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Unformatted text preview: 101 101 Strain, Force, and Pressure Force is that which results in acceleration (when forces don’t cancel). Strain is the change in shape of an object . . . . . . usually due to some force. (Force is usually called stress in this context.) Pressure is force per unit area. 101 EE 4770 Lecture Transparency. Formatted 8:35, 19 February 1999 from lsli10. 101 102 102 Strain Consider an object in two situations: with and without a force applied. Let a force be applied along a dimension. Let L 1 be the length of the object along the dimension when no force is applied. Let L 2 be the length when the force is applied. Then the object’s strain is defined to be L 2 L 1 L 1 . The symbol is usually used to denote strain. In most situations, strains of interest will be very small,   < . 0001. 102 EE 4770 Lecture Transparency. Formatted 8:35, 19 February 1999 from lsli10. 102 103 103 Strain Transducers Called strain gauges. Symbol: no common symbol. Construction Flexible card with strip of some conductor arranged in special pattern. Card is mounted (glued) onto the object being measured. Conductor is usually a metal or semiconductor. Pattern is chosen so that strain (to be measured) . . . . . . occurs along direction of current flow. Current is passed through conductor. 103 EE 4770 Lecture Transparency. Formatted 8:35, 19 February 1999 from lsli10. 103 104 104 Principle of Operation For Both Types Conductor maintains an almost constant volume with strain. That is, conductor is not compressible. Recall that the resistance of a conductor is R = ρ L A , where L is its length, A is its area, and ρ is its resistivity. Suppose force causes length of the conductor to decrease. Since volume does not change much, area must increase. Thus, resistance decreases. 104 EE 4770 Lecture Transparency. Formatted 8:35, 19 February 1999 from lsli10. 104 105 105 Model Function H t1 ( x ) = R (1 + G f x ), where G f is a constant . . . . . . called the gauge factor. For metal strain gauges, G f = 2. (An integer!) For semiconductor strain gauges G f is much higher. 105 EE 4770 Lecture Transparency. Formatted 8:35, 19 February 1999 from lsli10. 105 106 106 Complementary Pairs In some cases the strain . . . . . . in two places on the object . . . . . . will be of equal magnitude—but opposite sign. For example, a cantilever beam: Force Strain Gauges The upper part of beam is stretched (positive strain) . . . . . . and the lower part of beam is compressed (negative strain). The two strain gauges therefore . . . . . . form complementary pairs. 106 EE 4770 Lecture Transparency. Formatted 8:35, 19 February 1999 from lsli10. 106 107 107 Derivation of Gauge Factor for Ideal Metal Ideal metal’s properties: • Noncompressible. (Does not change volume.) • Resistivity is constant....
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This note was uploaded on 12/11/2011 for the course EE 4770 taught by Professor Staff during the Fall '99 term at LSU.
 Fall '99
 Staff

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