JP6590746B2 - Rotating machine vibration measuring device, rotating machine vibration measuring method and program - Google Patents

Description

  The present invention relates to a rotating machine vibration measuring device, a rotating machine vibration measuring method, and a program.

  A rotary machine including a steam turbine and a gas turbine is required to have sufficient vibration strength. Therefore, at the time of design, the vibrations of the turbine blades are measured to verify that the vibration characteristics of the turbine blades are as designed, or changes in the vibration characteristics due to changes in operating conditions are confirmed. As one of the techniques for measuring the vibration of the turbine blade, there is known a non-contact blade vibration measurement technique (BTT: Blade Tip Timing) for measuring the vibration of the turbine blade in a non-contact manner (see, for example, Patent Document 1). In this technique, a sensor that detects the passage of a turbine blade in a non-contact manner is disposed in the casing of the turbine blade, and the vibration amplitude of the turbine blade is calculated from the difference in passage time between when the turbine blade is vibrating and when it is not vibrating.

Japanese Patent No. 5293406

  However, in the non-contact blade vibration measurement technique, since the sensor is arranged in the casing, the sensor vibrates when the casing vibrates. Sensor vibrations may affect measurement errors in turbine blade vibration measurement. More specifically, when the vibration amplitude of the turbine blade is sufficiently larger than the vibration amplitude of the sensor, it can be evaluated that the influence of the vibration of the sensor is a negligible level. On the other hand, when the difference between the vibration amplitude of the turbine blade and the vibration amplitude of the sensor is small, the influence of the vibration of the sensor cannot be ignored. For example, since turbine blades used in gas turbines have high rigidity and small vibration amplitude, the influence of sensor vibration cannot be ignored.

  Moreover, the turbine shaft of the turbine used for a gas turbine may respond with torsional vibration. In this case, even if the turbine blades are not vibrating, a deviation occurs in the passage time of the turbine blades due to the torsional vibration of the turbine shaft. For this reason, in the non-contact blade vibration measurement technique, the vibration amplitude of the turbine blade is calculated to be larger than the actual vibration amplitude including the torsional vibration of the turbine.

  The present invention has been made in view of such circumstances, and an object of the present invention is to provide a rotating machine vibration measuring device, a rotating machine vibration measuring method, and a program for measuring vibrations of a rotating body with high accuracy.

  A rotating machine vibration measuring device of the present invention is arranged at a first predetermined position of a stationary body facing an outer periphery of a rotating body arranged in the rotating machine, and detects a passage of the rotating body in a non-contact manner, A second sensor that is disposed at a second predetermined position of the rotating shaft of the stationary body or the rotating body and detects vibration at the second predetermined position of the stationary body or the rotating shaft; and vibration of the stationary body or the rotating shaft Based on the model, a vibration calculation unit that calculates vibrations of the stationary body or the rotation shaft, vibrations at the second predetermined position of the stationary body or the rotation shaft calculated by the vibration calculation unit, and the second The stationary body or the rotating shaft calculated by the vibration calculating unit compared with the comparing unit that compares the stationary body or the vibration at the second predetermined position of the rotating shaft detected by the sensor. The vibration model used in the vibration calculation unit so that a difference between the vibration at the second predetermined position and the vibration at the second predetermined position of the stationary body or the rotating shaft detected by the second sensor is reduced. Based on a time difference between a gain setting unit that sets a gain of the state quantity, a passage time when the rotating body is detected by the first sensor, and a passage time of the rotating body in the reference state stored in the storage unit A stationary rotor calculated by the vibration calculating unit from a vibration waveform of the rotating body calculated by the first rotating body vibration calculating unit calculated by the first rotating body vibration calculating unit calculating the vibration of the rotating body; And a second rotating body vibration calculating unit that calculates a vibration of the rotating body by removing a displacement caused by vibration at the first predetermined position of the rotating shaft.

  According to this configuration, the vibration of the rotating body can be measured with high accuracy.

  In the rotary machine vibration measuring device of the present invention, the second sensor is disposed on the stationary body, detects vibration of the stationary body at the second predetermined position, and the vibration calculation unit is a vibration model of the stationary body. And the comparison unit calculates the vibration of the stationary body at the second predetermined position calculated by the vibration calculation unit and the stationary body detected by the second sensor. And the gain setting unit compares the vibration at the second predetermined position of the stationary body calculated by the vibration calculation unit and compared with the vibration at the second predetermined position. The gain of the state quantity of the vibration model used in the vibration calculation unit is set so that the difference from the vibration at the second predetermined position of the stationary body detected by the sensor is small, and the second rotating body vibration calculation is performed Department is front From the vibration waveform of the rotating body calculated by the first rotating body vibration calculating unit, removing the displacement of the first sensor due to the vibration at the first predetermined position of the stationary body calculated by the vibration calculating unit, It is preferable to calculate the vibration of the rotating body. According to this configuration, the vibration of the rotating body can be measured with high accuracy.

  In the rotating machine vibration measuring device of the present invention, the second sensor is disposed on the rotating shaft, detects torsional vibration at the second predetermined position of the rotating shaft, and the vibration calculating unit includes the rotating body and the A torsional vibration including the rotating body and the rotating shaft based on a torsional vibration model including a rotating shaft; and the comparing unit calculates the second of the rotating shafts calculated by the vibration calculating unit. The torsional vibration at a predetermined position is compared with the torsional vibration at the second predetermined position of the rotating shaft detected by the second sensor, and the gain setting unit is compared with the comparison unit, the vibration calculation unit The vibration so that a difference between the calculated torsional vibration of the rotation shaft at the second predetermined position and the torsional vibration of the rotation shaft at the second predetermined position detected by the second sensor is reduced. A gain of a state quantity of the vibration model used in the output unit is set, and the second rotating body vibration calculating unit calculates the vibration calculating unit from the vibration waveform of the rotating body calculated by the first rotating body vibration calculating unit. It is preferable to calculate the vibration of the rotating body by removing the displacement of the rotating body due to the torsional vibration at the first predetermined position of the rotating body calculated in step (1). According to this configuration, the vibration of the rotating body can be measured with high accuracy.

  In the rotating machine vibration measuring device of the present invention, the rotating machine vibration measuring device further includes an external force input unit that inputs an external force that acts on the rotating body including torque fluctuation, and the vibration calculating unit further includes the stationary body or the rotating shaft based on the external force. It is preferable to calculate the vibration. According to this configuration, the vibration of the rotating body can be measured with high accuracy.

