A straingauge measurement system is mounted on an airplane w

A strain-gauge measurement system is mounted on an airplane wing to measure wing oscillation and strain during wind gusts. The strain measurement system has a settling time of 2.5 second, and a ringing frequency of 80 Hz. Estimate the dynamic error in measuring a 35 Hz oscillation. Also, estimate the time lag in the response. Explain in words the meaning of this information. The output stage of a first-order transducer is to be connected to a second-order display stage device. The transducer has known time constant of 5 ms and static sensitivity of 0.05 V/degree C while the display device has values of sensitivity, damping ratio, and natural frequency of 1 V/V, 0.8, and 100 Hz, respectively. Determine the steady state response of this measurement system to an input signal of the form, T(t) = (30 + 2.5 sin 600t) degree C.

Solution

This document provides information to help you understand basic strain concepts, how strain gages work, and how to select the right configuration type.

In addition to the characteristics of the different strain gage configurations, you must consider the required hardware to properly condition and acquire strain measurements. For example, strain gages require voltage excitation, which is only available in certain conditioned measurement hardware.

1. What is strain?

In mechanical testing and measurement, you need to understand how an object reacts to various forces. The amount of deformation a material experiences due to an applied force is called strain. Strain is defined as the ratio of the change in length of a material to the original, unaffected length, as shown in Figure 1. Strain can be positive (tensile), due to elongation, or negative (compressive), due to contraction. When a material is compressed in one direction, the tendency to expand in the other two directions perpendicular to this force is known as the Poisson effect. Poisson’s ratio (v), is the measure of this effect and is defined as the negative ratio of strain in the transverse direction to the strain in the axial direction. Although dimensionless, strain is sometimes expressed in units such as in./in. or mm/mm. In practice, the magnitude of measured strain is very small, so it is often expressed as microstrain (µ), which is x 10-6.

The four different types of strain are axial, bending, shear, and torsional. Axial and bending strain are the most common (see Figure 2). Axial strain measures how a material stretches or compresses as a result of a linear force in the horizontal direction. Bending strain measures a stretch on one side of a material and the contraction on the opposite side due to the linear force applied in the vertical direction. Shear strain measures the amount of deformation that occurs from a linear force with components in both the horizontal and vertical directions. Torsional strain measures a circular force with components in both the vertical and horizontal directions.