CN113221054B - Medium damping calculation analysis method for vibration of mechanical vibration system in fluid medium - Google Patents

Abstract

The invention discloses a medium damping calculation analysis method for the vibration of a mechanical vibration system in a fluid medium, and a bagComprises the following steps: dividing the vibration damping of a vibrating object in a fluid medium into lateral damping R_m1And head-on damping R_m2Two types are adopted; side damping R_m1Calculating (1); head-on damping R_m2And (4) calculating. The invention discloses a medium damping calculation and analysis method for vibration of a mechanical vibration system in a fluid medium, which determines the classification and the source of the vibration damping by means of definition and content research of the vibration damping, correctly and deeply recognizes the mechanical vibration in the fluid medium, provides a method for calculating and analyzing the damping, lays a foundation for deep research and numerical analysis of the damping, the vibration and the resonance, and has clear scientific principle, simple and clear steps and strong operability.

Description

Medium damping calculation analysis method for vibration of mechanical vibration system in fluid medium

Technical Field

The invention relates to the technical field of fluid machinery and mechanical vibration, in particular to a medium damping calculation analysis method for vibration of a mechanical vibration system in a fluid medium.

Background

Vibration is common in nature, daily life, and industrial and agricultural production, and refers to the reciprocating motion of an object near a balance position. Resonance is a special state of vibration, and is a phenomenon that the amplitude of the system is increased significantly and reaches a maximum value when the excitation frequency of the system is equal to or close to the natural frequency of the system.

The mechanical vibration is divided into damping vibration and undamped vibration, and most of the mechanical vibration encountered in normal life and working environment is damping vibration. It is undeniable that the scientific community does not have sufficient knowledge of damping, and the definition is ambiguous, the classification is ambiguous, or even the source of damping cannot be clearly explained. At present, vibration damping is divided into two types, namely internal friction damping and radiation damping: one is that the mechanical energy of the system is reduced and converted into internal energy due to heat generation of frictional resistance, and the damping is called frictional damping; the other is that the system causes the vibration of surrounding particles, so that the energy of the system is gradually radiated to the periphery and becomes the energy of waves, and the damping is called radiation damping ".

This definition has three problems: (1) by mistake "frictional damping" is defined as "internal frictional damping", and "internal" and "external" between the vibrating system and the vibrating medium are not known, so that part of the literature misunderstands the frictional forces inside the material of the vibrating object as "internal friction", which in fact is already contained within the elastic restoring force. (2) It is not clear who gives who friction, nor is it specified where and how the friction acts, and therefore it is not possible to formulate a formula for calculating the frictional damping. (3) The so-called "radiation damping" is only damping imposed by the presence of the radiated wave and does not describe the presence, direction of action of the wave on the vibrating object as a resistance, making it less possible to physically express and mathematically calculate it. We have analyzed that it is possible that the industry recognizes that there is a second type of damping, but not clear the source, and propose this "radiation damping" to explain what forces, and what effects, are caused by the vibrations causing the pressure wave, but simply a "shadow damping", and it is not clear what forces, and what effects are produced, but only the energy of the wave, an explanation and definition of this is of ineffectiveness and tension.

Therefore, the industry cannot quantitatively calculate and analyze damping so as to influence the understanding of vibration and resonance in various boundaries, and cannot numerically simulate damping vibration to estimate the vibration amplitude of special vibration states such as resonance at present when computer numerical simulation is developed vigorously.

Disclosure of Invention

The invention aims to provide a medium damping calculation and analysis method for vibration of a mechanical vibration system in a fluid medium, which is used for solving the problem that the quantitative calculation and analysis of vibration damping cannot be carried out in the industry at present.

