chap12 - PROBLEM 12.1 KNOWN: A linear potentiometer having...

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Unformatted text preview: PROBLEM 12.1 KNOWN: A linear potentiometer having D = 0.1 mm 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 = = with A c = = -- 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 (1.5) cm of wire, thus N = = 462 9804 m 1.5 10 m-2 c h Then since each turn occupies approximately D = 0.1 mm the range is (9804) (0.1 mm) = 0.98 m 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. 2 4 6 8 10 12 14 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. 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....
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chap12 - PROBLEM 12.1 KNOWN: A linear potentiometer having...

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