Homework # 12004200456

Lim Myeong-Jun

Index(Axid) Stressδ & ε CurveCantileverStrain gageGage factorProblem solution

(Axid) Stress

M

xy

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

δ & ε CurveBrittle material ( ex. Glass)

Linear : elastic region => Not linear over a range

δn : Ultimate stress

δ & ε CurveDuctile material ( ex. Al, Steel)

δn : Ultimate Stressδy : yield Stressδ pl : Proportional Limit

δ & ε Curve

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

CantileverL

δ

F

F

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

Strain gageA 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.

Strain gageThe black line is electrical wire.

ρ A

L

+ V -

The equation shows relation between strain and resistance. If we push the strain, ρ, A and L was changed.

Strain gagewhen 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

Strain gage

Where μ : Poisson’s ratioεD : D/D = strain along the diametrical(horizontal) axis.εL : L/L = strain along the longitudinal(vertical) axis.

Strain gage & Gage factor

Piezoresistive effect

Dimensional effect

Gage factor

For mental strain gage : G = ~1.6For semi conductor strain gage : G = 100 ~ 170

high temperature coefficient

Gage factor The gauge factor GF is defined as:

where RG 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 mm2 in size.

With careful installation, the correct gauge, and the correct adhesive, strains up to at least 10% can be measured.

Problem # 3Gage factor : 10

Gage 1 & 2 : L -> L + LGage 3 & 4 : L -> L - L

F

Side view

Top view

1 2

3 4

1 2

L

F

Problem # 3

V0 = Av(Va – Vb)A : Differential-mode voltage gain

Cf) : Resistor

: variable Resistor

: Resistive Sensor

V 1

5V R4R1

R3 R2

IA-+

VbVa

Problem # 3

5V

R4R1

R3 R2

Va Vb

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.

Problem # 4Gage factor :

p-type Si strain gage S1 & S2 : G = 100n-type Si strain gage S3 & S4 : G = -100

1 3

F

Side view

Top view

1 3

2 4

1 3

Problem # 4

E

Problem # 4

Problem # 4

F

Side view

1 3

2 4

Use least squares method to find the calibration equation.

Force range : 0~100N

Problem # 6In 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?

Problem # 6

Gage factor : p-type Si strain gage S1 & S2 : G = 100n-type Si strain gage S3 & S4 : G = -100

24

13

Problem # 6

압력(mmHg)

저항 (Ω)

p-type

n-type

50

0 500

50.25

49.75

Problem # 6

1

Problem # 6

Thanks for your attention!!