JP2008129726A - Design device and design method for rotational structure - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a design device and a design method for a rotational structure, in which a finite element model of the rotational structure is changed so that the rotational structure can satisfy conditions relating to such design items as a critical speed, vibration amplitude and a bearing load. <P>SOLUTION: The design method for the rotational structure includes: creating an equation of motion for the finite element model of the rotational structure created by beam elements or beam elements and rigid disk elements, under the consideration of a power acting on the model (S104); analytically calculating sensitivity coefficients showing to which extent the design items change when changing certain design variables if the conditions of the design items are not satisfied (S114); and changing the finite element model by an optimization planning method by using the sensitivity coefficients (S116, S118). <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to the design of rotating structures.

  An apparatus for analyzing a physical characteristic value of a rotating structure rotating around a central axis and an apparatus for supporting the design are known. For example, the following Patent Document 1 describes a technique for analyzing vibration generated by unbalance of a rotating structure using a transfer matrix method and a mode analysis method, and using this to predict the effect of a balance weight. Yes. Patent Document 2 describes a technique for obtaining vibrations of a rotor blade using a finite element method and obtaining an optimum blade shape by a parameter study based on an experimental design method.

  Patent Documents 3 and 4 describe a technique for designing an optimum structure that satisfies a target natural frequency and a forced vibration level by iterative calculation using sensitivity analysis using a finite element method and strain energy. .

JP-A-6-331479 JP 2005-92358 A JP-A-8-83303 JP 2005-25554 A

  In the techniques disclosed in Patent Documents 1 and 2, the model can be analyzed based on the model of the rotating structure that defines the shape and other characteristics. In order to obtain a rotating structure that satisfies the design requirements, it is necessary to perform trial and error by changing the design variables indicating the shape and other characteristics (parameter study). This trial and error may take a long time to obtain the required performance. In particular, the operator's experience largely depends on which design variable is to be changed, and in the case of an operator having insufficient experience, there is a case where waste is increased.

  Further, in the above Patent Documents 3 and 4, a technique for performing optimization so as to satisfy the target requirement is shown, but it is unclear which parameter contributes to the design requirement and the efficiency. Well, it was not possible to adapt to the design conditions.

  An object of this invention is to provide the design apparatus which designs a rotary structure efficiently.

  In the design of the rotating structure according to the present invention, as a finite element model of the rotating structure, a rotating structure model formed by a plurality of beam elements, or a plurality of beam elements and at least one rigid disc element is used. A model in which the created rotating structure model is supported by a support element is used. The beam element is an element having rotational symmetry with respect to the central axis and a finite length in the central axis direction, and is a round bar-like element. By using a model formed of beam elements, it is possible to analytically determine the degree of change in performance when a model is deformed, that is, a coefficient indicating sensitivity, for a predetermined performance item. For example, when the length of one beam element is changed, it is analytically determined how much the critical speed, which is an example of the performance item of the rotating structure, changes. Further, the support element may be a support element constituted by an elastic / damping element, in particular, a support element comprising a linear spring / speed proportional damping.

  Specifically, the sensitivity coefficient can be obtained as follows. First, the equation of motion of the rotating structure is derived from the finite element model and the external force applied to the model. The sensitivity coefficient for the design variable of the finite element model is calculated for the characteristic matrix constituting the coefficient matrix of each term of the equation of motion, that is, each term of the elastic term, the damping term, and the spring term. This sensitivity coefficient can be obtained analytically because a beam element is used. Using the sensitivity coefficient of this characteristic matrix, the sensitivity coefficient for the design variable for the performance item can be expressed.

  If the sensitivity coefficient of each performance item with respect to the design variable of the finite element model is obtained, it can be estimated how to change the model in order to satisfy the design condition with respect to the performance item. Therefore, it is possible to calculate a model adapted to the design condition of the design item more efficiently than creating a model by trial and error.

  The performance items of the rotating structure include critical speed, vibration amplitude, and bearing load of the bearing that supports the rotating structure. For example, for a design condition in which the critical speed is defined as a multiple of the upper limit value of the rotational speed of use of the rotating structure, the finite element model is changed, that is, the design variable is changed so as to satisfy this condition. .

