principles
vibration of the vibrating used to measure the amount of intensity, the amount of vibration may be vibrator displacement, velocity or acceleration. If the amount of vibration exceeds the allowable range, the device will have a greater mechanical loads and dynamic noise, thus affecting its performance and service life, can cause serious failure of the early components. For example, the turbine blade breakage due to vibration produced, can cause serious accidents. Due to the increasing complexity of modern mechanical structure, increasing the speed of movement, vibration hazards more prominent. Conversely, the use of vibrating machinery principle, should produce the expected vibrations. In the field of mechanical engineering, as well as the fluid vibration, and the vibration of the solid and fluid coupling of vibration in addition to solid. Air compressor surge, is a fluid vibration.
only kinetic model of the known mechanical device, and the external excitation based on the working conditions, in order to analyze the dynamic characteristics Mechanical characteristics of the device. Dynamic analysis include: ① calculating or measuring the inherent characteristics of the natural frequencies of the mechanical equipment, mode shapes, stiffness and damping. The inherent characteristics can identify the causes generating vibrations, avoid resonance, and provide basic data for further dynamic analysis. ② calculated or determined dynamically in response to the displacement, velocity, acceleration, phase, spectral and vibration time history and other relevant point mechanical equipment is energized, according to the capability of dynamic response evaluation of mechanical equipment to withstand vibration and shock, find their weaknesses and waste link provide a basis for improved design. Equations of motion of the mechanical system may also be represented by the modal parameter called modal analysis. ③ Analysis Dynamic mechanical stability of the computing device, to determine the mechanical equipment is unstable, i.e., self-excited vibration is generated in critical conditions. Ensure the mechanical device may not cause self-excited vibration at its full performance, and stable operation.
type
is the simplest mechanical vibration particle harmonic vibration. Simple harmonic motion is a sinusoidal function over time sports. Such vibration may be regarded as the result of this plane in the vertical-axis projection uniform circular motion in the vertical plane of the point. It vibration displacement
x ( t ) = Acos ωt
wherein a is the amplitude, i.e. the maximum deviation from the equilibrium position, i.e. the maximum vibration displacement; t is the time; ω is the angular frequency (2π times the frequency sinusoid). It vibration velocity is
d x / d t = ωA sin ( ωt + π / 2)
it vibration acceleration
d2x / dt2 = ω2Asin (ωt + π)
is represented by a vector vibrations. Constant angular velocity vector ω in the counterclockwise direction of rotation, the mold displacement vector (magnitude of the vector) is the amplitude of the A , the mold velocity vector is the magnitude of velocity ωA , the acceleration mode is the acceleration vector magnitude ω 2A. 90 ° to the speed of advance than the displacement vector, acceleration leading to 180 ° MV ratio. The vibration starts this dot is not in an equilibrium position, which displacement can be expressed
x ( t ) = A sin ( ωt + ψ)
wherein [Psi] is the initial phase. The time required to complete a cycle of vibration is called. I.e. the reciprocal of the number of vibrations per unit time period, referred to as frequency. Vibration having a fixed period, a period elapsed after the start of the cycle returned to the state, which is called periodic vibration. Any periodic function, as long as certain conditions are met can be expanded into a Fourier series. Thus, a non-harmonic vibration cycle can be decomposed into a series of simple harmonic motion. There is no fixed oscillation period is called a non-periodic vibrations, for example, rotating machinery aperiodic vibration occurs first during starting, when only the rotating machine cycle to achieve uniform rotation generates vibrations.
The system consists of the elements of mass, stiffness and damping of the composition in a form, called a mechanical system. The actual mechanical structures are generally more complex, when analyzing vibration problems often it needs to be simplified by several "inelastic" Quality and mechanical model "massless" elastic element consisting of a mechanical system which is , called spring-mass system. With the characteristics of the elastic stiffness of the spring element is represented, it is required to shorten or springs per unit length of elongation is applied forces. For example, the vehicle body and front and rear axle as a mass, the tire and the plate spring as the elastic member, each link having a vibration energy dissipation acting as a damper, three together form a mechanical vibration system of automobile .
SDOF systems Number of independent coordinates determined desired motion state of a mechanical system, referred to as the number of degrees of freedom of the system. Vibration analysis need to ignore the actual mechanical configuration of a certain secondary factors, it is simplified kinetic model, while it determines the number of degrees of freedom. Simplified depends on the main features of the system itself and the accuracy of the analysis of the results desired, and finally through the field to simplify the test results are correct. The simplest system is a single degree of freedom spring-mass system, is a system which consists of a spring and a mass consisting of only one coordinate can be determined independently of its state of motion. As the case may be selected as an independent coordinate linear displacement, angular displacement may be selected as an independent coordinate. A vibration system in a line independent displacement coordinates, called linear vibration. A twist angle of the vibration system independent displacement coordinates, called torsional vibrations.
