mechanical vibration

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Mechanical vibration refers to that the object or particle Balance position Regular reciprocating motion nearby. Use of vibration Amount of vibration To measure, the vibration quantity can be the displacement, speed or acceleration 。

Chinese name: mechanical vibration
Foreign name: mechanical vibration
Type: Reciprocating motion

Main body: object Or particle
Location: his Balance position nearby
Instance: Spring vibrator

catalog

one principle
two features
three type

five Anti vibration measures
six Research History

principle

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Use of vibration Amount of vibration To measure, the vibration quantity can be the displacement, velocity or acceleration of the vibrating body. If the vibration exceeds the allowable range, the mechanical equipment will produce large dynamic load and noise, which will affect its working performance and service life, and even lead to Early failure 。 For example, Turbine blade Fracture caused by vibration can cause Serious accident 。 Due to the increasing complexity of modern mechanical structures, Movement speed With the increasing of vibration, the harm of vibration is more prominent. On the contrary, the mechanical equipment that uses the vibration principle shall be able to produce the expected vibration. In the field of mechanical engineering, besides solid vibration Fluid vibration , as well as solid fluid coupling vibration. Air compressor Of surge Is a fluid vibration.

features

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Programmable mechanical vibration table

Only when known mechanical equipment Dynamic model, external excitation and Working conditions Only on the basis of Dynamic characteristics 。 Dynamic analysis includes: ① calculating or measuring the natural frequencies of mechanical equipment at various stages Modal shape , stiffness and damping, etc Inherent characteristic 。 According to the inherent characteristics, the causes of vibration can be found to avoid resonance and provide for further dynamic analysis Basic data 。② Calculate or measure the displacement, speed acceleration , phase, spectrum and time history of vibration, etc dynamic response Check the ability of mechanical equipment to withstand vibration and shock according to dynamic response weak link And waste links to provide basis for improving design. It can also be established for Modal parameter Of the indicated mechanical system Equation of motion , called modal analysis. ③ Analysis and calculation of mechanical equipment dynamic stability It is determined that the mechanical equipment is unstable, that is, it generates self-excited vibration critical condition 。 Ensure that the mechanical equipment will not produce self-excited vibration and can work stably under the condition of giving full play to its performance.

type

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The simplest mechanical vibration is particle Simple harmonic vibration 。 The simple harmonic vibration is sine The motion of a function change. This vibration can be regarded as constant velocity in the vertical plane Circular motion The result of the projection of a point on the vertical axis in this plane. Its vibration displacement is

x ( t )= Acos ω t

Where A by amplitude , i.e. deviation Balance position Of Maximum , i.e. the maximum value of vibration displacement; t Is time; ω by Circular frequency ( Sine quantity 2 π times the frequency). Its vibration speed is

d x /d t = ω A sin( ω t +π/2)

its vibration acceleration by

d2x/dt2= ω 2Asin( ω t+π)

The vibration can also be expressed by vectors. Vector to wait angular velocity ω When rotating counterclockwise, the modulus (magnitude of the vector) of the displacement vector is the amplitude A The module of velocity vector is the amplitude of velocity ω A ， acceleration The mode of vector is the amplitude of acceleration ω 2A。 The velocity vector is 90 ° ahead of the displacement vector, and the acceleration vector is 180 ° ahead of the displacement vector. If the particle is not in the equilibrium position at the beginning of vibration, its displacement can be expressed by the following formula

x ( t )= A sin( ω t + ψ)

Where ψ by Initial phase 。 The time required to complete a vibration is called period. The reciprocal of the period is the number of vibrations per unit time, which is called frequency. The vibration with a fixed period returns to the state at the beginning of the period after a period, which is called Periodic vibration 。 Any one Periodic function , can be expanded into Fourier series 。 Therefore, an anharmonic periodic vibration can be decomposed into a series of simple harmonic vibrations. Vibration without fixed period is called Aperiodic vibration For example, the aperiodic vibration occurs first in the starting process of rotating machinery, and the periodic vibration occurs only when the rotating machinery reaches a uniform speed.