The invention provides a medium damping calculation analysis method for a mechanical vibration system vibrating in a fluid medium, which comprises the following steps:

step A: determining the source and classification of vibration damping;

the vibration damping of a vibrating object in a fluid medium is divided into lateral damping R according to the stress source of the vibrating object_m1And head-on damping R_m2Two types are adopted;

and B: side damping R_m1Calculating (1);

the side damping belongs to friction damping, and the calculation expression is as follows:

R_m1mu.l (formula 1)

Wherein μ is a hydrodynamic viscosity coefficient in the unit of N · s/m²(ii) a l is the length of the side surface of the vibrating object;

and C: head-on damping R_m2Calculating (1);

the head-on damping belongs to dynamic buoyancy damping, and the calculation expression is as follows:

R_m2rho.S.Δ x/Δ t (equation 3)

In the formula, rho is the density of the fluid, S is the frontal area of the vibrating object, Δ x is the vibration displacement of the object, and Δ t is the vibration period.

Compared with the prior art, the invention has the beneficial effects that:

the invention discloses a mechanical vibration system in fluid mediumThe medium damping calculation analysis method of vibration is based on the depth analysis of forced vibration equation, the stress analysis using vibrating object as isolator and the dimensional analysis of damping, especially the demonstration analysis of dynamic buoyancy, and divides the vibration damping of vibrating object in fluid medium into side damping R_m1And head-on damping R_m2Two types, and side damping R is proposed_m1And head-on damping R_m2The computational expression of (2) can be used for the computational analysis of the vibration damping encountered by mechanical vibration systems in fluid media such as air, water and the like. The invention discloses a calculation and analysis method of vibration damping in fluid medium, which determines the classification and source of the vibration damping by means of the definition and content research of the vibration damping, correctly and deeply recognizes the mechanical vibration in the fluid medium, provides a calculation and analysis damping method, lays a foundation for the deep research and numerical analysis of the damping, the vibration and the resonance, and has clear scientific principle, simple and clear steps and strong operability.

Drawings

Fig. 1 is a schematic view of analyzing vertical vibration stress of a rectangular solid object provided in embodiment 1 of the present invention.

Detailed Description

Example 1

Embodiment 1 provides a medium damping calculation analysis method of a mechanical vibration system vibrating in a fluid medium, wherein the vibrating medium is a fluid, the calculation analysis method including:

step A: determining the source and classification of vibration damping;

dividing the vibration medium damping of a vibrating object in a fluid medium into side damping R according to the stress source of the vibrating object_m1And head-on damping R_m2Two types are adopted;

wherein the side damping R_m1From the resistance experienced by the side of the object parallel to the direction of vibration, head-on damping R_m2Resulting from the resistance encountered by an object facing perpendicular to the direction of vibration.

Side damping R of vibrating objects_m1And head-on damping R_m2The derivation process of the calculation formula of (1):

1. referring to fig. 1, the vibrating object is set to be a rectangular parallelepiped spacer, and the length a, the width b, the thickness c, and the vibration amplitude Δ x in the thickness direction thereof are set to the vibrating object. Defining the surface of the object parallel to the vibration direction (the vertical direction in fig. 1, i.e., the thickness direction of the vibrating object) as a side surface (4 surfaces except the upper and lower surfaces of the object are side surfaces in 6 surfaces in fig. 1), and the surface perpendicular to the vibration direction as a facing surface (the upper and lower surfaces of the object in fig. 1), the resistance applied to the vibrating object by the fluid medium can be reduced to resistances acting on the two types of surfaces, i.e., a side resistance and a facing resistance.

2. The side surface of the vibrating object is parallel to the vibrating direction, and the resistance transmitted to the object by the fluid medium can only be friction force. An important index for characterizing the frictional force characteristics of a fluid is the dynamic viscosity coefficient μ, which is commonly expressed in N · s/m²Dimension [ mu ] thereof]＝MT^{- 1}L^-1Where M is a dimension symbol of quality, T is a dimension symbol of time, and L is a dimension symbol of geometric size. From dimensional analysis, the dynamic viscosity coefficient can be expressed as damping per unit length. If the length of the side of the vibrating object submerged in the fluid is l, or "wetted perimeter", as in fig. 1, l is 2a +2 b. From this, the side damping R_m1The expression is as follows:

R_m1mu.l (formula 1)

This expression explains the lateral damping R_m1Proportional to the dynamic viscosity coefficient mu of the dielectric fluid and proportional to the lateral length l of the vibrating body.

