KR102353883B1 - Low-voltage distribution panel having seismic isolation device for protecting electrical equipment from earthquake - Google Patents

Abstract

A low-voltage switchgear including a seismic device is provided. The seismic device included in the low-voltage switchgear of the present invention is provided to perform an operation of constructing a vibration system model for modeling vibration in a predetermined direction of the low-voltage switchgear; an operation of deriving a motion equation of the vibration system model and normalizing the motion equation; and a design variable determination operation for determining a spring constant and a damping coefficient of the seismic device that minimizes the maximum bending stress and vibration transmission rate of the low-voltage switchgear in the vibration system model. The operation of constructing the vibration system model considers the low-voltage switchgear and the seismic device as a column vibrating in the direction and constructs the vibration system model using the concentrated mass, spring constant, and damping constant of each of the low-voltage switchgear and the seismic device. The maximum bending stress is obtained by the following formula. According to the present invention, since the spring constant and damping constant of the seismic device can be determined in consideration of the physical characteristics of the low-voltage switchgear, it is possible to design a seismic device customized to a low-voltage switchgear and effectively protect the low-voltage switchgear from earthquakes.

Description

Low-voltage distribution panel having seismic isolation device for protecting electrical equipment from earthquake}

The present invention relates to a low-voltage switchgear, and more particularly, to a low-voltage switchgear including an earthquake-resistant device for protecting electrical equipment from earthquakes.

The recent earthquakes in Gyeongju and Pohang have raised a sense of crisis that Korea is not a safe zone from earthquakes. In particular, as the frequency of intraplate earthquakes is increasing like the Sichuan earthquake, the possibility of large-scale earthquakes in Korea is increasing.

In Korea, seismic design has been applied since 1988, when the seismic-resistance law was enacted. According to the earthquake damage prediction model announced by the Ministry of Public Safety and Security, the estimated amount of damage to buildings in Seoul is 427 trillion won, and the estimated amount of indirect damage is 427 trillion won, according to the earthquake damage prediction model announced by the Ministry of Public Safety and Security. 536 trillion, a huge amount of damage is expected.

Therefore, the government is continuously strengthening seismic design regulations as part of earthquake disaster prevention measures, and the earthquake-resistant construction market is expected to continue to grow as it is promoting measures to reinforce earthquake resistance of existing public facilities. In particular, earthquake-resistant technology is emerging as a future technology that can create high value-added in the overseas construction market as the damage caused by earthquakes has become large-scale due to global population growth and urbanization.

In general, seismic design refers to a structural design that determines the physical properties of a cross section so that all stresses of a structure are within an allowable stress so that the safety of a structure can be maintained and its function can be exerted when an earthquake occurs. The core of seismic design is to make a building respond to the horizontal force of seismic waves. Recently, seismic isolation technology that minimizes vibration transmission and vibration damping technology that offsets the impact of an earthquake by installing a vibration damping device in the structure are being applied to seismic design.

Currently, power supply facilities such as relay panels, or monitoring panels, distribution boards, communication panels, protection panels, control rooms, communication control lines, computer equipment, and control rooms are installed on the floor of the building by installing another floor plate. If you look at the configuration of the double floor system, first, vertical support bars are applied and attached with epoxy adhesive at regular intervals on the concrete slab floor. And the relay panel or switchboard and various facilities mentioned above are installed on this installation floor plate. A cushion pad is placed on the top of the head, and the support for fixing the upper position is connected to the vertical underground bar in all directions, respectively, and fixed with bolts to form a frame. On top of that, assemble the top plate in all directions according to the cushion pad groove and complete it.

Referring to Republic of Korea Patent Registration No. 10-1765683 (the title of the invention "a osseous anchor assembly and a osseous anchor construction method capable of absorbing vibrations of earthquakes using the same") An anchor construction method capable of absorption is also disclosed. In this method, the two-bone type anchor assembly, each with an angle adjustment head that can adjust the installation angle of the PC strand at the line and rear end of the PC strand, absorbs vibration during earthquakes or large-scale ground deformation, and during tension or large-scale ground deformation or earthquake. By preventing the bending phenomenon of the PC strand, the PC strand can exert the maximum tensile force by matching the axis of force in any condition.

However, these two-bone anchors cannot be additionally installed unless they are installed at the time of construction, and there is a limit that cannot be applied to already installed facilities. That is, these technologies could be applied to newly established equipment or facilities, but in equipment such as switchboards or relay panels that are currently operated, there is a problem that cannot be applied in equipment operation because power failure or relocation is required to install seismic reinforcing structures. Have.

Therefore, in order to improve the seismic performance of not only newly installed equipment, but also installed equipment, a technique for designing an earthquake-resistant device in consideration of the physical characteristics of the equipment is urgently required.

Republic of Korea Patent Registration No. 10-1765683 (Title of the invention: "Anchor assembly with ossicles and a construction method for ossicle-type anchors capable of absorbing vibrations from earthquakes using the same")

An object of the present invention is to provide a low voltage switchgear including a seismic device for designing a seismic device in consideration of the physical characteristics of the protection target facility in order to improve the seismic performance of the protection target facility in a predetermined direction.

를 만족하는 k_s 및 c_s 를 찾기 위하여,

The present invention for achieving the above objects relates to a low-voltage switchgear including a seismic device for protecting a facility to be protected from an earthquake. A low-voltage switchgear according to the present invention includes: a switchboard housing in which the low-voltage switchboard is mounted; a power lead-in line for supplying external power to the low-voltage switchboard; and an earthquake-resistant device for determining and applying a design variable that satisfies a predetermined design condition based on design constants for physical properties and dimensions of the low-voltage switchboard, which is a facility to be protected, wherein the earthquake-resistant device includes: a predetermined spring It has a constant and a damping coefficient, and a seismic mount installed between the ground and the facility to be protected so as to support the facility to be protected against the ground; design and model the vibration in a direction perpendicular to the gravity direction of the facility to be protected constructing a vibration system model to deriving a motion equation of the vibration system model and normalizing the motion equation; and in the vibration system model, a design variable determination operation of determining a spring constant and a damping coefficient of the seismic mount that minimizes the maximum bending stress and vibration transmission rate of the facility to be protected. In particular, the operation of constructing the vibration system model is performed by considering the low-voltage switchgear and the earthquake-resistant device as columns vibrating in the above direction, and using the concentrated mass, spring constant, and damping constant of each of the low-pressure switchboard and the earthquake-resistant device. It is characterized in that the vibration system model is constituted. In addition, the operation of determining the design variable includes determining the spring constant and damping coefficient of the seismic device in consideration of the maximum displacement limit value, the acceleration gain limit value, and the maximum bending stress of the low voltage switchgear and the seismic device. and constructing the vibration system model comprises:

To find k _s and c _s that satisfy

는 최대 굽힘 응력,

는 허용 가능 응력,

는 최대 상대 변위 응답,

는 저압 배전반의 허용가능 상대 변위,

는 가속도 이득,

는 허용가능 가속도 이득,

는 내진 장치의 최대 변위,

는 내진 장치의 허용가능 변위,

는 그 총합이 1인 가중 인자,

는

에 대한 스케일링 인자이다. 더 나아가, 상기 운동 방정식을 정규화하는 단계는, 상기 운동 방정식을

로서 모델링하고, 상기 진동계 모델에 인가된 최대 작용력을

로서 모델링하며, 여기에서,

은 고유 진동수(Natural frequency),

이고,

는 감쇠비(Damping ratio)이며,

는 지반가속도 스펙트럼,

이고, k 및 k _s 는 각각 상기 저압 배전반 및 상기 내진 장치의 스프링 상수, c 및 c _s 는 각각 상기 저압 배전반 및 상기 내진 장치의 감쇠 상수를 나타내고, x는 상기 방향에 있어서의 변위를 나타낸다. 바람직하게는, 상기 최대 굽힘 응력은,