  The rotating machine vibration measuring method of the present invention is a first sensor disposed at a first predetermined position of a stationary body facing the outer periphery of a rotating body disposed in the rotating machine, and detects the passage of the rotating body in a non-contact manner. A second vibration detecting step and a second sensor disposed at a second predetermined position of the rotating shaft of the stationary body or the rotating body to detect a vibration at the second predetermined position of the stationary body or the rotating shaft; Based on a vibration detection step, a vibration model for calculating the vibration of the stationary body or the rotating shaft based on a vibration model of the stationary body or the rotating shaft, and the stationary body or the rotation calculated in the vibration calculating step. The comparison step comparing the vibration at the second predetermined position of the shaft with the vibration at the second predetermined position of the stationary body or the rotating shaft detected at the second vibration detection step was compared at the comparison step. The vibration at the second predetermined position of the stationary body or the rotation shaft calculated in the vibration calculation step, and the vibration at the second predetermined position of the stationary body or the rotation shaft detected in the second vibration detection step. A gain setting step for setting a gain of a state quantity of the vibration model used in the vibration calculation step, a passage time when the rotating body is detected in the first vibration detection step, and a storage Calculated in the first rotating body vibration calculating step and the first rotating body vibration calculating step for calculating the vibration of the rotating body based on the time difference from the passing time of the rotating body in the reference state stored in the unit. The vibration of the rotating body is calculated by removing the displacement due to the vibration at the first predetermined position of the stationary body or the rotating shaft calculated in the vibration calculating step from the vibration waveform of the rotating body. Characterized in that it comprises a second rotating body vibration calculating step. According to this method, the vibration of the rotating body can be measured with high accuracy.

  The program of the present invention is a first vibration detection step of detecting the passage of the rotating body in a non-contact manner by a first sensor arranged at a first predetermined position of a stationary body facing the outer periphery of the rotating body arranged in the rotating machine. And a second vibration detecting step of detecting vibration at the second predetermined position of the stationary body or the rotating shaft with a second sensor arranged at a second predetermined position of the rotating shaft of the stationary body or the rotating body. A vibration calculating step of calculating a vibration of the stationary member or the rotating shaft based on a vibration model of the stationary member or the rotating shaft, and the first of the stationary member or the rotating shaft calculated in the vibration calculating step. The comparison of the vibration at the second predetermined position with the comparison at the second predetermined position and the vibration at the second predetermined position of the stationary body or the rotating shaft detected at the second vibration detection step The vibration at the second predetermined position of the stationary body or the rotating shaft calculated in the exiting step and the vibration at the second predetermined position of the stationary body or the rotating shaft detected in the second vibration detecting step. A gain setting step for setting a gain of a state quantity of the vibration model used in the vibration calculation step so that the difference is small, a passage time when the rotating body is detected in the first vibration detection step, and a storage unit Based on the time difference with the passage time of the rotating body in the stored reference state, the first rotating body vibration calculating step for calculating the vibration of the rotating body and the rotation calculated in the first rotating body vibration calculating step The second rotation for calculating the vibration of the rotating body by removing the displacement due to the vibration at the first predetermined position of the stationary body or the rotating shaft calculated in the vibration calculating step from the vibration waveform of the body Characterized in that to execute a vibration calculating step to the computer. According to this program, the vibration of the rotating body can be measured with high accuracy.

  According to the present invention, it is possible to realize a rotating machine vibration measuring device, a rotating machine vibration measuring method, and a program for measuring vibration of a rotating body with high accuracy.

FIG. 1 is a schematic diagram illustrating an example of the configuration of the rotating machine vibration measuring device according to the first embodiment. FIG. 2 is a cross-sectional view showing an example of the configuration of a turbine blade in which the rotary machine vibration measuring device according to the first embodiment is arranged. FIG. 3 is a front view schematically showing the configuration of the turbine blade in which the rotating machine vibration measuring device according to the first embodiment is arranged. FIG. 4 is a schematic diagram illustrating a detection signal detected by a non-contact sensor of the rotary machine vibration measuring device according to the first embodiment. FIG. 5 is a schematic diagram illustrating an example of the configuration of the rotating machine vibration measuring device according to the first embodiment. FIG. 6 is a schematic diagram illustrating an example of the configuration of the rotating machine vibration measuring device according to the second embodiment. FIG. 7 is a schematic diagram showing a vibration waveform obtained by the rotary machine vibration measuring apparatus according to the second embodiment. FIG. 8 is a schematic diagram showing a vibration waveform obtained by the rotary machine vibration measuring apparatus according to the second embodiment. FIG. 9 is a schematic diagram showing a vibration waveform obtained by the rotary machine vibration measuring apparatus according to the second embodiment. FIG. 10 is a schematic diagram showing a vibration waveform obtained by the rotary machine vibration measuring apparatus according to the second embodiment. FIG. 11 is a schematic diagram showing a vibration waveform obtained by the rotary machine vibration measuring apparatus according to the second embodiment. FIG. 12 is a schematic diagram showing a vibration waveform obtained by the rotary machine vibration measuring apparatus according to the second embodiment.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. In addition, this invention is not limited to each following embodiment, It can implement by changing suitably.

[First embodiment]
First, with reference to FIG. 1 thru | or FIG. 3, the outline | summary of the turbine blade 111 as a rotary body arrange | positioned at the steam turbine and gas turbine as a rotary machine is demonstrated, for example. FIG. 1 is a schematic diagram illustrating an example of the configuration of the rotating machine vibration measuring device according to the first embodiment. FIG. 2 is a cross-sectional view showing an example of the configuration of a turbine blade in which the rotary machine vibration measuring device according to the first embodiment is arranged. FIG. 3 is a front view schematically showing the configuration of the turbine blade in which the rotating machine vibration measuring device according to the first embodiment is arranged. 1 to 3 schematically show a plurality of turbine blades (rotary bodies) 111 and a casing (stationary body) 120.

  The plurality of turbine blades 111 are disposed radially outward from the turbine shaft (rotating shaft) 110. The turbine blade 111 rotates around the turbine shaft 110 when the turbine shaft 110 rotates. The turbine blade 111 is accommodated in the casing 120. The outer periphery of the turbine blade 111 faces the inner periphery of the casing 120. The plurality of turbine blades 111 are arranged at equal intervals in the circumferential direction of the turbine shaft 110. For explanation, in the present embodiment, eight turbine blades 111 are provided, and turbine blade numbers B1 to B8 are assigned counterclockwise.