3. The vibrating object is faced perpendicularly to the vibration direction, and the faced area of the vibrating object is S, as shown in FIG. 1, S is a-b. If the spaces on both sides of the vibrating object are assumed to be relatively large, the lateral flow of the facing fluid caused by the displacement delta x can be not considered, the fluid medium bears the thrust required by the movement delta x distance of the object to move away the fluid in the S.delta x volume, and the facing force transmitted by the medium to the vibrating object is the reaction force of the thrust borne by the fluid. This is a force of the fluid medium resisting the flow, which is expressed as a buoyancy force F on the object. The buoyancy force F is different from the static buoyancy force F of the object which is static and soaked in the fluid₁The buoyancy F is dynamic₂. Despite the static buoyancy F₁And dynamic buoyancy F₂Are all related to moving fluid mass, but static buoyancy F₁The buoyancy direction is always upward, and the buoyancy direction is the product of the moving mass and the gravity acceleration; and dynamic buoyancy F₂It is the product of the moving mass and the vibration acceleration, and the buoyancy direction is changed, always opposite to the motion direction. The dynamic buoyancy F₂The calculation expression of (a) is:

wherein rho is the density of the fluid, S is the frontal area of the vibrating object, Delta x is the vibration displacement of the object,

is the vibration acceleration.

The head-on damping R can be obtained by the analysis of the damping dimension_m2The calculation expression of (a) is:

R_m2rho · S · Δ x/Δ t (formula 3)

The formula 3 illustrates the head-on damping R_m2The fluid density rho, the frontal area S of the vibrating object and the vibration displacement Deltax are in direct proportion, and the vibration period Deltat is in inverse proportion.

And B, step B: side damping R_m1Calculating (1);

side damping R_m1The friction damping is calculated by the following expression:

R_m1mu.l (formula 1)

Wherein μ is a hydrodynamic viscosity coefficient in the unit of N · s/m²(ii) a l is the length of the side;

step C: head-on damping R_m2Calculating (1);

head-on damping R_m2Belongs to dynamic buoyancy damping, and the calculation expression is as follows:

R_m2rho.S.Δ x/Δ t (equation 3)

Where ρ is the fluid density, S is the head-on area, Δ x is the vibration displacement, and Δ t is the vibration period.

Although the invention has been described in detail above with reference to a general description and specific examples, it will be apparent to one skilled in the art that modifications or improvements may be made thereto based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.

Claims (1)

1. A medium damping calculation analysis method for a mechanical vibration system vibrating in a fluid medium is characterized by comprising the following steps:

step A: determining the source and classification of vibration damping;

the vibration damping of a vibrating object in a fluid medium is divided into lateral damping R according to the stress source of the vibrating object_m1And head-on damping R_m2Two types, wherein the side damping R_m1The resistance is born by the side face of the object parallel to the vibration direction, wherein the side face refers to the surface of the object parallel to the vibration direction; the head-on damping R_m2Resistance from the object facing perpendicular to the vibration direction, the facing being the surface perpendicular to the vibration direction;

and B: side damping R_m1Calculating;

the side damping belongs to friction damping, and the calculation expression is as follows:

R_m1mu.l (formula 1)

Wherein μ is a hydrodynamic viscosity coefficient in the unit of N · s/m²(ii) a l is the length of the side surface of the vibrating object;

step C: head-on damping R_m2Calculating (1);

the head-on damping belongs to dynamic buoyancy damping, and the calculation expression is as follows:

R_m2rho.S.Δ x/Δ t (equation 3)

In the formula, rho is the density of the fluid, S is the frontal area of the vibrating object, Δ x is the vibration displacement of the object, and Δ t is the vibration period.

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