로 얻어지고, 상기 설계 변수를 결정하는 동작은, 상기 내진 장치의 스프링 상수 및 감쇠 계수를,

및

로서 구하는 것을 특징으로 한다. 특히, 상기 설계 변수를 결정하는 동작은, 설계 변수를 최적화 알고리즘, 후발견적 알고리즘(meta-heuristic algorithm), 및 공학적 시행착오법(Engineer's trial and error method) 중 적어도 하나를 사용하여 결정하는 것을 특징으로 한다.is considered as a design constraint, where

is the maximum bending stress,

is the allowable stress,

is the maximum relative displacement response,

is the allowable relative displacement of the low voltage switchgear,

is the acceleration gain,

is the allowable acceleration gain,

is the maximum displacement of the seismic device,

is the permissible displacement of the seismic device,

is a weighting factor whose sum is 1,

Is

is the scaling factor for . Further, the step of normalizing the equation of motion, the equation of motion

modeled as, and the maximum applied force applied to the vibration system model

Modeled as , where

is the natural frequency,

ego,

is the damping ratio,

is the ground acceleration spectrum,

where k and k _s are spring constants of the low-voltage switchgear and the earthquake-proof device, respectively, c and c _s represent the damping constants of the low-voltage switchboard and the earthquake-proof device, respectively, and x represents the displacement in the direction. Preferably, the maximum bending stress is

Obtained as, the operation of determining the design variable, the spring constant and damping coefficient of the seismic device,

and

It is characterized in that it is obtained as In particular, the operation of determining the design variable is characterized in that the design variable is determined using at least one of an optimization algorithm, a meta-heuristic algorithm, and an Engineer's trial and error method. do.

According to the present invention, since the spring constant and damping constant of the seismic device can be determined in consideration of the physical characteristics of the facility to be protected, it is possible to design a seismic device customized to the facility to be protected, and to effectively protect the facility to be protected from horizontal earthquakes be able to protect

1A to 1C show a perspective view of a low voltage switchboard according to the present invention, and FIGS. 1D to 1F show a front view, a side view, and a rear view, respectively, of the low voltage switchboard according to the present invention.
1E is a flowchart schematically showing a method of designing an earthquake-resistant device applied to a low-voltage switchboard according to the present invention.
Fig. 2 is a block diagram schematically showing a seismic device design system in which the method of Fig. 1e can be implemented;
3 and 4 illustrate a vibration-proof vibration system model considered in the earthquake-resistant device design method of FIG. 1E .
5 shows the dimensions of the equivalent column.
6 shows an example of obtaining a design variable using the present invention.
7 is a graph modeling the impact from the ground to the seismic device.
8 is a graph showing the ground acceleration spectrum specified in Telcordia-GR-63-CORE, Zone 4, Issue 3).
Fig. 9 shows the discrete ground acceleration spectral input used in the analysis of Fig. 8;

In order to fully understand the present invention, the operational advantages of the present invention, and the objects achieved by the practice of the present invention, reference should be made to the accompanying drawings illustrating preferred embodiments of the present invention and the contents described in the accompanying drawings.

Hereinafter, the present invention will be described in detail by describing preferred embodiments of the present invention with reference to the accompanying drawings. However, the present invention may be embodied in various different forms, and is not limited to the described embodiments. In addition, in order to clearly explain the present invention, parts irrelevant to the description are omitted, and the same reference numerals in the drawings indicate the same members.

Throughout this specification, the term protection target facility will be used interchangeably as an implied name to encompass electrical equipment including a switchboard and a control panel.

1A to 1C show a perspective view of a low voltage switchboard according to the present invention, and FIGS. 1D to 1F show a front view, a side view, and a rear view, respectively, of the low voltage switchboard according to the present invention.

The low voltage switchboard 1100 of the present invention includes a body 1010 , a front panel 1020 , and a side panel 1030 . The main body is fixedly installed at the installation position, and the front panel 1020 is installed so that the main body can be opened. In addition, the low voltage switchgear may be accommodated in the switchgear housing, and external power is supplied to the low voltage switchboard through a power lead-in line. Cable trays may be installed to support and secure the power supply lines.

The switchboard housing may have a hollow hexahedral shape as shown in FIGS. 1A to 1F , a door is installed on the front side, and a power lead-in line for receiving external power may be connected. In addition, electrical equipment such as an operation lever for opening and closing the circuit breaker of the main circuit, an air switch, a voltmeter, an ammeter, a wattmeter, an accumulator, and a current relay may be mounted in the switchboard housing, and these electrical equipment are connected to the power supply line through the conductive part may be electrically connected.

1G is a flowchart schematically showing a method of designing an earthquake-resistant device applied to a low voltage switchboard according to the present invention, and FIG. 2 illustrates a system in which the method of FIG. 1G can be implemented.

The seismic device design method performed in the seismic device included in the low voltage switchboard according to the present invention includes the steps of receiving design constants such as physical dimensions and properties of the facility to be protected (S110), vibration in a predetermined direction of the facility to be protected Constructing a vibration system model modeling (S130), deriving a motion equation of the vibration system model, and normalizing the motion equation (S150), and in the vibration system model, the maximum bending stress and vibration transmission rate of the facility to be protected and determining the spring constant and damping coefficient of the earthquake-resistant device to be minimized (S170). In addition, it is determined whether the determined design variable satisfies the design, and if it is not satisfied, the step of re-determining and refining the design variable ( S190 ) is included. Each step is described below in detail in the corresponding part of the specification.

Fig. 2 is a block diagram schematically showing a seismic device design system in which the method of Fig. 1g can be implemented;

Referring to FIG. 2 , the seismic device design system according to the present invention includes user terminals 210 , 212 , 214 , a seismic device design server 250 , and a database 260 .

The user terminals 210 , 212 , and 214 are used to input design constants such as physical properties and dimensions of the facility to be protected, and receive design parameters determined by the seismic device design server 250 . The design constants input through the user terminals 210 , 212 , and 214 are transmitted to the seismic device design server 250 through the network 290 , and are stored in the database 260 .

The seismic device design server 250 includes a processor capable of implementing a design method as described in FIG. 1G . The design parameters determined by the seismic device design server 250 are transmitted to the user terminals 210 , 212 , and 214 through the network 290 again.

Hereinafter, the seismic device design method according to the present invention will be described in detail.

는 내진 장치(Seismic mount)를 탄성과 감쇠를 가진 칼럼(Column) 으로 간주하였을 때, 내진 장치의 스프링 상수와 감쇠 상수이다. 3 and 4 show a 1-DOF vibration system model for seismic analysis when a switchgear supported by a vibration isolator is subjected to a horizontal seismic motion. In the modeling of FIG. 3 , m is the mass of the switchboard considered as a concentrated mass, and k and c are the spring constant and damping constant of the column when the switchboard structure is regarded as a cantilever column, respectively. and

is the spring constant and damping constant of the seismic mount when the seismic mount is regarded as a column with elasticity and damping.

