Mechanics of Materials - University of Pittsburghqiw4/Academic/MEMS1082/Chapter9-3.pdf · 2011. 4....
24
Department of Mechanical Engineering MEMS1049 Mechatronics Chapter 9 Resistive Sensors 9-3
Transcript of Mechanics of Materials - University of Pittsburghqiw4/Academic/MEMS1082/Chapter9-3.pdf · 2011. 4....
Department of Mechanical Engineering
MEMS1049
MechatronicsChapter 9
Resistive Sensors 9-3
Department of Mechanical Engineering
Background Theory For Metal Strain Gauge Resistance R (Ohm Ω) and
resistivity ρ (Ωm)
For Semiconductors The piezoresistive effect describes the changing resistivity of a semiconductor due to applied mechanical stressstrain
Gauge factor G of a piezoresistive device
Axial strain
Stress
ALR ρ=
axial
RRGε∆
=
LL
axial∆
=ε
AForce
axial =σ
Department of Mechanical Engineering
Metal foil strain gauge
Strain gauge structure
Department of Mechanical Engineering
Strain gauge configurations
Various Strain Gauge Configurations
Department of Mechanical Engineering
Gauge Factor
Gauge factor of metal foil strain gaugeALR ρ=
wdw
hdh
AdA
whA
+=
=
AdA
LdLd
RdR
ALR
minus+=
minus+=
ρρ
ρ lnlnlnln
LdL
wdw
hdh νminus==
LdL
AdA ν2minus=
( ) ρρεν
νεερρ
dRdR
dR
dR
axial
axialaxial
++=
++=
21
2
Department of Mechanical Engineering
Gauge Factor
Gauge factor of metal foil strain gauge
( ) ρρεν dRdR axial ++= 21
( )axialaxial
dRdRε
ρρνε
++= 21
F Gauge factor Piezoresistive effect for semiconductors
axial
RdRFε
=
Department of Mechanical Engineering
Strain Gauge Bridge
Static bridge circuit for strain gauge In the balance state
High impedance VM
The unknown resistor R1
Department of Mechanical Engineering
Strain gauge bridge circuit
Dynamic unbalanced bridge circuit
Department of Mechanical Engineering
Leadwire effect in frac14 bridge circuit
If strain gauge located far from the bridge circuit
Lead wire resistance R΄ can be effect by temperature
Department of Mechanical Engineering
Temperature compensation
Temperature change can cause significant change in resistance Using a dummy gauge
Department of Mechanical Engineering
Stress measurement with strain gauge
Uniaxial stress
xx Eεσ =
AP
x =σ
xAEP ε=
Precision Strain Gages -1-Axis General Purpose
Department of Mechanical Engineering
Review Stress-strain
Hookrsquos Lawhellip
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Background Theory For Metal Strain Gauge Resistance R (Ohm Ω) and
resistivity ρ (Ωm)
For Semiconductors The piezoresistive effect describes the changing resistivity of a semiconductor due to applied mechanical stressstrain
Gauge factor G of a piezoresistive device
Axial strain
Stress
ALR ρ=
axial
RRGε∆
=
LL
axial∆
=ε
AForce
axial =σ
Department of Mechanical Engineering
Metal foil strain gauge
Strain gauge structure
Department of Mechanical Engineering
Strain gauge configurations
Various Strain Gauge Configurations
Department of Mechanical Engineering
Gauge Factor
Gauge factor of metal foil strain gaugeALR ρ=
wdw
hdh
AdA
whA
+=
=
AdA
LdLd
RdR
ALR
minus+=
minus+=
ρρ
ρ lnlnlnln
LdL
wdw
hdh νminus==
LdL
AdA ν2minus=
( ) ρρεν
νεερρ
dRdR
dR
dR
axial
axialaxial
++=
++=
21
2
Department of Mechanical Engineering
Gauge Factor
Gauge factor of metal foil strain gauge
( ) ρρεν dRdR axial ++= 21
( )axialaxial
dRdRε
ρρνε
++= 21
F Gauge factor Piezoresistive effect for semiconductors
axial
RdRFε
=
Department of Mechanical Engineering
Strain Gauge Bridge
Static bridge circuit for strain gauge In the balance state
High impedance VM
The unknown resistor R1
Department of Mechanical Engineering
Strain gauge bridge circuit
Dynamic unbalanced bridge circuit
Department of Mechanical Engineering
Leadwire effect in frac14 bridge circuit
