KR100719632B1 - Balancing method of the reciprocating compressor - Google Patents

Abstract

The present invention calculates the weight of the counterweight compensating for the unbalanced force due to the rotational mass and the reciprocating mass of the crank arm and the connecting rod of the reciprocating compressor, and calculates the rotational mass and the reciprocating mass according to the calculated inertia force The present invention relates to a balancing method of a reciprocating air compressor which can simplify the counterweight calculation by deriving the counterweight calculation formula.

)과, 피스톤과 연결봉 소단부를 포함하는 왕복질량(

)으로부터 관성력(Fp, Fr)에 대한 모멘트(Mp, Mr)를 계산하고, 상기 관성력에 대한 모멘트(Mp, Mr)로부터 평형추 설계식(Mb1, Mb2)을 구하되, 상기 모멘트(Mp, Mr)에 복소좌표를 적용하여 이루어짐을 특징으로 한다. The present invention is a balancing method for balancing the crank arm by installing a counterweight on both ends of the crank arm of the reciprocating air compressor, the rotating mass including the connecting rod end (

) And a reciprocating mass (including piston and connecting rod small ends)

Calculate the moments (Mp, Mr) for the inertia forces (Fp, Fr), and calculate the counterweight design formulas (Mb1, Mb2) from the moments (Mp, Mr) for the inertial forces, the moment (Mp, Mr) It is characterized by consisting of the complex coordinates applied to).

Complex coordinates, counterweight design, reciprocating compressor

Description

Balancing method of reciprocating compressor {BALANCING METHOD OF THE RECIPROCATING COMPRESSOR}

1 is a counterweight calculation model according to the balancing method of the first stage reciprocating compressor according to the present invention,

Figure 2 represents the motion of the reciprocating compressor using the complex coordinates used in the balancing method of the reciprocating compressor according to the present invention,

3 is a counterweight calculation model according to the balancing method of the two-stage in-line reciprocating compressor according to the present invention.

4 is a counterweight calculation model according to the balancing method of the W-type reciprocating compressor according to the present invention.

The present invention relates to a balancing method of a reciprocating air compressor. More specifically, the weight of the counterweight compensating for the unbalanced force due to the rotating mass and the reciprocating mass applied to the crank arm and the connecting rod of the reciprocating compressor is calculated using complex coordinates. The present invention relates to a balancing method of a reciprocating air compressor which can simplify the calculation of the counterweight by calculating the rotational mass and the reciprocating mass according to the obtained inertia force and inducing the counterweight calculation equation therefrom.

In general, a rotating machine does not coincide with the center of rotation of the rotating body and the center of mass of the rotating body does not coincide with the center of rotation of the rotating body, and thus a lot of vibration occurs when the rotating body rotates.

This vibration is not a big problem when the rotor rotates at low speed, but when it is rotated at high speed, the vibration caused by the imbalance of the center of mass and the rotation center can affect other equipment as well as destroy the rotor itself. It may also result in.

This imbalance is further increased as the rotation speed of the rotating body increases as described above, so that the dynamic load applied to the bearing supporting the rotating body becomes gradually larger.

In order to prevent rotation imbalance and vibration caused by the imbalance between the center of mass and the center of rotation, a method of precisely meshing each part and precisely engaging each other can be used, but there are many difficulties in precisely machining each element. In addition, accurate machining cannot completely eliminate the imbalance between the center of mass and the center of rotation.

Therefore, as a method for resolving the imbalance between the center of mass and the center of rotation, a method of installing counter weights corresponding to an unbalance amount is used, and the method of designing such a counterweight has a modern balance method and influence. There is a counting method.

The above-mentioned modern balance method needs to calculate the inertia force by using the piston acceleration equation made up of differential equations and use the same to calculate the counterweight, so it is difficult to derive because the equation is too complex, and the influence coefficient method uses the influence coefficient matrix and the initial vibration matrix. Since the imbalance matrix is obtained by using the method, the error is large and the calculation is difficult due to the deterioration of the matrix condition.

