JP4243639B2 - Rotating body misalignment calculating method and misalignment calculating system - Google Patents

Description

  The present invention relates to a method for calculating misalignment of a rotating body and a misalignment calculation system.

  In general, when the rotating body is bent or misaligned, the rotating body becomes unbalanced, which causes shaft vibration during operation. If this shaft vibration becomes excessive, an abnormality occurs in the bearing portion and normal operation cannot be performed. Further, if this excessive vibration further progresses, it may lead to a shaft breakage accident. Accordingly, in order to prevent such an accident, it is important to keep the shaft bending or misalignment of the rotating body within an allowable value.

  In addition to the gas turbine rotor, the rotating body that is the subject of the present invention includes a rotor for a rotating machine such as a steam turbine rotor, a compressor rotor, a turbine rotor, various pump rotors, and various blower rotors. .

  A gas turbine rotor will be specifically described as an example. FIG. 11 shows a general structural diagram of a gas turbine rotor. The gas turbine rotor 1 includes a compressor rotor unit 10 and a turbine rotor unit 20 and an intermediate shaft 25 that connects the compressor rotor unit 10 and the turbine rotor unit 20. Both the compressor rotor unit 10 and the turbine rotor unit 20 are implanted with blades 11 radially on the outer periphery. It is composed of an ellipsoidal rotor disk 50. The gas turbine rotor 1 has an integrated structure in which these rotor disks 50 are stacked in the rotor axial direction and fastened with spindle bolts 30 and both ends are supported by bearings S1 and S2.

  When a shaft bend occurs in the gas turbine rotor 1 having such a configuration, it causes shaft vibration. Further, the gap between the tip of the moving blade 11 mounted on the outer periphery of the rotor disk 50 and the outer casing (not shown) is adjusted to be substantially constant in the circumferential direction. When the shaft vibration becomes large, the tip of the rotor blade and the casing may interfere with each other and operation may become impossible. Therefore, it is necessary to adjust at the time of assembling the rotor so that the amount of shaft bending falls within the allowable value, and when the shaft bending exceeds the allowable value, it is necessary to correct the shaft bending.

  The following procedure is used to correct shaft bending. In the configuration of the gas turbine rotor 1 shown in FIG. 11, misalignment data including a misalignment amount and a misalignment angle is calculated for each rotor disk 50, and an axial bending distribution of the gas turbine rotor 1 is calculated. An example of the axial bending distribution is shown in FIG. The horizontal axis represents the distance of the rotor from the bearing S1, and the vertical axis represents the misalignment amount of each rotor disk 50.

  One of the factors that cause the shaft bending is that the thickness of the rotor disk 50 is not uniform. Therefore, depending on how the rotor disks 50 are stacked, the amount of misalignment of the rotor disks 50 may exceed an allowable value. In such a case, the rotor disk 50 to be corrected is selected from the axial curve distribution, the contact surface of the rotor disk 50 is cut, and the contact surface angle (α) between the rotor disks 50 is adjusted to be small. The shaft bending of the gas turbine rotor 1 is corrected (FIG. 13).

  FIG. 13 shows a state in which the shaft bending of the gas turbine rotor 1 has occurred. The relationship among the rotor disk 50, the rotor disk contact surface 51, the contact surface angle (α) between adjacent rotor disks 50, the amount of misalignment of the rotor shaft center, and the amount of deflection in the radial direction of the rotor disk 50 is shown.

  The amount of runout in the radial direction of the rotor disk 50 is determined by selecting a plurality of measurement points at equal intervals in the circumferential direction while rotating the rotor on the outer surface 52 of each rotor disk 50 and reading the displacement meter at each measurement point. It is obtained by measuring the radial displacement at the measurement point. That is, using the measurement start point as a reference (for convenience, the displacement amount at the measurement start point is set to 0), the displacement amount in the rotor radial direction relative to the measurement start point at each measurement point is used as the shake amount at each measurement point. Various known sensors are applied as the displacement meter. For example, in addition to a contact sensor such as a dial gauge, a non-contact sensor such as a laser sensor, a capacitance sensor, or an ultrasonic sensor can be used.

Misalignment data is calculated from the measured value of the shake amount at each measurement point. As shown in FIG. 13, the radial shake amount of the gas turbine rotor 1 is indicated by the fluctuation range of the distance between the outer surface 52 of the rotor disk 50 and the rotor rotation center. Here, the rotor center of rotation, means a straight line connecting the center of the bearing S ₁ and the bearing S _2. The figure center O ₁ of the cross section of the rotor disk 50 to be measured is calculated from the measured value of the shake amount on the outer surface 52 of the rotor disk 50, and the deviation between the calculated figure center O ₁ and the rotor rotation center O ₂ is calculated. Misalignment. Quantitative display of the misalignment obtained in this way is misalignment data consisting of the misalignment amount and misalignment angle.

Patent Documents 1 and 2 disclose a general method for calculating misalignment of a rotating body. Also, a method such as a least square method is shown as a means for calculating misalignment.
JP 2001-91244 A Japanese Patent Laid-Open No. 5-187816

  In general, when inspecting misalignment of a rotating body, it is necessary to capture data measured by the inspector at the site online, feed back the measurement result to the inspector instantly, and remeasure as necessary. For this purpose, it is desirable to select a simple calculation method. However, since the methods shown in Patent Document 1 and Patent Document 2 require a huge amount of calculation, a simpler method is desired.

  In addition, the outer surface of the rotating body may be inspected with rust or scratches. When such an abnormal outer surface happens to be selected as a measurement point, it cannot be said that the displacement meter is measuring a normal outer surface, and the measured value must be excluded as an abnormal value.

However, in the least square method applied to the conventional misalignment calculation method shown in Patent Document 1 and Patent Document 2, although it is originally a highly accurate calculation method, when measurement including an abnormal value is performed, The amount of misalignment is calculated by taking the abnormal value as it is.
Therefore, there is a problem that the expected accuracy cannot be obtained due to the influence of the abnormal value, and it is difficult to exclude the abnormal value.
On the other hand, in order to reduce the influence of abnormal values, it is necessary to select as many measurement points as possible, and there is a problem that enormous calculation is required.

  The present invention has been made to solve such problems, and an object of the present invention is to provide a misalignment calculation method and misalignment calculation system that are simpler than conventional methods.