  Returning to FIG. 1, the rotary machine vibration measuring apparatus 1 measures the vibration of the turbine blade 111 in a non-contact manner. The rotating machine vibration measuring device 1 includes a rotation speed sensor 2, a non-contact sensor (first sensor) 3, a contact sensor (second sensor) 4, and a calculation unit 10. Here, the vibration of the turbine blade 111 means that when the turbine shaft 110 rotates, the relative position of the turbine blade 111 to the turbine shaft 110 is displaced from the relative position of the turbine blade 111 to the turbine shaft 110 when the turbine shaft 110 is stopped. That is.

  The rotation speed sensor 2 detects the rotation speed of the turbine shaft 110. More specifically, the rotation speed sensor 2 detects the rotation speed of the turbine shaft 110 by detecting the reference position K of the turbine shaft 110. When the rotation speed sensor 2 detects the reference position K, the rotation speed sensor 2 outputs the detection signal to the calculation unit 10 as a reference signal. As shown in FIG. 4, the reference signal output from the rotation speed sensor 2 is pulsed. FIG. 4 is a schematic diagram illustrating a detection signal detected by a non-contact sensor of the rotary machine vibration measuring device according to the first embodiment. The interval between the reference signals is a cycle of one rotation of the turbine shaft 110.

  As shown in FIGS. 2 and 3, the non-contact sensor 3 is disposed at a first predetermined position (BTT measurement position) of the casing 120. The first predetermined position is an inner peripheral surface of the casing 120 and is a position facing the turbine blade 111. The non-contact sensor 3 detects passage of the turbine blade 111 in a non-contact manner. The non-contact sensor 3 detects the passage of the turbine blade 111 in a non-contact manner when the turbine shaft 110 rotates. More specifically, when the non-contact sensor 3 detects the passage of the turbine blade 111, the non-contact sensor 3 outputs a pulse-shaped detection signal to the arithmetic unit 10 as a blade passage signal. As shown in FIG. 4, the non-contact sensor 3 outputs a blade passage signal every time the turbine blade 111 passes. The blade passing signals are output at regular intervals as indicated by a solid line in the reference state where the turbine blade 111 is not vibrating. In the vibration state in which the turbine blade 111 is oscillating, the blade passage signal fluctuates in the interval as shown by the broken line. The non-contact sensor 3 is, for example, an optical sensor, a capacitance sensor, or an overcurrent sensor. In the present embodiment, 16 non-contact sensors 3 are provided, and sensor numbers S1 to S16 are assigned clockwise.

  The contact sensor 4 is disposed at a second predetermined position (vibration measurement position) of the casing 120 and detects vibration at the second predetermined position of the casing 120. The second predetermined position may be a position where the casing 120 vibrates, and preferably a position where the casing 120 vibrates larger than other positions is suitable. The contact sensor 4 is, for example, a strain gauge or an acceleration sensor. The contact sensor 4 is a representative point of the casing 120 and may be disposed at a position where it can be disposed. One or more contact sensors 4 may be arranged. As the number of contact sensors 4 increases, the vibration calculation unit 11 can obtain a more accurate result. The contact sensor 4 outputs the detected strain and acceleration to the calculation unit 10.

  The arithmetic unit 10 includes a memory and a CPU (Central Processing Unit). The arithmetic unit 10 may be realized by dedicated hardware, or may be realized by loading a program for realizing the function of the arithmetic unit 10 into a memory and executing the program. Good. As shown in FIG. 5, the calculation unit 10 includes a vibration calculation unit 11, a comparison unit 12, a gain setting unit 13, a first rotary body vibration calculation unit 14, a second rotary body vibration calculation unit 15, and an external force. And an input unit 16. FIG. 5 is a schematic diagram illustrating an example of the configuration of the rotating machine vibration measuring device according to the first embodiment.

  The vibration calculation unit 11 calculates the vibration of the casing 120 using a vibration model of the casing 120. The vibration model of the casing 120 is obtained by solving the equation of motion for the casing 120 based on the design data of the casing 120, for example, measurement data of the casing 120 and input data including external force acting on the turbine 100, and the vibration of the casing 120 is calculated. calculate. From the vibration of the casing 120 calculated in this way, vibration at a desired position of the casing 120 can be acquired. That is, the vibration calculation unit 11 is based on, for example, measurement data of the casing 120 or input data including external force acting on the turbine 100 at the first predetermined position or the second predetermined position of the casing 120 during operation with the input data. Vibration can be calculated. The vibration calculating unit 11 outputs the calculated vibration at the first predetermined position of the casing 120 to the second rotating body vibration calculating unit 15. The vibration calculation unit 11 outputs the calculated vibration at the second predetermined position of the casing 120 to the comparison unit 12.

  The comparison unit 12 compares the vibration at the second predetermined position of the casing 120 calculated by the vibration calculation unit 11 with the vibration at the second predetermined position of the casing 120 detected by the contact sensor 4. In other words, the comparison unit 12 compares the vibration at the arrangement position of the contact sensor 4 of the casing 120 calculated by the vibration calculation unit 11 with the vibration at the arrangement position of the contact sensor 4 of the casing 120 detected by the contact sensor 4. To do. The comparison unit 12 outputs the comparison result to the gain setting unit 13.

  The gain setting unit 13 compares the vibration at the second predetermined position of the casing 120 calculated by the vibration calculation unit 11 compared with the comparison unit 12 (the estimated value of vibration based on the vibration model) and the casing 120 detected by the contact sensor 4. The gain of the state quantity of the vibration model used in the vibration calculation unit 11 is set so that the difference (error) from the vibration at the second predetermined position (measured value of vibration) becomes small. The gain setting unit 13 feeds back the set gain to the vibration calculation unit 11. The processing of the vibration calculation unit 11, the comparison unit 12, and the gain setting unit 13 is repeated, and the vibration of the casing 120 calculated by the vibration calculation unit 11 converges to an actual measurement value.