The system composed of mass, stiffness and damping elements in a certain form is called mechanical system 。 The actual mechanical structure is generally complex. When analyzing its vibration problem, it is often necessary to simplify it to several "inelastic" masses and "massless" masses Elastic element Composed of mechanical model This is a mechanical system called spring mass system. The characteristics of the elastic element are expressed by the stiffness of the spring Unit length The force to be applied. For example, the body, front and rear axles of a car can be used as the mass, the leaf spring and tire can be used as the elastic elements, and each link with the effect of dissipating vibration energy can be used as the damping. The three together constitute a mechanical system for studying the vibration of a car.

Single degree of freedom system Determine the motion state The number of independent coordinates required, called the Degrees of freedom 。 When analyzing the vibration characteristics of an actual mechanical structure, it is necessary to ignore some Secondary factors , simplify it to dynamic model And determine its degrees of freedom. The degree of simplification depends on the main characteristics of the system itself and the accuracy of the required analysis and calculation results. Finally, the accuracy of the simplified results is verified through actual measurement. The simplest spring mass system is Single degree of freedom system It is a system composed of a spring and a mass, and only one independent coordinate can determine its motion state. According to the specific situation, you can select Linear displacement As an independent coordinate, you can also select angular displacement As independent coordinates. The vibration of the system with linear displacement as independent coordinate is called Linear vibration 。 The vibration of the system with torsion angle displacement as independent coordinate is called torsional vibration 。

Multi degree of freedom system Many practical engineering vibration problems often need to be simplified into two or more degrees of freedom Multi degree of freedom system 。 For example, when only the vertical up and down vibration of the vehicle is studied, it can be simplified as a single degree of freedom system with linear displacement to describe its motion. When studying the up and down vibration and the front and back swing of the vehicle, it should be simplified as a two degree of freedom system that describes its motion with linear displacement and angular displacement at the same time. Two degree of freedom systems generally have two different values natural frequency 。 When the system is based on any natural frequency free vibration Is called main vibration. When the system acts as the main vibration, the whole system has a certain vibration form, which is called the main vibration mode. Like the natural frequency, the main vibration mode is only determined by the physical property , and initial condition irrelevant. Multi degree of freedom system has multiple natural frequencies, and the lowest natural frequency is called the first natural frequency fundamental frequency 。 Study of beam transverse vibration When you use an infinite number of cross section The motion law of the beam is described in each instantaneous motion state. Therefore, a beam is a system with infinite degrees of freedom, also known as continuous system 。 The mass and stiffness of chords, rods, membranes, plates and shells are the same as those of beams, and they are distributed. Therefore, they are all continuous systems with infinite degrees of freedom, also known as Distributed system 。

Mechanics Vibration There are different classification method 。 According to the causes of vibration, it can be divided into free vibration , forced vibration and Self-excited vibration ； It can be divided into Simple harmonic vibration , anharmonic periodic vibration and random vibration; By vibration System structure The characteristics of parameters can be divided into linear vibration and nonlinear vibration ； According to the characteristics of vibration displacement, it can be divided into torsional vibration and Linear vibration 。

free vibration

After removing incentives or constraints, mechanical system The vibration that occurs. The vibration is only maintained by its elastic restoring force, and the vibration will gradually attenuate when there is damping. The frequency of free vibration only depends on the physical properties of the system itself, which is called the natural frequency of the system.

Forced vibration

mechanical vibration

Mechanical system is exposed to external environment Continuous incentive Vibration generated. Simple harmonic excitation is the simplest continuous excitation. Forced vibration contain Transient vibration and Steady state vibration 。 The vibration that changes with time during the initial period of vibration is called transient vibration. After a short time, the transient vibration disappears. The system constantly obtains energy from the outside to compensate for the energy dissipated by damping, so it can make continuous Constant amplitude vibration , the frequency of this vibration is Excitation frequency Same, called steady state vibration. For example, install one in the middle of the beam fixed at both ends Exciter The continuous constant amplitude vibration of the beam after the exciter is started for a short time is the steady vibration, and the vibration frequency is the same as that of the exciter. When the system is subjected to external force or other input, its corresponding Output This is called a response. When External incentives When the frequency of is close to the natural frequency of the system amplitude Will increase sharply. The excitation frequency is equal to that of the system resonance frequency Resonance will occur when. Resonance must be prevented when designing and using machinery. For example, to ensure rotation Mechanical safety Running, shaft Operating speed Should be in its various stages critical speed Out of a certain range.

