KR102128942B1 - anti-vibration design method of 2DOF Resonance Type Mixer - Google Patents

Abstract

The present invention relates to a vibration proof design method of a two-DOF resonance type mixer which comprises: a stirring unit; a driving unit; and a case accommodating the stirring unit and the driving unit, wherein the stirring unit is connected to and supported on an inner upper surface of the case by means of a first elastic body having stiffness k1, the stirring unit and the driving unit are connected to each other by means of a second elastic body having stiffness k2, and stirring unit is connected to and supported on an inner lower surface of the case by means of a third elastic body having stiffness k3. The vibration proof design method of a two-DOF resonance type mixer comprises the steps of: (a) obtaining a relational expression between the mass of the stirring unit and the mass of the driving unit that satisfy the condition in which the stirring unit resonates by the excitation frequency and the condition that prevents vibration from being transmitted to the case in a resonant state and determining the mass of the stirring unit and the mass of the driving unit based on the relational expression; and (b) determining the stiffness of the first to third elastic bodies satisfying the condition in which the excitation force of the driving unit is minimized, and static deflection of the stirring unit and the driving unit is equal to or less than a predetermined value.

Description

Anti-vibration design method of 2DOF Resonance Type Mixer}

The present invention relates to a dustproof design method of a two-degree-of-freedom resonant mixer.

A mixer is a device that mixes two or more types of powders or liquids, and is widely used for mixing fine chemical materials, bio materials, food, medicine, and cosmetic materials. There are various types of mixers using rotary blade type, magnetic field, vibration, and ultrasonic wave depending on the mixing method. Rotary wing mixers are used in most industrial sites and homes. However, when used for a long time, the rotor blade type mixer may be contaminated with impurities due to wear of the blade or the rotating shaft, or the material may be deformed due to collision of the blade and the material and heat of friction. In the case of biomaterials, food, pharmaceuticals, and cosmetic materials, these problems are the cause of defective products. A mixer developed to solve this problem is a vibrating mixer. The general vibrating mixer mixes the material by vibrating the container containing the material by generating an excitation force due to rotational imbalance. Resonant mixers that use resonance to create large vibrations with small excitation are prior art. However, since resonance is used, a large vibration occurs not only in the container for mixing the substance, but also in the entire case containing the mixer. In order to solve this problem, a resonant mixing technique using a balance weight is applied as the most recent technique. Nevertheless, the prior art has the following problems.

First, a resonant mixer that does not use a counterweight makes the vibration of the body case so large that it makes the stable mixing process difficult. In addition, the vibration of the motor part that generates the excitation force is also large, shortening the motor life. Second, a resonant mixer using a counterweight can solve the above problem, but the structure is complicated and heavy, resulting in high production cost and inconvenient management operation.

Korean Patent Publication No. 10-2014-0091557 (Publication date: 2014.07.21.)

The present invention provides a method for reducing severe vibration of a case occurring in a conventional two-degree-of-freedom resonant mixer without using a counterweight.

The present invention includes two new technical features as a method for reducing severe vibration of a case occurring in a conventional two-degree-of-freedom resonant mixer without using a counterweight. First, it is a technique that minimizes the excitation force required to create vibrations for mixing. This allows mixing with a small motor, which reduces the weight of the motor drive and reduces the vibration of the body. Second, it is a technology that minimizes the transmission of vibration to the case using the secondary resonance mode of the mixer system. By using the secondary resonance mode, vibration transmission can be reduced by canceling vibrations transmitted to the case through the container spring and vibrations transmitted to the case through the motor drive spring. The present invention provides a design technique for making the mass and spring stiffness of each part satisfy this condition. 1 is a block diagram of a resonant stirrer composed of a container part and a motor part, and FIG. 2 is a simple motion system for vibration analysis.

More specifically, the present invention to achieve the above-described technical problem,

Stirring unit; Drive unit; And a case accommodating the stirring unit and the driving unit,

The stirring portion is supported by being connected to the upper surface inside the case via the first elastic body of rigid k ₁ ,

The stirring portion and the driving portion are interconnected with a second elastic body of rigid k ₂ ,

In the dustproof design method of the two-degree-of-freedom resonant mixer, characterized in that the stirring unit is connected to and supported by a lower surface inside the case via a third elastic body of rigid k ₃ ,

(a) Obtain a relational expression between the mass of the stirring portion and the mass of the driving portion that satisfies the condition that the stirring portion is resonated by the excitation frequency and the condition for preventing vibration from being transmitted to the case in the resonant state, and based on the relational expression, the mass of the stirring portion and the mass of the driving portion Determining; And

(b) determining the stiffness of the first to third elastic bodies satisfying the condition that the excitation force of the driving portion is minimized, but the static deflection of the stirring portion and the driving portion is equal to or less than a predetermined value; We propose a dust-proof design method for a freedom mixer.