이 된다.In addition, U _g (t) is the displacement of the ground, y(t) is the vibration displacement of the switchboard, and y _s (t) is the displacement of the upper end of the seismic device. In the modeling of FIG. 3, the spring constant k is the bending stiffness of the switchboard approximated by a column, so if the switchboard is the same as the switchboard of FIG. 4, the spring constant of the column is

becomes this

- Seismic analysis

1) equation of motion

에 대하여 나타내면 다음과 같다.Using Newton's law of motion to derive the equation of motion for the mathematical model of Fig. 4, then the relative displacement

It is expressed as follows.

Here, the equivalent spring constant k _eq and the equivalent spring constant c _eq can be obtained as follows from the mathematical model of FIG. 3 , respectively.

Rewriting the equation of motion in Equation 1 in a normalized form is as follows.

은 고유 진동수(Natural frequency),

는 감쇠비(Damping ratio)이고, 이들 관계로부터

이다. In the above formula,

is the natural frequency,

is the damping ratio, and from these relationships

to be.

2) Relative vibration displacement frequency response (Frequency response)

와 수배전반의 진동 변위

, 그리고 기초가진 진동계의 상대 진동 변위 응답

을 각각 다음과 같은 조화진동이라고 가정하면, Meanwhile, the ground displacement

and vibration displacement of switchgear

, and the relative vibration displacement response of the vibration system with the basis

Assuming each of the following harmonic oscillations,

to be.

와 수배전반의 진동 변위 응답

, 그리고 상대진동 가속도 응답

는 다음과 같이 나타낼 수 있다.ground acceleration

and vibration displacement response of switchgear

, and the relative vibration acceleration response

can be expressed as

가 주어진다면 전달 함수법(Transfer function method)을 이용하여 진동계의 상대진동 변위 주파수 응답(Frequency response)

를 다음과 같이 구할 수 있다.If the ground acceleration spectrum

If given, the relative vibration displacement frequency response of the vibration system using the transfer function method

can be obtained as

은 진동수비(Frequency ratio)이다. 또한 위 식으로부터 최대 상대 변위

는 다음과 같이 구할 수 있다.in Equation 10

is the frequency ratio. Also from the above equation, the maximum relative displacement

can be obtained as

3) Displacement gain and Acceleration gain

는 지반 변위 진폭

에 대한 수배전반 변위 진폭

의 비율로 정의된다. 마찬가지로 가속도 이득(Acceleration gain) 또는 가속도 전달율(Acceleration transmissibility)

는 지반가속도 진폭

에 대한 수배전반 가속도 응답 진폭

의 비율로 정의된다. 여기에

의 관계를 대입하면 변위 이득

와 가속도 이득

를 다음과 같이 구할 수 있다.Displacement gain or Displacement transmissibility

is the ground displacement amplitude

switchgear displacement amplitude for

is defined as the ratio of Similarly, acceleration gain or acceleration transmissibility

is the ground acceleration amplitude

switchboard acceleration response amplitude for

is defined as the ratio of Here

Substituting the relation of

and acceleration gain

can be obtained as

은 진동수비(Frequency ratio)이고,

은 고유 진동수이며,

는 감쇠비(Damping ratio)이다. 미소 감쇠인 경우에, 위 수학식 12식으로부터 최대 변위 이득

와 최대 가속도 이득

는 각각 다음과 같이 구할 수 있다.in Equation 12

is the frequency ratio,

is the natural frequency,

is the damping ratio. In the case of small attenuation, the maximum displacement gain from Equation 12 above

and maximum acceleration gain

can be obtained as follows.

4) Displacement-, velocity-, acceleration-spectral response

가 주어진다면 수배전반 진동계의 상대 변위

를 대합적분(Superposition integration)을 이용하여 다음과 같이 구할 수 있다.Ground motion in the motion equation of Equation 3

If is given, the relative displacement of the switchgear vibration system

can be obtained as follows using superposition integration.

는 감쇠고유 진동수(Damped natural frequency)이다.in Equation 14

is the damped natural frequency.

의 최대 진폭(The maximum absolute value of the displacement), 즉

를 진동계의 "위 스펙트럼 응답(Spectral displacement of the system)"

으로 정의한다. 즉,Displacement response obtained by searching over the analyzed time interval

The maximum absolute value of the displacement, i.e.

is the “spectral displacement of the system”

to be defined as in other words,

과 가속도 스펙트럼 응답(Spectral acceleration)

은 각각 다음과 같이 된다.and the velocity spectral response (Spectral velocity)

Hyperacceleration Spectral Acceleration

are respectively as follows.

가 수학식 10에 나타낸 조화 해석법으로 구한 기초가진계의 주파수 응답

의 최대 값과 근사적으로 동일하다고 가정하면 근사적인 변위-, 속도-, 가속도- 스펙트럼 응답은 각각 다음과 같이 구해진다.If the response spectrum method is obtained by seismic analysis

The frequency response of the fundamental excitation system obtained by the harmonic analysis method shown in Equation 10

Assuming that it is approximately equal to the maximum value of , the approximate displacement-, velocity-, and acceleration-spectral responses are respectively obtained as follows.

5) Maximum stress and structural safety factor

The maximum shear force applied to the column, that is, the switchgear is as follows.

Using the approximate spectral response, the above equation becomes

를 위 식에 대입하면 칼럼(수배전반 구조물)에 걸리는 최대 전단력

은 다음과 같이 구해진다.Maximum relative displacement obtained from Equation 11

Substituting in the above formula, the maximum shear force applied to the column (switchboard structure)

is obtained as

Therefore, the maximum bending moment generated in the switchgear structure is obtained as follows.

From the theory of bending deformation of beams (columns), the maximum bending stress generated in the switchgear structure is defined as follows.

는 구조물(칼럼)에 작용하는 최대 굽힘 모멘트(Maximum bending moment)이고, d는 도5에 보인 바와 같이 칼럼의 중립축에서 단면의 외곽까지의 거리이다. L , I는 각각 은 칼럼의 길이와 단면 계수(Area moment of inertia)이다.in Equation 25

is the maximum bending moment acting on the structure (column), and d is the distance from the neutral axis of the column to the outer edge of the cross section as shown in FIG. L and I are the length and area moment of inertia of the column, respectively.

를 위 식에 대입하면 수배전반 구조물에 발생한 최대 응력

은 다음과 같이 구한다.Maximum relative displacement obtained from Equation (11)

Substituting in the above equation, the maximum stress generated in the switchgear structure

is obtained as follows.

Comparing the maximum bending stress obtained in Equation 25 or Equation 26 with the allowable stress of the column material, the structural safety factor S can be obtained as follows.

는 칼럼, 즉 수배전반 구조 재료의 허용 응력(Allowable stress)이다.here

is the allowable stress of the column, that is, the switchgear structure material.

은 집중질량으로 간주한 수배전반의 질량이고,

는 각각 수배전반 구조물을 외팔보 칼럼으로 간주하였을 때의 칼럼의 스프링상수와 감쇠상수이다. 그리고

는 내진마운트(Seismic mount)를 탄성과 감쇠를 가진 칼럼(Column) 으로 간주하였을 때, 내진마운트의 스프링상수와 감쇠상수이다. 그리고 U _g (t)는 지반의 변위이고, y(t)는 수배전반의 진동 변위이고, y _s (t) 는 내진 장치 상단의 변위이다. 도 3의 모델링에서 스프링 상수 k는 칼럼으로 근사시킨 수배전반의 굽힘 강성이므로 수배전반이 도 4의 수배전반과 동일하다면 칼럼의 전술된 k와 같다. Fig. 3 shows a 1-DOF vibration system model for seismic analysis when a switchgear supported on a vibration-proof mount is subjected to a horizontal seismic motion. In the modeling of Figure 3

is the mass of the switchgear considered as the concentrated mass,

are the spring constant and damping constant of the column when the switchgear structure is regarded as a cantilever column, respectively. and

is the spring constant and damping constant of the seismic mount when the seismic mount is regarded as a column with elasticity and damping. And U _g (t) is the displacement of the ground, y(t) is the vibration displacement of the switchboard, and y _s (t) is the displacement of the top of the seismic device. Since the spring constant k in the modeling of FIG. 3 is the bending stiffness of the switchboard approximated by a column, if the switchboard is the same as the switchboard of FIG. 4 , it is the same as the aforementioned k of the column.

