Dept. of Biomedical Engineering YOUNHO HONG RESISTIVE SENSORS

Stress (axial), Strain M x y A=xy F=mg On the surface, the average force per unit area is denoted as σ : “stress” [N/m²] L F F δ : “strain” [unitless]

Stress-Strain Curve Brittle Materials ( ex. glass, concrete) 1 : ultimate stress 2 : rupture # Do not have a yield point # ultimate strength and breaking strength are the same nonlinear over a wide range

Stress-Strain Curve Ductile material (ex. Al, steel) 1 : ultimate stress 2 : yield stress 3 : rupture 4 : elastic region 5 : plastic region A : Al B : steel For elastic region ( linear region ) [ σ ≤ σ PL] σ = E ε (E : Young’s modulus) σ PL cf) Less ductile materials such as aluminum and medium to high carbon steels do not have a well-defined yield point.

Cantilever L F F δ Al σ = E ε If a material of a cantilever is a aluminum, A and L are almost constant. L+ ε F F = αε

Strain gage (electrical wire) A L + - V ρ resistivity is low

Strain gage If A, L, ρ change at the same time, Poisson’s ratio L D L+ ∆L D- ∆D

Gage factor for metal strain gage, G : ~1.6 for semi-conductor strain gage, G : 100~ Ω -> Ω 100 Ω -> 101 Ω for a bit of changes of resistance, use Bridge Circuit method

Problems and Solutions Top view Bottom view Gage 1 Gage 2 Gage 3 Gage 4 Gage 1&2 : L => L + ∆L Gage 3&4 : L => L - ∆L f = ε AE ε = (1/AE)f (3) Four metal strain gages which gage factor is 10 are attached on a plain. By forcing F to the plain, Gage1 and 2 are expanded as long as ∆L, whereas Gage3 and 4 are shorten in the same length. It has a relation that ∆L/L = kf, k is constant. Design a bridge circuit getting output voltage in proportion to F, describe output voltage as F. Voltage source of the bridge circuit is dc 5[V].

Problems and Solutions Vo = Av(Va-Vb)

Problems and Solutions p-type Si strain-gage S1&S2 : G=100 n-type Si strain-gage S3&S4 : G=-100 Top view Bottom view Gage 1 Gage 3 Gage 2 Gage 4 (4) Consider to design a system measuring force by using both two P-type Si strain gages which gage factor is 100 and two N-type Si strain gages which one is -100.

Problems and Solutions R=200 Ω -5 ≤ Vo ≤ 5 Vo.max = Av*5*100* = Av*0.25 = 5V Av = 20 (b) Assuming that both top and bottom of cantilever is changed in the same length in case that forced. By forced F, maximum change of the length of strain gage is +0.05%, resistor is 200 without any load. Specify gain in order output to vary in the range between -5V to +5V. (c) Derive to calibrate this kind of instrument. f Vo Change f by using different metal, and measure Vo # Use least square method to find the calibration equation.

Problems and Solutions (6) Four metal strain gages are attached on the diaphragm below. Two of them which are p-type Si strain gages have 100 gage factor and the others which are n-type Si strain Gages have -100 gage factor. When the diaphragm is pressed, each of strain gages has the same strain and sensitivity is (1/100000)%/mmHG. When It isn’t pressed, resistance is 50. Assume the relation between pressure and strain is linear. (a)How much does each resistance of p-type and n-type Si strain gages change, when the pressure is changed ? The sensitivity is (1/100000)%/mmHG and the resistance is 50 when pressure is zero. So, when the pressure is 500mmHG, the resistance of p-type is and the resistance of n-type is (b) Design Bridge circuit with four strain gages. Make the positions of strain gages. p-type Si strain-gage S1&S2 : G=100 n-type Si strain-gage S3&S4 : G=-100

Problems and Solutions (c) Define the Voltage Gain of the op-amp. Input voltage is DC 1V. Output voltage changes 0-1V. Av =

Thank for your attention