The first means is a method for calculating the misalignment of a rotating body, based on measured values measured by a displacement meter at at least four measurement points along the circumferential outer surface while rotating the rotating body. Deriving the radial displacement amount of the rotating body, selecting any three points from the radial displacement amount and the measurement angle of each measurement point at all measurement points, and determining one circle determined by these three points was calculated as calculated circle, it calculates the value of the radial located on the calculated circle at the same measured angle and the measuring point for all of the measurement points from the calculated circle as calculated circle value, the diameter and the calculated circle value The difference from the amount of displacement in the direction is calculated as an error amount for each measurement point, and the error amount is summed to derive a total error amount value, and the number of combinations of the three measurement points for all measurement points is calculated. Repeat to calculate the total error amount and obtain From the total error amount for all combinations, the calculation circle with the smallest error is selected as the most probable circle, and the deviation between the center of the most probable circle and the rotation center of the rotating body is selected as the most probable circle. It is calculated as misalignment data.

  The second means is characterized in that, in the first means, the most probable circular misalignment data is a misalignment amount and a misalignment angle.

  The third means is that in the first or second means, when the most probable circle error amount, which is the difference between the calculated circle value in the most probable circle and the radial displacement amount, exceeds a reference value, the most probable The measurement value at the measurement point corresponding to the circle error amount is recognized as an abnormal value.

  When the most probable circle error amount exceeds a reference value in the third means, the fourth means remeasures the measurement value recognized as the abnormal value to obtain a remeasurement value, and the measurement value Is replaced with the remeasurement value.

  A fifth means is characterized in that, in any one of the first to fourth means, the rotating body is a gas turbine rotor.

The rotating means misalignment calculation system of the sixth means includes an input unit for setting at least four measurement points during one rotation of the rotating body, and at least 4 along the outer surface in the circumferential direction of the rotating body. A deflection amount detection unit for deriving a radial displacement amount of the rotating body based on a measurement value measured by a displacement meter at more than one measurement point, and the radial displacement amount derived by the deflection amount detection unit And a storage unit that stores the measurement angle of the measurement point, and a calculation unit that calculates the most probable circle misalignment data of the rotating body based on the data stored in the storage unit, the calculation unit including the storage unit Select any three points from the radial displacement amount and the measurement angle at all the measurement points stored in the section, calculate one circle determined by these three points as a calculation circle, and calculate from the calculation circle the same total and the measurement point for all of the measurement points Calculates the value of the radial in an angle on the calculated circle as calculated circle value, the difference between the displacement amount in the radial direction with the calculated circle value is calculated as the amount of error for each measurement point, the sum of said error amount Then, the error amount total value is derived, the calculation is repeated for the number of combinations of three measurement points for all measurement points, and the respective error amount total values are calculated, and the total error amount for all the obtained combinations is obtained. The calculation circle that minimizes the value from the values is selected as the most probable circle, and the deviation between the center of the most probable circle and the rotation center of the rotating body is calculated as the most probable circle misalignment data. Features.

  Seventh means, in the sixth means, when the calculation unit has a most probable circle error amount that is a difference between the calculated circle value in the most probable circle and the radial displacement amount exceeding a reference value, It comprises an abnormal value determination means for recognizing a measurement value at a measurement point corresponding to the most probable circle error amount as an abnormal value.

  According to an eighth means, in the seventh means, when the most probable circle error amount exceeds a reference value, the calculation unit calls the remeasured value acquired by the shake amount detection unit from the storage unit, A measurement value update means for replacing the measurement value with the remeasurement value is provided.

  According to the configuration of the invention relating to claim 1, since the most probable circular misalignment data can be calculated by a simple method, maintenance work such as disassembly and assembly of the rotating body is facilitated.

  According to the configuration of the invention according to claim 2, since the most probable circular misalignment data can be specified by the misalignment angle and the misalignment amount, it is easy to judge the validity of the data.

  According to the configuration of the invention relating to claim 3, when the most probable circle error amount exceeds the reference value, it is possible to easily determine whether or not the measured value is an abnormal value, so that maintenance work is easy.

  According to the configuration of the invention according to claim 4, when the most probable circle error amount exceeds the reference value, remeasurement can be immediately performed and replaced with the remeasurement value, so that the abnormal value can be reliably excluded and measured. Increased work reliability.

  According to the configuration of the invention relating to claim 5, since a simple and highly reliable measurement method can be adopted, the reliability of the regular inspection work of the gas turbine is improved.

  According to the configuration of the invention relating to claim 6, a simple and reliable center misalignment calculation system for a rotating body can be provided.

  According to the configuration of the invention relating to claim 7, since it is easy to determine whether or not the measured value is an abnormal value, a system with easy maintenance can be provided.

  According to the configuration of the invention according to claim 8, since the abnormal value of the measured value can be immediately eliminated, a system capable of providing quick and reliable maintenance can be realized.

  Embodiments of the present invention will be described with reference to the drawings. However, these are merely examples of the embodiments, and each invention described in the claims is limited to these embodiments. It is not a thing. The constituent elements of this embodiment include those that can be easily replaced by those skilled in the art or those that are substantially the same.

  The basic concept of the present invention will be described below with respect to the method of calculating the misalignment of the rotating body.

FIG. 1 shows a cross section of a cylindrical body that is a rotating body (gas turbine rotor), and shows a relationship between a measured value, a reference circle, and a calculation circle in the cross section. Along the circumferential direction of the rotary body, defines divided into a plurality (m pieces) to the measurement points X _{i (i} = 1~m) at equal intervals the outer surface of the rotating body, in Figure 1 the rotating body while one rotation in the process of the arrows, at each measurement point X _i, on the basis of the measurement value measured by the displacement meter 2 (distance to the outer surface of the rotating body from the installation position of the displacement gauge 2), the outer surface of the rotary body The amount of displacement a _i in the radial direction of the rotating body is derived.

Note that the measurement points X _i may be selected at equal intervals or not at equal intervals.
Further, a pitch angle (including the number of pulses of the tachometer 3) such that the number of measurement points m in one rotation of the rotating body is 4 or more is input, and each measurement point X _i (rotation angle θ) is based on the pitch angle. _i ) may be set at equal intervals. In this case, the angle of the last and the measurement point X _m as the first measurement point X ₁ in one rotation of the rotating body may be different from the above-mentioned pitch angle. Further, four or more measurement points X _i (rotation angle θ _i ) may be directly input and set. Further, the measurement point number m is inputted such that the measurement point number m in one rotation of the rotating body is 4 or more, and each measurement point X _i (i = 1 to m) is set based on the measurement point number m. May be.