  According to the present invention, since the finite element model is created by the beam element, the sensitivity coefficient of the performance item can be obtained analytically, and the amount of calculation can be reduced. Further, by changing the finite element model using the sensitivity coefficient, it is possible to efficiently adapt to the design conditions.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a block diagram showing a schematic configuration of a design system 12 including a rotating structure design apparatus 10 according to the present embodiment. The design apparatus 10 can be a computer that operates according to a program stored in the program storage unit 14, and each block in the design apparatus 10 is a block that indicates each function of the computer.

  The design apparatus 10 includes an input / output unit 16 that exchanges information with the outside. The input / output unit 16 can acquire the finite element model 18 created outside. Further, the finite element model 18 can be created in the design apparatus 10 by storing a program for creating a finite element model in the program storage unit 14. As will be described later, the finite element model 18 is a model created with a beam element or with a beam element and a rigid disk element. The input / output unit 16 receives an operation input from the operator 20, for example, an input of design conditions, an operation instruction of the design apparatus 10, and the like. Further, information is output from the input / output unit 16 to an output device 22 such as a display device or a printing device, and predetermined output is performed by the output device.

  The calculation processing unit 24 functions as a sensitivity coefficient calculation unit 26, a model change unit 28, a model evaluation unit 30, a dangerous speed calculation unit 32, a forced vibration calculation unit 34, and a bearing load calculation unit 36. These functions will be described later.

  Furthermore, the design apparatus 10 is provided with a design condition storage unit 38 that stores conditions relating to design items that are input by an operator. The design item is an item that becomes a constraint in designing the rotating structure, such as dangerous speed, forced vibration, and bearing load. For each, a design-acceptable range, that is, a design condition, is determined when designing each rotating structure, and a finite element model is adapted to satisfy this condition. In addition, the design apparatus 10 includes a sensitivity coefficient storage unit 40. The sensitivity coefficient indicates how much the design item changes when the design variable of the finite element model is changed. In particular, in the present embodiment, even if there is a change in the design variable of the finite element model, a new sensitivity coefficient can be obtained by substituting a new design variable into the analytical formula for the sensitivity coefficient obtained analytically. It is done. Furthermore, the design apparatus 10 includes a model storage unit 42 that stores a finite element model.

  Calculation of the sensitivity coefficient by the sensitivity coefficient calculation unit 26 is performed as follows. The sensitivity coefficient derives the equation of motion of the rotating structure from the finite element model and the force applied to the model, and the sensitivity coefficient (characteristic matrix) of the characteristic matrix that is the coefficient matrix of each term of this equation of motion to the design variable of the finite element model Sensitivity coefficient) for a predetermined performance item and a design variable for the design variable can be calculated using the sensitivity coefficient of the characteristic matrix. The calculation of the sensitivity coefficient is analytically obtained because the finite element model is created by the beam element, and is expressed as an expression including design variables. Therefore, when a certain design variable is given, the sensitivity coefficient for the design variable can be calculated by substituting the numerical value into the equation.

  The model change unit 28 changes the finite element model based on the evaluation by the model evaluation unit 30 and the sensitivity coefficient. Specifically, if the current finite element model fails to satisfy the design conditions, the design variables of the individual beam elements or rigid disk elements that make up the finite element model, such as the length and diameter of the beam element, are changed. To create a new finite element model. The design variable is changed at this time in a direction in which the design condition is satisfied for a design item for which the condition is not satisfied with reference to the sensitivity coefficient.

  The model evaluation unit 30 evaluates whether the conditions of each design item are satisfied using a finite element model. In this embodiment, the model evaluation unit 30 is configured such that the critical speed calculated by the critical speed calculation unit 32, the forced vibration amplitude calculated by the forced vibration calculation unit 34, and the bearing load calculated by the bearing load calculation unit 36 are predetermined. If there is an unsatisfied determination item, the model changing unit 28 is instructed to improve the item. The critical speed calculator 32 calculates the critical speed by solving a known eigenvalue problem of the equation of motion. In addition, the forced vibration calculation unit 34 and the bearing load calculation unit 36 calculate the amplitude and the bearing load by a known solution method of the forced vibration solution of the equation of motion.

