JP5839883B2 - Vibration analysis method for piping system - Google Patents

Description

  The present invention relates to a method for performing vibration analysis of a piping system in various plants such as a petrochemical factory, a chemical / food manufacturing factory, an iron mill, a machine manufacturing factory, a power plant, and a pipeline.

  In a piping system in a plant, vibration analysis of the piping system is performed, and some measures against vibration are taken based on the analysis result. As measures against vibration, for example, resonance with a device including a rotating body or a reciprocating body can be avoided, or rigidity against vibration can be improved.

However, the piping system in the plant has to have a complicated shape due to restrictions such as layout of various devices to which the piping is connected and generation of thermal stress. Therefore, even in the same type of piping system in the same plant, there are many cases where the piping system does not have the same shape. Moreover, even if it is the same kind of plant, the shape of a piping system differs normally for every plant.
Therefore, in the conventional vibration analysis method, a model is created for each piping system in each plant, and vibration analysis of the piping system is performed using this model.

As a conventional vibration analysis method for modeling a piping system and performing vibration analysis, for example, there are methods described in Non-Patent Documents 1 and 2.
Non-Patent Document 1 discloses a technique for diagnosing vibration of a multi-span pipe using an analysis model created by modeling the multi-span pipe. In this method, an analysis model is created by modeling a multi-span pipe by treating the pipe in the target multi-span pipe as a beam element, treating the valve as a concentrated mass, and treating the support as a spring element. In addition, the analysis model is optimized to match the vibration characteristics of the analysis model with the vibration characteristics of the actual machine. By using the analysis model obtained in this way, it is possible to evaluate the generated stress at an arbitrary location of the multi-span piping from the actual machine data obtained by the accelerometer.
Non-Patent Document 2 discloses a method of modeling a piping system in a pressurized water nuclear power plant (PWR plant) and calculating vibration stress generated in a branch pipe due to vibration of a mother pipe. In this method, the actual piping system is compared to the simplified model that assumes that the center of gravity of the piping system exists at the valve box position of the valve provided on the branch pipe (small-diameter piping) without vibration of the main pipe. Analysis is performed using a model that is corrected to take into account the deviation of the center of gravity position from the valve box and the vibration of the mother pipe itself.

Mamoru Tanaka and two others, “Development of Diagnostic and Monitoring System for Vibration Pipes”, Mitsubishi Heavy Industries Technical Review, Mitsubishi Heavy Industries, Ltd., Vol. 33, No. 4, p. 278-281 Miki Hiramatsu and one other, “Evaluation methods of Vibration Stress of Small Bore Piping”, INSUS JOURNAL, 2001, Vol. 8, p. 92-99

However, each of the methods described in Non-Patent Documents 1 and 2 needs to individually model the piping system of the plant to be analyzed, and it takes a lot of time to perform vibration analysis of the piping system. .
On the other hand, in order to shorten the analysis time, it is conceivable that the vibration analysis is limited to only the portion of the piping system that is thought to contribute greatly to vibration (the portion that easily shakes). It is impossible to accurately grasp the vibration characteristics of the. Therefore, even if the piping system is designed to achieve the desired vibration characteristics, it is clear that the piping system is not adequately equipped with vibration countermeasures during the trial operation of the plant that actually assembles the piping system and flows the fluid through the piping system. Therefore, the piping support structure is forced to be corrected, which may increase the cost.

  The present invention has been made in view of the above-described circumstances, and provides a vibration analysis method for a piping system and a vibration analysis apparatus for the piping system that can easily perform vibration analysis even for a piping system having a complicated shape. The purpose is to do.

  The vibration analysis method for a piping system according to the present invention is a vibration analysis method for a piping system having a piping and a plurality of support members that support the piping at a plurality of restraining points, and the piping system includes a plurality of piping systems for each restraining point. Based on the difference between the dividing step of dividing into the elements, the reference model fitting step of applying a reference model having a known natural frequency for each of the plurality of elements, and the reference model applied to each element A correction coefficient calculating step for obtaining a correction coefficient for each of the plurality of elements, and multiplying the natural frequency of a reference model applied to each element by the correction coefficient to obtain a natural frequency of each of the plurality of elements And a natural frequency calculating step.

In the above-mentioned vibration analysis method for piping systems, the reference model is applied to each of a plurality of elements obtained by dividing the piping system for each constraint point, and the known natural frequency of the reference model is corrected based on the difference between each element and the reference model. The natural frequency of each element is obtained by correcting with a coefficient. Instead of modeling a piping system with a complicated shape in this way, the piping system is divided into a plurality of elements, and the natural frequency of each element is obtained based on comparison with the reference model. Vibration analysis can be performed easily, and the time required for analysis can be greatly reduced. Therefore, it becomes possible to perform analysis over a wider range of the piping system, and it is possible to accurately grasp the vibration characteristics of the piping system. Therefore, it is possible to prevent a situation in which the piping support structure (support member) is forced to be corrected after the plant trial operation stage.
Further, since the natural frequency can be obtained for each element, it becomes clear which part (element) of the piping system should be subjected to vibration countermeasures. Therefore, at the piping system design stage, there is no risk of resonance with a device having a rotating body or a reciprocating body, and a piping system having excellent rigidity against vibration can be easily realized.