At this time, the relationship between the mass of the stirring unit and the mass of the driving unit is characterized in that it is represented by Equation 1 below.

<Equation 1>

(In the formula 1, m ₁ is the mass of the stirring unit, m ₂ is the mass of the driving unit, X ₁ /X ₂ is the amplitude ratio of the stirring unit to the driving unit, β is k ₃ /k ₁ ).

In addition, in the step (b), the minimum value of the excitation force is present regardless of the value of the elastic stiffness ratio α (k ₂ /k ₁ ).

In addition, as the α value increases, the elastic body stiffness k ₁ value that satisfies the minimum excitation force decreases, and the static deflection of the stirring portion and the driving portion increases.

According to the anti-vibration design method of the two-degree-of-freedom resonant mixer according to the present invention, first, since the mixing process is possible with the minimum excitation force, the size and weight of the motor driving part can be minimized, and vibration transmission to the body can also be reduced. By canceling and blocking the vibration transmitted to, mixing can be performed in a stable state, and third, since a system design technique that satisfies the above conditions is provided, a new market can be developed by developing products of various capacities.

In addition, the two-degree-of-freedom resonant mixer designed according to the present invention can be widely applied as a replacement for the existing rotary vane mixer for mixing of fine chemical materials, bio materials, food, pharmaceuticals, and cosmetic materials, and resonance with an existing balance weight It is possible to develop a system that simplifies the structure of the type mixer and reduces the production cost by reducing the weight, and increases the production capacity by increasing the capacity of the container.

1 is a schematic diagram of a two-degree-of-freedom resonant stirrer.
2 is a schematic diagram showing the resonant stirrer of FIG. 1 with a simple motion system.
3 is a graph showing the relationship between α and k ₁ and excitation force.
4 is a graph showing the relationship between α and the transfer force.
5 is a graph showing static deflection according to α.
6 is a vibration mode of the resonant stirrer.
7 is a frequency response curve of a resonant stirrer.

In the description of the present invention, when it is determined that a detailed description of a related known function or configuration may unnecessarily obscure the subject matter of the present invention, the detailed description will be omitted.

Embodiments according to the concept of the present invention may be modified in various ways and have various forms, and thus, specific embodiments will be illustrated in the drawings and described in detail in the present specification or application. However, this is not intended to limit the embodiment according to the concept of the present invention to a specific disclosure form, and it should be understood to include all modifications, equivalents, or substitutes included in the spirit and scope of the present invention.

The terms used herein are only used to describe specific embodiments, and are not intended to limit the present invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this specification, the terms "include" or "have" are intended to indicate that a feature, number, step, action, component, part, or combination thereof described is present, and one or more other features or numbers. It should be understood that it does not preclude the existence or addition possibilities of, steps, actions, components, parts or combinations thereof.

Hereinafter, the present invention will be described in more detail with reference to Examples.

The embodiments according to the present specification may be modified in various other forms, and the scope of the present specification is not interpreted to be limited to the embodiments described below. The embodiments of the present specification are provided to more fully describe the present specification to those skilled in the art.

<Example>

1. Vibration of resonant mixer

)은 스프링

으로 케이스에 연결되어 지지된다. 모터 구동부(

)는 스프링

로 케이스에 지지된다. 용기부와 모터 구동부의 운동을 결정하기 위해 뉴턴 제 2법칙을 적용하여 운동 방정식을 아래와 같이 구할 수 있다. FIG. 2 is a simplified structure of the mixer system of FIG. 1. Container part(

) Is spring

It is supported by being connected to the case. Motor drive (

) Is spring

It is supported by the furnace case. In order to determine the motion of the container part and the motor drive part, the equation of motion can be obtained as follows by applying Newton's second law.

와

를 조화운동으로 보면, 식 (1),(2)는 식 (3)의 행렬방정식으로 나타낼 수 있다.Displacement

Wow

Looking at the harmonic motion, Eqs. (1) and (2) can be expressed as the matrix equation of Eq. (3).

The characteristic equation for determining the resonant frequency of the system can be expressed by Equation (4), which is a condition where the matrix of the coefficient matrix becomes zero.

The amplitudes of the stirring part and the motor part derived from equation (3) are as shown in equations (5) and (6).