If strain gauge located far from the bridge circuit
Lead wire resistance R΄ can be effect by temperature
Department of Mechanical Engineering
Temperature compensation
Temperature change can cause significant change in resistance Using a dummy gauge
Department of Mechanical Engineering
Stress measurement with strain gauge
Uniaxial stress
xx Eεσ =
AP
x =σ
xAEP ε=
Precision Strain Gages -1-Axis General Purpose
Department of Mechanical Engineering
Review Stress-strain
Hookrsquos Lawhellip
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Metal foil strain gauge
Strain gauge structure
Department of Mechanical Engineering
Strain gauge configurations
Various Strain Gauge Configurations
Department of Mechanical Engineering
Gauge Factor
Gauge factor of metal foil strain gaugeALR ρ=
wdw
hdh
AdA
whA
+=
=
AdA
LdLd
RdR
ALR
minus+=
minus+=
ρρ
ρ lnlnlnln
LdL
wdw
hdh νminus==
LdL
AdA ν2minus=
( ) ρρεν
νεερρ
dRdR
dR
dR
axial
axialaxial
++=
++=
21
2
Department of Mechanical Engineering
Gauge Factor
Gauge factor of metal foil strain gauge
( ) ρρεν dRdR axial ++= 21
( )axialaxial
dRdRε
ρρνε
++= 21
F Gauge factor Piezoresistive effect for semiconductors
axial
RdRFε
=
Department of Mechanical Engineering
Strain Gauge Bridge
Static bridge circuit for strain gauge In the balance state
High impedance VM
The unknown resistor R1
Department of Mechanical Engineering
Strain gauge bridge circuit
Dynamic unbalanced bridge circuit
Department of Mechanical Engineering
Leadwire effect in frac14 bridge circuit
If strain gauge located far from the bridge circuit
Lead wire resistance R΄ can be effect by temperature
Department of Mechanical Engineering
Temperature compensation
Temperature change can cause significant change in resistance Using a dummy gauge
Department of Mechanical Engineering
Stress measurement with strain gauge
Uniaxial stress
xx Eεσ =
AP
x =σ
xAEP ε=
Precision Strain Gages -1-Axis General Purpose
Department of Mechanical Engineering
Review Stress-strain
Hookrsquos Lawhellip
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Strain gauge configurations
Various Strain Gauge Configurations
Department of Mechanical Engineering
Gauge Factor
Gauge factor of metal foil strain gaugeALR ρ=
wdw
hdh
AdA
whA
+=
=
AdA
LdLd
RdR
ALR
minus+=
minus+=
ρρ
ρ lnlnlnln
LdL
wdw
hdh νminus==
LdL
AdA ν2minus=
( ) ρρεν
νεερρ
dRdR
dR
dR
axial
axialaxial
++=
++=
21
2
Department of Mechanical Engineering
Gauge Factor
Gauge factor of metal foil strain gauge
( ) ρρεν dRdR axial ++= 21
( )axialaxial
dRdRε
ρρνε
++= 21
F Gauge factor Piezoresistive effect for semiconductors
axial
RdRFε
=
Department of Mechanical Engineering
Strain Gauge Bridge
Static bridge circuit for strain gauge In the balance state
High impedance VM
The unknown resistor R1
Department of Mechanical Engineering
Strain gauge bridge circuit
Dynamic unbalanced bridge circuit
Department of Mechanical Engineering
Leadwire effect in frac14 bridge circuit
If strain gauge located far from the bridge circuit
Lead wire resistance R΄ can be effect by temperature
Department of Mechanical Engineering
Temperature compensation
Temperature change can cause significant change in resistance Using a dummy gauge
Department of Mechanical Engineering
Stress measurement with strain gauge
Uniaxial stress
xx Eεσ =
AP
x =σ
xAEP ε=
Precision Strain Gages -1-Axis General Purpose
Department of Mechanical Engineering
Review Stress-strain
Hookrsquos Lawhellip
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Gauge Factor
Gauge factor of metal foil strain gaugeALR ρ=
wdw
hdh
AdA
whA
+=
=
AdA
LdLd
RdR
ALR
minus+=
minus+=
ρρ
ρ lnlnlnln
LdL
wdw
hdh νminus==
LdL
AdA ν2minus=
( ) ρρεν
νεερρ
dRdR
dR
dR
axial