The vibration analysis method of the piping system further includes a representative model preparation step of preparing a plurality of representative models with known natural frequencies before performing the reference model fitting step, and the reference model fitting step includes a plurality of the above-described representative model preparation steps. A representative model closest to each element from among the representative models may be selected as the reference model and applied to each element.
Thereby, if elements typically used in the piping system of the plant are prepared in advance as a representative model, vibration analysis of piping systems of arbitrary shapes in various plants can be performed easily and quickly.

The piping system vibration analysis method further includes a function calculation step for obtaining a function indicating a relationship between the natural frequency of the representative model and an influencing factor affecting the natural frequency before performing the correction coefficient calculation step. In the correction coefficient calculation step, the correction coefficient may be obtained using the function from the difference in the influence factors between each element and the reference model applied to the element.
In this manner, a function indicating the relationship between the natural frequency of the representative model and the influencing factors affecting the representative model is obtained in advance, and the correction coefficient is obtained using the function from the difference in influencing factors between each element and the reference model. Thus, the accurate natural frequency of each element can be obtained easily and quickly.

In the piping system vibration analysis method, the dividing step, the reference model fitting step, the correction coefficient calculation step, and the natural frequency calculation step may be repeated in two horizontal directions and three vertical directions that are orthogonal to each other. .
Plant piping systems are usually complex three-dimensional shapes, so vibrations in all directions can be a problem. For this reason, even if analysis is performed in one direction, it is often impossible to accurately know the vibration characteristics of the piping system. Therefore, as described above, by repeating the division process to the natural frequency calculation process in two directions that are orthogonal to each other in the horizontal direction and the vertical direction, the vibration characteristics of a complicated three-dimensional piping system can be reliably grasped. can do.

Further, when the division step to the natural frequency calculation step are repeated for the three directions, the minimum natural frequency for obtaining the minimum natural frequency among the natural frequencies of the elements calculated in the natural frequency calculation step for the three directions. You may further provide a calculation process.
From the minimum natural frequency obtained in this way, it is possible to know which vibration mode of which element of the piping system should be subjected to vibration countermeasures. Therefore, vibration countermeasures for the piping system can be performed efficiently.

  The piping system vibration analyzing apparatus according to the present invention is a piping system vibration analyzing apparatus including a pipe and a plurality of support members that support the pipe at a plurality of restraining points, and the piping system is provided for each of the restraining points. A difference between a dividing means for dividing the element into a plurality of elements, a reference model fitting means for applying a reference model having a known natural frequency for each of the plurality of elements, and a reference model applied to each element Correction coefficient calculation means for obtaining a correction coefficient based on each of the plurality of elements, and by multiplying the natural frequency of the reference model applied to each element by the correction coefficient, the natural frequency of each of the plurality of elements Natural frequency calculation means for obtaining

In the piping system vibration analysis apparatus, the reference model fitting means applies the reference model to each of a plurality of elements obtained by dividing the piping system by the dividing means, and the natural frequency calculation means performs the known natural vibration of the reference model. The natural frequency of each element is obtained by correcting the number with the correction coefficient obtained by the correction coefficient calculating means. Instead of modeling a piping system with a complicated shape in this way, the piping system is divided into a plurality of elements, and the natural frequency of each element is obtained based on comparison with the reference model. Vibration analysis can be performed easily, and the time required for analysis can be greatly reduced. Therefore, it becomes possible to perform analysis over a wider range of the piping system, and it is possible to accurately grasp the vibration characteristics of the piping system. Therefore, it is possible to prevent a situation in which the piping support structure (support member) is forced to be corrected after the plant trial operation stage.
Further, since the natural frequency can be obtained for each element, it becomes clear which part (element) of the piping system should be subjected to vibration countermeasures. Therefore, at the piping system design stage, there is no risk of resonance with a device having a rotating body or a reciprocating body, and a piping system having excellent rigidity against vibration can be easily realized.

The piping system vibration analysis apparatus further includes a storage unit storing a plurality of representative models with known natural frequencies, and a user interface having a display unit and an input unit for exchanging information with an operator. The reference model fitting means urges the operator to select a representative model closest to each element from the plurality of representative models stored in the storage means, and the operator selects the representative model using the input section. The representative model may be applied to each element as the reference model.
Thereby, if elements typically used in the piping system of the plant are prepared in advance as a representative model, vibration analysis of piping systems of arbitrary shapes in various plants can be performed easily and quickly.

