The maximum permissible effective bridge excitation voltage of a strain gauge (SG) is an important parameter given in the specifications. What is the significance of this value, how is it calculated, and what has to be taken into account in actual applications?

## Strain Gauges as Heating Elements

When strain is measured using strain gauges in a Wheatstone bridge, the strain gauges are electrical resistors. The applied voltage results in a loss of power in the form of heat in the strain gauge's measuring grid.

Heat needs to be dissipated, since excessive heat in the strain gauge results in incorrect measured values. These measurement errors result from:

• Apparent strain through thermal expansion of the strain gauge, which manifests itself as a zero drift.
• Deterioration of the strain gauge's self-temperature-compensation characteristics as a result of excessive differences in thermal expansion between the measuring body and the strain gauge.
• Exceeding temperature limits (e.g. of the adhesive) through additional heating such as when measurements are taken in a high temperature range.

It is essential to define reasonable limits, i.e. maximum permissible effective bridge excitation voltages, since heating of the strain gauge cannot be entirely avoided. Complying with these values guarantees a minimum measurement error.

In the following example, an increase in temperature compared to the measuring body of up to 5 °C is tolerated. Assuming measurements were taken at room temperature, the resulting measurement error is less than 1 µm/m. Even in the most unfavorable case,. in the range of the strain gauge's highest temperature dependence, the error normally is less than 10 µm/m.

### Factors That Influence Heating

The following factors have a significant impact on heating and thus on the maximum permissible bridge excitation voltage Umax:

1. Strain gauge resistance R - a higher resistance produces lower heating
2. Strain gauge grid area A - a larger area allows better heat dissipation
3. Thermal conductivity λ of the measuring body – impacts the 'efficiency' of heat dissipation
4. Special features - for example the strain gauge design (stacked measuring grids)

### Heat Flow Model

From the electrical point of view, the maximum permissible bridge excitation voltage at a defined maximum electric power P and a given resistance R is calculated as follows:

Thermal considerations involve establishing a heat flow model with a strain gauge bonded to a measuring body of infinite thermal capacity C.

A temperature gradient ΔT/d develops close to the strain gauge resulting from the temperature difference between the strain gauge and the measuring body. It is independent of the grid area and strain gauge resistance and can be regarded as a measure in fault analysis.

Empirical studies have shown that the measurement error limit is generally complied with at a temperature gradient of ΔT/d = 0.75² °C/mm in the area close to the strain gauge.

Fig. 1: Heat flow model for heat dissipation from the strain gauge to the measuring body.

The dissipated heat energy Q' in the heat flow model results from the strain gauge grid area A, the measuring body's specific thermal conductivity λ, and the temperature gradient ΔT/d:

In stationary mode, a balance is created between the electric power P and the heat energy Q' dissipated through the carrier to the measuring body.

## Calculating Maximum Permissible Bridge Excitation Voltage

Assuming that the electric heat generated in the model is dissipated completely via the measuring body, the following equation is obtained for the strain gauge's maximum permissible effective bridge excitation voltage  :

This equation determines the maximum effective bridge excitation voltage for different strain gauges based on the known parameters and the quantity empirically determined for the temperature gradient:

• Resistance R: Strain gauge property
• Measuring grid area A: The measuring grid area is the product of its length and width. It is evident that smaller strain gauges heat up faster than larger ones, and thus tolerate only a lower excitation voltage.
• Thermal conductivity λ: This property of the measuring body material has a significant influence on the maximum excitation voltage, since the variance between an excellent heat conductor such as aluminum and typical plastics is very high. The following table shows typical measuring body materials.
Measuring body material Thermal conductivity λ [W/m*K] HBM part number Correction factor for steel
Ferritic steel 50 1 1.00
Aluminum 236 3 2.17
Austenitic steel 15 5 0.55
Quarz glass/composite 0.76 6 0.12
Titanium/gray cast iron 22 7 0.03
Plastic < 0.05 8 0.03
Molybdenum 136 9 1.65

The right column in the table shows the correction factor to be used when only the maximum excitation voltage for strain gauges matched to steel is known, however, the strain gauge is installed on another material. It results from the following formula:

## Specifics of the Maximum Bridge Excitation Voltage

### Carrier Frequency

The effective value of the maximum bridge excitation voltage is reduced by 0.7 (1/√2 ) when sinusoidal carrier frequency is employed for bridge excitation. This means carrier frequency excitation is a better choice, since it heats up the strain gauge to a lesser degree than a DC voltage with the same value.

### Stacked Rosettes

With stacked rosettes, when the individual measuring grids are stacked one on top of the other, the upper measuring grids can dissipate heat to the measuring body to a lesser degree than the lower ones. The maximum permissible bridge excitation voltage therefore needs to be reduced by a factor of 0.7 (1/√2 ) with a T rosette with two stacked measuring grids and by a factor of 0.6 (1/√3 ) with a rosette with three measuring grids.

### Weldable Strain Gauges

With weldable strain gauges, the heat flow through the spot welds is reduced, which results in a lower maximum permissible effective bridge excitation voltage.

### Encapsulated Strain Gauges

The formula given above applies for encapsulated strain gauges, since this model takes into account only the heat dissipated from the strain gauge to the measuring body. Heat dissipation to the ambient air (convective heat transfer) is neglected, and is therefore not affected by the strain gauge covering.

### Laminated Strain Gauges

Strain gauges that can be laminated are typically used in environments with poor thermal conductivity. For this reason, the lowest possible bridge excitation voltage should be chosen.

### Extreme Conditions

If heating the strain gauge needs to be ruled out entirely, optical strain measurement should be chosen. Here, strain is measured through an optical interrogator using a Bragg grating. This is the best solution, for example, when measuring in a high-quality vacuum or in extremely low temperatures near absolute zero.

## Use in Practice

First, it should be noted that slightly exceeding the maximum permissible excitation voltage does not damage the strain gauge.  A measurement error primarily consisting of a zero offset simply needs to be taken into account. With dynamic measurements, even that is irrelevant.

A strain gauge's maximum effective excitation voltage is specified on its packaging or in the data sheet. It is essential to use the value matched to the measuring body material. Only in this case does the value specified for the thermal conductivity λ correspond to the material used for temperature response matching i.e. it can be taken directly. If only the value for strain gauges matched to steel is known, with the strain gauge being installed on another measuring body, use the table on page 3 to find the correction factor.

Second, it is important to remember that the value is maximum excitation voltage. The value used in the amplifier can be significantly lower. Since the heat to be dissipated increases quadratically with the excitation voltage, an excitation voltage below the maximum excitation voltage very quickly results in a significant minimization of the measurement error.

When using carrier frequency amplifiers, the factor of 0.7 (effective voltage value) to be applied already a safety margin, thus significantly reducing the measurement error that has to be expected.

Strain gauge measurements on materials with very poor thermal conductivity such as plastics are critical. The smallest possible excitation voltage and a strain gauge with the highest possible resistance should be chosen.

As a rule of thumb, an excitation voltage of 2.5 V can, for example, always be used with typical measurements on steel or aluminum, and with strain gauges with a minimum measuring grid length of 1.5 mm and a resistance of 350 ohms. This is far from the maximum effective excitation voltage so that no measurement error resulting from heating can occur.