axialaxial
++=
++=
21
2
Department of Mechanical Engineering
Gauge Factor
Gauge factor of metal foil strain gauge
( ) ρρεν dRdR axial ++= 21
( )axialaxial
dRdRε
ρρνε
++= 21
F Gauge factor Piezoresistive effect for semiconductors
axial
RdRFε
=
Department of Mechanical Engineering
Strain Gauge Bridge
Static bridge circuit for strain gauge In the balance state
High impedance VM
The unknown resistor R1
Department of Mechanical Engineering
Strain gauge bridge circuit
Dynamic unbalanced bridge circuit
Department of Mechanical Engineering
Leadwire effect in frac14 bridge circuit
If strain gauge located far from the bridge circuit
Lead wire resistance R΄ can be effect by temperature
Department of Mechanical Engineering
Temperature compensation
Temperature change can cause significant change in resistance Using a dummy gauge
Department of Mechanical Engineering
Stress measurement with strain gauge
Uniaxial stress
xx Eεσ =
AP
x =σ
xAEP ε=
Precision Strain Gages -1-Axis General Purpose
Department of Mechanical Engineering
Review Stress-strain
Hookrsquos Lawhellip
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Gauge Factor
Gauge factor of metal foil strain gauge
( ) ρρεν dRdR axial ++= 21
( )axialaxial
dRdRε
ρρνε
++= 21
F Gauge factor Piezoresistive effect for semiconductors
axial
RdRFε
=
Department of Mechanical Engineering
Strain Gauge Bridge
Static bridge circuit for strain gauge In the balance state
High impedance VM
The unknown resistor R1
Department of Mechanical Engineering
Strain gauge bridge circuit
Dynamic unbalanced bridge circuit
Department of Mechanical Engineering
Leadwire effect in frac14 bridge circuit
If strain gauge located far from the bridge circuit
Lead wire resistance R΄ can be effect by temperature
Department of Mechanical Engineering
Temperature compensation
Temperature change can cause significant change in resistance Using a dummy gauge
Department of Mechanical Engineering
Stress measurement with strain gauge
Uniaxial stress
xx Eεσ =
AP
x =σ
xAEP ε=
Precision Strain Gages -1-Axis General Purpose
Department of Mechanical Engineering
Review Stress-strain
Hookrsquos Lawhellip
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Strain Gauge Bridge
Static bridge circuit for strain gauge In the balance state
High impedance VM
The unknown resistor R1
Department of Mechanical Engineering
Strain gauge bridge circuit
Dynamic unbalanced bridge circuit
Department of Mechanical Engineering
Leadwire effect in frac14 bridge circuit
If strain gauge located far from the bridge circuit
Lead wire resistance R΄ can be effect by temperature
Department of Mechanical Engineering
Temperature compensation
Temperature change can cause significant change in resistance Using a dummy gauge
Department of Mechanical Engineering
Stress measurement with strain gauge
Uniaxial stress
xx Eεσ =
AP
x =σ
xAEP ε=
Precision Strain Gages -1-Axis General Purpose
Department of Mechanical Engineering
Review Stress-strain
Hookrsquos Lawhellip
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Strain gauge bridge circuit
Dynamic unbalanced bridge circuit
Department of Mechanical Engineering
Leadwire effect in frac14 bridge circuit
If strain gauge located far from the bridge circuit
Lead wire resistance R΄ can be effect by temperature
Department of Mechanical Engineering
Temperature compensation
Temperature change can cause significant change in resistance Using a dummy gauge
Department of Mechanical Engineering
Stress measurement with strain gauge
Uniaxial stress
xx Eεσ =
AP
x =σ
xAEP ε=
Precision Strain Gages -1-Axis General Purpose
Department of Mechanical Engineering
Review Stress-strain
Hookrsquos Lawhellip