According to the present invention, instead of modeling a piping system having a complicated shape as it is, the piping system is divided into a plurality of elements, and the natural frequency of each element is obtained based on comparison with the reference model. The vibration analysis of the system can be easily performed, and the time required for the analysis can be greatly shortened. Therefore, it becomes possible to perform analysis over a wider range of the piping system, and it is possible to accurately grasp the vibration characteristics of the piping system. Therefore, it is possible to prevent a situation in which the piping support structure (support member) is forced to be corrected after the plant trial operation stage.
Further, since the natural frequency can be obtained for each element, it becomes clear which part (element) of the piping system should be subjected to vibration countermeasures. Therefore, at the piping system design stage, there is no risk of resonance with a device having a rotating body or a reciprocating body, and a piping system having excellent rigidity against vibration can be easily realized.

It is a figure which shows the basic concept of the vibration analysis method of the piping system which concerns on one Embodiment of this invention, (A) shows a mode that a piping system is divided | segmented into a some element, (B) shows a reference | standard model for each element. It shows how to apply. It is a flowchart of the vibration analysis method of a piping system. (A) is a diagram showing a representative model consisting of L-shaped pipe and its supporting member, (B) is a natural frequency X _i and the influencing factors a _j of the representative model shown in FIG. 3 (A) It is a graph which shows the relationship. It is a figure which shows an example of the piping system which has a three-dimensional shape. It is a figure which shows a mode that the piping system shown in FIG. 4 is divided | segmented into an element about each of an XYZ direction, (A) shows the mode of element division in a X direction, (B) shows the mode of element division in a Y direction. (C) shows the state of element division in the Z direction. It is a figure which shows the structural example of the vibration analyzer of a piping system.

Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. However, the dimensions, materials, shapes, relative arrangements, and the like of the components described in this embodiment are not intended to limit the scope of the present invention unless otherwise specified, and are merely illustrative examples. Only.
In the following, a vibration analysis method for a piping system according to the present embodiment will be described first, and then a vibration analysis device for executing the vibration analysis method will be described.

  FIG. 1 is a diagram showing a basic concept of a vibration analysis method for a piping system according to this embodiment. FIG. 1 (A) shows a state in which the piping system is divided into a plurality of elements, and FIG. 1 (B) shows each element. Shows how the reference model is applied to. FIG. 2 is a flowchart of the piping system vibration analysis method according to the present embodiment.

  As shown in FIG. 1A, a piping system 1 that is a target of vibration analysis includes a piping 2 and a support member 3 that supports the piping 2 at a plurality of restraint points. In the case of a conventional vibration analysis method, the entire piping system 1 is modeled and vibration analysis is performed. In this embodiment, the piping system 1 is divided into a plurality of elements for each constraint point, and vibration analysis is performed.

As shown in FIG. 2, first, a plurality of representative models 4 _i (where i is a number assigned to each representative model) having a known natural frequency X _i0 are prepared (step S2). .
The representative model 4 _i is an element typically used in a piping system of a plant, and includes a pipe having an arbitrary shape and a support member 3 that supports both ends of the pipe. For example, an element composed of a straight pipe and a support member 3 that supports both ends of the straight pipe, an L-shaped pipe having only one bent portion, and an element composed of the support member 3 that supports both ends of the pipe, a bent portion A pipe having two places and extending in one plane and an element comprising a support member 3 that supports both ends of the pipe, a pipe having two bent parts and extending in three dimensions, and both ends of the pipe An element composed of the supporting member 3 to be supported, a pipe branched from the mother pipe, and an element composed of the supporting member 3 supporting the pipe are prepared as the representative model 4 _i . Natural frequency X _i0 of each representative model 4 _i may be determined by calculation, may be obtained by actual measurement using a mock-up test body simulating a respective representative model 4 _i.

なお、影響因子が所定の値ａ_ｊ０のときの各代表モデル４_ｉの固有振動数Ｘ_ｉが、上述した既知の固有振動数Ｘ_ｉ０である。つまり、上記式（１）は、代表モデル４_ｉの各影響因子を所定値ａ_ｊ０から任意の値ａ_ｊに変化させたとき、その固有振動数が既知の値Ｘ_ｉ０からどのように変化するかを表している。
ここでいう影響因子ａ_ｊとは、各代表モデルの固有振動数に影響する任意のパラメータであり、例えば、配管仕様、配管の延べ長さ、集中質点の位置、配管の屈曲部の位置、配管の分岐部の位置、配管内を流れる流体の種類、保温の有無、配管内を流れる流体の温度、配管の厚さ、配管に作用する負荷荷重、計算上の誤差などが影響因子の具体例として挙げられる。また、ここでいう関数ｆ_ｉｊ（ａ_ｊ）の形式は各影響因子ａ_ｊと固有振動数Ｘ_ｉとの関係を特定可能である限り特に限定されず、上記式（１）そのものに相当する数式であってもよいし、上記式（１）に相当する固有振動数Ｘ_ｉと影響因子ａ_ｊとの関係を示すグラフやテーブルであってもよい。 Next, proceeding to step S4, for each representative model 4 _i , a function f _ij (a _j ) indicating the relationship between the natural frequency X _i and the influence factor a _j is prepared (where i is in each representative model). And j is a number assigned to each influencing factor). The following relationship is established between the natural frequency X _i of the i-th representative model and the j-th influence factor a _j .