  FIG. 2 is a chart showing the flow of the design method of the rotating structure according to the present embodiment. First, a design target, that is, a condition regarding a design item is set by an operator (S100). Next, when a finite element model is separately created, it is read (S102). The equation of motion is determined by the finite element model and the force applied to the model (S104). The critical speed and forced vibration response are calculated from this equation of motion (S106, S108), and it is determined whether these solutions satisfy the design target related to the critical speed of the design target, the amplitude of the forced vibration, and the bearing load ( S110). If the design goal is satisfied, the finite element model used is determined as the designed model.

  If the design target is not satisfied in step S110, the sensitivity coefficient of each design item is calculated (S114), and the design variable is changed (updated) by the optimization planning method using this sensitivity coefficient (S116). It performs (S118).

  Hereinafter, the design of the rotating structure according to the present embodiment will be described with a specific example.

<Finite element model>
FIG. 3 is a diagram schematically showing a rotational structure 50 rotationally symmetric about a central axis supported by a support element 52 composed of a linear spring element and a damping element. The support element 52 is assumed to be a plain bearing or a rolling bearing. Assume a system in which two rigid disks 56 and 58 are fixed to an elastic shaft 54 supported by a support element 52 and having several parts with different diameters, and the rotating structure 50 rotates at a constant speed ω. A forcing force Fi (i = 1 to 4) acting on the rotating structure is applied to the left and right of the rigid disks 56 and 58, respectively.

  FIG. 4 is a diagram showing a finite element model 60 of the rotating structure 50 and the supporting element 52 of FIG. The rotating structure 50 is divided into elements in the z direction. In the example shown in the figure, it is divided into 12 elements indicated by circled numbers in the figure. The nodal point of the element is taken as the point of action of the forcing force such as the portion where the cross section of the shaft changes, the position of the center of gravity of the rigid disk, the support point of the spring / damping element, and the unbalanced weight. In the figure, the nodes are represented by numbers in parentheses. The nodes other than (5), (8), (9), and (12) are the nodes where the axial section changes, the node (5) is the center of gravity of the rigid disk 56, and the nodes (8) and (9) are supported. A support point by element 52. The nodes (3), (6), (11), and (13) are not only the point at which the axial cross section changes, but also the point of application of the forcing force F. The node (12) is the position of the center of gravity of the rigid disk 58.

  The rotating structure 50 is an example of modeling a turbocharger compressor, turbine, and shafts thereof. The rigid disks 56 and 58 correspond to the compressor and turbine impellers, and the elastic shaft 54 corresponds to the shaft. Yes. In the illustrated example, the elastic shaft 54 includes twelve portions having different diameters, but the number of these portions can be changed as appropriate. Further, the number of rigid disks and the attachment position with respect to the elastic shaft 54 can be changed as appropriate. Furthermore, it is also possible to handle a rotating structure composed of only an elastic shaft without a rigid disk.

There are three types of analysis elements: a beam element representing an elastic shaft portion, a rigid element representing a rigid disk (concentrated inertia element), and a linear spring / damping element. FIG. 5 is a diagram showing the configuration of the beam elements. The illustrated beam element is composed of an inner shaft 62 and an outer shaft 64. l is the length of the beam element, d ₁ and d ₂ are the outer diameters of the inner shaft 62 and the outer shaft 64, E ₁ and E ₂ are the longitudinal elastic modulus of the inner shaft 62 and the outer shaft 64, and G ₁ and G ₂ are the inner diameters Transverse elastic coefficients of the shaft 62 and the outer shaft 64, ρ ₁ and ρ ₂ represent the densities of the inner shaft 62 and the outer shaft 64, respectively. The beam element shown in the figure is a double shaft of inner and outer shafts, but a single, that is, a uniform round bar-like beam element may be used if necessary.

<Equation of motion>
Next, the equation of motion of the finite element model 60 is obtained. In FIG. 4, considering the vibration in the x and y directions, the equation of motion is derived by the finite element method. This whirling vibration includes rigid body vibration and bending vibration of the rotating structure. For the formulation of the equation of motion, see Toshio Yamamoto and Yukio Ishida, dynamics of rotating machinery, Corona. The outline is shown below.

