Mechanical Measurements Applications

ME 302

Chapters # 11,12,14,15 and 16

Chapter 11-Displacement and Dimensional Measurement

• Gauge Blocks • wringling blocks

together to make larger dimensions.

• αp = temperature coefficient of expansion of gaged part in ppm/º

• αb = temperature coefficient of expansion of gage block in ppm/º

L Lb 1 T 10 6 p b

Linear Variable Differential Transformers

LVDT For Linear

Displacement Measurements

Measuring Tools

Vernier Calipers; Resoln

0.001” & acc. ±0.001”

micrometer, Resolution

of 0.0001”

Dial Indicators

• Dials for Displacement Measurements

Chapter 12; Strain Measurements

a dL

LL2 L1

L1

LL1

Metallic Gauges

R LA

LCD2

If you have a conductor of resistivity , the resistance across that conductor is

If you strain this conductor axially, its length will increase while its cross sectional area will decrease. Taking the total differential of R,

dR R

d RL

dL R CD2

d CD2

1

CD2 Ld dL 2L dD

D

dR

RdL

L 2

dD

Dd

Metallic Gauges

dR /R

dL /L1 2

dD /D

dL /L d /dL /L

dR

RdL

L 2

dD

Dd

a dL

L

L dD

D

L

a

F dR /R

dL /LdR /R

a

1 2v d /dL /L

For most strain gauges, = 0.3. If the resistivity is not a function of strain, then F only depends on poisson’s ratio, and F ~ 1.6.

Gage factor

Strain Gauge

lateral strain

axial strain

L

a

F dR /R

dL /LdR /R

a

1 2v d /dL /L

1

F

RR

F and R are supplied by the manufacturer, and we measure ∆R.

Strain Gage Bridge Circuit

eo

ei

R1 /R

4 2 R1 /R

1

F

RR

eo eiF

4 2F

Bridge with 2 strain gages

The bending strain on the top gage is equal and opposite of the one on the bottom.

Wheatstone Bridge

eo ei

R2

R1 R2

R4

R3 R4

make R2 = R4 = R

eo ei

R

R1 R

R

R3 R

eo ei

R

R1

1R

R3

1

eo

ei

R1

R1

1

R3

Multiple Gauge BridgeMost strain gauge measurement systems allow us to make 1, 2, 3 or all 4 legs of the bridge strain gauges. There are many reasons to do this that we will talk about now.

Going back to our fundamental bridge equations from chapter 6,

Eo E i

R1

R1 R2

R3

R3 R4

Say that unstrained, all of these have the same value. If they are then strained, the resultant change is Eo is

dEo Eo

Rii1

4

dRi

Eo

Multiple Gauges

Make the following assumptions:

•All gauges have the same nominal resistance (generally true)

•All gauges have matched gauge factors (must be purchased as set)

Then:

Eo

E i

F

41 2 4 3 Eo

Chapter 13; Force Measurements

Torque & Power Measurements

Torque T = FRPower P = T

Chapter 14 Pressure

Measuring pressure is also very common and can be accomplished very cheaply or very accurately (not usually both). We are going to discuss several sensor types that are available.

Cheap Rugged, fast

Accurate

Static and Dynamic PressureDynamic Pressure = Total Pressure - Static Pressure

Use of Manometers

Deadweight Testers

Elastic Pressure Transducers

Bourdon Tube Gauge

Pressure Measurements in a Moving Fluid

Chapter 15 Flow Measurements

Obstruction Meters

P1 P2

V2

2 V12

2gc

Qideal V2A2 A2

1 A2 /A1 2 1/ 2

2gc P1 P2

Rotameter or Area meter

Q AwC2g f f w

A f w

1/ 2

Aw 4

D by 2 d2

2% full scale

Vortex Shedding Meters

Q K1

K1 d3

4St

Pitot probe errors

Thermal Anemometry

Particle Image Velocimetry

PIV

Chapter 16 Temperature Measurements

The manner in which a thermometer is calibrated needs to correspond to how it used. Under normal circumstances, you can get accuracy from ±0.2 to ±2°C.

Thermometry based on thermal expansion

Liquid-in-glass thermometers

Bimetalic ThermometersIf you take two metals with different thermal expansion coefficients and bond them together, they will bend in one direction if the temperature rises above the temperature at which the boding was done and in the other if it gets less.

Resistance Temperature Detectors RTD

R1

R2

R3 r1

RRTD r3

RRTD R3 r1 r3

R R0 1 A T T0

Thermistors

R R0e 1/T 1/T0

Usually made of a semiconductor and have the following properties:Much larger dR/dT than RTD’s, so more sensitiveRuggedFast Response

16.5 Thermoelectric Temperature Measurement

In this section, we will learn about perhaps the most important temperature measuring technique--Thermocouples.

“Electromotive Force”

Thermoelectric EffectsSeebeck Generates voltages across two dissimilar materials when a temperature difference is present.

Peltier Moves heat through dissimilar materials when current is applied.

ThermocouplesThermocouples measure the difference in temperature between two points. One of those points at a known temperature.

Error Sources in Temperature Measurements

Conduction: Your probe can conduct heat to/from the environment to/from your desired measurement location

Analysis of Conduction Error

qxdx qx hPdx T(x) T

T T

q kAdT

dx

m hP

kA

d2dx 2 m2 0

x w

coshmx

coshmL

0 w

T 0 T

Tw T

1

coshmL

T 0 T Tw T

coshmL

L

P/A = 4/D for round

16.8 Radiative Temperature Measurements (Pyrometry)

Eb T 4

Temperatures greater than 500ºC = 5.67•10-8 W/m2K4

Total Radiation Pyrometry

q TA4 TB

4

The radiative heat transfer between two ideal bodies A and B