Strain Gauge Force Sensors

Introduction

A strain gauge works because a mechanical deformation changes its resistance. Strain gauges are the basic part of most force sensors.

flowchart LR
    F["Force"] --> D["Deformation"]
    D --> R["Change in<br/>resistance"]
    R --> V["Output voltage"]

How it works

The resistance of a conductor is:

$$R=\rho \frac{L}{A}$$

where $\rho$ is the resistivity, $L$ is the length and $A$ is the area. When a force stretches the gauge, $L$ increases and $A$ decreases, so $R$ changes.

Wheatstone bridge

A Wheatstone bridge changes the small change in resistance into a voltage that is proportional to the strain.

$$V_{out}=\frac{R_2}{R_1+R_2}{V}_{in}-\frac{R_4}{R_3+R_4}{V}_{in}=\frac{R_2{R}_3-R_1{R}_4}{(R_1+R_2)(R_3+R_4)}{V}_{in}$$

If the bridge is balanced at the start, so that $R_2{R}_3=R_1{R}_4$, then $V_{out}=0$. Any change in the gauge resistance $R_2$ from a deformation unbalances the bridge and gives a non zero output.

Problem and solution

Changes in the ambient temperature change the gauge resistance, even when no force is applied. You can fix this by:

• balancing the bridge from time to time
• using two gauges and taking the difference of their outputs