1. Homework # 1 2004200456 Lim Myeong-Jun

2. Index (Axid) Stress δ & ε Curve Cantilever Strain gage Gage factor Problem solution

3. (Axid) Stress M x y A F = M * g A = x * y On the surface, the average force per unit area is denoted as δ. “ stress ” cf) Pressure F is sometimes called “ Load ” ε : Strain(unitless) L δ F F

4. δ & ε Curve Brittle material ( ex. Glass) Linear : elastic region => Not linear over a range δn : Ultimate stress

5. δ & ε Curve Ductile material ( ex. Al, Steel) δn : Ultimate Stress δy : yield Stress δ pl : Proportional Limit

6. δ & ε Curve For elastic region (linear region) (δ ≤ δpl) δ = E * ε ∵ E : Young’s modulus ( Modulus of elastivity)

7. Cantilever L δ F F E : constant, A & L : almost constant ∴ If we know ε, then we can find F (force).

8. Strain gage A strain gauge (alternatively: strain gage) is a device used to measure the strain of an object. Invented by Edward E. Simmons and Arthur C. Ruge in 1938, the most common type of strain gauge consists of an insulating flexible backing which supports a metallic foil pattern. The gauge is attached to the object by a suitable adhesive, such as cyanoacrylate. As the object is deformed, the foil is deformed, causing its electrical resistance to change. This resistance change, usually measured using a Wheatstone bridge, is related to the strain by the quantity known as the gauge factor.

9. Strain gage The black line is electrical wire. ρ A L +V-+V- The equation shows relation between strain and resistance. If we push the strain, ρ, A and L was changed.

10. Strain gage when you differentiate each variable, The third equation’s ‘-’ sign means that opposite change as compared with change of resistance. -> R ∝ L, R ∝ 1/A Total change of resistance

11. Strain gage Where μ : Poisson’s ratio εD : △ D/D = strain along the diametrical(horizontal) axis. εL : △ L/L = strain along the longitudinal(vertical) axis.

12. Strain gage & Gage factor Piezoresistive effect Dimensional effect Gage factor For mental strain gage : G = ~1.6 For semi conductor strain gage : G = 100 ~ 170 high temperature coefficient

13. Gage factor The gauge factor GF is defined as: where R G is the resistance of the undeformed gauge, ΔR is the change in resistance caused by strain, and ε is strain. For metallic foil gauges, the gauge factor is usually a little over 2. For a single active gauge and three dummy resistors, the output v from the bridge is: where BV is the bridge excitation voltage. Foil gauges typically have active areas of about 2-10 mm 2 in size. With careful installation, the correct gauge, and the correct adhesive, strains up to at least 10% can be measured.

14. Problem # 3 Gage factor : 10 Gage 1 & 2 : L -> L + △ L Gage 3 & 4 : L -> L - △ L F Side view Top view 1 2 3 4 1 2 L F

15. Problem # 3 V0 = Av(Va – Vb) A : Differential-mode voltage gain Cf) : Resistor : variable Resistor : Resistive Sensor IA -+-+ Vb Va

16. Problem # 3 VaVb

17. Problem # 3 - The constant 50 defined by gage factor(10) and voltage source(5v). - Av is changeable factor by resistor connected IA(Instrument Amplifier) - k is given by structure and material. - There are linearity between Vo and F.

18. Problem # 4 Gage factor : p-type Si strain gage S1 & S2 : G = 100 n-type Si strain gage S3 & S4 : G = -100 1 3 F Side view Top view 1 3 2 4 1 3

19. Problem # 4 E

21. F Side view 1 3 2 4 Use least squares method to find the calibration equation. Force range : 0~100N

22. Problem # 6 In the below pressure sensor, diaphragm is equipped with two p- type Si strain gage of gage factor of +100 and two n-type Si strain gage of gage factor of -100. As pressure is placed in the diaphragm, the same strain occurs in the each strain gage and the responsiveness is 10 -5 %/mmHg. As not, the strain gage is 50. suppose the relationship between pressure and strain is linear. (a) When pressure is changed from 0 to 50mmHg, What is the resistance of the p-type and Si strain gage changed? (b) Sketch the bridge circuit consisting of four strain gage and mark where each strain gage is placed. (c) Let the driving power source have voltage of 1 and add instrumentation amplifier for the final output to be converted from 0 to 1V. What is the gain?

23. Problem # 6 Gage factor : p-type Si strain gage S1 & S2 : G = 100 n-type Si strain gage S3 & S4 : G = -100 2424 1313

24. Problem # 6 압력 (mmHg) 저항 (Ω) p-type n-type 50 0 500 50.25 49.75

25. Problem # 6 1

27. Thanks for your attention!!