【正文】 ing 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 mass 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。 100 g is ~ in. Measuring Vibratory Displacement Optical Techniques. If displacement is large enough, as at low frequencies, it can be measured with a scale, calipers, or a measuring microscope. At higher frequencies, displacement measurement requires more sophisticated optical techniques. Highspeed movies and video can often be used to measure displacements and are especially valuable for visualizing the motion of plex structures and mechanisms. The two methods are limited by resolution to fairly large displacements and low frequencies. Strobe lights and stroboscopic photography are also useful when displacements are large enough, usually in., to make them practical. The change in intensity or angle of a light beam directed onto a reflective surface can be used as an indication of its distance from the source. If the detection apparatus is fast enough, changes of distance can be detected as well. The most sensitive, accurate, and precise optical device for measuring distance or displacement is the laser interferometer. With this apparatus, a reflected laser beam is mixed with the original incident beam. The interference patterns formed by the phase differences can measure displacement down to 100 nm. NIST and other national primary calibration agencies use laser interferometers for primary calibration of vibration measurement instruments at frequencies up to 25 kHz. Electromagic and Capacitive Sensors. Another important class of noncontact, specialpurpose displacement sensors is the general category of proximity sensors. These are probes that are typically built into machinery to detect the motion of shafts inside journal bearings or the relative motion of other machine elements. The sensors measure relative distance or proximity as a function of either electromagic or capacitive (electrostatic) coupling between the probe and the target. Because these devices rely on inductive or capacitive effects, they require an electrically conductive target. In most cases, they must be calibrated for a specific target and specific material characteristics in the gap between probe and target. Electromagic proximity sensors are often called eddy current probes because one of the most popular types uses eddy currents generated in the target as its measurement mechanism. More accurately, this type of sensor uses the energy dissipated by the eddy currents. The greater the distance from probe to target, the less electromagic coupling, the lower the magnitude of the eddy currents, and the less energy they drain from the 6 probe. Other electromagic probes sense the distortion of an electromagic field generated by the probe and use that measurement to indicate the distance from probe to target. Capacitive proximity sensor systems measure the capacitance between the probe and the target and are calibrated to convert the capacitance to distance. Capacitance is affected by the dielectric properties of the material in the gap as well as by distance, so calibration can be affected by a change of lubricant or contamination of the lubricant in a machine environment. Contact Techniques. A variety of relative motion sensors use direct contact with two objects to measure relative motion or distance between them. These include LVDTs, cable position transducers (stringpots), and linear potentiometers. All of these devices depend on mechanical linkages and electromechanical transducers. Seismic Displacement Transducers. These devices, discussed in detail later, were once popular but now are seldom used. They tend to be large, heavy, and short lived. Double Integration of Acceleration. With the increasing availability and decreasing cost of digital signal processing, more applications are using the more rugged and more versatile accelerometers as sensors, then double integrating the acceleration signal to derive displacements. While older analog integration techniques tended to be noisy and inaccurate, digital processing can provide quite highquality, highaccuracy results. Measuring Vibratory Velocity Transducers. Some of the earliest highfrequency vibration measurements were made with electrodynamic velocity sensors. These are a type of seismic transducer that incorporates a mag supported on a soft spring suspension system to form the seismic (spring mass) system. The magic member is suspended in a housing that contains one or more multiturn coils of wire. When the housing is vibrated at frequencies well above the natural frequency of the spring mass system, the mass (mag) is isolated from the housing vibration. Thus, the mag is essentially stationary and the housing, with the coils, moves past it at the velocity of the structure to which it is attached. Electrical output is generated proportional to the velocity of the coil moving through the magic field. Velocity transducers are used from ~10 Hz up to a few hundred Hz. They tend to be large and heavy, and eventually wear and produce erratic outputs. Laser Vibrometers. Laser vibrometers or laser velocimeters are relatively new instruments capable of providing high sensitivity and accuracy. They use a frequencymodulated (typically around 44 MHz) laser beam reflected from a vibrating surface. The reflected beam is pared with the original beam and the Doppler frequency shift is used to calculate the velocity of the vibrating surface. Alignment and standoff distance are critical. Becau