Note that the natural frequency X _i of each representative model 4 _i when the influence factor is the predetermined value a _j0 is the above-described known natural frequency X _i0 . That is, the above equation (1) shows how the natural frequency changes from the known value X _i0 when each influence factor of the representative model 4 _i is changed from the predetermined value a _j0 to an arbitrary value a _j. Represents.
The influence factors a _j here is any parameter that affects the natural frequency of each representative models, for example, pipe specifications, total length of pipe, the position of the centralized mass, the position of the bent portion of the pipe, the pipe Specific examples of influential factors include the position of the branch of the pipe, the type of fluid flowing in the pipe, the presence or absence of heat, the temperature of the fluid flowing in the pipe, the thickness of the pipe, the load applied to the pipe, and the calculation error Can be mentioned. The form of the function f _ij (a _j ) here is not particularly limited as long as the relationship between each influence factor a _j and the natural frequency X _i can be specified, and a mathematical expression corresponding to the above formula (1) itself. It may be a graph or a table showing the relationship between the natural frequency X _i corresponding to the above formula (1) and the influence factor a _j .

FIG. 3A is a diagram showing a representative model 4 _i composed of an L-shaped pipe and its support member, and FIG. 3B is a diagram showing the natural frequency X of the representative model 4 _i shown in FIG. It is a graph which shows the relationship between _i and each influence factor _aj .
As shown in FIG. 3A, the representative model 4 _i is configured by an L-shaped pipe having only one bent portion 5 and a support member 3 that supports both ends of the pipe from below. The bent portion 5 is located between the straight pipe portion and the straight tube portion of the length L2 of the length L1, total length of the representative model 4 _i is represented by L1 + L2.
As shown in FIG. 3B, the total length a _{1 of} the pipe, the thickness a _{2 of} the pipe, the type of fluid a _{3 in} the pipe, the fluid temperature a _{4 in} the pipe, the position a of the bent portion 5 in the pipe _5. A function f _i1 indicating a relationship between a total of seven influence factors a _{j of} a load applied to the pipe (equivalent to the pipe length) a ₆ and a calculation error a ₇ and the natural frequency X _i of the representative model 4 _i (A ₁ ) to f _i7 (a ₇ ) are prepared. The functions f _i1 (a ₁ ) to f _i7 (a ₇ ) may be obtained by calculation, or may be obtained by actual measurement using a mock-up specimen that represents the representative model 4 _i .

Subsequently, the process proceeds to step S6 in FIG. 2, and the piping system 1 is divided into a plurality of elements 6 _k (where k = 1, 2,..., M) for each restraint point (position of the support member 3) (FIG. 1). (See (A)). Here, the division into the elements of the piping system 1 is performed on the basis of the restraint point (the position of the support member 3) because the restraint point is a vibration separation point (the elements adjacent beyond the restraint point This is because vibration of each element can be handled independently. In other words, each element 6 _{k obtained} by dividing the piping system 1 for each constraint point is the smallest unit that can handle vibration independently.

For each element divided in this way, the one closest to each element 6 _k is selected from the plurality of representative models 4 _i prepared in step S2, and this is selected as the reference model 7 _k (where k = 1,2, ..., m) as fit to each element _{6 k} (step S8).
Fitting the reference model 7 _k to each element 6 _k, specifically performed as follows. That is, in the example shown in FIG. 1 (B), since the element ₆₁ is made of a pipe and its supporting member 3 has a bent portion 5 only two places, as a reference model ₇₁ selects the closest representative model to Element 6 applies to ₁ Also elements 6 ₂ to become a straight pipe and its supporting member 3, fit the element 6 ₂ as reference model 7 ₂ selects the closest representative model thereto. Furthermore, although elements 6 _m since composed of piping and the support member 3 has a bent portion 5 only one place, applying to the element 6 _m as a reference model 7 _m and selects the closest representative model thereto.

Each reference model 7 _k is selected from a plurality of representative models 4 _i , and naturally corresponds to one of the representative models 4 _i . Therefore, the natural frequency of the reference model 7 _{k is known as} the natural frequency X _i0 of the representative model 4 _i corresponding to the reference model (the natural frequency when each influencing factor is the predetermined value a _j0 ). For the relationship between the natural frequency X _i of the model 7 _k and each influence factor a _j , the function f _ij (a _j ) calculated for the representative model 4 _i corresponding to the reference model can be applied as it is.

