# Determining the Maximum Excitation Voltage of a Strain Gauge

The maximum permissible effective bridge excitation voltage of a strain gauge (SG) is a crucial factor given in the specifications. What is the importance of this value, how is it determined, and what has to be considered in actual applications?

## Strain Gauges as Heating Elements

Strain gauges are electrical resistors when performing strain measurement in a Wheatstone bridge. The applied voltage causes a power loss in the form of heat in the measuring grid of the strain gauge. It is necessary to dissipate heat from the strain gauge because excessive heat leads to incorrect measured values. Reasonable limits, i.e., maximum permissible effective bridge excitation voltages, need to be defined as it is not entirely possible to completely avoid heating of the strain gauge. Adhering to these values ensures a minimum measurement error.

## Factors Influencing Heating of Strain Gauges

The following are the factors that significantly influence heating of strain gauges and therefore their maximum permissible bridge excitation voltage (Umax):

• Strain gauge grid area ‘A’ as larger area facilitates better heat dissipation
• Strain gauge resistance ‘R’ as higher resistance results in lower heating
• Special features such as the design of a strain gauge (stacked measuring grids)
• Thermal conductivity ‘λ’ of the measuring body as it influences the 'efficiency' of heat dissipation

## Heat Flow Model

The maximum permissible bridge excitation voltage can be calculated at a given resistance R and a defined maximum electric power P as follows:

Thermal considerations involve devising a heat flow model (Figure 1) with a strain gauge that is attached to a measuring body of infinite thermal capacity C. A temperature gradient ΔT/d develops close to the strain gauge due to the temperature difference between the measuring body and the strain gauge. It is not influenced by the strain gauge resistance and grid area and can be considered as a measure in error analysis. Empirical studies have proven that the measurement error limit is complied with at a temperature gradient of ΔT/d = 0.75°C/mm in the area in proximity to the strain gauge.

Figure 1 Heat flow model for heat dissipation from the strain gauge to the measuring body. Image credit: Hottinger Baldwin Messtechnik GmbH

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

In stationary mode, the electric power P is in balance with heat energy Q' dissipated via the carrier to the measuring body.

## Estimation of Maximum Permissible Bridge Excitation Voltage

If the electric heat produced in the model is completely dissipated through the measuring body, then the maximum permissible effective bridge excitation voltage of the strain gauge is:

The above equation calculates the maximum effective bridge excitation voltage for various strain gauges based on the known parameters and the quantity empirically calculated for the temperature gradient. The typical measuring body materials are summarized in Table 1.

Table 1. 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 correction factor shown in Table 1 can be used only when the maximum excitation voltage for strain gauges corresponding to steel is known:

## Specifics of the Maximum Bridge Excitation Voltage

### Carrier Frequency

Carrier frequency excitation is preferred as the degree of heating of the strain gauge by it is lower than a DC voltage with the same value.

### Stacked Rosettes

Stacked rosettes, involving stacking of the individual measuring grids on top of one another, allows the upper measuring grids to dissipate heat to the measuring body to a lesser degree when compared to the lower ones.

### Encapsulated Strain Gauges

For encapsulated strain gauges, the heat dissipation from the gauge to the measuring body is only considered, but the heat dissipated to the ambient air is ignored. Hence, this model is unaffected by the strain gauge covering.

### Weldable Strain Gauges

The heat flow via the spot welds is decreased with weldable strain gauges, thus leading to a lower maximum permissible effective bridge excitation voltage.

### Laminated Strain Gauges

Laminated strain gauges are generally used in areas with poor thermal conductivity. Hence, it is necessary to select the lowest possible bridge excitation voltage.

### Extreme Conditions

Optical strain measurement is a better choice in cases where heating the strain gauge is not desirable. This approach uses a Bragg grating to measure strain through an optical interrogator. This is ideal to perform measurement in very low temperatures close to absolute zero or in a high-quality vacuum.

## Conclusion

The strain gauge will not be damaged if the voltage value is slightly above the maximum permissible excitation voltage. A measurement error principally comprising a zero offset simply needs to be considered. However, it is also irrelevant with dynamic measurements. The maximum effective excitation voltage of a strain gauge is mentioned on its packaging or in the data sheet. The value corresponding to the measuring body material needs to be used.

However, the maximum effective excitation voltage of a strain gauge can be taken directly when the thermal conductivity value corresponding to the material utilized for temperature response matching. If only the value for strain gauges corresponding to steel is known and the strain gauge is mounted on another measuring body, then correction factor needs to be determined using Table 1.

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.

For materials with very poor thermal conductivity like plastics, it is recommended to select the smallest possible excitation voltage and a strain gauge with the highest possible resistance.

This information has been sourced, reviewed and adapted from materials provided by HBM, Inc.

## Citations

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