Hioki MR8740, Instruction Manual

Page: 399 / 424

Appendix 2 Reference
A
9
Appe
ndix
This section describes how to determine the scaling conversion ratio when measuring with strain
gauges and the Model 8969 and U8969 Strain Unit.
The appropriate conversion formula for stress depends on how the strain gauges
are used.
Three methods are available depending on whether one, two or four strain
gauges are used for measurement. The two-gauge method is used for tempera-
ture compensation.
E: Young modulus, ν : Poisson ratio, ε : Distortion measurement value
T ensile and Compressive Stress Measurement: Stress ( σ ) = E × ε
For temperature compensation with two or four gauges, position the gauges per-
pendicularly.
Stress (
σ
) is obtained by 1 / (1 +
ν
) for two gauges, and by 1 / {2 (1 +
ν
)} for four
gauges.
Bending Stress Measurement: Stress (
σ
) = E
× ε
For temperature compensation with two or four gauges, stress (
σ
) is obtained as
a multiple of ½ or ¼, respectively.
Torsional Stress Measurement: Stress ( σ ) = E / {2 (1 + ν )} × ε (two-gauge case)
For the four-gauge case, it is half of that.
Refer to the strain gauge instruction manual for combinations of strain gauges
for each measurement.
Example. Measuring Compressive Stress
Using the one-gauge method for an aluminum measurement object having a
Young's modulus of 73 (GPa) according to the following Table,
σ = 73 × 10
9
× Measurement Value (in με units) × 10
-6
(in με units)
) = 73 × Measurement Value (in kPa units)
= 7.44
*
× Measurement Value (in gf/mm
2
units)
*: 1 Pa = 1.01971621× 10
-7
kgf/mm
2
Unit: gf/mm
2
, Conversion Ratio = 7.44 gf/mm
2
Enter this value as the scaling conversion ratio
See: "7.4 Converting Input Values (Scaling Function)" (p.146)
Appendix 2.6 Scaling Method When Using Strain
Gauges
Mechanical properties of industrial materials
Material
Modulus of Elasticity
(Young's Modulus)
Poisson's Ratio
E (GPa) ν
Carbon Steel (0.1 to 0.25% C)
205 0.28 to 0.3
Carbon Steel (> 0.25% C) 206 0.28 to 0.3
Spring Steel (Quenched) 206 to 211 0.28 to 0.3
Nickel Steel 205 0.28 to 0.3
Cast Iron 98 0.2 to 0.29
Brass (Cast) 78 0.34
Phosphor Bronze 118 0.38
Aluminum 73 0.34
Concrete 20 to 29 0.1