ただし、Ｘ_ｋはｋ番目の要素４_ｋの固有振動数である。また、Ｘ_ｋ０はｋ番目の要素に当てはめられた基準モデル７_ｋの固有振動数（影響因子がａ_ｊ０のときの固有振動数）であって、その基準モデル７_ｋに対応する代表モデル４_ｉ（ステップＳ８で選択された代表モデル４_ｉ）の固有振動数Ｘ_ｉ０（影響因子がａ_ｊ０のときの固有振動数）から既知である。また、ｆ_ｋｊ（ａ_ｊ）はｋ番目の要素６_ｋに当てはめられた基準モデル７_ｋの固有振動数Ｘ_ｋと各影響因子ａ_ｊとの関係を示す関数であって、その基準モデル７_ｋに対応する代表モデル４_ｉについてステップＳ４で算出済みの関数ｆ_ｉｊ（ａ_ｊ）を用いる。また、ａ_ｊは各要素の影響因子の実際の値であり、ａ_ｊ０は基準モデルの影響因子の値（既知の固有振動数Ｘ_ｋ０に対応する影響因子の値）である。
具体的には、図１（Ｂ）に示す例の場合、各要素６_ｋ（ｋ＝１，２，…，ｍ）に当てはめられた基準モデル７_ｋの各影響因子の値ａ_ｊ０と、各要素の各影響因子の値ａ_ｊとの相違を上記式（２）にて考慮し、補正係数α_ｋ（ｋ＝１，２，…，ｍ）を算出する。 Next, using the function f _{ij (a j)} showing the relationship between the natural frequency X _i of each representative model 4 _i that are prepared and influence factors a _j in step S4, the fitted to each element and the element A correction coefficient α _k based on the difference of the influence factor a _{j from} the reference model 7 _k is calculated (step S10). The correction coefficient α _k is obtained from the following equation.

However, X _k is the natural frequency of the k-th element 4 _k . X _k0 is the natural frequency (the natural frequency when the influence factor is a _j0 ) of the reference model 7 _k applied to the k-th element, and the representative model 4 _i corresponding to the reference model 7 _k It is known from the natural frequency X _i0 (the natural frequency when the influence factor is a _j0 ) of (representative model 4 _i selected in step S8). _Further, a function showing a relationship between f kj _{(a j)} is the k-th element ₆ natural frequency of the reference model _{7 k,} which is fitted to the _{k X k} and the influencing factors _{a j,} the reference model _{7 k} The function f _ij (a _j ) calculated in step S4 is used for the representative model 4 _i corresponding to. Further, a _j is the actual value of the influence factor of each element, and a _j0 is the value of the influence factor of the reference model (the value of the influence factor corresponding to the known natural frequency X _k0 ).
Specifically, in the case of the example shown in FIG. 1B, the value a _j0 of each influencing factor of the reference model 7 _k applied to each element 6 _k (k = 1, 2,..., _M ), The correction coefficient α _k (k = 1, 2,..., M) is calculated in consideration of the difference from the value a _j of each influence factor of the element in the above equation (2).

Thereafter, by multiplying the correction coefficient alpha _k obtained in known natural frequency X _k0 in step S10 of the reference model 7 _k, which is fitted to each of the elements 6 _k, the actual natural frequency X _k of the elements 6 _k (= X _k0 × α _k ) is calculated.

In step S14, it is determined whether or not the natural frequency _Xk of each element _6k has been calculated in two horizontal directions and three vertical directions orthogonal to each other. About three directions unless calculated natural frequencies _{X k} is completed (NO determination at step S14), and repeats the processing of step S6~S12 respect to the other direction back to the step S6.
On the other hand, if the calculation of the eigenfrequency _{X k} is completed for three directions (YES determination at step S14), and proceeds to step S16, the minimum of the natural frequency of _{X k} of the elements _{6 k} determined for three directions The natural frequency is obtained (the smallest of the 3 × k natural frequencies is obtained). From this minimum natural frequency, it is possible to know which element _6k in which direction in the piping system 1 should be subjected to vibration countermeasures in which direction of vibration mode. Therefore, vibration countermeasures for the piping system 1 can be efficiently performed.

  Here, the division into elements of the piping system 1 when the vibration analysis of the piping system 1 is performed in each of two horizontal directions and three vertical directions orthogonal to each other will be described with a specific example.

  FIG. 4 is a diagram illustrating an example of the piping system 1. FIG. 5 is a diagram showing a state in which the piping system 1 shown in FIG. 4 is divided into elements for each of two orthogonal horizontal directions (XY directions) and vertical directions (Z directions). FIG. FIG. 5B shows a state of element division in the Y direction, and FIG. 5C shows a state of element division in the Z direction.

  The piping system 1 shown in FIG. 4 has devices A and B connected to both ends. The piping system 1 includes two bent portions 5 between the devices A and B, and is supported at the restraint points 8 (8A to 8E) by the support member. The restraint point 8A is a connection portion between the device A and the piping system 1, and the piping system 1 is restrained in all directions of XYZ by the device A (an example of a support member) at the restraint point 8A. The piping system 1 is restricted only in the Z direction by a piping support 9 (an example of a support member) at a restraint point 8B, and is restrained in the XY direction by the piping support 9 at a restraint point 8C. Further, at the restraint point 8D, the piping system 1 is restrained in the Z direction by a piping support 9 (an example of a support member). Furthermore, the piping system 1 is restrained in all directions of XYZ at a restraint point 8E which is a connection portion with the device B (an example of a support member).