The reference circle is not an element directly related to the configuration of the present invention, but is displayed for convenience as a circle whose graphic center coincides with the rotation center O _{2 of the} rotating body. When the rotating body is a rotor for a rotating machine, the reference circle is a perfect circle, and the center of the reference circle is the rotation center O _{2 of the} rotating body.

Calculated circle is determined from the shake amount of the measured value P _{i (measured} angle theta _i and radial displacement of a _i) at each measurement point X _i. If each measurement point X _i (and measurement angle θ _i ) is determined with respect to the number m of measurement points in the circumferential direction, and arbitrary three points are selected from the measurement values P _i at each measurement point X _i , the three points Only one circle can be determined. A circle determined by these three points is a calculated circle. Calculation circle, of the m measurement points X _i, is to be determined by a combination of the measurement points X _i of three arbitrary points, there is a combination of a total of _{(m C 3)} street. Here, ( _m C ₃ ) means the total number of combinations in which all three combinations are selected when arbitrary three points are selected for m measurement points X _i . Therefore, if n = ( _m C ₃ ), there are n calculation circles.

In the present invention, arbitrary three points are selected from all measurement points X _i (i = 1 to m), and one calculation circle is calculated from these three points. Next, for each measurement point X _i , the radial deviation between each measurement value P _j and the calculated circle, that is, the displacement amount a _{i in} each radial direction and the calculated circle value (the significance of the calculated circle value will be described later). The difference is calculated as an error amount Δ _{i, j} . An error amount total value ΔS _j is calculated from each error amount Δ _{i, j} . Next, calculation circles determined from other combinations of the three measurement points X _i (i = 1 to m) are sequentially calculated, and the error amount total value ΔS _j is similarly calculated for each calculation circle.

After calculating the total error amount value [Delta] S _j for all calculated circles, all total error amount value ΔS _{j (j} = 1~n) minimum total error amount value smallest things in ΔS _{j (j} = a) It was selected as the calculated circle corresponding to the minimum total error amount value [Delta] S _a and most probable circle. The most probable circle is regarded as displaying the figure closest to the cross section of the rotating body among all the calculated circles, and the center of the most probable circle is considered as the figure center. The deviation between the center of the most probable circle and the rotation center O ₂ is the misalignment (eccentric distance e). Which quantitatively show this misalignment state is the most probable circle misalignment data consisting of eccentricity e and misalignment angle theta _a. The calculation of the eccentricity e and the misalignment angle theta _a, the degree of misalignment of the rotating body can be easily determined, it is easy to validity of the judgment of the data.

For each calculated circle, one error amount Δ _{i, j} is calculated for each measurement point X _i , and one error amount total value ΔS _j can be calculated for each calculated circle. Further, one most probable circle is determined for all measurement points X _i (i = 1 to m).

The above method will be specifically described with reference to FIG. In FIG. 1, each measurement value at each measurement point X _i is represented by P _i (θ _i , a _i ). Here, the symbol “i” is selected from any one of “1” to “m”, and the measurement point X _i means the “i” -th measurement point from the measurement start point (X ₁ ). To do. Sign "theta _i" represents the measured angle in the clockwise direction around the measurement starting point of the measurement points X _i (X _1), symbol "a _i" is the amount of displacement of said radial at the measurement points X _i .

  From a combination of arbitrary three measurement points, one calculation circle can be determined by a method described later (Formula 4). Further, n calculation circles can be finally determined from a combination of arbitrary three points of all measurement points by the same method.

Next, the significance of the calculated circle value Q _{i, j} will be described with reference to FIG. The calculated circle value Q _{i, j} is a value on one calculated circle selected from arbitrary three points among all the measurement points X _i (i = 1 to _m ). Calculated circle value Q _{i, j} is the point corresponding to the measurement points X _i, i.e., have the same measured angle theta _i and the measurement point X _i, is a value calculated from the calculated circle. The calculated circle value Q _{i, j} is indicated by the sign “Q _{i, j} (θ _i , b _{i, j} )”. Here, as described above, the symbol “θ _i ” indicates the measurement angle in the clockwise direction from the measurement start point (X ₁ ) of the measurement point X _i , and the symbol “b _{i, j} ” indicates that the measurement angle is “ The calculated value on the calculated circle which is “θ _i ” is shown. The calculated circle value Q _{i, j} (θ _i , b _{i, j} ) can be calculated from the calculated circle and the measurement angle θ _i if the calculated circle is determined. In the case of m measurement points, since there are n calculation circles, the symbols “i” and “j” displayed below are any of “i” from “1” to “m”. The symbol “j” means a point selected from any one of “1” to “n”. That is, the symbol “i” indicates the rank number of the measurement point from the measurement start point (X ₁ ) for m measurement points, and the symbol “j” is targeted for n calculation circles. Indicates the rank number of the calculated circle.

The difference between each measured value P _i (θ _i , a _i ) and the corresponding calculated circle value Q _{i, j} (θ _i , b _{i, j} ) is expressed as an error amount Δ _{i, j at} each measurement point X _i . In this case, the error amount Δ _{i, j} is expressed by equation (1).
(Expression 1) Δ _{i, j} = [P _i (θ _i , a _i ) −Q _{i, j} (θ _i , b _{i, j} )] ²

In Equation 1 _, the difference between the measured value P _i and the calculated circle value Q _{i, j} is squared to eliminate the influence of the plus / minus sign of the difference value between the two, and the measured value includes an abnormal value. This is because the difference between the abnormal value and the normal value is further expanded in consideration of the case where the abnormal value is selected, and the abnormal value is easily selected.

Next, with respect to the target calculation circle, the error amount Δ _{i, j} is calculated by Equation 1 for all measurement points X _i (i = 1 to _m ).

Further, the error amounts Δ _{i, j} are summed for the target calculation circle. The error amount total value ΔS _j is expressed by Equation 2.
(Expression 2) ΔS _j = Σ (Δ _{i, j} )
For the target calculation circle, the total error amount ΔS _j is obtained by adding the error amounts Δ _{i, j} at each measurement point shown in Equation ₁ from the measurement point X ₁ to the measurement point X _m .

Next, another calculation circle is determined in the same manner from any other combination of three measurement points. Further, the error amount Δ _{i, j} and the error amount total value ΔS _j are calculated for each calculation circle using Equation 1 and Equation 2. Incidentally, each because one total error amount value [Delta] S _j can be calculated for each calculated circle, for the n calculated circles, the n total error amount value [Delta] S _j can be calculated.