-Beam element characteristic matrix-
FIG. 6 shows contact displacement at both ends of the beam element. u and v represent translational displacements in the x and y directions, and θx and θy represent rotational displacements (deflection angles) around the x and y axes. A contact displacement vector q _e ^s of the beam element is defined as shown in Equation (1). Here, i and j indicate both ends of the beam element.

式（３）に用いられるＳｙｍ．は、この部分の行列の各要素が、行列の左下半分の各要素を左上から右下に延びる対角線で対象に配置したものであることを示す。以下同様である。 The element mass matrix M ^b is expressed by equations (2) and (3).

Sym. Used in Equation (3). Indicates that each element of this part of the matrix is the lower left half of the matrix arranged on the target by a diagonal line extending from upper left to lower right. The same applies hereinafter.

式（５）に用いられるＳｋｅｗ−ｓｙｍ．は、この部分の行列の各要素が、行列の左下半分の各要素について符号を逆転し、これらを左上から右下に延びる対角線で対象に配置したものであることを示す。以下同様である。 The element gyro matrix G ^b is expressed by equations (4) and (5).

Skew-sym. Used in equation (5). Indicates that the elements of this part of the matrix are those in which the signs of the elements in the lower left half of the matrix are reversed and these are arranged on the object with diagonal lines extending from the upper left to the lower right. The same applies hereinafter.

Further, the element stiffness matrix K ^b is expressed by equations (6) and (7).

-Rigid element characteristic matrix-
The mass of the rigid element is concentrated at the position of the center of gravity. Nodal center of gravity and i, as defined in Figure 6, representing the nodal displacement vector q _e ^d in rigid element in equation (8).

The element mass matrix M ^d is expressed by equations (9) and (10). Mi is the mass of the rigid element, Idi is the moment of inertia around the x-axis (or around the y-axis) of the rigid element, and Ipi is the moment of inertia around the z-axis of the rigid element. In the rotating body, due to the symmetry, the moment of inertia around the x axis is usually equal to the moment of inertia around the y axis.

-Spring / damping element characteristic matrix-
It is assumed that the support reaction force of the spring / damping element is concentrated on one node. Here, only the spring / damping constant in the translation direction is considered, and the rotational component is not considered. However, a coupled component in the x direction and the y direction is considered. The contact displacement vector q _e ^sd of the spring / damping element is expressed by Expression (11).

The element stiffness matrix K ^sd and the element attenuation matrix C ^sd are expressed as in Expressions (12) and (13).

  Kxx and Kyy represent translational spring constants in the x and y directions, and Kxy and Kyx represent coupled spring constants in the x and y directions. Kθxθx and Kθyθy represent rotational spring constants about the x and y axes, and Kθxθy and Kθyθx represent coupled spring constants about the x and y axes. Cxx and Cyy represent translational damping constants in the x and y directions, and Cxy and Cyx represent coupled damping constants in the x and y directions. Cθxθx and Cθyθy represent rotational damping constants about the x and y axes, and Cθxθy and Cθyθx represent coupled damping constants about the x and y axes.

-Unbalance force-
In many cases, since the whirling vibration of the rotating structure is excited by unbalance, the unbalance forcing force of the rotating structure is formulated here. If the magnitude of unbalance of the node i is Ui and the phase angle is αi, the forcing vector at the node i is expressed by the following equation (14).

ｔは時間、ｊは虚数単位を表す。他の任意の周期外力を扱う場合も、このような調和関数を重ね合わせることで定式化が可能である。

t represents time and j represents an imaginary unit. In the case of handling other arbitrary periodic force, it can be formulated by superposing such harmonic functions.

-Equation of motion of the whole system-
The equation of motion (15) of the entire system is obtained by assembling the element characteristic matrix and the force vector for all elements. q represents a displacement vector of all nodes, and F represents a force vector. M, G, C, and K are a mass matrix, a gyro matrix, an attenuation matrix, and a stiffness matrix of the entire system, and are represented by the sum of each element matrix as in Expression (16).