2. Resonant frequency

에 대한 스프링 강성비를 사용하여

,

로 표시하면 특성 방정식 (4)를 식(7)로 나타낼 수 있다. 식(7)에 공진주파수 값을 적용하면 질량과 스프링상수 사이의 관계를 얻을 수 있다.The resonance frequency is set to 60 Hz.

Using the spring stiffness ratio for

,

When expressed as, the characteristic equation (4) can be expressed as equation (7). By applying the resonance frequency value to equation (7), the relationship between mass and spring constant can be obtained.

3. Transmission power offset

The transmission force to the case passes through a path in which the vibration of the motor driving portion is transmitted through the spring k3 and a path in which the vibration of the container portion is transmitted through the spring k1. In order to cancel the sum of the two transmission paths to zero, the direction of the force transmitted between the two paths is made to be opposite so that the condition (8) of the condition for canceling the transmission force can be satisfied.

)

를 사용하여 얻을 수 있다.From Eq. (7) and Eq. (8), the spring constant ratio (

)

Can be obtained using

4. System Design

By applying equations (5) and (6) to equation (8) and using equation (9), the mass of the container can be determined. However, in the case of spring stiffness, the case where the condition is satisfied is not determined as one, so an appropriate spring constant value should be selected. First, the vibration acceleration of the container part satisfies 100 g at 60 Hz, but the excitation force of the motor part is minimized. Additionally, it is possible to derive an appropriate spring stiffness value by limiting the static deflection range of the spring.

으로 설정하고 용기부 진폭대비 모터부 진폭의 비를 0.2로 설정하였다. 이 값은 믹서의 크기에 따라 조절이 가능하다. 식(5)에 가진 주파수

에서 용기부의 진동 가속도

를 만족시키는 조건을 적용하면, 가진력

는 아래와 같이 나타낼 수 있다.Container mass

And the ratio of the amplitude of the motor portion to the amplitude of the container portion was set to 0.2. This value can be adjusted according to the size of the mixer. Frequency in Equation (5)

Vibration acceleration of container part

Applying the condition that satisfies the

Can be represented as below.

의 값에 따라 스프링 상수

과 가진력

의 상관관계를 나타낸 그래프이다. 감쇠는 스프링 연결부의 마찰로 인한 작은 감쇠를 고려하여,

의 작은 값을 부여하였다. 본 발명에서 규명한 흥미로운 현상은

에 무관하게 최소 가진력이 존재한다는 사실이다. 즉, 본 발명이 제공하는 최소 가진력으로 공진시켜 요구치인 100g의 믹싱 가속도를 얻을 수 있다. 종래에는 과도한 가진력을 사용하였므로 요구치를 초과하는 믹싱 가속도를 얻을 수는 있었으나, 모터 구동부의 중량이 증가하고 케이스의 진동이 커지는 문제가 발생했다.3 is a spring constant ratio

Spring constant according to the value of

Overexcitation

It is a graph showing the correlation of. The damping takes into account the small damping due to the friction of the spring connection,

Was given a small value of. Interesting phenomenon identified in the present invention

It is true that regardless of the minimum excitation force exists. That is, it is possible to obtain a mixing acceleration of 100 g, which is a required value, by resonating with the minimum excitation force provided by the present invention. In the prior art, since excessive excitation force was used, mixing acceleration exceeding a required value could be obtained, but the weight of the motor drive portion increased and the vibration of the case increased.

에 따른 케이스로 전달력의 변화를 보인다.

가 증가하고 감쇠가 작아질수록 케이스 전달력은 감소한다. 그러나 도 3에서

가 증가하면 최소 가진력을 만족하는 스프링 상수

값이 감소한다. 스프링 상수가 너무 작아지면 시스템이 취약해지므로 허용 가능한 범위에서 적절한 스프링 강성을 정해야 한다. 이 문제는 스프링의 정적 처짐 식 (10)을 사용하여 해결이 가능하다. 4 is a spring constant ratio

According to the case, it shows the change of transmission power.

And the damping decreases, the case transfer force decreases. However, in Figure 3

Increases, the spring constant satisfies the minimum excitation force

Value decreases. If the spring constant becomes too small, the system becomes vulnerable, so the proper spring stiffness should be determined within an acceptable range. This problem can be solved using the static deflection equation (10) of the spring.

과

는 각각 용기부와 모터부의 정적 처짐이다. 도 5은

에 따른 정적 처짐의 변화다.

가 증가하면서 정적 처짐의 값도 증가한다. 정적 처짐을 1mm로 설정하면, 스프링 상수비

=11로 결정된다. 이 스프링 상수는 도 4에서 15[N] 아래의 작은 힘만 전달한다.

and

Is the static deflection of the container part and the motor part, respectively. Figure 5

It is the change of static deflection according to.