- Seismic analysis

- Equation of Motion

에 대하여 나타내면 다음과 같다.After deriving the equation of motion for the mathematical model of Fig. 3 (d) above using Newton's law of motion, the relative displacement

It is expressed as follows.

Here, the equivalent spring constant k _eq and the equivalent spring constant c _eq can be obtained as follows from the mathematical model of FIG. 3 , respectively.

이므로 도 3 (c)의 모델은 다음 도 4 (a)와 같이 Zener model이 된다.However, in the case of seismic mount switchgear, most

Therefore, the model of Fig. 3 (c) becomes a Zener model as shown in Fig. 4 (a).

(또는 응력과 변형률)의 관계는 비선형이지만 테일러 급수 전개를 이용하여 선형함수로 나타내면 다음과 같다.Figure 4 (a) is a non-linear viscoelastic suspension model combined with two springs and one damper, the so-called Zener model. Force F and deformation in Zener model

The relationship between (or stress and strain) is non-linear, but when expressed as a linear function using Taylor series expansion, it is as follows.

는 각각 다음 수학식 4로 주어지는 Relaxation times이며,

은 수학식 5로 주어지는 Relaxed modulus이다.here

are each relaxation times given by the following Equation 4,

is a relaxed modulus given by Equation (5).

이므로

이다.In case of switchgear supported by seismic mount

Because of

to be.

Therefore, we get the following equation:

Meanwhile, in the equivalent spring-attenuator suspension of FIG. 4(b), the relationship between the acting force and the deformation can be expressed by the following equation.

Comparing the above equations, the equivalent spring constant and equivalent damping coefficient of the Zener model suspension become as follows.

Therefore, if the equivalent spring constant and the equivalent damping coefficient are applied to the equation of motion, it becomes the equation of motion for the model of FIG.

은 고유 진동수(Natural frequency),

이고,

는 감쇠비(Damping ratio)이며,

이다.In the above formula,

is the natural frequency,

ego,

is the damping ratio,

to be.

- Relative displacement response of switchgear and relative displacement response of seismic mount

와 수배전반의 진동 변위

, 기초가진 진동계의 상대진동 변위 응답

, 그리고 내진 장치의 변위

와 내진 장치의 상대 변위

를 각각 다음과 같이 조화진동으로 가정한다.ground displacement

and vibration displacement of switchgear

, Relative vibration displacement response of a vibration system with a basis

, and the displacement of the seismic device

and the relative displacement of the seismic device

Each is assumed to be a harmonic vibration as follows.

와 수배전반의 진동 변위 응답

, 수배전반의 상대가속도 응답

, 내진 장치의 가속도 응답

, 내진 장치의 상대가속도 응답

은 다음과 같이 나타낼 수 있다.ground acceleration

and vibration displacement response of switchgear

, Relative acceleration response of switchgear

, the acceleration response of the seismic device

, the relative acceleration response of the seismic device

can be expressed as

는 지반 가속도 스펙트럼 입력이다. 만약 지반가속도 스펙트럼

가 입력으로 주어진다면, 진동계의 운동방정식의 해인 수배전반의 상대변위 주파수응답(Displacement Frequency Response)

는 전달함수법(Transfer function method)을 이용하여 다음과 같이 구할 수 있다.here

is the ground acceleration spectrum input. If the ground acceleration spectrum

If is given as an input, the displacement frequency response of the switchgear, which is a solution to the equation of motion of the vibration system, is

can be obtained as follows using the transfer function method.

은 진동수비(Frequency ratio),

은 고유 진동수,

이고,

는 감쇠비(Damping ratio)이며,

이다. 또한 위 식으로부터 수배전반의 최대 상대변위

를 다음과 같이 구할 수 있다.in the above expression

Silver frequency ratio,

is the natural frequency,

ego,

is the damping ratio,

to be. Also, from the above equation, the maximum relative displacement of the switchgear

can be obtained as

를 다음과 같이 정의하면, Relative displacement of the seismic mount in the switchgear vibration system model of Fig. 4 (a)

If we define as:

는 다음의 관계를 가진다.By applying the above relational expressions, the relative displacement frequency response of the seismic mount

has the following relation.

On the other hand, in the switchgear vibration system model of FIG. 4(b), the following relational expression is established from the relationship between the force and displacement acting on the series spring of the vibration system.

는 내진 장치-수배전반 진동계의 질량 m에 작용하는 최대 작용력이고,

는 내진 장치의 스프링 상수, k는 수배전반(구조물)의 스프링 상수, 그리고

는 진동계의 등가 스프링 상수로서

와 k가 직렬연결된 스프링 상수이다. 이들을 정리하면 내진마운트의 최대 상대변위

는 다음과 같이 된다.in the above expression

is the maximum force acting on the mass m of the seismic device-switchboard vibration system,

is the spring constant of the seismic device, k is the spring constant of the switchboard (structure), and

is the equivalent spring constant of the vibrating system.

and k are spring constants connected in series. If these are arranged, the maximum relative displacement of the seismic mount

becomes as follows.

에 걸리는 최대 작용력(Maximum force)

는 다음과 같이 구할 수 있다.Switchgear mass in the switchgear vibration system model of Fig. 4(b)

Maximum force applied to

can be obtained as

이므로 수학식 48에서 구한 최대 상대변위

위 수학식 55에 대입하면 내진마운트-수배전반 진동계의 질량

에 작용하는 최대 작용력

은 다음과 같이 구해진다.By the way,

Therefore, the maximum relative displacement obtained from Equation 48

Substituting into Equation 55 above, the mass of the seismic mount-switchboard vibration system

maximum force acting on

is obtained as

은 고유 진동수,

이고,

는 감쇠비(Damping ratio)이며,

이다.here

is the natural frequency,

ego,

is the damping ratio,

to be.

에 작용하는 최대 작용력

를 수학식 55에 대입하면 내진마운트의 최대 상대변위

는 결국 다음과 같이 구한다.The mass of the seismic mount-switchboard vibration system obtained from Equation 56 above

maximum force acting on

Substituting in Equation 55, the maximum relative displacement of the seismic mount

is finally obtained as

- Displacement-, velocity-, acceleration-spectral response

가 주어진다면 수배전반 진동계의 상대 변위

를 대합적분(Superposition integration)을 이용하여 다음과 같이 구할 수 있다.On the other hand, in the equation of motion, the ground motion

If is given, the relative displacement of the switchgear vibration system

can be obtained as follows using superposition integration.

는 감쇠고유진동수(Damped natural frequency)이다.from above

is the damped natural frequency.

의 최대 진폭(The maximum absolute value of the displacement), 즉

를 진동계 내진 해석에서의 "변위 스펙트럼 응답(Spectral displacement of the system)"

으로 정의한다. 즉,Displacement response obtained by searching over the analyzed time interval

The maximum absolute value of the displacement, i.e.

“Spectral displacement of the system” in the seismic analysis of the vibration system.

to be defined as in other words,

과 가속도 스펙트럼 응답(Spectral acceleration)

은 각각 다음과 같이 된다.to be. In addition, the spectral velocity of the seismic analysis of the vibration system

Hyperacceleration Spectral Acceleration

are respectively as follows.