<Sensitivity analysis>
-Sensitivity coefficient of characteristic matrix-
Formulate the sensitivity coefficient for each element characteristic matrix of the equation of motion. Here, the sensitivity coefficient with respect to the dimensions (d ₁ , d ₂ , l) of the elastic beam element shown in FIG. 5 is shown. Sensitivity coefficients for the rigid element inertia values (Mi, Idi, Ipi), bearing spring damping constants, and forcing components are defined by the characteristic matrix definition equations (9), (10), (12), (13 ), The description will be omitted.

The sensitivity coefficient of the beam element with respect to the mass matrix M ^b is expressed by the following equations (17) to (20). That is, the sensitivity coefficient with respect to the design variable d ₁ is represented by Expression (17), the sensitivity coefficient with respect to the design variable d ₂ is represented by Expression (18), and the sensitivity coefficient with respect to the design variable l is represented by Expression (19).

Sensitivity coefficient for gyro matrix G ^b of the beam element, the following equation (21) - a (24).

The sensitivity coefficient for the stiffness matrix K ^b of the beam element is expressed by the following equations (25)-(28).

The sensitivity coefficient of the unbalance forcing force shown in the equation (14) is expressed by the following equations (29) and (30). Here, the unbalanced magnitude Ui of each node and the phase angle αi are set as design variables.

The sensitivity coefficients of the mass matrix M, the gyro matrix G, the attenuation matrix C, and the stiffness matrix K of the entire system are expressed by the following formula (31) by assembling the sensitivity coefficients of the individual element specifying matrices for all elements. Here, s represents a design variable.

Further, the element mass matrix M ^d of the rigid body element is represented by the following expressions (31-1) and (31-2) from Expression (9) by definition. The element gyro matrix G ^d , the element stiffness matrix K ^sd of the spring / damping element, and the element damping matrix C ^sd are similarly derived from the definition expressions (10), (12), and (13).

式（３４）において、ｐは固有振動数、φは固有ベクトルを表す。 −Dangerous speed sensitivity coefficient−
Consider the critical speed (resonance speed) of unbalanced forced vibration. The critical speed of unbalanced vibration is the rotational speed that matches the fixed natural frequency. In order to calculate the critical speed, substituting equation (33), which is a free vibration solution, into equation of motion (32) of free vibration, equation (34) is obtained.

In Expression (34), p represents the natural frequency, and φ represents the eigenvector.

Ｍ，Ｋは対称行列、Ｇは歪対称行列なので、式（３５）は、エルミート行列の固有値問題となる。したがって、得られる固有値ω²が正であれば、ωは実数となり、危険速度が実在することとなる。 Here, when the critical speed condition p = ω is considered, the eigenvalue problem shown in the equation (35) regarding ω ² and φ is obtained.

Since M and K are symmetric matrices and G is a distortion symmetric matrix, Equation (35) is an eigenvalue problem of Hermitian matrix. Therefore, if the obtained eigenvalue ω ² is positive, ω is a real number, and a dangerous speed exists.

φrは危険速度における固有ベクトルである。固有ベクトルの大きさは任意であるので、ここでは、式（３７）の正規条件を定める。記号＊は、共役転置を表す。

Assuming that the r-th critical speed is ωr, ωr satisfies Expression (36).

φr is the eigenvector at the critical speed. Since the size of the eigenvector is arbitrary, the normal condition of Expression (37) is defined here. The symbol * represents a conjugate transpose.

Differentiating equation (36) by design variable s yields equation (38), and taking conjugate transpose of both sides of equation (36) yields equation (39).

Multiplying φr ^* from the left of both sides of Equation (38) and considering Equation (37) and Equation (39), the sensitivity coefficient for the critical speed ωr is Equation (40).

-Sensitivity coefficient of vibration amplitude-
Substituting the solution of the unbalanced forced vibration equation of motion (15) into the equation of motion as equation (41) yields equation (42).

Therefore, the amplitude of the forced vibration at the rotational speed ω is expressed by Equation (43).

When the equation (42) is differentiated by the design variable s, the equation (44) is obtained.