The value of static sag increases with increasing. If the static deflection is set to 1mm, the spring constant ratio

=11. This spring constant transmits only a small force below 15[N] in FIG. 4.

5. Resonance mode

Through this analysis process, it is possible to determine the specifications of the mixer system that satisfies 100 g of vibration acceleration at 60 Hz while minimizing motor excitation and case transmission. Table 1 shows the specifications of the resonant mixer when the container mass is set to 5 kg.

<Table 1> Specification of two degree of freedom resonant stirrer

을 다르게 해도 동일한 해석 방법을 통해 시스템의 제원을 결정할 수 있다.The present invention is the mass of the container

Even if is different, the specifications of the system can be determined through the same analysis method.

6 is a vibration mode and natural frequency of the resonant mixer determined by the proposed method. The second natural frequency is 60 Hz, and the container part and the motor part vibrate in opposite phases. Therefore, when resonating in the secondary mode, the container portion and the motor driving portion vibrate in opposite directions, and the transmission force to the case is canceled. In addition, the amplitude ratio of the motor portion to the container portion is 0.2, which is advantageous for the durability of the motor. The vibration response characteristic of this system is finally confirmed by the frequency response curve of FIG. 7. When vibrating at the second natural frequency of 60 Hz, the vibration acceleration (Acc1) of the container part satisfies the target value of 100 g. At this time, the motor part (Acc2) vibrates at an acceleration of 20g, which is 1/5, and the phases of the container part (Phase1) and the motor part (Phase2) are opposite directions. In conclusion, when resonating in the secondary resonance mode, the transmission force to the case is minimized with minimal excitation force, and the vibration of the motor part is limited to about 1/5 of the vibration of the container part.

The present invention is not limited to the above embodiments, but may be manufactured in various different forms, and those skilled in the art to which the present invention pertains have other specific forms without changing the technical spirit or essential features of the present invention. It will be understood that can be carried out. Therefore, it should be understood that the embodiments described above are illustrative in all respects and not restrictive.

Claims (5)

Stirring unit; Drive unit; And a case accommodating the stirring unit and the driving unit,
The stirring portion is supported by being connected to the upper surface inside the case via the first elastic body of rigid k ₁ ,
The stirring portion and the driving portion are interconnected with a second elastic body of rigid k ₂ ,
In the dustproof design method of the two-degree-of-freedom resonant mixer, characterized in that the stirring unit is connected to and supported by a lower surface inside the case via a third elastic body of rigid k ₃ ,
(a) Obtain a relational expression between the mass of the stirring portion and the mass of the driving portion that satisfies the condition that the stirring portion is resonated by the excitation frequency and the condition that prevents vibration from being transmitted to the case in the resonant state, and based on the relational expression, the mass of the stirring portion and the mass of the driving portion Determining; And
(b) determining the stiffness of the first to third elastic bodies satisfying the condition that the excitation force of the driving portion is minimized, but the static deflection of the stirring portion and the driving portion is equal to or less than a predetermined value;
Dustproof design method of a two-degree-of-freedom resonant mixer comprising a. According to claim 1,
The relationship between the mass of the stirring unit and the mass of the driving unit is a method for anti-vibration design of a two-degree-of-freedom resonant mixer, which is represented by Equation 1 below:
<Equation 1>

(In the formula 1, m ₁ is the mass of the stirring unit, m ₂ is the mass of the driving unit, X ₁ /X ₂ is the amplitude ratio of the stirring unit to the driving unit, β is k ₃ /k ₁ ). According to claim 1,
In the step (b), a method for anti-vibration design of a two-degree-of-freedom resonant mixer, characterized in that a minimum excitation force exists regardless of the value of the elastic stiffness ratio α (k ₂ /k ₁ ). According to claim 3,
As the α value increases, the elastic rigidity k ₁ value that satisfies the minimum excitation force decreases, and the static deflection method of the two-degree-of-freedom resonant mixer is characterized in that the static deflection of the stirring portion and the driving portion increases. According to claim 1,
Excitation frequency 60Hz, stirring part acceleration 100 × 9.81m/s ² , static deflection 1mm, stirring part mass 5kg and driving part amplitude ratio (X ₁ /X ₂ ) under conditions of 0.2, vibration at minimum excitation force condition and resonance In order to satisfy all the conditions to prevent delivery to this case,
The drive mass is set to 25kg, and k ₁ to k ₃ values are 50,043 N/m, 550,470 N/m, and 250,220 N/m, respectively.

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