The present invention is to solve the above problems, the weight of the balance weight easier and more accurate to solve the imbalance of the center of mass and rotation center to reliably drive the crank arm more stable and reduce the vibration It is an object to provide a balancing method of an air compressor.

Furthermore, an object of the present invention is to provide a balancing method of a reciprocating air compressor that can easily calculate the weight of the counterweight by calculating the inertia force using the complex coordinates and calculating the weight of the counterweight using the same.

)과, 피스톤과 연결봉 소단부를 포함하는 질량(

)으로부터 관성력(Fp, Fr)에 대한 모멘트(Mp, Mr)를 계산하고, 상기 관성력에 대한 모멘트(Mp, Mr)로부터 평형추 설계식(Mb1, Mb2)을 구하되, 상기 관성력(Fp, Fr)에 복소좌표를 적용하여 이루어짐을 특징으로 한다. The present invention for achieving the above object is a mass (including a connecting rod end)

), And the mass (including piston and connecting rod small ends)

Calculate the moment (Mp, Mr) for the moment of inertia (Fp, Fr), and the counterweight design formula (Mb1, Mb2) from the moment (Mp, Mr) for the moment of inertia, the inertia (Fp, Fr) It is characterized by consisting of the complex coordinates applied to).

The reciprocating mass inertia force Fp and the rotational mass inertia force Fr are

,

이며,

,

Is,

The weight of the counterweight (Mb1, Mb2) is

와

임을 특징으로 한다.

Wow

It is characterized by that.

Mr is a rotating mass including the large end of the connecting rod,

Mp is the reciprocating mass including the piston and the small end of the connecting rod,

ℓ is the distance between Mb1 and Mb2,

s is the distance between Mr and Mb1 or Mb2.

에 의해 구해짐을 특징으로 한다. In addition, the residual unbalance force generated after the installation of the counterweight obtained by the above-described counterweight (Mb1, Mb2) calculation formula is

It is characterized by being obtained by.

Hereinafter, the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art can easily understand and reproduce.

1 is a counterweight calculation model in a balancing method of a first stage reciprocating compressor according to the present invention.

The sign according to the counterweight calculation in the balancing method of the reciprocating compressor according to the present invention is as follows.

)가 걸리고, 연결봉의 끝단에는 연결봉의 대단부를 포함하는 질량(

)이 걸린다. As shown in FIG. 1, the piston includes a mass including a piston and a connecting rod small end (

), And at the end of the connecting rod, the mass (including the large end of the connecting rod)

Takes

In the description below, ω is the rotational speed of the shaft, R is the length of the crank arm, L is the length of the connecting rod, Mr is the rotating mass moment including the connecting rod end, Mp is the reciprocating mass moment including the piston and connecting rod small end, Mb1, Mb2 The weight of the counterweight, Fp, is the inertia force by Mp and Pr.

The counterweight calculation process for calculating the counterweight weight according to the balancing method of the reciprocating air compressor of the present invention is as follows.

)과, 피스톤과 연결봉 소단부를 포함하는 질량(

)으로부터 피스톤의 관성력(Fp, Fr)을 구한 후 회전축으로부터 s만큼 떨어진 곳에서의 관성력에 대한 모멘트(Mp, Mr)를 구하며, 상기 모멘트(Mp, Mr)로부터 평형추의 무게를 구한다. In the balancing method according to the present invention, the process of deriving the counterweight design equation, first, the mass including the connecting rod end (

), And the mass (including piston and connecting rod small ends)

The moment of inertia (Mp, Mr) for the inertia force at a position s away from the rotation axis after obtaining the inertial force (Fp, Fr) of the piston from the (), and the weight of the counterweight from the moment (Mp, Mr).

First, the inertial force (Fp) of the piston by the reciprocating mass can be expressed by the following formula by a conventional method used conventionally.