Therefore, the sensitivity coefficient of the forced vibration amplitude Q is expressed by equations (45) and (46).

When the sensitivity coefficient of the forced amplitude at the critical speed ωr is considered, ωr is also a function of the design variable s, and therefore, the equation (47) is substituted for the equation (46).

−Bearing load sensitivity coefficient−
Due to the unbalanced vibration of the rotating body, a load is generated in the bearing (spring / damping element) that supports the rotating body. The bearing load Fix generated in the x direction of the bearing node i is expressed by the following equation (48).

The sensitivity coefficient of the bearing load at an arbitrary rotational speed ω is given by equation (49), and the sensitivity coefficient of the bearing load at the critical speed ωr is given by equation (50).

−Summary of sensitivity coefficient−
Sensitivity coefficients of design items such as critical speed, vibration amplitude, and bearing load are mass matrix M, gyro matrix G, damping, as shown in equations (40), (45)-(47), and (50). It is expressed by a matrix C, a stiffness matrix K, and sensitivity coefficients thereof, and further a sensitivity coefficient of unbalance forcing force. The characteristic matrix is analytically obtained, for example, as shown in equations (2), (4), (6), and the like, and by substituting specific numerical values for design variables such as diameters d ₁ and d ₂ , It can be obtained as a specific numerical value. Therefore, the sensitivity coefficient can be easily obtained as a numerical value regarding a specific finite element model. This is because the axis is modeled by a beam element.

  If the sensitivity coefficient of the design item for the design variable is analytically determined, that is, if it is expressed by an expression using the design variable as a variable, the sensitivity coefficient can be obtained by substituting a specific design variable into this expression. Can be requested. Whether the design variable value should be increased or decreased in order to satisfy the design condition for the design item can be determined by looking at the sign of the sensitivity coefficient. If the design condition is not satisfied, a new finite element model is created by increasing or decreasing the value of the design variable according to the sensitivity coefficient for the design item. Thus, if an initial model is set, the model can be changed by the design device without depending on the operator's instruction, and the labor of the operator can be omitted.

  For the model of FIG. 7, the optimization problem of unbalanced forced vibration is solved using sequential linear programming using a sensitivity coefficient as the optimization programming. In FIG. 7, the rotating structure is composed of beam elements and is supported by two bearings 52-1, 52-2 (spring / damping elements). The unbalance which becomes the forcible force is set at four points of nodes U3, U8, U17 and U22. The design variables are the diameter and axial length l1, l2 of the beam element of the shaded portion in FIG.

  8 and 9 show the unbalanced forced vibration amplitude (node number 1) and bearing load in the initial specifications. The curve Fx1 in FIG. 8 indicates the load on the bearing 52-1, and the curve Fx2 indicates the load on the bearing 52-2. The normal rotation speed of the rotating machine is set to 3750 Hz. In the initial specifications, it can be seen that there is a critical speed in the bending secondary mode near the normal rotational speed.

  Constraint conditions for moving the critical speed ω2 of the bending secondary mode shown in FIGS. 8 and 9 to the higher speed side than the normal rotation speed and making the vibration amplitude u1 (ω1) at the critical speed of the bending primary mode below a certain value. The optimization problem for reducing the weight of the rotating structure is set as in the following equation (51).

  Here, q represents a design variable vector. The results of solving this optimization problem by sequential linear programming are shown in FIGS. FIG. 10A shows the initial model, and FIG. 10B shows the model after optimization. In the model after optimization, the axial lengths l1 and l2 of the beam elements, which are design variables, are each shortened by 5 mm. FIG. 11 is a diagram illustrating the vibration displacement A of the initial model and the vibration displacement B of the optimization model. It can be understood that the maximum amplitude at the critical speed ω1 in the bending primary mode is equal to or less than the condition value (0.38), and the critical speed in the bending secondary mode is equal to or greater than the condition value (3900 Hz).

  Further, an optimization problem for reducing the weight of the rotating structure is set as shown in the following equation (52) under the constraint condition that the bearing load at the normal rotational speed is reduced to a certain value or less.

  FIG. 12 shows the initial state and the optimized bearing load. (A) shows the bearing load of the bearing 52-1, (b) shows the bearing load of the bearing 52-2, the curve A shows the initial model, and the curve B shows the optimization model.

