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BASIC SENSORS AND PRINCIPLES Introduction of Resistive Sensor ① Strain gages • Measurement of extremely small displacement ① Potentiometers • Translational and Rotational displacement ② FSR and so on… (Axial) Stress On the surface, The average force per area is denoted as A = xy F A F = mg (N ) (m 2 ) F is sometimes called as “LOAD” ; Stress -solid (cf. Pressure) -liquid, gas Strain L F ( m) L ( m) F ; Strain (unitless) & CURVE ① Brittle material (ex. glass) n rupture Broken : Brittle material’s property ; Non-linear Linear region ; elastic region (like spring) Not linear ; over a wide range & CURVE ys ② Ductile material (ex. Al, Steel) n PL rupture PL rupture rupture ; Al elastic region plastic region For elastic region ( Linear region ) ( < PL ) ; Steel elastic region plastic region E Young’s modules (cf. y = kx) (modules of elasticity) In Summary, so far... F A E L Cantilever E L F F E A L E : constant A & L are almost constant AE F AE L ; Provided that you know , it is possible to measure F Strain gage is widely used to measure F The Principle of Weighing Machine F • None of our business, • All about for mechanics in terms of a variety of structures. F mg Able to derive ‘m’ Strain Gages L Substrate A : resistivity Electrical wire 8XL L R A All variables changed for volume constant Eight Electrical X times length ; The relation between Strain and Resistor F F Length Length ( elastic region ) Strain Gages Partial Derivative in order to know the relation to each component R L L R A A L R A R RL L L A A R L L 2 RA 2 A A A A Strain Gages R R RL RA Measurable size L L d dL 2 dA A A A R L A R L A Resistor Strain Strain Gages Poisson’s ratio with D L D L L D D D R L (1 2 ) R L Piezo-resistive effect Dimensional effect Strain Gages R Gage factor R R R G 1 2 L L L L • For metal strain gage • For semiconductor strain gage G : ~1.6 G : 100 ~ 170 (High temperature coefficient) Problem (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]. Problem (3) G ① ② R R 10 R 10 L L R L L Gage1& 2 : L L L Gage3& 4 : L L L ③ ④ Load cell : force sensor (Structure + Strain gage) ① ② Top view L k f L f AE 1 f AE Problem (3) ③ ② Vo Av(Va VB ) ① ④ And LPF Register Variable Register Resistive Sensor R1 R R R R Va 5 5 5 R1 R3 R RR R 2R R4 R R R R Vb 5 5 5 R2 R4 R RR R 2R 10 R L Vo Av 5 Av 10 2R L Vo 50 Avkf Part of it is your design 5 X 10 Your design Given by structure and material Problem (4) Consider to design a system measuring force by using both two Ptype Si strain gages which gage factor is 100 and two N-type Si strain gages which one is -100. (a)Design a circuit including a bridge circuit having four strain gages as well as instrumentation amplifier in order to magnify output. Specify the type of each strain gage composing the bridge circuit. (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. Problem (4) P-type Si Strain gage S1 & S2 : G = 100 N-type Si Strain gage S3 & S4 : G = -100 G S3 S1 S1 S3 <Top View> R L R L S4 S2 S2 S4 <Bottom View> Problem (4) S3 S4 Vo Av(Va VB ) S1 S2 And LPF Va R1 R R R R E E E R1 R3 R RR R 2R Vb R4 R R R R E E E R2 R4 R RR R 2R Problem (4) R R L Av 5 G L Vo AvE Vomax Av 5 100 0.0005 Av 0.25 5V 5 Av 20 0.25 max L 0.0005 L R 200 Problem (4) Calibration F : 0 – 100N Change f by using different mass to measure V0 Use Least Square Method to find the Calibration Eqution. Problem (6) 2 P-type Si strain gages and 2 N-type Si strain gages are attached below diaphragm of Pressure sensor. In case of pressure on diaphragm, same strain occur at the each strain gage with its sensitivity of 105 %/mmHg, its resistor is 50 without any pressure. Assuming that it is linear between pressure and strain. Catheter Liquid Sensor S3 S4 Diaphragm S2 S1 Problem (6) (a) In variation of pressure from 0 to 500mmHg , how each resistor of P-type and N-type Si strain gages changed. R Ro G Sensitivity pressure RP 50 100 0.0000001 500 50.005 RN 50 100 0.0000001 500 49.995 Problem (6) (b) Design a bridge circuit included 4 strain gages and specify each strain gage in the circuit. S3 S1 S4 S2 Problem (6) (c) Add instrumentation Amplifier to vary from 0V to 1V with dc 1V. Specify its gain. S3 S4 Vo Av(Va VB ) S1 S2 And LPF Va R1 R R R R E E E R1 R3 R RR R 2R Vb R4 R R R R E E E R2 R4 R RR R 2R Problem (6) R Vo AvE R L Av 1 G L max Vomax Av 1100 0.0000001 Av 0.00001 1V 1 Av 100000 0.00001 L 0.00005(@ 500mmHg ) L R 50