App-18
IM 701240-01E
Appendix 9
Basic Defining Equation of Strain
Definition of Strain
∆
L/L =
ε
(1)
ε
:
Strain
L:
Initial length of the material
∆
L:
Amount of change due to external strain
Definition of the Gauge Factor
Gauge factor (K) refers to the ratio between the mechanical strain and the change in the
resistance of the strain gauge resistor.
(
∆
R/R)=K
×ε
(3)
ε
= =
(2)
∆
R/R
K
∆
L
L
R: Gauge resistance
∆
R: Amount of change in resistance when a strain is received
Normally, K=2.0. However, the value varies depending on the strain gauge material.
General Equation of the Measured Voltage (V) and Strain (
ε
) of the Wheatstone
Bridge (1 Gauge Method)
If we assume V to be the voltage measured on the bridge and E to be the voltage
applied to the bridge,
V = (1/4)
×
E
×
(
∆
R/R)
(4)
From equation (3),
(
∆
R/R) = K
×
ε
Thus, V = (1/4)
×
E
×
K
×
ε
(5)
• When Determining the Strain (
ε
) from the Measured Voltage (V) (Strain Gauge (1
Gauge Method))
If we derive
ε
from equation (5)
ε
= (4/K)
×
(V/E)
(6)
• When Determining the Measured Value of the Strain Gauge Sensor (e) from the
Voltage Measured on the Bridge (V) (Strain Gauge Sensor)
Assuming e to be the measured value (measured value of the strain gauge sensor:
mV/V unit) and substituting
ε
= e in equation (6),
ε
= (4/K)
×
(V/E)
(7)
In the case of a strain gauge sensor, set the Gauge Factor (K) to 2 on the SL1400. If
you change the value of K, conversion is made using the above equation.