After calculating the error amount total value ΔS _j for n calculation circles, the smallest error amount total value among the error amount total values ΔS _j is selected, and the calculated circle having this minimum error amount total value is the most probable circle. And The most probable circle is regarded as displaying the graphic closest to the cross section of the rotating body among all the calculated circles, and the center of the most probable circle is considered as the graphic center of the cross section. The misalignment between the center of the most probable circle and the rotation center O ₂ of the rotating body is referred to as misalignment. In FIG. 1, the eccentric distance e, which is the length between the rotation center O ₂ of the rotating body and the most probable circle center, is the misalignment amount. In addition, an angle θ _a indicating the direction of misalignment from the measurement start point in the clockwise direction is the misalignment angle. Incidentally, the rotation center O _2, as described above, the same meaning as the rotor rotational center O ₂ shown in FIG. 13.

  If the misalignment is determined by such a method, data can be acquired by a simple method as compared with the least square method or the like which is the prior art disclosed in Patent Document 1 and Patent Document 2.

  Even if the measured value includes an abnormal value, the abnormal value is surely excluded in the process of calculating the most probable circle. That is, since the calculated circle is a circle determined from arbitrary three measured values, there is always a calculated circle that does not include an abnormal value. Accordingly, the circle with the smallest total error amount is necessarily selected as the most probable circle from the calculated circles that do not include an abnormal value. Further, since the abnormal value can be specifically identified, the abnormal value can be excluded and replaced with the measured value after remeasurement (remeasured value). On the other hand, in the least square method or the like, which is a conventional technique shown in Patent Document 1 and Patent Document 2, an outlier value is taken in and the misalignment is calculated. Moreover, since an abnormal value cannot be specified, it is difficult to exclude an abnormal value and replace it with a remeasured value.

  Next, a method for calculating a calculated circle from the measured value and quantitatively evaluating the error amount using the plane coordinates will be outlined below.

The change of the shake when the rotating body having the misalignment is rotated can be approximated to the shake of the eccentric disk cam. FIG. 3 shows a conceptual diagram of the eccentric disk cam. In FIG. 3, the eccentric disk cam is composed of a rotating disk A and a follower B, and the follower B is composed of a flat plate C and a shaft portion D fixed thereto. The follower B is in contact with the peripheral surface of the rotating disk A through a flat plate C at a contact P. The follower B has a structure in which the shaft portion D can only move in the axial direction (vertical direction on the paper surface of FIG. 3) in the restraining member E, and the follower B as a whole according to the rotation of the rotating disk A. Has a structure that can move up and down. Further, the rotating disk A rotates around a rotation center O ₂ that is eccentric from the figure center O ₁ by an eccentric distance e. In such a eccentric disc cams, if the rotary disk A is rotated about the rotation center O ₂ eccentric, follower B along with change in the rotation angle beta, it moves up and down with respect to the paper surface.

FIG. 4 shows how the contact point P varies with the movement of the rotating disk A. FIG. 4 shows that when the rotating disk A rotates about the rotation center O ₂ and the rotation angle β changes clockwise from 0 ° to 360 ° in increments of 45 °, the contact P is the contact P _1. from to the contact point P _9, which shows how the changes in the vertical direction with respect to the rotation angle beta.

According to FIG. 4, the state where the rotation angle β is “0 °” means a state where the axis of the disk center O ₁ , the rotation center O ₂ and the axis portion D coincide with each other in the vertical direction (on the paper surface). The center O ₂ exists between the contact P (P ₁ ) and the disk center O ₁ . In this state, the chord Z ₁ Z ₂ forming the diameter of the rotating disk A is on a vertical line in which the axes of the disk center O ₁ , the rotation center O ₂ and the shaft portion D coincide with each other in the vertical direction of the drawing. The rotation angle β that changes with the rotation of the rotating disk A is the chord Z ₁ Z ₂ and the vertical line (a straight line in the vertical direction with respect to the paper surface that connects the rotation center O ₂ and the axis of the shaft portion D). ) And the clockwise angle.

In FIG. 4, when the relative positional relationship in the vertical direction with respect to the rotation center O ₂ of the contact P is viewed, the position of the contact P moves up and down as the rotation angle β changes. The locus of the contact P draws a sine curve (substantially the same even if called a cosine curve) as will be described later. At the position where the rotation angle β is “0 °”, the height of the contact P (P ₁ ) shows the minimum value (the vertical distance between the flat plate C and the rotation center O ₂ is minimum), and the rotation angle β is “180 °. ", The contact P (P ₅ ) indicates the maximum value (the vertical distance between the flat plate C and the rotation center O ₂ is maximum).

The difference between the maximum value (P ₅ ) and the minimum value (P ₁ ) of the displacement of the contact P is the maximum swing width. This maximum deflection width is twice the amount of misalignment of the rotating disk A, that is, the eccentric distance e between the graphic center O ₁ and the rotating center O ₂ of the rotating disk A. Further, the rotation angle β in FIG. 4 is synonymous with the measurement angle θ in FIG. 1, and in the following description, the rotation angle β is replaced with the measurement angle θ.

Assuming that the displacement of the follower B of the eccentric disk cam, that is, the displacement in the vertical direction of the contact point P is “y”, the displacement y is expressed by the following equation (3).
(Equation 3) y = e (1-cos θ)

Equation (3) means the displacement of the follower B when the rotating disk A is rotated by the measurement angle θ, that is, the displacement of the contact P, and is represented by a sine curve passing through the origin of the y-θ coordinate. Further, as described above, the state where the measurement angle “θ” is “0 °” means a state where the axis of the disk center O ₁ , the rotation center O ₂ and the axis D are coincident, and the displacement of the contact point P is minimum. Means the position. The displacement y at this time is “0”. It can be considered that the displacement y of the contact point P corresponds to a change in the radial deflection of the rotating body causing the misalignment in the present invention.

In the measurement of the amount of shake in the radial direction of the rotating body, the displacement at the measurement start point is set to “0”, and the displacement at other measurement points is measured as a change in the reading of the displacement meter with reference to this measurement start point. On the other hand, in Equation 3, when the measurement angle θ is “0 °”, the displacement y is “0”. In general, when measuring the roundness of a rotating body having misalignment, the position at which the measurement angle θ is “0” (the position at which the displacement is minimized) is unknown at the start of measurement. Therefore, when the measurement angle θ is “θ _a ” and the displacement y is “y _a ”, actual measurement is started, and this point is set as a measurement start point (X ₁ ). In addition, coordinate conversion of Formula 3 is performed so that the measurement angle at this time is “0 °” and the displacement Y is “0”.