As shown on the left side of FIG. 5 (A), when the restraint points 8 (8A to 8E) that restrain the piping system 1 in the X direction are extracted, only the restraint points 8A, 8C, and 8E are obtained. Therefore, when the piping system 1 is divided for each restraint point 8 (8A, 8C, 8E), two elements (6 _1X , 6 _2X ) are obtained as shown on the right side of FIG. That is, when divided into a plurality of elements piping system 1 for each constraint points in the X direction, the two elements _{6 1X, 6 2X} is obtained, each element _{6 1X, 6 2X} by performing subsequent steps S8~S12 Accordingly, the natural frequency _Xk is calculated.
Further, as shown on the left side of FIG. 5B, when the restraint points 8 (8A to 8E) that restrain the piping system 1 in the Y direction are extracted, only the restraint points 8A, 8C, and 8E are obtained. Therefore, when the piping system 1 is divided for each restraint point 8 (8A, 8C, 8E), two elements (6 _1Y , 6 _2Y ) are obtained as shown on the right side of FIG. That is, when divided into a plurality of elements piping system 1 for each constraint points in the Y direction, the two elements _{6 1Y, 6 2Y} is obtained, the element _{6 1Y, 6 2Y} each by performing subsequent steps S8~S12 Accordingly, the natural frequency _Xk is calculated.
Similarly, as shown on the left side of FIG. 5C, when the constraint points 8 (8A to 8E) that extract the piping system 1 in the Z direction are extracted, only the constraint points 8A, 8B, 8D, and 8E are obtained. Become. Therefore, when the piping system 1 is divided for each restraint point 8 (8A, 8B, 8D, 8E), three elements (6 _1Z , 6 _2Z , 6 _3Z ) are obtained as shown on the right side of FIG. That is, when the piping system 1 is divided into a plurality of elements for each constraint point with respect to the Z direction, three elements 6 _1Z , 6 _2Z , 6 _3Z are obtained, and then the elements 6 _1Z , 6 are performed by performing steps S8 to S12. _{2Z, 6} natural frequency _{X k} with respective _3Z is calculated.
In the present embodiment, the element division in the XYZ directions and the calculation of the natural frequency for each element are sequentially performed by returning from step S14 to step S6 in FIG.

Next, a vibration analysis device for a piping system using the above-described vibration analysis method will be described. FIG. 6 is a diagram illustrating a configuration example of a vibration analysis apparatus for a piping system.
As shown in FIG. 1, the vibration analysis apparatus 10 mainly includes a CPU 20 that performs processing necessary for vibration analysis of the piping system 1 and storage means (memory) 30 in which information necessary for vibration analysis of the piping system 1 is stored. And an input unit 42 and a display unit 44, and a user interface 40 for exchanging information between the CPU 20 and the operator.

The storage unit 30 stores a plurality of representative models 4 _i prepared in advance together with the known natural frequency X _i0 . Further, a function f _ij (a _j ) obtained in advance for each representative model 4 _i and indicating the relationship between the natural frequency X _i and the influence factor a _j is also stored in the storage unit 30. The memory | storage means 30 provides such information to CPU20 side according to the request | requirement from CPU20 side.

