Strain gauge compensation theory and method
1. Self-temperature compensation
Strain gauges are usually installed on a surface whether it is for stress analyses or sensor production, without any external forces applied to the surface. When environmental temperature changes, the resistance of the strain gauge changes accordingly. This phenomenon is called the strain gauges thermal output. This thermal output is the result of interactions and superposition of the resistance temperature coefficient of grid materials, the sensitive grid materials and the linear expansion coefficient. The effects of these factors is described in the formula below:
In this formula αg and βg refer to the resistance temperature coefficient of the grid material and the linear expansion coefficient of the strain gauge. K refers to the strain gauges gauge-factor and βs refers to the linear expansion coefficient of the tested object . Δt refers to the relative change in temperature of the tested subject and environment. Common strain gauges often have a large thermal output as shown in figure 1. Thermal output is the biggest source of errors in static strain measurements. When temperature increases the dispersion and therefore the thermal output value increases. Ideally the thermal output of strain gauges should be zero. To meet this requirement a self-temperature compensating strain gauge is used. In figure 2 the typical thermal output of a constantan and a self-temperature compensating karma strain gauge are displayed.
Figure 1: Thermal output curve of strain gauges on different steel materials
By adjusting the composition ratio of the alloys of the strain gauge sensitivity grid material, and make use of cold rolling and proper heat treatment, the internal crystalline structure of the gauge material can be altered in a way it will compensate the changes of the material due to temperature change. This way the change in Thermal output can be kept very close to zero and the standards for highprecision sensors and stress analysis can be met. Note that the self-temperature compensation is only in a small temperature range from approximately + 20℃ up to +250℃ .
Figure 2: Thermal output for Self-Temperature compensated Karma and Constantan alloy strain gauges
Choice in self-temperature compensation
Currently ZEMIC offers a range of different Self-Temperature compensated strain gauges which are divided in ranges of compensations for different materials from which the test surface is made of. ZEMIC currently offers the following:
- 9: Titanium test surfaces with a typical expansion coefficient of 8.8 x 10⁻⁶ / ℃
- 11: Martensitic, Age hardenable-stainless and alloy steel test surfaces with a typical expansion coefficient of 11.3 x 10⁻⁶ / ℃
-16: Copper-based and austenitic stainless steel test surfaces with a typical expansion coefficient of 16 x 10⁻⁶ / ℃
-23: Aluminium-alloy test surfaces with a typical expansion coefficient of 23.2 x 10⁻⁶ / ℃
-27: Magnesium-alloy test surfaces with a typical expansion coefficient of 26.1 x 10⁻⁶ / ℃
When the temperature compensation of the strain gauge matches the test surface material, the thermal output of that test surface will be compensated within the temperature range and no further adjustments have to be made to this thermal output.
When the temperature self-compensating strain gauges test surface has a slight difference in material composition, or the self-temperature compensation of the strain gauge does not match the temperature coefficient of the material, a half or full bridge of strain gauges should be used to compensate the thermal output brought influences.
A quarter bridge setup for high precision stress measurements should consist of one strain gauge attached to a compensation object which has the same material as the test surface. In addition the compensation strain gauge and the strain gauge which is applied to the test surface should be of the same lot. The two strain gauges should be under the same temperature and environmental conditions and located next to each other in the Wheatstone bridge.
2. Self-creep compensation
Creep characteristics exist due to the elasticity of a spring element. This is a material characteristic. Due to this characteristic, a transducers output increases with the passing of time (Positive creep). This characteristic is depending on several variables such as the spring element material, structure, strain field, span, heat treatment and test temperature. The backing material of the strain gauges and the bonding adhesive have a very high viscoelasticity which results in an output decrease over time. On the other hand the grid material of the strain gauge has anelastic properties which results in a positive output change over time. The accumulation of these two make that a strain gauge can have either a positive or negative creep under fixed load. The direction and value of this compensation can be adjusted by modifying the design of the grid structure, backing material ratio and key technology parameters. For example, by changing the dimensions of the end grid and fixing the other parameters, a curve as seen in figure 3 can be created. After selecting the material of a spring element, a strain gauge can be selected with the same creep as the element but in the opposite direction. This way the creep can be compensated to a value close to 0. In the same way, during the production of transducers, the creep error which is caused by other factors can be compensated. In this way the creep value could be brought to a minimum and within specifications of the transducer. ZEMIC offers a wide variety of strain gauges for which the creep factor should be decided by the transducers manufacturers. The N* and T* codes in the strain gauge naming system
are designated referrals to the creep code. Different codes refer to different creep values. For ZEMIC strain gauges the rule is as follows: the creep difference between two neighbouring codes is 0.01-0.015%FS/30min.
N9 > N7 > N5 > N3 > N1 > N0 > N8 > N6 > N4 > N2 > T0 > T2 > T4 > T6 > T8 > T1 > T3 > T5
Figure 3: Creep compensation and effect of creep
Choice in self-creep compensation
It is advised when using strain gauges for the first time to select one or two models with a great difference in creep values and bond them to the spring element. The actual creep code will be determined according to the actual value of the creep and the difference with the applied strain gauges.
When selecting a strain gauge for transducers with the same spring materials and structure, the smaller the capacity the more positive creep will occur. Therefore the lower the capacity of the transducer, the bigger negative creep code should be chosen.
Different element materials show different creep characteristics. Therefore, different creep codes should be selected for the steel and aluminium transducers with the same capacity and structure.
The creep value of transducers is depending on many variables such as spring elements, strain gauge type, adhesive used as well as the way of sealing, the protective coating etc. The direction and magnitude of the creep however can be predicted to a certain amount and this should therefore be taken into account when selecting a strain gauge creep code.