The shake equation after the coordinate conversion is expressed by Equation 4 on the XY coordinates.
(Equation 4) Y = e [1-cos (X + θ _a )] − y _a

This equation is a shake equation that is the basis of the misalignment calculation method according to the present invention. Here, the measurement angle X means a measurement angle (rotation angle) from the measurement start point. The displacement Y means a displacement amount with respect to the measurement angle X. The angle “θ _a ” is called an initial angle, and the displacement “y _a ” is called an initial displacement. The eccentric distance e between the rotation center O ₂ and the figure center O ₁ of the eccentric disc cam shown in FIG. 3 corresponds to the amplitude of the sine curve of Formula 4 (1/2 of the total deflection width).

Expression 4 variables X, by substituting the measured value of the three measurement points in Y, Sadamari constants _e, θ _a, y _a, wherein the one calculated circle is determined.

  FIG. 2 shows the relationship between the measured value of the rotating body shown in FIG. 1, the reference circle, and the calculated circle, expanded to the XY coordinates. In FIG. 2, the horizontal axis X indicates the measurement angle from the measurement start point, and the vertical axis Y indicates the displacement at the measurement point. The shake equation represented by Equation 4 is represented by a sine curve passing through the origin O on the XY coordinates shown in FIG.

In FIG. 2, the calculated circle is indicated by a solid line. Since the reference circle is a perfect circle and the displacements for all measurement angles are considered to be “0”, the reference circle coincides with the X axis. The origin O is the measurement start point. The measurement points in the circumferential direction of the rotating body are displayed as measurement points X _i corresponding to the measurement angle θ _i by dividing the X axis from 0 to 360 ° into m pieces on the XY coordinates. Measurement values _{P i} for each measurement point _{X i} is the measured value. The relationship between the original coordinates y-θ coordinate and XY coordinate is shifted by the measurement angle “θ _a ” on the X axis and the displacement “y _a ” on the Y axis. The amplitude of this sine curve (1/2 of the total runout width) corresponds to the misalignment amount. The initial angle “θ _a ” corresponds to the misalignment angle.

As described above, the calculation circle determined from the measurement values at the arbitrary three measurement points in FIG. 1 developed on the XY coordinates corresponds to the locus of the calculation circle in FIG. In FIG. 1, a calculation circle determined from three points of measurement values P ₁ , P ₂ , and P _m for the measurement points X ₁ , X ₂ , and X _m is displayed as an example. The calculated circle shown in FIG. 2 is displayed by expanding the calculated circle in FIG. 1 as a sine curve on XY coordinates. 1 and 2 show only one calculated circle (jth calculated circle), but there are actually n number of calculated circles determined from Equation (4).

Further, the error amount Δ _{i, j} displayed in Equation 1 is expressed as a difference between the measured value P _i and the calculated circle value Q _{i, j} on the calculated circle in FIG. More specifically, the measurement value of the shake amount is displayed as P _i (θ _i , a _i ) at the measurement point X _i (measurement angle θ _i ) on the X axis. The calculated circle value on the calculated circle is displayed as Q _{i, j} (θ _i , b _{i, j} ). Accordingly, the error amount Δ _{i, j} can be displayed as a difference between the measured value P _i (θ _i , a _i ) and the calculated circle value Q _{i, j} (θ _i , b _{i, j} ). However, as described above, from the viewpoint of the plus / minus sign difference between the measured value and the calculated circle value and the ease of selecting the abnormal value, the error amount Δ _{i, j} is expressed by the following equation (1). As shown, the difference between the measured value and the calculated circle value is squared.

Next, an error amount Δ _{i, j} is calculated, and an error amount total value ΔS _j is calculated. After calculating the error amount total value ΔS _j for each calculated circle, if the smallest minimum error amount total value ΔS _j (j = a) is selected, the calculated circle having this minimum error amount total value ΔS _a is the most probable circle. It becomes.

The difference between the center of the most probable circle finally selected and the rotation center O ₂ (center of the reference circle) is the most probable circle misalignment data. That is, the most probable circular misalignment data is represented by the misalignment amount and misalignment angle. In Figure 2, the misalignment amount is calculated as the amplitude of the sine curve of the most probable circle, the misalignment angle is calculated as the initial angle theta _a. The misalignment amount and misalignment angle thus determined are the most probable circular misalignment data obtained by the present invention.

  If the number of measurement points m in the circumferential direction during one rotation of the rotating body is increased, the calculation accuracy of misalignment increases, but the calculation amount increases. On the other hand, if the number of measurement points m is reduced, the accuracy of misalignment calculation is degraded. However, from the viewpoint of the present invention, the number of measurement points m needs to be at least 4 or more. This is because the basic idea of the present invention is not established when the number of divisions is 3 or less.

  Next, a specific procedure for calculating the misalignment of the rotating body will be described with reference to FIG.

First, in order to determine the number of measurement points in the circumferential direction of the rotating body (gas turbine rotor), the number of measurement points m that is at least 4 or more in the circumferential direction of the rotating body is set (input). Each measurement point X _i (rotation angle θ _i ) is determined from the determined number m of measurement points along the circumferential outer surface of the rotating body.

Then, while rotating the rotating member, for each measurement point X _i, on the basis of the measured measurement values by the displacement meter 2 (distance between the displacement meter 2 installed position and the outer surface), the shake amount detecting means 62 (described later) Thus, the amount of shake of the rotating body (radial displacement amount a _i ) is derived (step S1).
As described above, various values can be used for the radial displacement amount a _i .

Calculating the number of combinations of three measurement points (calculated circle number n) from the measurement point X _i (step S2). The number of combinations (the number of calculated circles n) can be determined by n = ( _m C ₃ ).

  Three arbitrary measurement points are selected (step S3). One calculated circle is determined from the three selected points.

  The measured values of the selected three points are substituted into Equation 4 to determine a calculation circle (step S4).

Based on the determined calculated circle, calculated circle values Q _{i, j} (θ _i , b _{i, j} ) are calculated for all measurement points X _i . From each measured value P _i (θ _i , a _i ) and calculated circle value Q _{i, j} (θ _i , b _{i, j} ), the error amount Δ _{i, j} at each measurement point X _i is calculated by the equation (1). Calculate (step S5).

For each calculated circle, the error amount total value ΔS _j is calculated by the equation (2). By completing this step, the calculation of one error amount total value ΔS _j for one calculated circle is completed (step S6).

The calculation from step S3 to step S6 is repeated for the number of combinations of three measurement points (the number of calculated circles n) for all the measurement points m (step S7). By repeating the calculation for all the combinations (the number of calculated circles n), the total error amount ΔS _j (j = 1 to n) can be calculated for each of n calculated circles.