가 수학식 47에 나타낸 조화해석법으로 구한 기초가진계의 주파수응답

의 최대값과 근사적으로 동일하다고 가정하면, 도 4 (b) 진동계에 대한 내진해석의 근사적인 변위-, 속도-, 가속도-스펙트럼응답은 각각 다음과 같이 구해진다.If the response spectrum method is obtained by seismic analysis

The frequency response of the fundamental excitation system obtained by the harmonic analysis method shown in Equation 47

Assuming that it is approximately equal to the maximum value of , the approximate displacement-, velocity-, and acceleration-spectral responses of the seismic analysis for the vibration system in Fig. 4 (b) are respectively obtained as follows.

- Maximum bending deformation, bending stress, structural safety factor of switchgear structure

이므로, 최대 굽힘변형

는 다음의 관계를 가진다.The bending deformation of the switchgear structure (column) due to the action force of the switchgear is

Therefore, the maximum bending deformation

has the following relation.

와 수학식 57에서 구한

를 위 식에 대입하면 수배전반 구조물의 최대 굽힘변형

는 결국 다음과 같이 구해진다.obtained from Equation 48

and obtained from Equation 57

By substituting in the above formula, the maximum bending deformation of the switchgear structure is

is eventually obtained as

이고,

는 감쇠비(Damping ratio)이며, 등가 스프링상수로부터

이다.From here

ego,

is the damping ratio, from the equivalent spring constant

to be.

Therefore, the maximum applied force (shear force) applied to the switchgear structure (column) is as follows.

Therefore, the maximum bending moment generated in the switchgear structure (column) is obtained as follows.

From the bending deformation theory of the beam (column), the maximum bending stress generated in the switchgear structure (column) is defined as follows.

는 구조물(칼럼)에 작용하는 최대 굽힘모멘트(Maximum bending moment)이고, d는 도 5에 보인 바와 같이 칼럼의 중립축에서 단면의 외곽까지의 거리이다. L, I는 각각 은 칼럼의 길이와 단면계수(Area moment of inertia)이다. 그리고

이고,

는 감쇠비이며,

이다.in the above expression

is the maximum bending moment acting on the structure (column), and d is the distance from the neutral axis of the column to the outer edge of the section as shown in FIG. 5 . L and I are the length and area moment of inertia of the column, respectively. and

ego,

is the damping ratio,

to be.

는 다음과 같이 구할 수 있다.When the maximum bending stress obtained in Equation 69 and the allowable stress of the column material are compared, the structural safety factor

can be obtained as

는 칼럼, 즉 수배전반 구조 재료의 허용응력(Allowable stress)이다.here

is the allowable stress of the column, that is, the switchgear structure material.

- Displacement gain and Acceleration gain

에 대한 수배전반 변위진폭

의 비율로 정의된다. 마찬가지로 가속도이득(Acceleration gain) 또는 가속도전달율(Acceleration transmissibility) T _a 은 지반가속도 진폭

에 대한 수배전반 가속도응답 진폭

의 비율로 정의된다. 수학식 47로 구해진 수배전반 상대변위 응답

에

의 관계를 대입하면 변위전달율 T _d 와 가속도전달율 T _a 를 각각 다음과 같이 구할 수 있다. When the vibration system of Fig. 4 (b) receives harmonic fundamental excitation, displacement gain or displacement transmissibility T _d is the ground displacement amplitude

Displacement amplitude of switchgear for

is defined as the ratio of Similarly, acceleration gain or acceleration transmissibility T _a is the ground acceleration amplitude

Switchgear acceleration response amplitude for

is defined as the ratio of The switchgear relative displacement response obtained by Equation 47

to

Substituting the relationship of , the displacement transmission rate T _d and the acceleration transmission rate T _a can be obtained as follows, respectively.

은 진동수비(Frequency ratio)이고,

은 고유진동수,

이고,

는 감쇠비(Damping ratio)이며,

이다. 미소 감쇠인 경우에, 최대 변위이득

와 최대 가속도이득

는 각각 다음과 같이 구할 수 있다.from above

is the frequency ratio,

is the natural frequency,

ego,

is the damping ratio,

to be. In the case of small damping, the maximum displacement gain

and maximum acceleration gain

can be obtained as follows.

- Vibration reduction and static deflection

인 경우에 변위전달율은 다음과 같이 된다.When the switchgear vibration system of Fig. 3 (d) or Fig. 4 (b) receives a harmonic seismic load, a slight attenuation in the displacement transfer rate T _d of Equation 72, that is,

In the case of , the displacement transfer rate becomes

인 방진영역(Vibration isolation region)에서 진동저감율(Vibration reduction ratio)

은 다음과 같이 정의한다.

Vibration reduction ratio in the vibration isolation region

is defined as

에 대하여,

에서의 진동저감율 R을 내진마운트의 방진성능으로 정하고자 하는데 진동저감율 R은 극대화될수록 좋은 성능이므로 목적함수 최소화 문제에 적합한 성능함수로 변환하기 위하여 진동저감율 역수(Inverse of the vibration reduction ratio)를 다음과 같이 정의한다.design variables

about,

To determine the vibration reduction ratio R as the vibration-proof performance of the earthquake-resistant mount, the vibration reduction ratio R is a better performance as it is maximized. define together.

- Energy absorption efficiency of the anti-seismic mount

의 조건을 만족해야 한다. 즉, 지진의 주된 진동수(Dominant frequency of ground motion) f _g 는

의 조건을 만족하여야 한다. 그러므로 충격진동해석 이론을 적용한 완충효율 분석을 적용할 때에 이러한 전제조건이 만족되는지를 반드시 우선적으로 확인하여야 한다.In the design analysis process described above, a vibration analysis theory assuming ground excitation as harmonic excitation was applied. In order to apply the shock vibration analysis, if the shock duration is sufficiently shorter than the natural period, the vibration analysis by shock and the buffer theory can be applied. Therefore, in order for a ground earthquake to become an impact force,

must satisfy the conditions of That is, the dominant frequency of ground motion f _g is

must satisfy the conditions of Therefore, when applying the buffer efficiency analysis applying the shock vibration analysis theory, it is necessary to first check whether these prerequisites are satisfied.

If the ground excitation acts at a moment sufficiently shorter than the natural period of the vibration system (Impulsive base excitation), the vibration analysis by impact and the cushioning theory can be applied.

In this way, when the ground vibration satisfies the shock condition, the ground vibration shock applied to the switchboard in the switchboard vibration system model of FIG. 4 (b) is modeled as shown in FIG. 7 below.

는 지반가진의 충격지속시간(Impulse duration time)으로서 지반가진을 Half sine함수로 가정하고 지반가진의 주된 주파수(Dominant frequency of ground motion)를 f _g 라 하면 다음의 관계를 가진다.in Fig.

is the impulse duration time of the ground excitation, assuming that the ground excitation is a half sine function and f _g is the dominant frequency of ground motion, it has the following relationship.

에 의한 충격량(Impulse)은 다음과 같이 가정한다.maximum ground excitation force

Impulse by , is assumed as follows.

가 가해질 때 진동계의 응답

는 대합적분법(Convolution integral or Duhamel integral)으로 구하면 다음과 같다.The amount of impact in the switchgear vibration system modeling of Fig. 4 (b)

The response of the vibrating system when

If is obtained by the convolution integral or Duhamel integral, it is as follows.