  The first rotor vibration calculation unit 14 is based on a time difference ΔT between the passage time when the turbine blade 111 is detected by the non-contact sensor 3 and the passage time of the turbine blade 111 in the reference state stored in advance in the storage unit. The vibration of the turbine blade 111 is calculated. In the present embodiment, the first rotating body vibration calculation unit 14 measures the time of the blade passage signal, which is the passage time when the turbine blade 111 is detected by the non-contact sensor 3 in the vibration state, with the time counter, Based on the time difference ΔT from the passage time, the vibration of the turbine blade 111 is calculated. As a method for calculating the vibration of the turbine blade 111 based on the time difference ΔT between the vibration state and the reference state, for example, a known decimal point method or a multipoint method including a single point method may be used. The one-point method is a method in which one non-contact sensor 3 is arranged in the casing 120 and the time difference during which the turbine blade 111 passes through the non-contact sensor 3 is measured to reproduce the vibration amplitude of the turbine blade 111. The multipoint method is a method in which a large number of non-contact sensors 3 are arranged in the casing 120, and the time when the turbine blades 111 pass through the individual non-contact sensors 3 is measured to reproduce the vibration waveform of the turbine blades 111. . When the turbine blade 111 is not vibrating, the time difference ΔT calculated by the time difference calculation unit 6 is zero.

  The second rotating body vibration calculating unit 15 is a displacement ΔX caused by vibration at the first predetermined position of the casing 120 calculated by the vibration calculating unit 11 from the vibration waveform of the turbine blade 111 calculated by the first rotating body vibration calculating unit 14. And the vibration of the turbine blade 111 is calculated. In other words, the second rotating body vibration calculating unit 15 uses the vibration at the BTT measurement position of the casing 120 calculated by the vibration calculating unit 11 from the vibration waveform of the turbine blade 111 calculated by the first rotating body vibration calculating unit 14. The displacement ΔX of the turbine blade 111 is removed, and the vibration of the turbine blade 111 is calculated.

Here, using the time difference ΔT of the passage time and the peripheral speed V _B of the turbine blade tip, the vibration amplitude X _B of the turbine blade 111 is calculated by the following equation (1).
X _B = ΔT × V _B (1)

Second rotating body vibration calculation unit 15 subtracts the displacement ΔX from the vibration amplitude X _B, calculates the vibration of the actual turbine blades 111.

  The external force input unit 16 can input an external force acting on the turbine 100 including torque fluctuation. When an external force is input, the external force input unit 16 outputs the input external force to the vibration calculation unit 11. The external force may not be input.

  Next, a rotating machine vibration measuring method using the rotating machine vibration measuring apparatus 1 having the above configuration will be described. The rotating machine vibration measuring method according to the present embodiment includes a first vibration detecting step, a second vibration detecting step, a vibration calculating step, a comparing step, a gain setting step, a first rotating body vibration calculating step, A two-rotor vibration calculation step.

  First, the rotary machine vibration measuring device 1 causes the first vibration detection step to be executed. More specifically, the rotating machine vibration measuring device 1 uses the non-contact sensor 3 to detect passage of the turbine blade 111 in a non-contact manner. The rotating machine vibration measuring device 1 causes the calculation unit 10 to output a blade passage signal of the turbine blade 111 detected by the non-contact sensor 3.

  The rotary machine vibration measuring device 1 causes the second vibration detection step to be executed together with the first vibration detection step. More specifically, the rotating machine vibration measuring device 1 detects the vibration at the second predetermined position of the casing 120 by the contact sensor 4 disposed at the second predetermined position of the casing 120. The rotating machine vibration measuring device 1 causes the calculation unit 10 to output the vibration at the second predetermined position of the casing 120 detected by the contact sensor 4.

  The rotating machine vibration measuring device 1 executes a vibration calculating step. More specifically, in the rotary machine vibration measuring apparatus 1, the vibration calculation unit 11 calculates the vibration of the casing 120 based on the vibration model of the casing 120.

  The rotating machine vibration measuring device 1 executes a comparison process. More specifically, in the rotary machine vibration measuring device 1, the comparison unit 12 uses the vibration at the second predetermined position of the casing 120 calculated by the vibration calculation unit 11 and the second predetermined position of the casing 120 detected by the contact sensor 4. Compare with vibration at.

  The rotating machine vibration measuring device 1 executes a gain setting process. More specifically, in the rotary machine vibration measuring device 1, the gain setting unit 13 detects the vibration at the second predetermined position of the casing 120 calculated by the vibration calculating unit 11 and detected by the contact sensor 4. The gain of the state quantity of the vibration model used in the vibration calculation unit 11 is set so that the difference from the vibration at the second predetermined position of the casing 120 becomes small. In the rotating machine vibration measuring apparatus 1, the gain setting unit 13 feeds back the set gain to the vibration calculating unit 11. The vibration calculation process, the comparison process, and the gain setting process are repeated, and the vibration of the casing 120 calculated in the vibration calculation process converges to an actual measurement value.

  The rotating machine vibration measuring device 1 causes the first rotating body vibration calculating step to be executed. More specifically, in the rotary machine vibration measuring apparatus 1, the time difference between the passage time when the turbine blade 111 is detected by the non-contact sensor 3 in the first rotor vibration calculation unit 14 and the passage time of the turbine blade 111 in the reference state. Based on the above, the vibration of the turbine blade 111 is calculated.

  The rotating machine vibration measuring device 1 causes the second rotating body vibration calculating step to be executed. More specifically, the rotary machine vibration measuring device 1 is calculated by the vibration calculating unit 11 from the vibration waveform of the turbine blade 111 calculated by the first rotating body vibration calculating unit 14 by the second rotating body vibration calculating unit 15. The displacement ΔX of the turbine blade 111 due to the vibration at the first predetermined position of the casing 120 is removed, and the vibration of the turbine blade 111 is calculated.

As described above, according to the present embodiment, when calculating the vibration amplitude X _B of the turbine blade 111, it subtracts the displacement ΔX of the turbine blade 111 due to vibration at the BTT measurement position of the casing 120. Thereby, this embodiment can remove the measurement error resulting from the vibration of the non-contact sensor 3, and can measure the vibration of the turbine blade 111 with high accuracy. For this reason, in the present embodiment, even if the difference between the vibration amplitude of the turbine blade 111 and the vibration amplitude of the non-contact sensor 3 is small and the influence of the vibration of the non-contact sensor 3 cannot be ignored, the turbine blade 111 Can be measured with high accuracy. For this reason, this embodiment is suitable also for vibration measurement of the turbine blade 111 of a gas turbine with high rigidity and small vibration amplitude, for example.