Next, the minimum error amount total value ΔS _j (j = a) is selected from the n error amount total values ΔS _j (j = 1 to n), and the most probable circle is determined (step S8). By determining the most probable circle, a calculated circle value corresponding to each measured value for the most probable circle, that is, the most probable circle calculated circle value can be calculated. The error amount between the most probable circle and the measured value, that is, the most probable circle error amount Δ _{i, a} is determined from the most probable circle calculated circle value and each measured value P _i .

Then, for each measured value P _i, it is determined whether or not the necessity of determining abnormal value (step S9).

The reason for following this procedure is as follows. Even if the measured value includes an abnormal value, the most probable circle determined is the correct most probable circle. That is, normal with respect to the total number of measurement points X _i, outliers occurring is very small. Therefore, even if it contains an abnormal value on the measurement values P _i, in the process of calculating the calculated circle by a combination of any three points, always a combination of three points does not include the abnormal value measured value P _i present To do. That is, since calculated circle always exists that does not include the abnormal value, even if tentatively containing outliers measurement values P _i, the most probable circle to be finally determined, including the abnormal measurement values P _i There will be no correct most probable circle. In other words, it is used to determine the measurement value most probable circle while containing an abnormal value to P _i, there is no difficulty in determining the most probable circle. Therefore, if you want to proceed easily with misalignment calculation, correct misalignment data can be obtained correctly even if you perform misalignment calculation without determining the abnormal value of each measured value, and misalignment calculation work as it is Can be terminated.

If determination is not required in the process of determining whether or not abnormal value determination is necessary, the most probable circular misalignment data is calculated (step 10), and the misalignment calculation operation ends. Misalignment data of the most probable circle is the deviation between the rotational center O ₂ and the center of the most probable circle consists eccentricity e and misalignment angle theta _a. Specifically, the misalignment amount corresponds to the amplitude of the sine curve of the most probable circle, the misalignment angle theta _a corresponds to the initial angle theta _a. Even when the most probable circle is determined, the most probable circle misalignment data is calculated, and the operation is terminated without determining whether or not the abnormal value determination is necessary, the present invention is substantially the same as the present invention. Are included in the technical scope of the present invention.

  When it is determined that the abnormal value determination is necessary, the next abnormal value determination means determines which measurement value is abnormal. That is, in the following Step 11 and Step 12, the presence / absence of an abnormal value and the recognition of the abnormal value are performed.

Specifically, the most probable circle error amount Δ _{i, a} corresponding to the most probable circle among the error amounts Δ _{i, j} for each measurement point X _i calculated in step S7 for the determined most probable circle. And determine whether or not the most probable circle error amount Δ _{i, a} (i = 1 to m) is within the reference value for all measurement points X _i (step S11).

When the most probable circle error amount Δ _{i, a} (for example, i = f) exceeds the reference value, the measurement value P _f at the measurement point X _f is recognized as an abnormal value (step S12).

If all the most probable circle errors Δ _{i, a} (i = 1 to m) are within the reference value, it is determined that normal measurement has been performed, and the most probable circle misalignment data is calculated. The deviation calculation work ends (step S10). Most probable circle misalignment data is shifted length of the rotation center and the center of the most probable circle consists misalignment amount (eccentricity e) and misalignment angle theta _a. Specifically, the misalignment amount corresponds to the amplitude of the sine curve of the most probable circle, misalignment angle corresponds to the initial angle theta _a.

If certified measurement P _f and outliers, and review of all the measurement values P _i in the next measurement value updating means _(i = 1~m). In other words, the measurement value update unit performs remeasurement for all measurement points X _i (i = 1 to m) in the displacement meter 2 and the shake amount detection unit 62 (and the tachometer 3), and acquires remeasurement values. Then, the measured value P _i (i = 1 to m) is replaced with the remeasured value (step S13).

When updating of the measured value X _i (i = 1 to m) is completed, the process returns to the start and recalculation is performed. The calculation procedure of steps S1 to S9 shown in FIG. 5 is repeated until the most probable circle error amount Δ _{i, a} (i = _{1 to} m) falls within the reference value. finish.

Note that, when an abnormal value occurs, instead of performing remeasurement of all the measurement points P _i (i = 1 to m), remeasurement may be performed only for the measurement point _Xf where the abnormal value has occurred. That is, the calculated measurement point X _f is re-measured, the error amount Δ _{f, a} is recalculated by the equation 1 based on the measured value P _f after replacement, and the calculated circle calculated from the most probable circle The most probable circle error amount Δ _{i, a} (i = 1 to m) is calculated based on the value and the remeasured value after the replacement. It is only necessary to confirm that the most probable circle error amount Δ _{i, a} (i = 1 to m) is within the reference value.

  Next, the configuration of the rotational misalignment calculation system of the rotating body will be described with reference to FIG. The misalignment calculation system 60 includes a gas turbine rotor 1 (rotary body), a displacement meter 2, a tachometer 3, an input unit 61, a shake amount detection unit 62, a storage unit 63, a calculation unit 64, and a display unit 65. .

In the input unit 61, the circumferential division number (measurement number m) of the gas turbine rotor 1 (rotating body) for selecting the number of measurement points, and the pitch angle (pulses of the tachometer 3) such that the measurement number m is 4 or more. Or an initial value required for starting misalignment calculation work such as four or more measurement points X _i (rotation angle θ _i ).

The shake amount detection unit 62 selects or derives at least four or more measurement points X _i during one rotation of the gas turbine rotor 1 in the circumferential direction along the outer surface of the rotating body. Further, the displacement meter 2 is installed close to the outer surface of the gas turbine rotor 1. In addition, about the drive source (not shown) and the tachometer 3 which rotate a rotary body, you may divert the thing of a gas turbine apparatus. While rotating the gas turbine rotor 1, the measurement value from the displacement meter 2 at each measurement point X _i is read, and this measurement value is stored in the storage unit 63 as the radial displacement amount a _i . If necessary, the measurement value from the tachometer 3 is also stored in the storage unit 63 as the measurement angle θ _i (not necessary if the measurement angle θ _i has already been set). The misalignment data to be measured is a radial displacement amount a _i and a measurement angle θ _i (rotation angle). As the displacement meter 2, various known sensors are applied. For example, in addition to a contact sensor such as a dial gauge, a non-contact sensor such as a laser sensor, a capacitance sensor, or an ultrasonic sensor can be used.