를 다음과 같이 구할 수 있다.Therefore, the maximum shock response

can be obtained as

는

이고, 도 7의 짧은 충격지속시간

동안 지반가진 충격에 의해 스프링이 최대변형

까지 변형될 때 스프링의 최대 탄성에너지(Maximum elastic energy) E _e 는 다음과 같다.Deflection of the spring in the switchgear vibration system modeling of FIG. 4 (b)

Is

and the short impact duration of FIG.

The maximum deformation of the spring due to the shock of the ground during

The maximum elastic energy E _e of the spring when deformed to

In the case of a conservation system (non-damping vibration system), the maximum elastic deformation energy and the maximum kinetic energy are the same according to the energy conservation law, so in Equations 80 and 81, the following holds.

Therefore, the natural frequency of the vibration system can be obtained as follows.

는 다음과 같이 결정할 수 있다. Therefore, the spring constant of the seismic mount

can be determined as

Equation 84 is a relational expression for determining the spring constant of a vibration-proof mount made of only elastic springs when a shocking ground excitation is given.

가 주어진다면, 스프링의 최대변위는

범위의 값을 가져야 하므로 선택 가능한 스프링상수는 다음 식으로 결정할 수 있다.In other words, when a ground vibration is shockingly applied to a switchboard supported only by a spring, the allowable displacement of the spring, a design limiting condition, is

If is given, the maximum displacement of the spring is

Since it has to have a value in the range, the selectable spring constant can be determined by the following formula.

는 에너지흡수 효율(Energy absorption efficiency)로서 지반가진에 의한 최대충격에너지(Maximum impact energy) E _i 에 대한 완충장치에 의해 흡수된 에너지(Energy absorbed by isolator) E _a 의 비율로 정의된다. On the other hand, the buffering efficiency of the seismic mount

is energy absorption efficiency, and is defined as the ratio of energy absorbed by isolator E _{a to} the maximum impact energy E _{i caused by ground excitation.}

에 의한 충격에너지 E _i 는 다음과 같다.The maximum impact force in the seismic impact model of Fig. 7 (c)

The impact energy E _{i by}

And the energy absorbed by the earthquake-proof switchgear mount is the elastic strain energy of the spring up to the elastic strain energy of the earthquake-proof mount springs are the same as the maximum kinetic energy is the maximum energy absorbed by the end E _a vibration mounting as follows.

는 다음과 같이 나타낼 수 있다.Substituting Equation 87 and Equation 88 into Equation 86, the buffering efficiency of the seismic mount

can be expressed as

은 수배전반 진동계의 고유진동수이고,

은 진동계의 고유주파수(Cyclic natural frequency of the vibration system)이다. here

is the natural frequency of the switchgear vibration system,

is the cyclic natural frequency of the vibration system.

의 역수(Inverse of the energy absorption efficiency)를 다음과 같이 정의한다.Buffer efficiency to convert to a performance function suitable for the objective function minimization problem

The inverse of the energy absorption efficiency is defined as follows.

However, since Equations 89 and 90 are established only when the natural frequency of the vibration system has a value smaller than the frequency, there is a limit to using it as an objective function in the process of optimal designing of an earthquake-resistant mount that needs to examine the natural frequency over a wide area.

- Dynamic design of seismic mount

Dynamic design of seismic mount refers to determining the seismic mount spring constant and damping coefficient, which are design parameters of the seismic mount, in order to satisfy the seismic safety of the switchgear and at the same time achieve the anti-vibration effect by using seismic analysis and the anti-vibration theory of the basic vibration system.

- DEFINITION OF DESIGN PROBLEMS

를 극소화시키면서 동시에 수배전반의 방진성능의 척도인 진동전달율 T _d 도 극소화시키도록 내진마운트의 스프링상수 k _s 와 감쇠계수 c _s 를 설계하는 것이다. 그런데 설계변수인 k _s 와 c _s 는 무차원 변수인 고유진동수

과 감쇠비

로 변환할 수 있으므로 목적함수를 무차원화 변수인

와

의 함수로 표현할 수 있다. 그러므로 설계문제는, 수학식 91을 최소화하는 설계변수

를 찾는 것으로 정의할 수 있다.The design includes the maximum bending stress generated in the structure when the switchgear with seismic device is subjected to an earthquake load;

It is to design the spring constant k _s and damping coefficient c _s of the seismic mount to minimize the vibration transmission rate T _{d , which} is a measure of the vibration-proof performance of the switchgear, while minimizing . However, the design variables k _s and c _s are dimensionless variables, natural frequencies.

and damping ratio

can be converted to , so the objective function can be converted to a dimensionless variable

Wow

can be expressed as a function of Therefore, the design problem is the design variable that minimizes Equation 91.

can be defined as finding

: 설계 변수

의 검색 범위,From here,

: design parameters

search scope of,

: 설계 변수

의 검색 범위,

: design parameters

search scope of,

: 가진 입력의 진동 변위 제약,

: vibration displacement constraint of excitation input,

: 보호 대상 설비의 진동 변위 제약

: Vibration displacement restriction of the equipment to be protected

: 가속도 이득 제약,

: acceleration gain constraint,

: 구조적 응력 제약이 설계 제약으로서 고려되고,

는 최대 굽힘 응력,

는 허용 가능 응력,

는 최대 상대 변위 응답,

는 보호 대상 설비의 허용가능 상대 변위,

는 가속도 이득,

는 허용가능 가속도 이득,

는 내진 장치의 최대 변위,

는 내진 장치의 허용가능 변위,

는 그 총합이 1인 가중 인자,

는

에 대한 스케일링 인자이다.

: structural stress constraint is considered as design constraint,

is the maximum bending stress,

is the allowable stress,

is the maximum relative displacement response,

is the permissible relative displacement of the equipment to be protected,

is the acceleration gain,

is the allowable acceleration gain,

is the maximum displacement of the seismic device,

is the permissible displacement of the seismic device,

is a weighting factor whose sum is 1,

Is

is the scaling factor for .

과 감쇠비

가 결정되면, 원래 설계변수인 내진마운트의 스프링상수 k _s 와 감쇠계수 c _s 를 다음 관계식으로부터 구하게 된다.From the above optimal design problem, the optimal natural frequency of the switchgear vibration system with seismic device through the optimal solution search process

and damping ratio

When is determined, the spring constant k _s and damping coefficient c _s of the seismic mount, which are the original design variables, are obtained from the following relational expressions.

- Determination of optimal design parameters

In order to obtain the design variables, the optimal solution is searched for by using the Graphical Optimization Method, which is relatively simple among optimization techniques and can visually check the changes in functions using graphs. The schematic optimization method is a simple method to search for the solution of an optimal design problem involving one or two design variables. That is, when there is only one design variable, the optimal value (minimum value or maximum value) can be easily found in the graph of the objective function for the design variable. Also, when there are two design variables, the optimal value can be easily found from the contour plots of the objective function and constraints.

Since the seismic mount dynamic design problem also has two design variables, the optimal design value can be easily determined by applying the Graphical Optimization Method.

을 2 ~ 20 Hz범위에서 적절한 증분으로 변화시키고, 동시에 다른 설계변수

를 0.1 ~ 0.7 범위에서 적절한 증분으로 변화시키면서 목적함수와 제한조건들을 계산하여 계산결과 데이터를 파일에 기록한다. Briefly explaining the method of searching for the optimal solution, the design variables in the optimal design problem of the switchgear supported on the seismic mount defined by Equation 91

is changed in appropriate increments in the range of 2 to 20 Hz, while at the same time other design parameters

Calculating the objective function and constraint conditions while changing in an appropriate increment in the range of 0.1 to 0.7, and recording the calculation result data in a file.

