The Need for Temperature Compensation in a Strain Gauge

Key Takeaways

• The thermally-induced apparent strain can be viewed as an error caused by temperature changes in strain measurements. The temperature compensation in the strain gauge is necessary to reduce the thermal effect on the measurements.

• The main reasons for establishing thermal compensation in strain gauges are thermal expansion of the measuring object, the thermal expansion of the sensing element in the strain gauge, and the temperature coefficient of resistance of the strain gauge connecting wires and sensing elements.

• The active-dummy method and self-temperature compensation methods are used to overcome the error in strain measurement caused by temperature variations. 

Strain gauges are commonly used sensing elements in aerospace engineering.

The strain gauge is a common sensing element in rotating machines, automobiles, aerospace applications, ships, rail monitoring systems, and civil structural damage inspection tools. The strain measurement utilizes different principles based on methods such as optical, mechanical, and electrical methods. In electrical strain gauges, electrical quantities like resistance, capacitance, inductance, and photoelectric effects are utilized for measuring strain. The basic principle of operation of resistive electrical strain gauge is that the metallic resistive sensing element changes length when it experiences strain. The elongation and contraction of the sensing element change the electrical resistance of it. This resistance change is proportional to the product of the gauge factor and the strain. 

Usually, the rate of resistance change is measured using bridge structures and therefore, the strain borne on the object is determined. However, the electrical resistance is vulnerable to temperature changes. According to the material and its coefficient of linear expansion, there will be either elongation or contraction of the sensing element under thermal effects and this will introduce thermally-induced apparent strain. This strain can be viewed as an error caused by temperature change. The temperature compensation in the strain gauge is necessary to reduce the thermal effect on the strain gauge measurements. 

Temperature Compensation in Strain Gauge 

For strain measurement, the active resistive strain gauges are made as an arm of bridge structures (for example, the Wheatstone bridge) to form a quarter bridge circuit. Any change in the resistance of the sensing element unbalances the Wheatstone bridge and produces a non zero output voltage. This output voltage is a function of the strain to be measured. The figure above shows the quarter bridge active strain gauge circuit arrangement, where RS is the strain gauge nominal resistance. The other arms are arranged such that  R₁= R₂ and R₃= R_S. The ratio of voltages present is given by the equation:

where GF is the gauge factor and is the strain. The only unknown present in the equation above is the strain, which is mathematically calculated. 

In ideal resistive strain gauges, the change in resistance should result only from the strain. However, as the measuring object material and strain sensing elements are temperature sensitive, there will be apparent strain due to temperature variations. The temperature-compensated strain gauge overcomes all these thermal effects and produces an accurate measurement. 

In a bonded resistive type strain gauge, the metallic resistive sensing element is bonded to the object under measurement. The thermal effects on the strain gauge can be expansion or contraction of the measuring object or sensing element. The three main reasons for establishing thermal compensation in strain gauges are: 

1. The object under test may have a certain coefficient of thermal expansion which results in either expansion or contraction of the object under temperature change. The strain is induced due to temperature and an error occurs, as the actual strain value is not obtained under this scenario. With temperature compensation, we can obtain the true value of strain borne on the object. 

2. The coefficient of thermal expansion of the sensing element in the strain gauge causes elongation or contraction of it. The changes in temperature make unwanted changes in the sensing element length and this causes error in strain reading. This temperature compensation technique can make the strain measurement free of such effects. 

3. The wires used in the strain gauge circuit connection and the sensing element may have either a positive or negative temperature coefficient of resistance. If the temperature coefficient is positive, the resistance value increases with the rise in temperature and vice versa for a negative temperature coefficient. The resistance change that is dependent on temperature, but independent of the strain is not needed in strain measurement systems. The increase or decrease in resistance due to temperature can be omitted by using temperature compensation in strain gauges. 

Temperature Compensation Techniques

The quarter bridge system of strain gauge measurement, otherwise called the one-gauge system, is highly sensitive to temperature fluctuations. There are various temperature compensation techniques used in strain gauges. 

Active-Dummy Compensation Method

The active dummy method employs a Wheatstone bridge arrangement with two or four strain gauges. In a two-gauge system (half-bridge configuration ), one active strain gauge and one dummy gauge are connected in adjacent arms of the Wheatstone bridge. 

The active and dummy strain gauges are made of the same material. The active strain gauge bonded to the object measures the strain, whereas the dummy strain gauge is unbonded. Both are kept under the same temperature conditions. This makes the thermally-induced strain in active and dummy strain gauges equal. As both the strain gauges undergo identical thermal changes, the ratio of resistances and output voltages remain unaffected. The adjacent placement of the active and dummy gauges helps to compensate for the thermally-induced strain under the balanced bridge conditions. 

In a four-gauge system or full-bridge configuration, three dummy gauges are present along with an active strain gauge, and thus the thermal effects are compensated. 

Self-Temperature Compensating Method

In a self-temperature compensated gauge, the linear expansion of the measuring object due to temperature variations is compensated by adjusting the temperature coefficient of resistance of the sensing element. With the advent of self-compensated strain gauges, the requirements of identical dummy strain gauges is considerably reduced. The thermally-induced strain in strain gauges obeys the following equation:

where α is the temperature coefficient of resistance of the sensing element. mand sare the coefficients of linear expansion of the measuring object and sensing element, respectively. From the equation above, it is clear that by controlling the value of , the thermally-generated strain can be reduced to zero:

Under the condition, t_emp=0, the temperature coefficient of resistance, , is a function of the gauge factor and the coefficient of linear expansions, , as given by equation 3, above. Heat treatment is used for controlling the temperature coefficient of resistance of the sensing element.

Strain gauge measurements are employed in various mechanical, civil, and electrical systems that are sensitive to thermal effects. Even though thermal management is available in every engineering design, the temperature compensation in the strain gauge is essential for achieving accurate strain measurements. If the procurement of identical dummy strain gauges required in the active-dummy method is a problem, you can use the self-temperature compensated strain gauges for error-free strain measurements. 

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