)와, 2차 회전성분(

)을 도 2에 도시한 바와 같이 복소좌표로 표시하여 관성력을 아래와 같이 표현할 수 있다. The inertial force of the piston expressed as above is too complicated and difficult to guide. In particular, in the case of having a different arrangement angle and a reciprocating amount, such as a multi-stage compressor, it is difficult to calculate the unbalance amount using this equation.

) And the second rotational component (

) Can be expressed in complex coordinates as shown in FIG.

로 표현되고, 직선운동은 전방회전을 나타내는

와 후방회전을 나타내는

의 벡터합으로 나타난다. In this way, the rotational and linear motions are represented by the complex coordinates using the complex coordinates. The circular motion represents the forward rotation.

Where linear motion represents forward rotation

Indicating backward and

It is represented by the vector sum of.

와

, 2차 회전성분의

와

의 합으로 표현될 수 있으며, 아래와 같이 표현된다. Therefore, the above equation is the first rotational component

Wow

Of secondary rotational components

Wow

It can be expressed as the sum of and is expressed as follows.

The inertia force for reciprocating mass

The inertia force on the rotating mass

이다.

to be.

이다. In the above equation, λ is the connecting rod ratio of the crank arm length (R) and the connecting rod length (L)

to be.

로 정의하고

Defined as

To sum up the above expression,

이다.

to be.

Calculating the moment (Mr) for the rotational mass and the moment for the reciprocating mass (Mp) in the part away from S in the axial direction for the inertial force expressed by the above formula,

to be.

The counterweight design equation can be obtained from the moment (Mr) for the rotational mass and the moment (Mp) for the reciprocating mass calculated as above.

In deriving the counterweight design equation, the equilibrium ratio is 50% so that only half of the rotating mass and the reciprocating mass are balanced, and the weight of the counterweight is given by considering the force and moment equilibrium equations.

Where l is the distance between counterweights and s is the distance between the end of the crank arm and the counterweight.

The weight of the counterweight above is simplified as follows when l = 2s, ie when two counterweights are installed at the same distance from the crank arm.

That is, when two counterweights are installed at the same distance from the crank arm, the weights of the two counterweights become equal.

The residual unbalance force (Fre) generated after installing the counterweight calculated by the counterweight calculation equation as above is obtained by the following equation.

Thus, in order to completely remove the residual unbalance force left after the counterweight is installed, the reverse primary rotational component opposite to the primary rotational component, the reverse secondary rotational component and the reverse primary rotational component opposite to the secondary rotational component It is possible to apply a mechanism with a second rotational component opposite to.

3 illustrates a counterweight calculation model according to a balancing method of a two-stage in-line reciprocating compressor.

As shown in the figure, a reciprocating compressor having two cylinders and a two-stage crankshaft was arranged to offset the directions of inertial forces by arranging the cylinders in-line.

Counterweights Mb1 and Mb2 are provided at opposite ends of the crank arm, respectively.

,

, 피스톤과 연결봉 소단부를 포함하는 질량

,

로부터 피스톤의 관성력(Fp, Fr)을 구한 후 회전축으로부터 s만큼 떨어진 곳에서의 관성력에 대한 모멘트(Mp, Mr)를 구하며, 상기 모멘트(Mp, Mr)로부터 평형추의 무게를 구한다. Mass with connecting rod end

,

, Mass including piston and connecting rod small end

,

The moment of inertia (Mp, Mr) for the inertia force at a position s away from the rotation axis after obtaining the inertia force (Fp, Fr) of the piston from the piston, and the weight of the counterweight from the moment (Mp, Mr).

First, the inertial force (Fp) of the piston by reciprocating mass is obtained by the same process as in the first stage reciprocating compressor described above,

The inertia force can be expressed as follows by displaying the first and second rotational components in complex coordinates.

The inertia force for reciprocating mass

The inertia force on the rotating mass

이다.

to be.

이고,

이다. Λ above is the connecting rod ratio of the crank arm length (R ₁ , R ₂ ) and the connecting rod length (L ₁ , L ₂ )

ego,

to be.

