河南理工大学万方科技学院本科毕业论文A Practical Approach to Vibration Detection and MeasurementPhysical Principles and Detection TechniquesBy: John Wilson, the Dynamic Consultant, LLCThis tutorial addresses the physics of vibration; dynamics of a spring mass system; damping; displacement, velocity, and acceleration; and the 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 period 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 direction 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.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 stiffness 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 = MAW = MgK = F/d = W/dd = F/K = W/K = Mg/KDynamics of a Spring Mass SystemThe 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 board, 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 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 energy 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 as 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. This 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 call 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, RI, and Tr1. As the forcing frequency approaches the natural frequency, 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, however, 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 fffn. This condition is called resonance. Isolation. If the forcing frequency is increased above fn, R decreases. 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 natural frequency is proportional to the square root of stiffness, K, and inversely proportional to the square root of