The CPU 20 includes a dividing unit 22, a reference model fitting unit 24, a correction coefficient calculation unit 26, a natural frequency calculation unit 28, and a minimum natural frequency calculation unit 29.
Based on the design data of the piping system 1 input by the operator via the input unit 42 of the user interface 40, the dividing unit 22 converts the piping system 1 into a plurality of elements 6 _k (k = 1, 2, ..., m).
The reference model fitting unit 24 applies the reference model 7 _k to each of the elements 6 _k obtained by the dividing process by the dividing unit 22. Specifically, the operator is prompted to select the one closest to each element 6 _k from the plurality of representative models 4 _i stored in the storage unit 30 via the display unit 44 of the user interface 40. Then, the representative model 4 _i selected by the input unit 42 of the user interface 40 by the operator is applied to each element 6 _k as the reference model 7 _k . Note that, from the viewpoint of reducing the burden on the operator, the reference model fitting unit 24 uses only the ones that are relatively close to each element 6 _k among the plurality of representative models 4 _i stored in the storage unit 30 as candidates. May be displayed.
The correction coefficient calculation unit 26 calculates the correction coefficient α _k based on the difference in the influence factor a _j between each element 6 _k and the reference model 7 _k using the above equation (2). At this time, the natural frequency X _i0 of the representative model 4 _i corresponding to the reference model 7 _k applied to each element 6 _k is received from the storage means 30, and the natural frequency is _{obtained as} the natural frequency of the reference model 7 _{k. Used} as _Xk0 . Further, receiving the function _f ij a _{(a j)} from the memory means 30 previously obtained with respect to the representative model _{4 i} corresponding to the reference model _{7 k,} which is fitted to each of the elements _{6 k,} a The function _f ij _{(a j)} used as a function _f kj _{(a j)} showing the relationship between the natural frequency _{X k} and the influencing factors _{a j} of the reference model _{7 k.}
The natural frequency calculation unit 28 multiplies the natural frequency X _k0 of the reference model 7 _k applied to each element 6 _k by the correction coefficient α _k obtained by the correction coefficient calculation unit 26 to obtain the value of each element 6 _k . The actual natural frequency X _k (= X _k0 × α _k ) is calculated.
Such a series of processing is repeated by the dividing unit 22, the reference model fitting unit 24, the correction coefficient calculating unit 26, and the natural frequency calculating unit 28, and two horizontal and vertical three directions (XYZ directions) orthogonal to each other. for, the natural frequency of _{X k} of the elements _{6 k} is calculated.
The minimum natural frequency calculation unit 29 obtains the minimum natural frequency among the natural frequencies X _k of each element 6 _k obtained by the natural frequency calculation unit 28 (the minimum among the 3 × k natural frequencies). Ask for things). As a result, it is possible to know which element 6 _k in which direction of the piping system 1 should be subjected to vibration countermeasures in which direction of vibration mode. The minimum natural frequency obtained by the minimum natural frequency calculation unit 29 is displayed on the display unit 44 of the user interface 40.

As described above, in the present embodiment, dividing step of dividing the pipeline 1 into a plurality of elements 6 _k for each constraint points 8 and (step S6), and for each of the plurality of elements 6 _k, the natural frequency X _k0 reference model 7 _k as the reference model fitting process fitting (step S8), and the elements 6 _k and a plurality of elements 6 _k the correction coefficient alpha _k based on the difference between the reference model 7 _k, which is fitted to the element which is known correction coefficient calculating step of calculating for each (step S10) and, by multiplying the correction coefficient alpha _k to the natural frequency X _k of the reference model 7 _k, which is fitted to each of the elements 6 _k, each unique multiple elements 6 _k by a natural frequency calculating step of calculating frequency X _k (step S12), the perform vibration analysis piping system 1.
Instead of modeling the piping system 1 having a complicated shape as it is, the piping system 1 is divided into a plurality of elements 6 _k , and the natural frequency of each element 6 _k is compared with the reference model 7 _k. by determining the X _k, it is possible to easily perform vibration analysis piping system 1 can greatly reduce the time required for analysis. Therefore, it is possible to perform analysis over a wider range of the piping system 1, and the vibration characteristics of the piping system 1 can be accurately grasped. Therefore, it is possible to prevent a situation in which the piping support structure (support member) is forced to be corrected after the plant trial operation stage.
Moreover, since the resulting natural frequency X _k for each element 6 _k, or to be subjected to vibration measures become clear to the pipe system 1 throat point (element 6 _k). Therefore, at the design stage of the piping system, there is no fear of resonance with a device having a rotating body or a reciprocating body, and the piping system 1 having excellent rigidity against vibration can be easily realized.

In the above-described embodiment, before the reference model fitting step (step S8), the representative model preparation step (step S2) for preparing a plurality of representative models 4 _i with known natural frequencies X _j0 is performed. did. Then, in the reference model fitting process (step S8), and it was set to fit the nearest representative model from among a plurality of representative model 4 _i to each element 6 _k is selected as reference model 7 _k to each element 6 _k.
Thus, if the elements typically used in the piping system 1 of the plant are prepared in advance as the representative model 4 _i , vibration analysis of the piping system 1 of any shape in various plants can be performed easily and quickly. it can.

In the embodiment described above, prior to the correction coefficient calculation step (step S10), and shows the relationship between the influence factors a _j that affects the natural frequency X _i and said intrinsic frequency X _i representative model 4 _i A function calculation step (step S4) for _{obtaining the} function f _ij (a _j ) is performed. In the correction coefficient calculation step (step S10), the correction coefficient α is calculated using the function f _ij (a _j ) based on the difference in the influence factor a _j between each element 6 _k and the reference model 7 _k applied to the element. _k was calculated. Specifically, the correction coefficient α using the function f _ij (a _j ) calculated in step S4 for the representative model 4 _i corresponding to the reference model 7 _k as f _kj (a _j ) in the above equation (2). _{Find k} .
Thus, it is possible to obtain an accurate natural frequency X _k of the elements 6 _k conveniently and quickly.