In the above expression

로 정의하고

Defined as

To sum up the above expression,

The inertia force for reciprocating mass

The inertia force on the rotating mass

이다.

to be.

The counterweight design equation can be obtained from the moment (Mr) for the rotational mass and the moment (Mp) for the reciprocating mass from the calculated inertial force, from which the counterweight design equation can be derived. In deriving the counterweight design equation, the equilibrium ratio is 50% so that only half of the rotating mass and the reciprocating mass are balanced, and the weight of the counterweight is given by considering the force and moment equilibrium equations.

Where ℓ is the distance between the counterweights, ℓ ₁ is the distance between one counterweight and the inflection part, ℓ ₂ is the distance between the other counterweight and the inflection part, and s ₁ is the distance between the end of the crank arm and one counterweight. And s ₂ is the distance between the end of the crank arm and the other counterweight.

s ₁ = s ₂ = s ₀ , ℓ ₁ = ℓ ₂ = ℓ ₀ , M _p1 = M _p2 = M _p , M _r1 = M _r2 = M _r , ℓ ₀ = 2s ₀ , that is, the same distance from the crank arm If two counterweights are installed on the counterweight, the counterweight weight is simplified as follows.

That is, when two counterweights are installed at the same distance from the crank arm, the weights of the two counterweights become equal.

The residual unbalance force (Fre) generated after installing the counterweight calculated by the counterweight calculation equation as above is obtained by the following equation.

Thus, in order to completely remove the residual unbalance force left after the counterweight is installed, the reverse primary rotational component opposite to the primary rotational component, the reverse secondary rotational component and the reverse primary rotational component opposite to the secondary rotational component It is possible to apply a mechanism with a second rotational component opposite to.

As another example, FIG. 4 illustrates a counterweight calculation model according to a balancing method of a W-type reciprocating compressor.

As shown in the drawing, a reciprocating compressor having three cylinders and a first stage crankshaft was arranged to offset the inertial forces in the horizontal direction by arranging the cylinders in a W-shape.

Counterweights Mb1 and counterweights Mb2 are provided at opposite ends of the crank arm, respectively.

피스톤과 연결봉 소단부를 포함하는 질량들

,

,

로부터 피스톤의 관성력(Fp, Fr)을 구한 후 회전축으로부터 S_R, S_L 만큼 떨어진 곳에서의 관성력에 대한 왕복질량에 대한 모멘트(M_R, M_M, M_L)와 회전질량에 대한 모멘트(Mr)를 구하며, 상기 모멘트(M_R, M_M, M_L, Mr)로부터 평형추의 무게를 구한다. Mass with connecting rod end

Masses including piston and connecting rod small end

,

,

The moment of inertia (M _R , M _M , M _L ) and the moment of rotation mass (Mr) for the reciprocal mass of the inertia force at a distance S _R , S _L from the rotation axis after obtaining the inertia forces (Fp, Fr) of the piston from ) And the weight of the counterweight from the moments (M _R , M _M , M _L, Mr).

First, the inertial force (Fp) of the piston by reciprocating mass is obtained by the same process as in the first stage reciprocating compressor described above,

The inertia force can be expressed as follows by displaying the first and second rotational components in complex coordinates.

The inertia force for reciprocating mass

The inertia force on the rotating mass

이다.

to be.

In the above expression

to be.

From the moment of inertia calculated as above, the counterweight design equation can be obtained from the moment (M _R , M _M , M _L ) for the rotating mass and the moment (Mr) for the reciprocating mass. In deriving the counterweight design equation, the equilibrium ratio is 50%, and considering the force and moment equilibrium equations, the counterweight weight is as follows.

Where ℓ is the distance between counterweights, ℓ _L is the distance between the left and center cylinders, ℓ _R is the distance between the right and center cylinders, and S _L is the distance between the end of the crank arm and the Distance and S _R is the distance between the end of the crank arm and the portion to which the right connecting rod is connected.