Each measurement point X _i of the gas turbine rotor 1 is selected in advance by putting marking lines or the like at the measurement positions of all the measurement points X _{i on} the outer surface of the gas turbine rotor 1. Displacement of a _i in the radial direction at each measurement point X _i, while rotating the gas turbine rotor 1 at a low speed, when it reaches the measurement position of the predetermined measurement point X _i, the readings of the displacement meter 2 as a measurement value It is automatically imported. Position X _i of the measurement point confirms the marking line such as a preset measuring position in CCD sensor or the like (not shown). Measurement of per rotor disk determines the measurement starting point, by 1 rotation of the gas turbine rotor 1 while checking the position of the measurement points X _i, collects the measured values of all the measurement points X _i. As the measurement point X _i , only the measurement start point may be selected on the outer surface of the rotor disk, and the other measurement points may be selected based on the rotation angle from the measurement start point detected by the tachometer 3.

  The calculation unit 64 includes a misalignment calculation unit 641, an abnormal value determination unit 642, and a measurement value update unit 643.

The misalignment calculating means 641 reads all the measured values P _i from the storage unit 63, sets the first stored radial displacement amount a ₁ as an initial value, and for each of the radial displacement amounts a _i , respectively. The new radial displacement amount a _i is calculated by subtracting the radial displacement amount a ₁ (radial displacement amount a _i −radial displacement amount a ₁ → radial displacement amount a _i ).
Instead of this, each data stored in the storage unit 63 may be used as the radial displacement amount a _i as it is. Further, a value obtained by subtracting each data stored in the storage unit 63 from a distance (known) between the rotation center O ₂ of the rotating body and the installation position of the displacement meter 2 may be used as the radial displacement amount a _i. (In this case, the radial displacement amount a _i is from the rotation center O ₂ ). Furthermore, virtually each reference circle and the radius of the reference circle are subtracted from the distance (known) between the rotation center O ₂ of the rotating body and the installation position of the displacement meter 2 imaginarily. The obtained value may be used as the radial displacement amount a _i .

Based on Equation 4, three measurement points are selected to determine a calculation circle. A calculated circle value Q _{i, j} corresponding to each measurement point X _i is calculated from the determined calculated circle. Next, an error amount Δ _{i, j} is calculated from the measured value P _i and the calculated circle value Q _{i, j at} each measurement point X _i based on the equation (1). Further, an error amount total value ΔS _j is derived from the error amount Δ _{i, j} by Equation (2). By similar processing, other calculated circles are determined from other combinations of the three measurement points, and an error amount total value ΔS _j for each calculated circle is derived. The minimum error amount total value ΔS _a is determined from the error amount total value ΔS _j , and the calculated circle for this is set as the most probable circle. The deviation between the center of the most probable circle and the rotation center O ₂ of the rotating body is calculated, and the most probable circle misalignment data consisting of the eccentric distance e and the misalignment angle θ _a is determined and stored in the storage unit 63.

The abnormal value determination unit 642 determines whether or not the error amount with respect to the most probable circle, that is, the most probable circle error amount Δ _{i, a} is within the reference value with respect to the most probable circle determined by the misalignment calculation unit 641. . It is desirable that all the most probable circle error amounts Δi _{, a} fall within the reference value. When the most probable circle error amount Δ _{i, a} (for example, i = f) exceeds the reference value, the measured value P _f (or the radial displacement amount a _f ) is recognized as an abnormal value.

When the measurement value P _f is recognized as an abnormal value, the measurement value update unit 643 issues a remeasurement instruction to the displacement meter 2 and the shake amount detection unit 62. The remeasurement value acquired by the shake amount detection unit 62 by remeasurement is temporarily stored in the storage unit 63 and then called by the measurement value update unit 643. The measurement value is updated by replacing the measurement value with the remeasurement value. finish. The misalignment calculation procedure shown in FIG. 5 is repeated with reference to the updated measurement value.

The display unit 65 displays the most probable circular misalignment data composed of the misalignment amount and misalignment angle called from the storage unit 63. Further, if the abnormal value occurs, the measured value P _f in the target measurement point X _f and the measurement point X _f, and displays the error amount delta _{f, a.} An example of the input / output screen of this system is shown in FIG.

According to this system, the most probable circular misalignment data (eccentric distance e and misalignment angle θ _a ) can be acquired by a simple method, and it is easy to identify an abnormal value. The amount and misalignment angle can be calculated easily.

  A specific example of the misalignment calculation method when normal measurement is performed will be described below by taking the rotor disk constituting the gas turbine rotor 1 as an example. In this embodiment, the misalignment data is calculated by dividing the rotor disk into eight equal parts in the circumferential direction and measuring the shake amount at each measurement point.

In FIG. 7, as Example 1, the measurement values and the most probable circle calculation circle values for the measurement angles of eight measurement points are shown, and the misalignment amount and the misalignment angle constituting the most probable circle misalignment data are shown. . In this embodiment, an example in which three points X ₁ , X _4, and X ₅ are employed as measurement points for calculating a calculation circle is shown. The most probable circle calculated circle value means a calculated circle value at each measurement point with respect to the most probable circle in this embodiment. In FIG. 8, this relationship is graphically represented as the relationship between the reference circle, the most probable circle, and the measured value, and the misalignment amount and misalignment angle are displayed. In the case of this example, the most probable circle error amount at each measurement point was within the reference value, and both the misalignment amount and misalignment angle were small, and there was no problem in practical use.

An example in the case where an abnormal value occurs in the measured value when measuring the rotor disk of the gas turbine rotor 1 is shown below. In this embodiment, a case where an abnormal value occurs at one measurement point (measurement point X ₅ ) out of eight measurement points is shown.

In Example 2 of FIG. 7, the measured value and the most probable circle calculation circle value for each measurement point are shown, and the misalignment amount and misalignment angle are also shown. In this embodiment, three points X ₁ , X ₂ and X ₈ are employed as measurement points for calculating the calculated circle. FIG. 9 shows the most probable circle error amount for the measured value and the most probable circle calculation circle value in this example. In FIG. 7, according to the present invention, even when the abnormal value shown in Example 2 occurs, the final misalignment amount and misalignment angle are almost the same numerical values as in Example 1 during normal measurement. Even in the case of abnormal measurement, it has practically no effect on the calculation accuracy of misalignment. Meanwhile, according to FIG. 9, the measurement points X _5, compared to the other measurement points, indicating a large amount of error by orders of magnitude exceeding the reference value far. Therefore, according to the present invention, it is easy to identify a measurement point where an abnormal value has occurred by referring to the most probable circle error amount.