Draw graphs of objective function and constraint from the calculation result data file.

과

을 결정할 수 있다. 이렇게 최적의 고유진동수

과 감쇠비

가 결정되면, 원래 설계변수인 내진마운트의 최적 스프링상수 k _s 와 최적 감쇠계수 c _s 를 수학식 92 및 수학식 93을 이용하여 결정할 수 있다. 이를 좀더 상세히 설명하면 다음과 같다.Since the design problem is an objective function minimization problem, the optimal solution

class

can be decided This optimal natural frequency

and damping ratio

When is determined, the optimum spring constant k _s and the optimum damping coefficient c _s of the seismic mount, which are the original design variables, can be determined using Equations 92 and 93. This will be described in more detail as follows.

Step 1: Design parameter data input, calculation

During the design process, the design parameters necessary for the calculation of the objective function and constraints are calculated. For example, in the switchgear model of FIG. 3, the switchgear was assumed as a lumped parameter model consisting of a column spring and a lumped mass. If given as 6, the design parameters of the switchgear required for the calculation of the product function and the constraints are as follows.

(1) Switchgear structure (assumed as a column in FIG. 6) Length L (m).

(2) Switchgear structure (assumed as a column in Fig. 6) Width B (m).

(3) Depth W (m) of switchgear structure (assumed as a column in FIG. 6).

(4) Axial-sectional distance d (m) of the switchgear structure (assumed as the column in FIG. 6).

(5) Plate thickness t (m) of the switchgear structure (assumed as the column in FIG. 6)

(6) The longitudinal modulus of elasticity E (Pa) of the switchgear structure (assumed as the column in FIG. 6).

.(7) Structural damping ratio of switchgear structure (assumed as the column in FIG. 6)

.

(8) Section modulus I of switchgear structure (column),

Assuming that the switchgear structure has a uniform column structure as shown in FIG. 6, the section modulus is calculated. If the excitation direction of the ground acceleration is in the y-direction, the section modulus I _y is calculated as follows.

If the excitation direction of the ground acceleration is in the x-direction, the section modulus I _x must be calculated.

(9) Spring constant k of switchgear structure

Assuming that the switchgear structure has a uniform column structure as shown in FIG. 6, the spring constant can be calculated as follows.

The damping coefficient c of the switchgear structure can be calculated as follows.

(11) switchboard mass m ,

의 가중치:

(12) objective function

weight of:

(13) Scaling factors of individual objective functions:

는 허용응력의 1/3정도인 50 MPa 정도로 정한다. In a multipurpose function design problem, each design variable is normalized and converted into a single objective function. In this process, scaling factors for each objective function must be set for normalization. In general, it is appropriate to use the initial design value of the objective function or the expected average value as the scaling factor. In the design problem of this study, it is not easy to predict to what extent the maximum stress of the switchgear structure will be generated as a result of the seismic analysis. The scale factor of the maximum stress, which is an individual objective function,

is set to about 50 MPa, which is about 1/3 of the allowable stress.

는 0.03 정도로 정한다. 다른 개별 목적함수인 방진성능 즉,

에서의 변위전달율은 일반적인 방진시스템의 전달율이 0.2 ~ 0.5 정도인 점을 고려하면 진동저감율 역수

의 스케일링 인수

는 0.2 정도로 정한다. 이러한 제약들은 이해의 편의를 위해 선택된 것으로서, 본 발명을 한정하는 것이 아님에 유의한다.It is difficult to predict the magnitude of the maximum displacement of the switchgear (which is the maximum relative displacement) X _max , but it is a scaling factor considering the maximum vibration displacement of the switchgear.

is set to about 0.03. Anti-vibration performance, which is another individual objective function,

Considering that the transmission rate of a general vibration isolation system is about 0.2 to 0.5, the displacement transmission rate at

scaling factor of

is set to about 0.2. It should be noted that these constraints are selected for convenience of understanding and do not limit the present invention.

와 가속도

: 표 2 참조.(14) Ground acceleration spectrum input: excitation frequency

and acceleration

: See Table 2.

와

.

Wow

.

By converting the ground acceleration spectrum of Telcordia's seismic design standard "GR-63-CORE Zone-4, Issue 3, March 2006" shown in FIG. 8 and Table 1 into a discrete spectrum input as shown in FIG. 9 and Table 2, It was used to calculate the objective function and constraint conditions of the optimal design process.

coordinate point Frequency (Hz) Value of A _g (f) [ g] One 0.3 0.5 2 0.6 2.0 3 2.0 5.0 4 5.0 5.0 5 15.0 1.6 6 50.0 1.6

coordinate point Frequency f _k (Hz) Value of A _g (f _k ) [ g] One One 2.961 2 2 2.0 3 3 5.0 4 4 5.0 5 5 5.0 6 6 4.12 7 7 3.51 8 8 3.07 9 9 2.71 10 10 2.44 11 11 2.21 12 12 2.02 13 13 1.86 14 14 1.72 15 15 1.6 16 17 1.6 17 19 1.6 18 21 1.6 19 23 1.6 20 25 1.6

(15) Main ground excitation frequency f _g (Hz): 4 Hz

(16) Search range of design variable natural frequency f _n

(Hz), 즉

(rad/s)의 범위에 있다. 그러므로 방진마운트 수배전반의 고유진동수는

(rad/s), 또는

(Hz)의 범위에 있어야 한다. 또한 아래 표 3의 방진장치들의 고유진동수를 참고하여 고유진동수 탐색범위를 1 ~ 20 Hz로 정한다.In the seismic analysis, the frequency range of the seismic acceleration input is

(Hz), i.e.

(rad/s). Therefore, the natural frequency of the anti-vibration mount switchgear is

(rad/s), or

(Hz) should be in the range. Also, referring to the natural frequencies of the vibration isolators in Table 3 below, the natural frequency search range is set to 1 ~ 20 Hz.

Table 3 is a table showing typical characteristic frequencies of passive isolators.

의 탐색범위- Design variable equivalent damping ratio

search scope of

정도라는 경험적 지식을 고려한다. The damping ratio of the anti-vibration system is

Consider the empirical knowledge of degree.

= 0.1 ~ 0.7로 정한다. The search range of the design variable damping ratio can be

= 0.1 ~ 0.7.

- Allowable values of objective function and constraint

Seismic Mount Vibration Displacement Allowable Value: X _s,a

Allowable value of switchgear relative vibration displacement: X _a

Acceleration gain allowable value: T _a,a

Allowable stress of switchgear structure:

Allowable values for static deflection of seismic mount springs:

- Step 2: Calculation of objective function and constraint conditions in the design variable search range

를 2 ~ 20 Hz 범위에서 1 Hz 단위로 변화시키고, 다른 설계변수

를 0.15 ~ 0.7 범위에서 0.05 단위로 변화시키면서, 두 설계변수 변화의 경우의 수마다, 가진주파수 f _k 의 5개 입력 주파수에서의 지반 가진입력 A _g (f _k )에 대하여 수학식 97의 목적함수와 수학식 101의 제한조건들을 계산하여 데이터 파일로 저장한다. design variables

is changed in increments of 1 Hz in the range of 2 to 20 Hz, and other design variables

The objective function of Equation 97 for the ground excitation input A _g (f _k ) at five input frequencies of the excitation frequency f _{k for} each number of cases of change of the two design variables while changing in units of 0.05 in the range of 0.15 to 0.7 and Equation 101 are calculated and saved as a data file.