In contrast, conventionally, the displacement ΔX due to vibration of the non-contact sensor 3 has been calculated include the oscillation amplitude X _B of the turbine blade 111. For this reason, the vibration amplitude of the turbine blade 111 is calculated to be larger than actual, and the calculated vibration of the turbine blade 111 includes a measurement error.

  According to the present embodiment, the contact sensor 4 may be disposed at a representative point of the casing 120, so that the number of contact sensors 4 disposed in the casing 120 can be suppressed. For this reason, this embodiment is suitable also for vibration measurement of the turbine blade 111 of the rotating machine in operation, for example.

[Second Embodiment]
Next, an outline of the rotating machine vibration measuring apparatus according to the present embodiment will be described with reference to FIGS. FIG. 6 is a schematic diagram illustrating an example of the configuration of the rotating machine vibration measuring device according to the second embodiment. In the present embodiment, parts that are different from the first embodiment will be described in order to avoid duplicate descriptions, and parts that have the same configuration as the first embodiment will be given the same reference numerals or corresponding reference numerals. To do.

  As shown in FIG. 6, the rotating machine vibration measuring device 1 </ b> A measures the vibration of the turbine blade 111 of the turbine 100 connected to the generator 130 and the turbine 150 in a non-contact manner. The rotating machine vibration measuring device 1A includes a rotation speed sensor 2, a non-contact sensor 3, a torsional vibration sensor 4A1 to a torsional vibration sensor 4A3, and an arithmetic unit 10A.

  As shown in FIG. 7, the rotating machine vibration measuring device 1 </ b> A calculates the vibration of the turbine blade 111 by removing the influence of torsional vibration generated in the turbine shaft 110. FIG. 7 is a schematic diagram showing a vibration waveform obtained by the rotary machine vibration measuring apparatus according to the second embodiment. The turbine shaft 110 generates, for example, a torsional vibration having a vibration mode (1) having a natural frequency F1 and a vibration mode (2) having a natural frequency F2. In this case, at the BTT measurement position of the casing 120, it is difficult to measure the torsional vibration of the turbine shaft 110 due to the structure of the turbine 100. In the example shown in FIG. 7, the torsional vibration is measured at the torsional vibration measuring position (1) on the inlet side of the generator shaft (rotating shaft) 140 and the torsional vibration measuring position (2) on the outlet side of the turbine shaft (rotating shaft) 160. measure. In the vibration mode (1), the torsional fluctuation angle at the torsional vibration measurement position (1) is θ1, and the torsional fluctuation angle at the torsional vibration measurement position (2) is θ2. In the vibration mode (2), the torsional fluctuation angle at the torsional vibration measurement position (1) is θ3, and the torsional fluctuation angle at the torsional vibration measurement position (2) is θ4. The rotating machine vibration measuring device 1A, for example, based on the torsional vibration response measured at the torsional vibration measurement position (1) and the torsional vibration response measured at the torsional vibration measurement position (2), Estimate vibration response. Then, the vibration of the turbine blade 111 is accurately calculated by removing the torsional vibration response as a measurement error.

Returning to FIG. 6, the torsional vibration sensor 4A1 to the torsional vibration sensor 4A3 are arranged on the rotation shaft and detect torsional vibration at the second predetermined position (torsional vibration measurement position) of the rotation shaft. Here, the rotating shaft includes a turbine shaft 110, a generator shaft 140 connected to the turbine shaft 110, and another turbine shaft 160. In the present embodiment, the torsional vibration sensor 4A1 is disposed on the inlet side of the generator shaft 140 at a position where the torsional vibration of the generator shaft 140 is measured. The torsional vibration sensor 4A2 is disposed at a position where the torsional vibration of the turbine shaft 160 is measured on the inlet side of the turbine shaft 160 of the turbine 150 following the turbine 100 where the non-contact sensor 3 is disposed. Torsional vibration sensor 4 </ b> A <b> 3 is arranged at a position for measuring the torsional vibration of turbine shaft 160 on the outlet side of turbine shaft 160. The torsional vibration sensor 4A1 to the torsional vibration sensor 4A3 are, for example, a strain gauge or an acceleration sensor. Torsional vibration sensor 4A1 to torsional vibration sensor 4A3 outputs the detected strain and acceleration to arithmetic unit 10A. More particularly, the torsional vibration sensor 4A1~ torsional vibration sensor 4A3 calculates the torsional vibration analysis system 4B1~ torsional vibration analysis system variations angle theta ₁ ~ torsional fluctuation angle theta ₃ torsional 4B3, and outputs to the operation unit 10A.

  The calculation unit 10A includes a vibration calculation unit 11A, a comparison unit 12A1 to a comparison unit 12A3, a gain setting unit 13A1 to a gain setting unit 13A3, a first rotating body vibration calculating unit 14, and a second rotating body vibration calculating unit 15A. And an external force input unit 16.

  The vibration calculation unit 11A performs torsional vibration including the turbine shaft 110, the generator shaft 140, and the turbine shaft 160 based on a vibration model of torsional vibration including the turbine blade 111, the turbine shaft 110, the generator shaft 140, and the turbine shaft 160. calculate. The vibration calculation unit 11A outputs the calculated torsional vibrations of the turbine shaft 110, the generator shaft 140, and the turbine shaft 160 to the comparison unit 12A and the second rotating body vibration calculation unit 15A. The torsional vibration model requires time for calculation when there are many degrees of freedom. For this reason, it is preferable that the vibration model of torsional vibration is reduced to the mode dimension related to the torsional vibration mode that affects the estimation of torsional vibration at the BTT measurement position of the non-contact sensor 3.

  The comparison unit 12A1 to the comparison unit 12A3 include the torsional vibration at the second predetermined position of the generator shaft 140 or the turbine shaft 160 calculated by the vibration calculation unit 11A and the generator shaft 140 detected by the torsional vibration sensor 4A1 to the torsional vibration sensor 4A3. Alternatively, the torsional vibration at the second predetermined position of the turbine shaft 160 is compared. The comparison unit 12A outputs the comparison result to the gain setting unit 13A. More specifically, the comparison unit 12A1 calculates the torsional vibration at the position where the torsional vibration sensor 4A1 of the generator shaft 140 calculated by the vibration calculation unit 11A and the torsional vibration sensor 4A1 of the generator shaft 140 detected by the torsional vibration sensor 4A1. The torsional vibration at the arrangement position is compared. The comparison unit 12A1 outputs the comparison result to the gain setting unit 13A1. The comparison unit 12A2 includes the torsional vibration at the position where the torsional vibration sensor 4A2 of the turbine shaft 160 calculated by the vibration calculation unit 11A and the torsion at the position where the torsional vibration sensor 4A2 of the turbine shaft 160 detected by the torsional vibration sensor 4A2. Compare with vibration. Comparison unit 12A2 outputs the comparison result to gain setting unit 13A2. The comparison unit 12A3 includes the torsional vibration at the arrangement position of the torsional vibration sensor 4A3 of the turbine shaft 160 calculated by the vibration calculation unit 11A and the torsion at the arrangement position of the torsional vibration sensor 4A3 of the turbine shaft 160 detected by the torsional vibration sensor 4A3. Compare with vibration. The comparison unit 12A3 outputs the comparison result to the gain setting unit 13A3.

