reference to FIG. The dynamic characteristic calculation method according to the present embodiment is different from the dynamic characteristic calculation method according to the third embodiment in that the step of exciting the turbo compressor 1 with the shaker 32 is omitted. The other points are the same as in the third embodiment, and steps S501 to S506 shown in FIG. 7 are the same steps as steps S401, S402, and S404 to S407 shown in FIG. Is omitted.

  As in the present embodiment, even if vibration is not performed by the vibration generator 32, the rotor 25 is vibrated due to the operation of the turbo compressor 1, so that dynamic characteristics can be measured. Therefore, by omitting the step of vibrating by the vibrator 32, the cost and labor of installing the vibrator 32 can be saved, so that the dynamic characteristics of each mechanical element of the rotor system 20 can be measured more easily. .

[Others]
The present invention is not limited to the above embodiment, and the elements of the above embodiment can be appropriately combined or variously modified without departing from the spirit of the present invention.

  In the above embodiment, the rotary shaft 21 is taken up as a mechanical element whose dynamic characteristics can be calculated in advance, and the bearing 23 is taken up as a mechanical element whose dynamic characteristics are difficult to calculate in advance. Or it can change suitably whether it treats as an unknown parameter. For example, it is also possible to calculate the dynamic characteristics related to the impeller 22 and the seal member 24 by setting the parameters of the dynamic characteristics related to the mechanical elements other than the rotating shaft 21 such as the impeller 22 and the seal member 24 as unknown numbers.

  In the above embodiment, the modeling of the rotor system 20 (steps S201 and S301) is performed before the operation of the turbo compressor 1 is started (steps S202 and S302). Modeling may be executed after the operation is started.

1 Turbo compressor (turbo machine)
DESCRIPTION OF SYMBOLS 10 Housing 20 Rotor system 21 Rotating shaft 22 Impeller 23 Bearing 24 Seal member 31 Vibration sensor (vibration detection means)
32 Exciter 34 Vibration sensor 40 Base system 41 Support member 100 Dynamic characteristic calculation device 101 Modeling unit 102 Mode analysis unit 103 Dynamic characteristic calculation unit

Claims (6)

A turbomachine dynamic characteristic calculation method for compressing or pumping fluid by rotating an impeller connected to a rotating shaft,
By expressing the characteristic matrix in the vibration equation of the rotor system of the turbomachine by a known parameter relating to a machine element whose dynamic characteristic can be calculated in advance and an unknown parameter relating to a machine element whose dynamic characteristic is difficult to calculate in advance, A modeling step of modeling the rotor system by a vibration equation;
A vibration detecting step for detecting vibration generated in the rotor system;
Based on the vibration signal data detected in the vibration detection step, a mode analysis step for calculating the eigenvalue and vibration mode of the rotor system;
A dynamic characteristic calculation step for calculating the unknown parameter from the vibration equation obtained in the modeling step and the eigenvalue and vibration mode calculated in the mode analysis step;
A dynamic characteristic calculation method for a turbomachine, comprising:   The turbo machine dynamic characteristic calculation method according to claim 1, wherein the modeling is performed by including in the unknown parameter a parameter related to a dynamic characteristic of a base system that supports the rotor system.   The turbo machine dynamic characteristic calculation method according to claim 1, wherein in the vibration detection step, vibration is applied by a vibration exciter provided outside the turbo machine. In the mode analysis step, the signal data is frequency-analyzed to calculate the eigenvalue and vibration mode of the rotor system,
4. The dynamic characteristic calculation method for a turbomachine according to claim 1, wherein the unknown parameter is calculated by a least square method in the dynamic characteristic calculation step. 5. A turbomachine dynamic characteristic calculation device that compresses or pumps fluid by rotating an impeller coupled to a rotating shaft,
By expressing the characteristic matrix in the vibration equation of the rotor system of the turbomachine by a known parameter relating to a machine element whose dynamic characteristic can be calculated in advance and an unknown parameter relating to a machine element whose dynamic characteristic is difficult to calculate in advance, A modeling unit for modeling the rotor system by a vibration equation;
A mode analysis unit for calculating the eigenvalue and vibration mode of the rotor system based on signal data output from vibration detection means for detecting vibration generated in the rotor system;
A dynamic characteristic calculation unit that calculates the unknown parameter from the vibration equation obtained by the modeling unit and the eigenvalue and vibration mode calculated by the mode analysis unit;
A dynamic characteristic calculation apparatus for a turbomachine, comprising:   6. The dynamic characteristic calculation apparatus for a turbomachine according to claim 5, wherein the modeling is performed by including a parameter related to a dynamic characteristic of a base system supporting the rotor system in the unknown parameter.

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