In the above-described embodiment, the dividing step (step S6), the reference model fitting step (step S8), the correction coefficient calculating step (step S10), and the natural frequency calculating step (step S12) are performed in two horizontal directions orthogonal to each other. It was made to repeat about three directions, a direction and a perpendicular direction.
Plant piping systems are usually complex three-dimensional shapes, so vibrations in all directions can be a problem. For this reason, even if analysis is performed in one direction, it is often impossible to accurately know the vibration characteristics of the piping system. Therefore, as described above, the vibration characteristics of the complicated three-dimensional piping system 1 can be ensured by repeating the division process to the natural frequency calculation process in two horizontal directions and a vertical direction that are orthogonal to each other. I can grasp it.

Furthermore, in the above-described embodiment, the minimum natural frequency calculating step (step) for obtaining the minimum natural frequency among the natural frequencies X _k of the elements 6 _k calculated in the natural frequency calculating step (step S12) in three directions. S16) was further performed.
Thus it was minimal from the natural frequency obtained in, for either direction vibration mode of which element 6 _k of the pipeline 1 can know to be subjected to vibration countermeasures. Therefore, vibration countermeasures for the piping system 1 can be efficiently performed.

  As mentioned above, although embodiment of this invention was described in detail, it cannot be overemphasized that this invention is not limited to this, In the range which does not deviate from the summary of this invention, various improvement and deformation | transformation may be performed.

  For example, in the above-described embodiment, an example in which steps S6 to S12 are repeated in the XYZ directions has been described. However, when it is sufficient to perform vibration analysis in a specific direction, steps S6 to S12 are performed only in that direction. Also good.

  In the above-described embodiment, the example in which the vibration analysis apparatus 10 (see FIG. 6) is used to implement the vibration analysis method illustrated in FIG. 2 is described. However, the vibration analysis method according to the present invention uses the vibration analysis apparatus 10. You may go without using it. At this time, all or part of steps S2 to S16 may be automated.

DESCRIPTION OF SYMBOLS 1 Piping system 2 Piping 3 Support member 4 _i representative model 5 Bending part 6 _k element 7 _k reference model 8A-8E Restriction point 9 Piping support 10 Vibration analyzer 20 CPU
22 division unit 24 reference model fitting unit 26 correction coefficient calculation unit 28 natural frequency calculation unit 29 minimum natural frequency calculation unit 30 storage means (memory)
40 User interface 42 Input section 44 Display section

Claims (7)

A vibration analysis method for a piping system having a piping and a plurality of support members for supporting the piping at a plurality of restraint points,
A dividing step of dividing the piping system into a plurality of elements for each of the restraint points;
A reference model fitting step of applying a reference model having a known natural frequency for each of the plurality of elements;
A correction coefficient calculation step for obtaining a correction coefficient for each of the plurality of elements based on a difference in influence factors that are parameters affecting the natural frequency between each element and the reference model applied to the element;
A vibration of a piping system, comprising: a natural frequency calculation step of obtaining the natural frequency of each of the plurality of elements by multiplying the natural frequency of the reference model applied to each element by the correction coefficient. analysis method. Before performing the reference model fitting step, further comprising a representative model preparation step of preparing a plurality of representative models with known natural frequencies,
2. The piping system vibration analysis according to claim 1, wherein, in the reference model fitting step, a representative model closest to each element is selected from the plurality of representative models as the reference model and applied to each element. Method. Before performing the correction coefficient calculation step, further comprising a function calculation step for obtaining a function indicating a relationship between the natural frequency of the representative model and an influencing factor affecting the natural frequency,
3. The piping system according to claim 2, wherein, in the correction coefficient calculation step, the correction coefficient is obtained using the function from a difference in the influence factors between each element and the reference model applied to the element. Vibration analysis method.   4. The method according to claim 1, wherein the dividing step, the reference model fitting step, the correction coefficient calculating step, and the natural frequency calculating step are repeated in three horizontal directions and a vertical direction that are orthogonal to each other. A vibration analysis method for a piping system according to claim 1.   5. The piping according to claim 4, further comprising a minimum natural frequency calculating step for obtaining a minimum natural frequency among the natural frequencies of each element calculated in the natural frequency calculating step in the three directions. System vibration analysis method. A vibration analysis device for a piping system comprising a piping and a plurality of supporting members that support the piping at a plurality of restraint points,
Dividing means for dividing the piping system into a plurality of elements for each of the restraint points;
A reference model fitting means for fitting a reference model having a known natural frequency for each of the plurality of elements;
Correction coefficient calculation means for obtaining a correction coefficient for each of the plurality of elements based on a difference in influencing factors that are parameters affecting the natural frequency between each element and a reference model applied to the element;
A vibration of a piping system, characterized by comprising: natural frequency calculation means for multiplying the natural frequency of a reference model applied to each element by the correction coefficient to obtain the natural frequency of each of the plurality of elements. Analysis device. Storage means for storing a plurality of representative models with known natural frequencies;
A user interface having a display unit and an input unit for exchanging information with an operator;
The reference model fitting means prompts the operator to select a representative model closest to each element from the plurality of representative models stored in the storage means, and the operator selects the representative model using the input section. The piping system vibration analysis apparatus according to claim 6, wherein a representative model is applied to each element as the reference model.

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