Ss = S _L = S ₀ , ℓ _R = ℓ _L = ℓ ₀ , M _R = M _M = M _L = M _P , i.e. when two counterweights are installed at the same distance from the crank arm, the counterweight above Is simplified as follows:

That is, when two counterweights are installed at the same distance from the crank arm, the weights of the two counterweights become equal.

The residual unbalance force (Fre) generated after installing the counterweight calculated by the counterweight calculation equation as above is obtained by the following equation.

Thus, in order to completely remove the residual unbalance force left after the counterweight is installed, the reverse primary rotational component opposite to the primary rotational component, the reverse secondary rotational component and the reverse primary rotational component opposite to the secondary rotational component It is possible to apply a mechanism with a second rotational component opposite to.

While the invention has been described with reference to the preferred embodiments, many modifications and variations are possible without departing from the scope and spirit of the invention as set forth by the claims below.

As described in detail above, the present invention is a counterweight design formula for calculating the weight of the counterweight from the moment obtained from the equation to calculate the inertial force by using the complex coordinates to display the rotational and linear motion in complex numbers It is effective to obtain the counterweight more easily by obtaining the.

While the present invention has been described with reference to the accompanying drawings, it will be apparent to those skilled in the art that many various obvious modifications are possible without departing from the scope of the invention from this description. Accordingly, the invention can only be construed limited by the words of the appended claims.

Claims (4)

In the balancing method of balancing the crank arm by installing a counterweight at both ends of the crank arm of the reciprocating air compressor, The moment (Mp, Mr) for the inertia forces (Fp, Fr) is calculated from the mass (m _r ) including the connecting rod end and the mass (m _p ) including the piston and the connecting rod small end, and the moment for the inertia force ( Obtain the counterweight design equations (Mb1, Mb2) from Mp, Mr), Balancing method of the reciprocating air compressor, characterized in that the equation is simplified by applying a complex coordinate to the inertial forces (Fp, Fr). The method of claim 1, In the case of single stage reciprocating compressor, the inertia force

ego, The counterweight weight (Mb1, Mb2) is Wow

Balancing method of reciprocating air compressor, characterized in that. here, Fp is the inertia force for reciprocating mass Fr is the inertia force for rotating mass Mr is the moment with respect to the mass including the large end of the connecting rod Mp is the moment for reciprocating mass including the piston and the small end of the connecting rod R is the length of the crank arm L is the length of connecting rod ℓ is the distance between Mb1 and Mb2, s is the distance between Mr and Mb1 or Mb2 The method of claim 1, When the two stage in-line reciprocating compressor

ego, Counterweight (Mb1, Mb2)

Balancing method of reciprocating air compressor, characterized in that. Fp is the inertia force for reciprocating mass Fr is the inertia force for rotating mass Mr ₁ and Mr ₂ are moments relative to the mass including the ends of the connecting rods Mp ₁ and Mp ₂ are moments for the reciprocating mass including the piston and the small end of the connecting rod R ₁ and R ₂ are the lengths of the crank arms L ₁ , L ₂ is the length of connecting rod ℓ ₁ is the distance between one counterweight and the inflection ℓ ₂ is the distance between the counterbalance and the inflection s ₁ is the distance between the end of the crank arm and the counterweight on one side s ₂ is the distance between the end of the crank arm and the counterweight on the other side The method of claim 1, In the case of single stage W-type reciprocating compressor, the inertia force

ego, Counterweight (Mb1, Mb2)

Balancing method of reciprocating air compressor, characterized in that. Fp is the inertia force for reciprocating mass Fr is the inertia force for rotating mass Mr is the moment of mass including the great end of the connecting rod M _R , M _M and M _L are moments of reciprocating mass including the piston and the small end of the connecting rod R is the length of the crank arm L _L , L _R is the length of connecting rod ℓ _L is the distance between the left and center cylinders ℓ _R is the distance between the right cylinder and the center cylinder S _L is the distance between the end of the crank arm and the part where the left connecting rod is connected S _R is the distance between the end of the crank arm and the part where the right connecting rod is connected

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