Self-excited vibration

stay nonlinear vibration The vibration of the system is only maintained by the excitation generated by itself. Self-excited vibration In addition to vibration elements, the system also has non oscillatory energy, regulation and feedback links. Therefore, when there is no external excitation, it can also produce a stable periodic vibration, and the alternating force to maintain the self-excited vibration is generated by the motion itself and controlled by the feedback and regulation links. As soon as the vibration stops, the alternating force also disappears. Self-excited vibration and initial condition The frequency is equal to or close to the natural frequency of the system. For example, the wing Flutter The creeping of the machine tool table when moving at low speed on the sliding guide rail, the swing of the clock pendulum and the vibration of the piano string are all self-excited vibrations.

Vibration test

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mechanical vibration

Since application Mechanical impedance 、 system identification and modal analysis People have successfully solved many complex vibration problems since the technology of vibration vibration. When the excitation is known, designing the vibration characteristics of the system to make its response meet the required requirements is called vibration design. Study the characteristics of the system under the condition that the excitation and response of the system are known experimental data The method combined with mathematical analysis to determine the mathematical model , called system identification. If known Mechanical structure Equation of motion System identification is simplified to parameter identification. Parameter identification can be performed in frequency domain It can also be carried out in the time domain, and some need to be carried out in the frequency domain and time domain at the same time. The study of excitation under the condition that the characteristics and responses of the system are known is called Environmental prediction 。 Vibration design, system identification and environment prediction can be summarized as the basic contents of modern vibration research. In the field of mechanical engineering, to ensure Safety of mechanical equipment With reliable operation, the vibration monitoring and diagnosis of mechanical structures have also attracted people's attention. stay research method On, Vibration test Yes and theoretical analysis Used in combination with calculation.

Anti vibration measures

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When designing mechanical equipment, the vibration of the designed object should be carefully considered: linear vibration or nonlinear vibration; Vibration degree; hold Amount of vibration The method of controlling within the allowable range. It's a decision design scheme Problems that need to be solved. When the vibration of existing mechanical equipment exceeds the allowable range, vibration reduction measures shall be taken. In order to reduce the vibration of mechanical equipment, various types of Shock absorber 。 To reduce the vibration of mechanical equipment surrounding environment Vibration isolation measures can be taken to reduce the impact of ambient vibration on mechanical equipment. When the system is subjected to transient excitation, its force, displacement, speed and acceleration change suddenly, which is called impact. General mechanical equipment can withstand weak impact, but cannot withstand strong impact. In order to protect mechanical equipment from being damaged by strong impact, buffer measures can be taken to reduce the impact of impact. For example, when the aircraft lands, tires Landing gear And buffer pillar, etc Impact energy To protect the safe landing of the aircraft. reduce Mechanical noise The fundamental way of noise source If necessary, silencer can also be equipped.

Research History

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1656~1657, Netherlands C. Huygens first proposed Physical pendulum And created Simple pendulum Mechanical clock. At the beginning of the 20th century, people's concern about mechanical vibration was mainly focused on avoiding resonance, so the focus of research was on mechanical structure natural frequency And determination of vibration mode. In 1921, H. Holzer of Germany proposed a solution Torsional vibration of shafting The calculation method of natural frequency and mode shape of. In the 1930s, the research on mechanical vibration began from Linear vibration It develops to nonlinear vibration. Since the 1950s, the research of mechanical vibration has developed from regular vibration to irregular vibration, which can only be described by probability and statistics random vibration 。 because Automatic control theory And electronics computer In the past, the calculation of multi degree of freedom system, which was considered very difficult, has become an easy problem to solve. vibration theory And the development of experimental technology, making vibration analysis machine design An important tool in.

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