App-13
IM DL850E-01EN
Appendix
Appendix 3 Fundamental Equations for Defining Strain
Definition of Strain
ΔL/L = ε ...............................................(1)
ε: Strain
L: Initial length of the material
ΔL: 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.
(ΔR/R) = K × ε ............................(3)
ε =
ΔL ΔR/R
L K
=
........................
(2)
R: Gauge resistance
ΔR: Amount of change in resistance when strain is applied
Normally, K = 2.0. However, the value varies depending on the strain gauge material.
General Equation for the Measured Voltage (V) and Strain (ε) of a 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 × (ΔR/R) ........................(4)
From equation (3),
(ΔR/R) = K × ε
Thus, V = (1/4) × E × K × ε .................(5)
When Determining the Strain (e) from the Measured Voltage (V) (Using a Strain Gauge and the 1 Gauge
Method)
If we derive e 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 th
e strain gauge sensor: mV/V unit) and
substituting ε = e in equation (6),
e = (4/K) × (V/E) ...........................(7)
In the case of a strain gauge sensor, set the gauge factor (K) to 2 on the DL850E/DL850EV. If you change the
value of K, the values are converted through the use of the above equation.
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