1、1 英文原文 A Practical Approach to Vibration Detection and Measurement Physical Principles and Detection Techniques By: John Wilson, the Dynamic Consultant, LLC This tutorial addresses the physics of vibration； dynamics of a spring mass system； damping； displacement, velocity, and acceleration； and the
2、operating principles of the sensors that detect and measure these properties. Vibration is oscillatory motion resulting from the application of oscillatory or varying forces to a structure. Oscillatory motion reverses direction. As we shall see, the oscillation may be continuous during some time per
3、iod of interest or it may be intermittent. It may be periodic or nonperiodic, i.e., it may or may not exhibit a regular period of repetition. The nature of the oscillation depends on the nature of the force driving it and on the structure being driven. Motion is a vector quantity, exhibiting a direc
4、tion as well as a magnitude. The direction of vibration is usually described in terms of some arbitrary coordinate system (typically Cartesian or orthogonal) whose directions are called axes. The origin for the orthogonal coordinate system of axes is arbitrarily defined at some convenient location.
5、Most vibratory responses of structures can be modeled as single-degree-of-freedom spring mass systems, and many vibration sensors use a spring mass system as the mechanical part of their transduction mechanism. In addition to physical dimensions, a spring mass system can be characterized by the stif
6、fness of the spring, K, and the mass, M, or weight, W, of the mass. These characteristics determine not only the static behavior (static deflection, d) of the structure, but also its dynamic characteristics. If g is the acceleration of gravity: F = MA W = Mg K = F/d = W/d d = F/K = W/K = Mg/K Dynami
7、cs of a Spring Mass System The dynamics of a spring mass system can be expressed by the systems behavior in free vibration and/or in forced vibration. Free Vibration. Free vibration is the case where the spring is deflected and then released and allowed to vibrate freely. Examples include a diving b
8、oard, a bungee jumper, and a pendulum or swing deflected and left to freely oscillate. Two characteristic behaviors should be noted. First, damping in the system causes the amplitude of the oscillations to decrease over time. The greater the damping, the faster the amplitude decreases. Second, the 2
9、 frequency or period of the oscillation is independent of the magnitude of the original deflection (as long as elastic limits are not exceeded). The naturally occurring frequency of the free oscillations is called the natural frequency, fn: (1) Forced Vibration. Forced vibration is the case when ene
10、rgy is continuously added to the spring mass system by applying oscillatory force at some forcing frequency, ff. Two examples are continuously pushing a child on a swing and an unbalanced rotating machine element. If enough energy to overcome the damping is applid, the motion will continue as long a
11、s the excitation continues. Forced vibration may take the form of self-excited or externally excited vibration. Self-excited vibration occurs when the excitation force is generated in or on the suspended mass； externally excited vibration occurs when the excitation force is applied to the spring. Th
12、is is the case, for example, when the foundation to which the spring is attached is moving. Transmissibility. When the foundation is oscillating, and force is transmitted through the spring to the suspended mass, the motion of the mass will be different from the motion of the foundation. We will cal
13、l the motion of the foundation the input, I, and the motion of the mass the response, R. The ratio R/I is defined as the transmissibility, Tr: Tr = R/I Resonance. At forcing frequencies well below the systems natural frequency, R I, and Tr 1. As the forcing frequency approaches the natural frequency
14、, transmissibility increases due to resonance. Resonance is the storage of energy in the mechanical system. At forcing frequencies near the natural frequency, energy is stored and builds up, resulting in increasing response amplitude. Damping also increases with increasing response amplitude, howeve
15、r, and eventually the energy absorbed by damping, per cycle, equals the energy added by the exciting force, and equilibrium is reached. We find the peak transmissibility occurring when ff fn. This condition is called resonance. Isolation. If the forcing frequency is increased above fn, R decreases.
16、When ff = 1.414 fn, R = I and Tr = 1； at higher frequencies R I and Tr 1. At frequencies when R I, the system is said to be in isolation. That is, some of the vibratory motion input is isolated from the suspended mass. Effects of Mass and Stiffness Variations. From Equation (1) it can be seen that n
17、atural frequency is proportional to the square root of stiffness, K, and inversely proportional to the square root of weight, W, or mass, M. Therefore, increasing the stiffness of the spring or decreasing the weight of the mass increases natural frequency. Damping Damping is any effect that removes
18、kinetic and/or potential energy from the spring mass system. It is usually the 3 result of viscous (fluid) or frictional effects. All materials and structures have some degree of internal damping. In addition, movement through air, water, or other fluids absorbs energy and converts it to heat. Inter
19、nal intermolecular or intercrystalline friction also converts material strain to heat. And, of course, external friction provides damping. Damping causes the amplitude of free vibration to decrease over time, and also limits the peak transmissibility in forced vibration. It is normally characterized
20、 by the Greek letter zeta ( ) , or by the ratio C/Cc, where c is the amount of damping in the structure or material and Cc is critical damping. Mathematically, critical damping is expressed as Cc = 2(KM)1/2. Conceptually, critical damping is that amount of damping which allows the deflected spring m
21、ass system to just return to its equilibrium position with no overshoot and no oscillation. An underdamped system will overshoot and oscillate when deflected and released. An overdamped system will never return to its equilibrium position； it approaches equilibrium asymptotically. Displacement, Velo
22、city, and Acceleration Since vibration is defined as oscillatory motion, it involves a change of position, or displacement (see Figure 1). Figure 1. Phase relationships among displacement, velocity, and acceleration are shown on these time history plots. Velocity is defined as the time rate of change of displacement； acceleration is the time rate of change of velocity. Some technical disciplines use the term jerk to denote the time rate of change of acceleration.