  The gain setting unit 13A1 to the gain setting unit 13A3 are torsional vibrations (torsion by a vibration model) at the second predetermined position of the generator shaft 140 or the turbine shaft 160 calculated by the vibration calculation unit 11A, compared by the comparison units 12A1 to 12A3. The difference (error) between the estimated value of vibration) and the torsional vibration (actually measured value of vibration) at the second predetermined position of the generator shaft 140 or the turbine shaft 160 detected by the torsional vibration sensor 4A1 to the torsional vibration sensor 4A3 becomes small. As described above, the gain of the state quantity of the vibration model used in the vibration calculation unit 11A is set. The gain setting unit 13A1 to the gain setting unit 13A3 feed back the set gain to the vibration calculation unit 11A. More specifically, the gain setting unit 13A1 compares the torsional vibration at the arrangement position of the torsional vibration sensor 4A1 of the generator shaft 140 calculated by the vibration calculating unit 11A and the power generation detected by the torsional vibration sensor 4A1 compared by the comparison unit 12A1. The gain of the state quantity of the vibration model used in the vibration calculation unit 11A is set so that the difference from the torsional vibration at the arrangement position of the torsional vibration sensor 4A1 on the axis 140 becomes small. The gain setting unit 13A2 compares the torsional vibration at the arrangement position of the torsional vibration sensor 4A2 of the turbine shaft 160 calculated by the vibration calculating unit 11A and the torsion of the turbine shaft 160 detected by the torsional vibration sensor 4A2 compared by the comparison unit 12A2. The gain of the state quantity of the vibration model used in the vibration calculation unit 11A is set so that the difference from the torsional vibration at the position where the vibration sensor 4A2 is arranged becomes small. The gain setting unit 13A3 compares the torsional vibration at the arrangement position of the torsional vibration sensor 4A3 of the turbine shaft 160 calculated by the vibration calculating unit 11A and the torsion of the turbine shaft 160 detected by the torsional vibration sensor 4A3 compared by the comparison unit 12A3. The gain of the state quantity of the vibration model used in the vibration calculation unit 11A is set so that the difference from the torsional vibration at the position where the vibration sensor 4A3 is disposed becomes small.

  The first rotor vibration calculation unit 14 calculates the vibration of the turbine blade 111. Here, the vibration of the turbine blade 111 calculated by the first rotor vibration calculation unit 14 will be described with reference to FIGS. 8 to 12.

  An example of the basic shape of the vibration waveform of the turbine blade 111 is shown in FIG. FIG. 8 is a schematic diagram showing a vibration waveform obtained by the rotary machine vibration measuring apparatus according to the second embodiment. FIG. 9 shows an example of a vibration waveform of the turbine blade 111 measured with the multipoint method in a state where the torsional vibration is not generated in the turbine shaft 110. FIG. 9 is a schematic diagram showing a vibration waveform obtained by the rotary machine vibration measuring apparatus according to the second embodiment. FIG. 10 shows an example of the vibration waveform of the turbine blade 111 in a state where torsional vibration is generated in the turbine shaft 110, which is measured by the multipoint method. FIG. 10 is a schematic diagram showing a vibration waveform obtained by the rotary machine vibration measuring apparatus according to the second embodiment. FIG. 11 shows an example of a vibration waveform of the turbine blade 111 measured with the one-point method in a state where the torsional vibration is not generated in the turbine shaft 110. FIG. 11 is a schematic diagram showing a vibration waveform obtained by the rotary machine vibration measuring apparatus according to the second embodiment. FIG. 12 shows an example of the vibration waveform of the turbine blade 111 in a state where torsional vibration is generated in the turbine shaft 110, which is measured by the one-point method. FIG. 12 is a schematic diagram showing a vibration waveform obtained by the rotary machine vibration measuring apparatus according to the second embodiment. Thus, in any method, in the state where the torsional vibration is not generated in the turbine shaft 110, the vibration amplitude of the turbine blade 111 calculated by the first rotor vibration calculation unit 14 and the actual turbine blade 111 are calculated. The vibration amplitude of the same. Further, in the state where the torsional vibration is generated in the turbine shaft 110, the vibration waveform of the turbine blade 111 is displaced to the turbine shaft 110 by the torsional vibration.

  The second rotating body vibration calculating unit 15A is a turbine based on torsional vibration at the BTT measurement position of the turbine shaft 110 calculated by the vibration calculating unit 11A from the vibration waveform of the turbine blade 111 calculated by the first rotating body vibration calculating unit 14. The displacement ΔX of the blade 111 is removed, and the vibration of the turbine blade 111 is calculated.

Here, using the time difference ΔT of the passage time and the peripheral speed V _B of the turbine blade tip, the vibration amplitude X _B of the turbine blade 111 is calculated by the above-described equation (1).

Further, the displacement ΔX of the turbine blade 111 due to torsional vibration at the BTT measurement position of the turbine shaft 110 is equal to the radial distance R from the center of the turbine shaft 110 at the tip of the turbine blade and the torsion of the turbine shaft 110 at the measurement position of the non-contact sensor 3. Using the vibration angular displacement θ, it is calculated by equation (2).
ΔX = R × θ (2)

Second rotating body vibration calculation unit 15A subtracts the ΔX from the vibration amplitude X _B, calculates the vibration of the actual turbine blades 111.

  Next, a rotating machine vibration measuring method using the rotating machine vibration measuring apparatus 1A having the above configuration will be described. The rotating machine vibration measuring method according to the present embodiment includes a first vibration detecting step, a second vibration detecting step, a vibration calculating step, a comparing step, a gain setting step, a first rotating body vibration calculating step, A two-rotor vibration calculation step. The first vibration detection step and the first rotating body vibration calculation step are the same processes as in the first embodiment.