  By applying the misalignment calculation method of the present invention, the most probable circle can be specified relatively easily and accurately, and the most probable circle misalignment data can be acquired. Moreover, since it is easy to specify an abnormal value, it is possible to easily exclude the abnormal value and replace it with a remeasured value.

As mentioned above, although embodiment of this invention was described, it cannot be overemphasized that this invention is not limited to said embodiment, A various change may be added to the specific structure within the scope of the present invention. .
For example, the shake amount detection means 62, the storage section 63, and the calculation section 64 (center misalignment calculation means 641, abnormal value determination means 642, measurement value update means 643) are in the form of individual electronic circuit units (IC unit cards). However, the present invention is not limited to this, and includes those in the form of a program (or sequence) or storage memory in an electronic computer.

For the measurement value P _i and the measurement angle θ _i , the data from the displacement meter 2 and the tachometer 3 are continuously measured while the gas turbine rotor 1 is rotated once, and the continuous data is stored in the storage unit 63. Then, at least four or more arbitrary points may be extracted, and the radial displacement amount a _i and the measurement angle θ _i may be derived and stored based on this.

The relationship of the measured value, reference | standard circle, and calculation circle concerning the best form for implementing this invention is shown. The relationship between the measured value on the XY coordinates, the reference circle, and the calculated circle is shown. The conceptual diagram of an eccentric disk cam is shown. The relationship between the rotation angle of an eccentric disk cam and the displacement of a contact is shown. The misalignment calculation procedure according to the best mode for carrying out the present invention will be described. 1 shows a configuration of a misalignment calculation system. The data concerning Example 1 and 2 concerning the best form for implementing this invention are shown. FIG. 2 shows a diagram of a relationship between a measured value and a most probable circle related to Example 1 according to the best mode for carrying out the present invention. FIG. The most probable circle error amount at each measurement point regarding Example 2 according to the best mode for carrying out the present invention is shown. An example of the input / output screen of the misalignment calculation system is shown. The structure of a gas turbine rotor is shown. The shaft curve distribution of a gas turbine rotor is shown. The shaft bending generation | occurrence | production state figure of a gas turbine rotor is shown.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Gas turbine rotor 2 Displacement meter 3 Tachometer 10 Compressor rotor part 11 Rotor blade 20 Turbine rotor part 30 Spindle bolt 50 Rotor disk 60 Center misalignment calculation system 61 Input part 62 Shaking amount detection means 63 Storage part 64 Calculation part 65 Display part 641 misalignment calculating unit 642 abnormal value determining section 643 measurement update unit X _i measurement points P _i measurement Q _{i, j} calculated circle value theta _i measured angle theta _a misalignment angle α rotor contact surface angle β angle of rotation a of the disc _i- direction displacement amount b _{i, j} calculated circle value Δ _{i, j} error amount ΔS _j error amount total value e eccentric distance m number of measurement points n number of calculated circles O ₁ figure center (disk center)
O ₂ rotation center

Claims (8)

A method for calculating misalignment of a rotating body,
Deriving the radial displacement of the rotating body based on the measured values measured by the displacement meter at least four measurement points along the circumferential outer surface while rotating the rotating body,
Select any three points from the radial displacement amount and the measurement angle of each measurement point at all measurement points, and calculate one circle determined by these three points as a calculation circle,
A radial value on the calculated circle is calculated as a calculated circle value at the same measurement angle as the measurement point for all the measurement points from the calculated circle,
The difference between the calculated circle value and the radial displacement amount is calculated as an error amount for each measurement point,
The error amount is summed to derive a total error amount value,
Repeat the calculation for the number of combinations of three measurement points for all measurement points to calculate the total error amount,
From the total error amount for all combinations obtained, select the calculation circle that minimizes it as the most probable circle,
Calculating the deviation between the center of the most probable circle and the rotation center of the rotating body as the most probable circle misalignment data,
A method for calculating misalignment of a rotating body.   The method of claim 1, wherein the most probable circular misalignment data includes a misalignment amount and a misalignment angle.   When the most probable circle error amount, which is the difference between the calculated circle value and the radial displacement amount in the most probable circle, exceeds the reference value, the measurement value at the measurement point corresponding to the most probable circle error amount is an abnormal value. The center misalignment calculation method for a rotating body according to claim 1 or 2, wherein   When the most probable circle error amount exceeds a reference value, the measurement value recognized as the abnormal value is remeasured to obtain a remeasurement value, and the measurement value is replaced with the remeasurement value. The method for calculating misalignment of a rotating body according to claim 3.   The method for calculating misalignment of a rotating body according to claim 1, wherein the rotating body is a gas turbine rotor. In the rotational misalignment calculation system for a rotating body,
An input unit for setting at least four or more measurement points in one rotation of the rotating body;
A shake amount detection unit for deriving a radial displacement amount of the rotating body based on a measurement value measured by a displacement meter at least four measurement points along the circumferential outer surface of the rotating body;
A storage unit for storing the radial displacement amount derived by the shake amount detection unit and the measurement angle of the measurement point;
A calculation unit that calculates the most probable center misalignment data of the rotating body based on the data stored in the storage unit,
The calculation unit is
Select any three points from the radial displacement amount and the measurement angle at all measurement points stored in the storage unit, and calculate one circle determined by these three points as a calculation circle,
A radial value on the calculated circle is calculated as a calculated circle value at the same measurement angle as the measurement point for all the measurement points from the calculated circle,
The difference between the calculated circle value and the radial displacement amount is calculated as an error amount for each measurement point,
The error amount is summed to derive a total error amount value,
Repeat the calculation for the number of combinations of three measurement points for all measurement points to calculate the total error amount,
From the total error amount for all combinations obtained, select the calculation circle that minimizes it as the most probable circle,
A system for calculating misalignment of a rotating body, wherein the misalignment between the center of the most probable circle and the center of rotation of the rotating body is calculated as the most probable circular misalignment data.   When the most probable circle error amount, which is the difference between the calculated circle value and the radial displacement amount in the most probable circle, exceeds a reference value, the calculation unit calculates the measurement point corresponding to the most probable circle error amount. The system for calculating misalignment of a rotating body according to claim 6, further comprising an abnormal value determining unit that recognizes the measured value as an abnormal value. The calculation unit, when the most probable circle error amount exceeds a reference value, calls the remeasurement value acquired by the shake amount detection unit from the storage unit, and replaces the measurement value with the remeasurement value. Update means,
The rotational misalignment calculation system for a rotating body according to claim 7.

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