Hioki MR8827, Instruction Manual

Page: 413 / 436

A
8
For Reference
Appendix 2.5 Scaling Method for Strain Gauges
This section describes how to determine the scaling conversion ratio when performing measurement with
strain gauges and the 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 temperature compensation.
E: Young's modulus, ν : Poisson's ratio, ε : Distortion measurement value
Tensile and Compressive Stress Measurement: Stress ( σ ) = E × ε
For temperature compensation with two or four gauges, position the gauges perpendicularly.
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 (with two gauges)
When using four gauges, that the values are halved.
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 with a Young's modulus of 73 (GPa)
according to the following calculation:
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
=1N/m
2
Unit: gf/mm
2
, Conversion Ratio = 7.44 gf/mm
2
Enter this value as the scaling conversion ratio
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
Refer to “8.5 Convert Input Values (Scaling Function)” (p. 151).