  The rotary machine vibration measuring device 1A causes the second vibration detection step to be executed together with the first vibration detection step. More specifically, the rotary machine vibration measuring device 1A includes a torsional vibration sensor 4A1 to a torsional vibration sensor 4A3 disposed at a second predetermined position of the generator shaft 140 or the turbine shaft 160, and a second predetermined of the generator shaft 140 or the turbine shaft 160. The position torsional vibration is detected. The rotating machine vibration measuring apparatus 1A causes the calculation unit 10A to output torsional vibrations at the second predetermined position of the generator shaft 140 or the turbine shaft 160 detected by the torsional vibration sensor 4A1 to the torsional vibration sensor 4A3.

  The rotating machine vibration measuring device 1A executes a vibration calculating step. More specifically, in the rotary machine vibration measuring apparatus 1A, the vibration calculating unit 11A is configured to generate power from the turbine shaft 110 and the power generation based on a vibration model of torsional vibration including the turbine blade 111, the turbine shaft 110, the generator shaft 140, and the turbine shaft 160. Torsional vibration including the machine shaft 140 and the turbine shaft 160 is calculated.

  The rotating machine vibration measuring device 1A executes the comparison process. More specifically, in the rotating machine vibration measuring device 1A, the comparison unit 12A1 to the comparison unit 12A3 are arranged at positions where the torsional vibration sensors 4A1 to 4A3 of the generator shaft 140 and the turbine shaft 160 calculated by the vibration calculation unit 11A are arranged. The torsional vibration is compared with the torsional vibration at the position where the torsional vibration sensor 4A1 and the torsional vibration sensor 4A3 of the turbine shaft 160 are detected by the torsional vibration sensor 4A1 torsional vibration sensor 4A3.

  The rotating machine vibration measuring device 1A executes a gain setting step. More specifically, in the rotary machine vibration measuring apparatus 1A, the gain setting unit 13A1 to the gain setting unit 13A3 compares the generator shaft 140 and the turbine shaft 160 calculated by the vibration calculating unit 11A compared by the comparison unit 12A1 to the comparison unit 12A3. Torsional vibrations at the arrangement positions of torsional vibration sensor 4A1 torsional vibration sensor 4A3, and arrangement positions of torsional vibration sensor 4A1 and torsional vibration sensor 4A3 of generator shaft 140 and turbine shaft 160 detected by torsional vibration sensor 4A1 torsional vibration sensor 4A3 The gain of the state quantity of the vibration model used in the vibration calculation unit 11A is set so that the difference from the torsional vibration at is small.

  The rotating machine vibration measuring device 1A executes a second rotating body vibration calculating step. More specifically, in the rotating machine vibration measuring device 1A, the second rotating body vibration calculating unit 15A is calculated based on the time difference between the passing time between the vibration state calculated by the first rotating body vibration calculating unit 14 and the reference state. From the vibration waveform of the turbine blade 111, the displacement ΔX of the turbine blade 111 due to torsional vibration at the BTT measurement position of the turbine shaft 110 calculated by the vibration calculation unit 11A is removed, and the vibration of the turbine blade 111 is calculated.

As described above, according to the present embodiment, when calculating the vibration amplitude X _B of the turbine blade 111, it subtracts the displacement ΔX by torsional vibration at the BTT measurement position of the turbine shaft 110. Thereby, this embodiment can remove the measurement error resulting from the torsional vibration of the turbine shaft 110, and can measure the vibration of the turbine blade 111 with high accuracy.

  In the above-described embodiment, the vibration model of the casing 120 and the vibration model of torsional vibration are used. However, in the same way, bending vibration models (shaking models) of vertical and horizontal axes may be used. . More specifically, the turbine generated by the shaft bending vibration at the BTT measurement position of the turbine shaft 110 calculated based on the shaft bending vibration model from the vibration waveform of the turbine blade 111 calculated by the first rotor vibration calculation unit 14. It is also possible to calculate the vibration of the turbine blade 111 by removing the displacement ΔX of the blade 111.

  Further, the vibration calculation unit may calculate the vibration of the turbine blade 111 by arbitrarily combining the vibration model of the casing 120, the vibration model of the torsional vibration, and the bending vibration model of the shaft described above.

  Now, the rotating machine vibration measuring device, the rotating machine vibration measuring method, and the program according to the present embodiment have been described so far, but may be implemented in various different forms other than the above-described embodiments.

  Each component of the calculation unit 10 of the illustrated rotary machine vibration measuring device 1 is functionally conceptual and may not necessarily be physically configured as illustrated. That is, the specific form of each component is not limited to that shown in the drawing, and all or a part of the component is functionally or physically distributed or arbitrarily distributed in arbitrary units according to the processing load or usage status of each component. You may integrate.

  The configuration of the calculation unit 10 of the rotary machine vibration measuring apparatus 1 is realized by, for example, a program loaded in a memory as software. The above embodiment has been described as a functional block realized by cooperation of these hardware or software. That is, these functional blocks can be realized in various forms by hardware only, software only, or a combination thereof.

DESCRIPTION OF SYMBOLS 1 Rotating mechanical vibration measuring device 2 Rotational speed sensor 3 Non-contact sensor (first sensor)
4 Contact sensor (second sensor)
DESCRIPTION OF SYMBOLS 10 Calculation part 11 Vibration calculation part 12 Comparison part 13 Gain setting part 14 1st rotary body vibration calculation part 15 2nd rotary body vibration calculation part 16 External force input part 110 Turbine shaft (rotary shaft)
111 Turbine blade (rotary body)
120 casing (stationary body)

Claims (6)

