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chap12

# chap12 - PROBLEM 12.1 KNOWN A linear potentiometer having D...

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PROBLEM 12.1 KNOWN: A linear potentiometer having D = 0.1 mm ρ e = 1.7 × 10 -8 -m R = 1 k FIND: a) for a core diameter of 1.5 cm, determine the range b) plot loading error as a function of displacement SOLUTION: a) In order to determine the number of turns of wire, N R L A L RA e c c e = = ρ ρ with A c = × = × - - π 4 0 1 10 7 854 10 3 2 9 . . m m 2 c h yields L = × × = - - 1000 7 854 10 1 7 10 462 9 8 m - m m 2 b gc h . . One turn takes π (1.5) cm of wire, thus N = × = 462 9804 m 1.5 10 m -2 π c h Then since each turn occupies approximately D = 0.1 mm the range is (9804) (0.1 mm) = 0.98 m

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b) The loading error for a voltage dividing circuit is found from (6.37) as ( 29 ( 29 ( 29 1 / 1 / 1 1 2 1 1 1 + - + + - + - = - = m T T T m T T i i o i o i L R R R R R R R R R R R R E E E E E E e In terms of output voltage the length may be written, assuming an infinite meter resistance, from (6.8) E L L E R R E o x T i x T i = = yielding deflection scale - full of percentage a as error loading 100 = × i l E e A plot is shown below. 0 2 4 6 8 10 12 14 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Length (m) % Loading Error 1000 Ohms 10000 Ohms 100000 Ohms
PROBLEM 12.2 KNOWN: Numerous applications for linear displacement sensors. FIND: Develop specifications for a selected application for a linear displacement sensor . SOLUTION : A list of potential applications is provided in the problem statement. These applications include several measurements that would easily be accomplished by a potentiometric or LVDT position sensor having an accuracy of ± 1 mm, including seat position and throttle position sensors for automotive applications. There exist applications where errors must be on the order of microns, and a variety of sensors exist that can meet such a stringent repeatability requirement, although absolute accuracy can be a significant challenge. Applications include machine tools and rapid prototyping systems.

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PROBLEM 12.3 KNOWN: Potentiometers are primarily either wire-wound or conductive plastic in their construction. FIND: Compare and contrast the design of wire-wound and conductive plastic potentiometers. SOLUTION: Conductive plastic potentiometers provide continuous analog output, where wire-wound potentiometers have resolution limited by the size of the wire that forms the winding. However, production of conductive plastic having a constant resistivity, which produces a linear relationship between displacement and resistance, is not perfect. Both designs are widely applied in a variety of devices.
PROBLEM 12.4 KNOWN: LVDT and potentiometric displacement transducers. FIND: Compare and contrast the use of LVDT and potentiometric displacement transducers. SOLUTION: The LVDT has the following positive characteristics: Because there is no contact between the movable core and the coil structure, friction is extremely low, and provides for essentially infinite life Truly analog behavior, so that resolution is limited only by the output measuring system employed Very good repeatability Somewhat greater cost The potentiometric sensor, has the following positive characteristics; Lower cost Good repeatability

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PROBLEM 12.5
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chap12 - PROBLEM 12.1 KNOWN A linear potentiometer having D...

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