MDOF system are practical engineering vibration problems, it often requires multiple degrees of freedom simplified system of two or more degrees of freedom. For example, when only the vertical vibration in the vertical direction research automobiles, to be reduced to single degree of freedom system described linear displacement movement thereof. When vertical vibration of automobile and swing back and forth, should be reduced to a line and angular displacements which also describes two degrees of freedom motion systems. 2 degrees of freedom systems generally have two different values of the natural frequencies. When the system according to any of the natural frequency of free vibration, called the main vibration. When primary vibration system, the system having a vibration modes is determined, called the primary vibration mode. And the natural frequency of the primary vibration mode as determined only, regardless of the initial conditions in the physical properties of the system itself. Multiple degrees of freedom system having a plurality of natural frequencies, the lowest natural frequency as a first-order natural frequency, referred to as the fundamental frequency. Study lateral vibration beam, the beam is necessary to use an unlimited number of cross-section of each instantaneous movement state of the movement of the beam is described. Therefore, a beam is a infinite number of degrees of freedom of the system, also known as continuous systems. Chord, rods, films, panels, stiffness and mass of the shell same beam has a property distribution. Therefore, they are an infinite number of degrees of freedom with a continuous system, also called the distribution system.
mechanical vibrations have different classification methods. By reason of vibration can be divided into free vibration, forced vibration and self-excited vibration; according to the law can be divided into simple harmonic vibration, the non-harmonic and random vibration cycles; by vibration characteristics of the structure parameters of the system can be divided into linear vibration and nonlinear vibration; by the vibration displacement characteristic can be divided into linear vibration and torsional vibration. After
free vibration
to remove the bound or excitation, mechanical vibration occurring. Vibration rely on its elastic restoring force to maintain when there is vibration damping will gradually decay. Free vibration frequency depends only on the physical properties of the system itself, referred to as the natural frequency of the system.
Forced Vibration
mechanical system excited by external vibrations continuously generated. Harmonic excitation is the simplest persistent excitation. The forced vibration comprising a vibration transient and steady-state oscillation. Time-varying vibration in the vibrating period starts occurring, called transient vibration. After a short time, the transient vibration disappears. The system continuously obtained from the external energy to compensate for the energy dissipated by the damper, it is possible to make constant vibration amplitude, the vibration frequency and the same excitation frequency, referred to as steady-state vibrations. For example, fixed at both ends in the middle of a cross member mounted exciter, continuous vibration amplitude after a short time of actuation beam exciter is made steady state vibration, the vibration frequency of the same frequency as the exciter. When the system by an external force or other input action, which is called in response to the corresponding output. When the frequency close to the natural frequency of the external excitation system, the amplitude of the system will increase dramatically. Excitation frequency equal to the system resonance frequency of the resonance. In the design and use of mechanical resonance must be prevented. For example, in order to ensure safe operation of the rotating machine, working speed of the shaft should be in a range which is outside of each of the first critical speed.
self-excited vibration
in the nonlinear vibration, the system only by its own vibration excitation generated maintained. In addition to self-excited vibration system having a vibrating element itself, but also with non-oscillatory energy, and feedback control element links. Thus, the absence of which can also produce a stable period when the outside vibration excitation, to maintain self-excited vibration by the alternating movement of the force itself and is controlled by a feedback and control element. A vibration stop, this alternating force disappeared. And self-excited vibration initial conditions independent of a frequency equal to or close to the natural frequency. The aircraft flight wing flutter, the machine table moving crawling low on the sliding guide, clocks pendulum swing and the vibration of the strings are all self-excited vibration.
Vibration
Since the mechanical impedance applications, system identification and modal analysis techniques, it has been successfully resolved many complex vibration problems. In the case of the known excitation, the vibration characteristics of the system design, it is required to respond to meet the requirements, the design called vibration. Systematic study under conditions known excitation and response characteristics of the system, i.e., the mathematical model of a vibration system by the method of experimental data and mathematical analysis of the combination, known as system identification. If the general form of the equation of motion of the mechanical structure is known, the simplified system identification parameter identification. Parameter identification may be performed in the frequency domain may be performed in the time domain, while others need to be in the frequency domain and time domain. Study at excitation and response characteristics of the known system, known as environmental prediction. Vibration design, system identification and environmental prediction can be summarized as the three basic elements of the modern study of vibration. In the field of mechanical engineering, machinery and equipment to ensure safe and reliable operation, vibration monitoring and diagnosis of mechanical structures also attracted attention. In the research method, vibration measurement is employed in combination with the theoretical analysis and calculation.
anti-vibration measures
When designing machinery and equipment, should be carefully designed in consideration of the object which vibrations occur: linear or nonlinear vibration vibration; level of vibration; the vibration the method of controlling the amount of the allowable range. This needs to be addressed when deciding the design problem. When the existing machinery and equipment vibration occurs exceeds the allowable range, damping measures need to be taken. In order to reduce the vibrations of the machine itself can be configured of various types of dampers. To reduce the effects of mechanical vibration equipment on the surrounding environment, or reduce the effects of vibration on the surrounding environment, machinery and equipment, vibration isolation measures can be taken. When systems are transient excitation, its force, displacement, velocity, acceleration, sudden change phenomenon, known as shock. General machinery and equipment withstand the impact of a weak, but can not afford a strong impact. In order to protect the machinery and equipment as not strong shock and damage mitigation measures can be taken to mitigate the impact of shocks. The aircraft landing, tires, landing gear strut and buffer, respectively, and subjected to absorbing some of the impact energy, so as to protect a safe landing. The fundamental way to reduce the mechanical noise is mainly controlling a vibration noise source, in case of need, the muffler may be disposed.
studying history
1656 ~ 1657 years, the Netherlands C. Huygens first proposed the theory of the physical pendulum, and created a mechanical pendulum clock. Early 20th century, mechanical vibration issues of concern focused on avoiding resonance, therefore, it is to focus on natural frequencies and mode shapes to determine the mechanical structure. 1921, Germany H. Holzer proposed natural frequencies and mode shapes of the calculated shaft torsional vibration solution. 1930s, research began to develop mechanical vibration of the linear vibration to the nonlinear vibration. Since the 1950s, studies of the development of mechanical vibration from the vibration of the rules to use probability and statistical methods to describe random vibration irregular vibration ── its laws. Since the development of automatic control theory and computer, and multi-degree of freedom in the past that computing system difficulties I am truly has become a problem easily solved. Development of vibration theory and experimental techniques, an important tool for vibration analysis in mechanical design becomes.