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Leadwire effect in frac14 bridge circuit
If strain gauge located far from the bridge circuit
Lead wire resistance R΄ can be effect by temperature
Department of Mechanical Engineering
Temperature compensation
Temperature change can cause significant change in resistance Using a dummy gauge
Department of Mechanical Engineering
Stress measurement with strain gauge
Uniaxial stress
xx Eεσ =
AP
x =σ
xAEP ε=
Precision Strain Gages -1-Axis General Purpose
Department of Mechanical Engineering
Review Stress-strain
Hookrsquos Lawhellip
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Temperature compensation
Temperature change can cause significant change in resistance Using a dummy gauge
Department of Mechanical Engineering
Stress measurement with strain gauge
Uniaxial stress
xx Eεσ =
AP
x =σ
xAEP ε=
Precision Strain Gages -1-Axis General Purpose
Department of Mechanical Engineering
Review Stress-strain
Hookrsquos Lawhellip
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Stress measurement with strain gauge
Uniaxial stress
xx Eεσ =
AP
x =σ
xAEP ε=
Precision Strain Gages -1-Axis General Purpose
Department of Mechanical Engineering
Review Stress-strain
Hookrsquos Lawhellip
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Review Stress-strain
Hookrsquos Lawhellip
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Review Planar stress
Principal stresses
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial stress
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Stress measurement with strain gauge
Biaxial strain gauges for measuring axial strain 090deg gauge pattern
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Stress measurement with strain gauge
General state of planar stress on the surface of a component
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Stress measurement with strain gauge
Common rosette configurations
For rectangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Stress measurement with strain gauge
Three -Element Strain Gage Rosettes Pre-Wired
Rectangular strain gage rosette
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Stress measurement with strain gauge
For equiangular rosette configuration
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Stress measurement with strain gauge
For T rosette configuration
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
Department of Mechanical Engineering
Piezoresistive strain sensors
( )axialaxial
dRdRε
ρρνε
++= 21
The change in resistivity may be related as follows
bull where i and j take values from 1 to 6 denoting the parameters in the corresponding strain direction and γ is the piezo-resistive coefficient Material such as single crystal silicon has a cubic crystal structure of which γ can be described using three constants γ11 γ12 and γ44
- MEMS1049
- Slide Number 2
- Metal foil strain gauge
- Strain gauge configurations
- Gauge Factor
- Gauge Factor
- Strain Gauge Bridge
- Strain gauge bridge circuit
- Leadwire effect in frac14 bridge circuit
- Temperature compensation
- Stress measurement with strain gauge
- Review Stress-strain
- Review Planar stress
- Review Planar stress
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Stress measurement with strain gauge
- Piezoresistive strain sensors
- Piezoresistive strain sensors
-
![The z Transform - UTKweb.eecs.utk.edu/~hli31/ECE316_2015_files/Chapter9.pdf · Existence of the z Transform! The z transform of x[n]=αnun−n [0], α∈ is X(z)=αnun−n [0]z−n](https://static.fdocument.org/doc/165x107/5e6f952567c1d8438c5967ae/the-z-transform-hli31ece3162015fileschapter9pdf-existence-of-the-z-transform.jpg)
