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                       allow operation up to 80,000 rpm [16]. High-speed operation requires careful consideration of the effects
                       of centrifugal stresses on the sensed quantity as well as of critical (vibration inducing) speed ranges.
                       Torsional oscillations associated with resonances of the shaft elasticity (characterized by its spring con-
                       stant) with the rotational inertia of coupled masses can corrupt the measurement, damage the transducer
                       by dynamic excursions above its rated overload torque, and even be physically dangerous.
                         Housings either float on the shaft bearings or are rigidly mounted. Free floating housings are restrained
                       from rotating by such “soft” means as a cable, spring, or compliant bracket, or by an eccentric external
                       feature simply resting against a fixed surface. In free floating installations, the axes of the driving and
                       driven shafts must be carefully aligned. Torsionally rigid “flexible” couplings at each shaft end are used
                       to accommodate small angular and/or radial misalignments. Alternatively, the use of dual flexible cou-
                       plings at one end will allow direct coupling of the other end. Rigidly mounted housings are equipped
                       with mounting feet or lugs similar to those found on the frame of electric motors. Free-floating models
                       are sometimes rigidly mounted using adapter plates fastened to the housing. Rigid mountings are preferred
                       when it is difficult or impractical to align the driving and driven shafts, as for example when driving or
                       driven machines are changed often. Rigidly mounted housings require the use of dual flexible couplings
                       at both shaft ends.
                         Modular transducers designed for zero or limited rotation applications have no need for bearings. To
                       ensure that all of the torque applied at the ends is sensed, it is important in such “reaction”-type torque
                       transducers to limit attachment of the housing to the shaft to only one side of the sensing region. Whether
                       rotating or stationary, the external shaft ends generally include such torque coupling details as  flats,
                       keyways, splines, tapers, flanges, male/female squares drives, etc.
                       Electrical Considerations
                       By their very nature, transducers require some electrical input power or excitation. The “raw” output
                       signal of the actual sensing device also generally requires “conditioning” into a level and format appro-
                       priate for display on a digital or analog meter or to meet the input requirements of data acquisition
                       equipment. Excitation and signal conditioning are supplied by electronic circuits designed to match the
                       characteristics of the specific sensing technology. For example, strain gage bridges are typically powered
                       with 10–20 V (DC or AC) and have outputs in the range of 1.5–3.0 mV per volt of excitation at the rated
                       load. Raising these millivolt signals to more usable levels requires amplifiers having gains of 100 or more.
                       With AC excitation, oscillators and demodulators (or rectifiers) are also needed. Circuit elements of these
                       types are normal when inductive elements are used either as a necessary part of the sensor or simply to
                       implement noncontact constructions.
                         Strain gages, differential transformers, and related sensing technologies require that electrical components
                       be mounted on the torqued member. Bringing electrical power to and output signals from these components
                       on rotating shafts require special methods. The most direct and common approach is to use conductive
                       means wherein brushes (typically of silver graphite) bear against (silver) slip rings. Useful life is extended
                       by providing means to lift the brushes off the rotating rings when measurements are not being made. Several
                       “noncontacting” methods are also used. For example, power can be supplied via inductive coupling between
                       stationary and rotating transformer windings [12–15], by the illumination of shaft-mounted photovoltaic
                       cells [20], or even by batteries strapped to the shaft [21] (limited by centrifugal force to relatively low speeds).
                       Output signals are coupled off the shaft through rotary transformers, by frequency-modulated (infrared)
                       LEDs [19,20], or by radio-frequency (FM) telemetry [21]. Where shaft rotation is limited to no more than
                       a few full rotations, as in steering gear, valve actuators or oscillating mechanisms, hard wiring both power
                       and signal circuits is often suitable. Flexible cabling minimizes incidental torques and makes for a long and
                       reliable service life. All such wiring considerations are avoided when noncontact technologies or construc-
                       tions are used.
                       Costs and Options
                       Prices of torque transducers reflect the wide range of available capacities, performance ratings, types,
                       styles, optional features, and accessories. In general, prices of any one type increase with increasing
                       capacity. Reaction types cost about half of similarly rated rotating units. A typical foot-mounted, 565 Nm

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