- Calculation of objective function:

Individual objective functions:

single objective function:

- constraint calculation:

- Calculation result data: "Save file"

- Step 3: Graph the objective function and constraints

Graph the objective function and constraints computed in step 2 from the data file:

,

의 변화 조합의 경우마다 목적함수들의 계산 데이터.- Objective function graph:

,

Computational data of the objective functions for each change combination of .

,

의 변화 조합 경우마다 제한조건들의 계산 데이터.- Graph of constraint:

,

The computed data of the constraint in each case of the change combination of the constraint.

- Step 4: Determination of optimal design variables and termination conditions

과

값을 찾고, 제한조건 그래프들에서 해당 설계변수 값에서 모든 제한조건들이 만족되는지 확인한다. 제한조건들이 모두 만족되면 최적의

과

로 결정하고, 하나라도 만족되지 않으면 탐색범위 내에서 그 다음으로 목적함수가 낮은 점을 찾아서 해당 설계변수가 제한조건들을 만족하는지를 확인하는 과정을 반복한다. 그리하여 탐색범위 내에서 모든 제한조건을 만족하는 경우를 찾으면 최적의

과

로 결정한다. 최적의 고유진동수

과 감쇠계수

를 찾으면 원래 설계변수인 내진마운트의 최적 스프링상수 k _s 와 최적 감쇠계수 c _s 를 수학식 101과 수학식 102를 이용하여 결정하고 설계과정을 종료한다. - Design variable corresponding to the point where the objective function is the minimum in the objective function graph drawn in step 3

class

Find the value, and check whether all constraints are satisfied at the value of the design variable in the constraint graphs. When all the constraints are satisfied, the optimal

class

, and if even one is not satisfied, the process of checking whether the design variable satisfies the constraint conditions is repeated by finding the point with the next lowest objective function within the search range. Therefore, if a case that satisfies all the constraint conditions within the search range is found, the optimal

class

to be decided by Optimal natural frequency

and damping factor

Once found, the optimal spring constant k _s and the optimal damping coefficient c _s of the seismic mount, which are the original design variables, are determined using Equations 101 and 102, and the design process is terminated.

If a satisfactory solution cannot be found within the search range, the search range is appropriately modified by reviewing whether the search range of the design variables and the allowable values of the constraints are appropriate. repeat

Although the present invention has been described with reference to the embodiment shown in the drawings, which is only exemplary, those skilled in the art will understand that various modifications and equivalent other embodiments are possible therefrom. For example, even when the ground motion is in the vertical direction, seismic analysis can be performed using the same mathematical modeling and theoretical formulas as described above. However, in this case, the spring constants k and k _eq , the damping constants c and c _eq , and the input ground motion u _g (t) must be applied in the vertical direction, respectively, and the applied force and stress acting on the switchgear are also vertical in the calculation process. It should be noted that the directional tensile-compressive force and thus the tensile-compressive stress have to be calculated.

In addition, the method according to the present invention can be implemented as computer-readable codes on a computer-readable recording medium. The computer-readable recording medium may include any type of recording device in which data readable by a computer system is stored. Examples of the computer-readable recording medium include ROM, RAM, CD-ROM, magnetic tape, floppy disk, optical data storage device, etc. include In addition, the computer-readable recording medium may store computer-readable codes that can be executed in a distributed manner by a network-connected distributed computer system.

In terms of terms used herein, the singular expression should be understood to include the plural expression unless the context clearly dictates otherwise, and terms such as "comprises" refer to the described feature, number, step, operation, element. , parts or combinations thereof are to be understood, but not to exclude the possibility of the presence or addition of one or more other features or numbers, step operation components, parts or combinations thereof. In addition, terms such as "... unit", "... group", "module", and "block" described in the specification mean a unit that processes at least one function or operation, which is hardware, software, or hardware. and a combination of software.

Accordingly, this embodiment and the drawings attached to this specification only clearly show a part of the technical idea included in the present invention, and within the scope of the technical idea included in the specification and drawings of the present invention, those skilled in the art can easily It will be apparent that all inferred modified examples and specific embodiments are included in the scope of the present invention.

The present invention can be applied to a seismic device for improving the seismic performance of a switchgear.

210, 212, 214: user terminal
250: seismic device design server 260: database

Claims (8)

A low-voltage switchgear comprising an earthquake-resistant device for protecting a facility to be protected from earthquakes,
a switchboard enclosure in which the low voltage switchboard is mounted;
a power lead-in line for supplying external power to the low-voltage switchboard; and
An earthquake-resistant device for determining and applying a design variable that satisfies a predetermined design condition based on design constants for physical properties and dimensions of the low-voltage switchgear, which is a facility to be protected; and
The seismic device is:
has a predetermined spring constant and damping coefficient, and an earthquake-resistant mount installed between the ground and the facility to be protected to support the facility to be protected against the ground;
constructing a vibration system model for modeling vibration in a direction perpendicular to the direction of gravity of the facility to be protected;
deriving a motion equation of the vibration system model and normalizing the motion equation; and
In the vibration system model, a design variable determination operation for determining the spring constant and damping coefficient of the earthquake-resistant mount that minimizes the maximum bending stress and vibration transmission rate of the facility to be protected; low voltage switchgear. According to claim 1,
The operation of constructing the vibration system model is,
The low-pressure switchboard and the earthquake-resistant mount are regarded as columns vibrating in the direction, and the vibration system model is constructed using the concentrated mass, spring constant, and damping constant of each of the low-pressure switchboard and the earthquake-resistant mount, characterized in that, Low voltage switchgear with seismic devices. 3. The method of claim 2,
The operation of determining the design variable is,
A low-voltage switchgear including an earthquake-resistant device, characterized in that the spring constant and damping coefficient of the earthquake-resistant mount are determined in consideration of the maximum displacement limit value, the acceleration gain limit value, and the maximum bending stress of the low-pressure switchboard and the earthquake-resistant mount. 4. The method of claim 3,
The operation of constructing the vibration system model is,

To find k _s and c _s that satisfy

is considered as a design constraint,
From here,

is the maximum bending stress,

is the allowable stress,

is the maximum relative displacement response,

is the allowable relative displacement of the low voltage switchgear,

is the acceleration gain,

is the allowable acceleration gain,

is the maximum displacement of the seismic mount,

is the allowable displacement of the seismic mount,

is a weighting factor whose sum is 1,

Is

A low-voltage switchgear comprising an earthquake-resistant device, characterized in that it is a scaling factor for. 5. The method of claim 4,
The operation of normalizing the equation of motion is,
the equation of motion

modeled as
The maximum operating force applied to the vibrating system model is

modeled as
From here,

is the natural frequency,

ego,

is the damping ratio,

is the ground acceleration spectrum,

where k and k _s are the spring constants of the low-voltage switchboard and the earthquake-resistant mount, respectively, c and c _s are the damping constants of the low-voltage switchboard and the earthquake-resistant mount, respectively, and x is the displacement in the direction A low-voltage switchgear including an earthquake-proof device. 6. The method of claim 5,
The maximum bending stress is

A low-voltage switchgear comprising an earthquake-resistant device, characterized in that obtained by 7. The method of claim 6,
The design variable determination operation is
The spring constant and damping coefficient of the seismic mount,

and

A low-voltage switchgear comprising a seismic device, characterized in that obtained as. 8. The method of claim 7,
The design variable determination operation is
A low-voltage switchgear comprising an earthquake-resistant device, characterized in that the design parameters are determined using at least one of an optimization algorithm, a meta-heuristic algorithm, and an Engineer's trial and error method.

Images