A first sensor that is disposed at a first predetermined position of a stationary body facing an outer periphery of a rotating body disposed in a rotating machine, and detects the passage of the rotating body in a non-contact manner;
A second sensor that is disposed at a second predetermined position of the rotating shaft of the stationary body or the rotating body and detects vibration at the second predetermined position of the stationary body or the rotating shaft;
Based on a vibration model of the stationary body or the rotating shaft, a vibration calculating unit that calculates vibration of the stationary body or the rotating shaft;
The vibration at the second predetermined position of the stationary body or the rotating shaft calculated by the vibration calculating unit and the vibration at the second predetermined position of the stationary body or the rotating shaft detected by the second sensor. A comparison section to compare;
The stationary body or the rotating shaft at the second predetermined position calculated by the vibration calculating unit, compared with the comparison unit, and the stationary body or the rotating shaft detected by the second sensor. A gain setting unit that sets a gain of a state quantity of the vibration model used in the vibration calculation unit so that a difference between vibrations at two predetermined positions is small;
The first rotating body that calculates the vibration of the rotating body based on the time difference between the passing time when the rotating body is detected by the first sensor and the passing time of the rotating body in the reference state stored in the storage unit A vibration calculator;
From the vibration waveform of the rotating body calculated by the first rotating body vibration calculating unit, the displacement due to vibration at the first predetermined position of the stationary body or the rotating shaft calculated by the vibration calculating unit is removed, A rotating machine vibration measuring apparatus comprising: a second rotating body vibration calculating unit that calculates vibration of the rotating body. The second sensor is disposed on the stationary body, detects vibration of the stationary body at the second predetermined position,
The vibration calculation unit calculates the vibration of the stationary body based on the vibration model of the stationary body,
The comparison unit compares the vibration at the second predetermined position of the stationary body calculated by the vibration calculation unit with the vibration at the second predetermined position of the stationary body detected by the second sensor;
The gain setting unit is configured to compare the vibration at the second predetermined position of the stationary body calculated by the vibration calculating unit and the second predetermined of the stationary body detected by the second sensor, compared with the comparison unit. Set the gain of the state quantity of the vibration model used in the vibration calculation unit so that the difference from the vibration at the position is small,
The second rotating body vibration calculating unit is configured to generate a vibration at the first predetermined position of the stationary body calculated by the vibration calculating unit from a vibration waveform of the rotating body calculated by the first rotating body vibration calculating unit. The rotary machine vibration measuring apparatus according to claim 1, wherein the vibration of the rotating body is calculated by removing the displacement of the first sensor. The second sensor is disposed on the rotating shaft, detects torsional vibration at the second predetermined position of the rotating shaft,
The vibration calculating unit calculates a torsional vibration including the rotating body and the rotating shaft based on a vibration model of a torsional vibration including the rotating body and the rotating shaft,
The comparison unit compares the torsional vibration at the second predetermined position of the rotating shaft calculated by the vibration calculating unit with the torsional vibration at the second predetermined position of the rotating shaft detected by the second sensor. And
The gain setting unit compares the torsional vibration at the second predetermined position of the rotating shaft calculated by the vibration calculating unit and the second of the rotating shaft detected by the second sensor, compared by the comparing unit. Set the gain of the state quantity of the vibration model used in the vibration calculation unit so that the difference with the torsional vibration at a predetermined position becomes small,
The second rotating body vibration calculating unit is configured to obtain a torsional vibration at the first predetermined position of the rotating body calculated by the vibration calculating unit from a vibration waveform of the rotating body calculated by the first rotating body vibration calculating unit. The rotary machine vibration measuring apparatus according to claim 1, wherein the vibration of the rotating body is calculated by removing the displacement of the rotating body due to the rotation. An external force input unit for inputting an external force acting on the rotating body including torque fluctuation,
4. The rotating machine vibration measuring device according to claim 1, wherein the vibration calculating unit further calculates vibration of the stationary body or the rotating shaft based on the external force. 5. A first vibration detecting step of detecting the passage of the rotating body in a non-contact manner with a first sensor arranged at a first predetermined position of a stationary body facing the outer periphery of the rotating body arranged in the rotating machine;
A second vibration detecting step of detecting vibration at the second predetermined position of the stationary body or the rotating shaft with a second sensor disposed at a second predetermined position of the rotating shaft of the stationary body or the rotating body;
Based on a vibration model of the stationary body or the rotating shaft, a vibration calculating step of calculating vibration of the stationary body or the rotating shaft;
The vibration at the second predetermined position of the stationary body or the rotation shaft calculated in the vibration calculation step, and the vibration at the second predetermined position of the stationary body or the rotation shaft detected in the second vibration detection step. A comparison process for comparing
The vibration at the second predetermined position of the stationary body or the rotating shaft calculated at the vibration calculating step and the stationary body or the rotating shaft detected at the second vibration detecting step compared at the comparison step. A gain setting step of setting a gain of a state quantity of the vibration model used in the vibration calculation step so that a difference from the vibration at the second predetermined position becomes small;
First calculating the vibration of the rotating body based on the time difference between the passing time when the rotating body is detected in the first vibration detecting step and the passing time of the rotating body in the reference state stored in the storage unit. A rotating body vibration calculating step;
From the vibration waveform of the rotating body calculated in the first rotating body vibration calculating step, the displacement due to vibration at the first predetermined position of the stationary body or the rotating shaft calculated in the vibration calculating step is removed, And a second rotating body vibration calculating step of calculating the vibration of the rotating body. A first vibration detecting step of detecting the passage of the rotating body in a non-contact manner with a first sensor arranged at a first predetermined position of a stationary body facing the outer periphery of the rotating body arranged in the rotating machine;
A second vibration detecting step of detecting vibration at the second predetermined position of the stationary body or the rotating shaft with a second sensor disposed at a second predetermined position of the rotating shaft of the stationary body or the rotating body;
Based on a vibration model of the stationary body or the rotating shaft, a vibration calculating step of calculating vibration of the stationary body or the rotating shaft;
The vibration at the second predetermined position of the stationary body or the rotation shaft calculated in the vibration calculation step, and the vibration at the second predetermined position of the stationary body or the rotation shaft detected in the second vibration detection step. A comparison process for comparing
The vibration at the second predetermined position of the stationary body or the rotating shaft calculated at the vibration calculating step and the stationary body or the rotating shaft detected at the second vibration detecting step compared at the comparison step. A gain setting step of setting a gain of a state quantity of the vibration model used in the vibration calculation step so that a difference from the vibration at the second predetermined position becomes small;
First calculating the vibration of the rotating body based on the time difference between the passing time when the rotating body is detected in the first vibration detecting step and the passing time of the rotating body in the reference state stored in the storage unit. A rotating body vibration calculating step;
From the vibration waveform of the rotating body calculated in the first rotating body vibration calculating step, the displacement due to vibration at the first predetermined position of the stationary body or the rotating shaft calculated in the vibration calculating step is removed, A program for causing a computer to execute a second rotor vibration calculation step for calculating vibration of the rotor.

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