It is a block diagram which shows schematic structure of the design system containing the design apparatus of the rotating structure of this embodiment. It is a chart which shows the flow of design of the rotation structure of this embodiment. It is a figure which shows schematic structure of a rotation structure. It is a figure which shows the finite element model of a rotating structure. It is a figure which shows a beam element. It is explanatory drawing of the displacement of a beam element. It is a figure which shows a finite element model (initial model). It is a figure which shows the displacement of the node of the number 1 of an initial model. It is a figure which shows the bearing load of an initial model. It is a figure which shows an initial model and an optimization model. It is a figure which shows the change of the displacement of the node by optimization. It is a figure which shows the change of the bearing load by optimization.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 10 Design apparatus of rotating structure, 14 Program storage part, 24 Calculation processing part, 26 Sensitivity coefficient calculation part, 28 Model change part, 30 Model evaluation part, 32 Critical speed calculation part, 34 Forced vibration calculation part, 36 Bearing load calculation 38, design condition storage unit, 40 sensitivity coefficient storage unit, 42 model storage unit, 50 rotating structure, 52 support element, 54 elastic shaft, 56, 58 rigid disk, 60 finite element model.

Claims (6)

A design device for designing a rotating structure that rotates around a central axis so as to satisfy a condition regarding a predetermined performance item,
A finite element including a rotating structure model created by a plurality of beam elements coaxial with the central axis of the rotating structure, or a plurality of beam elements and at least one rigid disk element, and a supporting element for supporting the rotating structure model A finite element model acquisition means for acquiring a model;
Sensitivity coefficient calculation means for analytically calculating a sensitivity coefficient for the design variable of the finite element model of the predetermined performance item;
An adaptation model calculation means for changing the finite element model so as to satisfy the condition regarding the predetermined performance item by an optimization programming method using a sensitivity coefficient, and calculating an adaptation model;
An apparatus for designing a rotating structure. The rotating structure design apparatus according to claim 1,
The sensitivity coefficient calculation means includes
A motion equation deriving means for deriving a motion equation of the rotating structure from the finite element model and the force applied to the rotating structure;
A characteristic matrix sensitivity coefficient calculating means for analytically calculating a sensitivity coefficient for a design variable of a finite element model of a characteristic matrix that is a coefficient matrix of each term of the equation of motion;
A performance item sensitivity coefficient calculating means for calculating a sensitivity coefficient of the predetermined performance item with respect to a design variable of the finite element model using a sensitivity coefficient of the characteristic matrix;
Having
Design device for rotating structures. It is a design apparatus of the rotation structure object according to claim 2,
The predetermined performance items include dangerous speed and vibration amplitude,
The adaptation model calculation means includes
A dangerous speed calculating means for calculating a dangerous speed from the equation of motion;
Vibration amplitude calculating means for calculating vibration amplitude at the time of forced vibration from the equation of motion;
Have
Repeat changes to the finite element model until the critical speed and vibration amplitude conditions are met,
Design device for rotating structures. It is a design apparatus of the rotation structure object according to claim 3,
The predetermined performance item includes a bearing load of a bearing that supports the rotating structure,
The adaptive model calculation means has a bearing load calculation means for calculating a bearing load from the equation of motion, and repeats the change of the finite element model until the condition of the bearing load is satisfied.
Design device for rotating structures.   A computer-readable program for causing a computer to operate as the rotating structure design apparatus according to any one of claims 1 to 4. A design method for designing a rotating structure rotating around a central axis so as to satisfy a condition related to a predetermined performance item,
A finite element including a rotating structure model created by a plurality of beam elements coaxial with the central axis of the rotating structure, or a plurality of beam elements and at least one rigid disk element, and a supporting element for supporting the rotating structure model Creating a model,
Analytically calculating a sensitivity coefficient for the design variable of the finite element model of the predetermined performance item;
A step of changing a finite element model to satisfy a condition regarding the predetermined performance item by an optimization programming method using a sensitivity coefficient, and calculating a fitting model;
A method for designing a rotating structure.

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