Glance at any transducer specification and you will notice that a specification is always provided which expresses the maximum error that can be expected upon variation of temperature. Qualification such as 0.002% FS per °F are quite common and refer to the temperature caused shifts in “zero” reading and temperature caused sensitivity changes which could be experienced as the temperature changes. The very existence of temperature specifications should in fact alert readers that the transducer they are about to purchase or use is not just sensitive to force, but is equally sensitive to temperature in a number of ways….some not so obvious, and some obvious.
This article explains why transducers are sensitive to temperature and methods employed by users and manufacturers to minimize thermal effects which could degrade the accuracy of their system or perhaps damage the transducer.
Thermal expansion is considered to be one of the most obvious effects of temperature. All materials expand as they get warmer (with some special exceptions for materials that are going through internal structural changes on an atomic level). Not only do these materials expand, but most engineering materials also expand at defined rates. Most steels expand at a rate of 6 parts per million per °F, meaning a steel part that was initially 1.000000″ long will grow to 1.000006″ if its temperature increased 1 °F. Stainless steels of the non-magnetic type expand at a rate of 9 ppm, aluminum at a rate of 13 ppm, and some plastics at rates of over 40 ppm.
These numbers appear to be very small at first glance. However, in a few instances they can produce quite sizeable effects; such as motions of several inches of fluid in a small tube of liquid which is called a thermometer, or some bridges which change their length by several feet or more. Getting practical, a number of large tank weighing systems make use of multiple load cells for suspending the tank. If the tank is steel and goes through a temperature change, it will change the distance between the load cells which if not allowed, can cause inaccuracies to develop in the load cells, or perhaps even physical damage.
To attain some idea of the magnitude of the effects, one can assume that a tank is supported by 4 load cells and is made of steel, with a distance of 100 inches between the load cells. If the tank is placed outside and the temperature differs between 0 °F and 100 °F (not everyone lives in southern California), the tank can be expected to expand and then contract by 0.060″ (0.000006 x 100″ x 100°F). This type of calculation is not completely correct as it does not take into account that the base that the load cells are mounted on also expands and then contracts; however, it does offer an indication of “possible” expansions which must be permitted.
Sixty thousandths of an inch sounds fairly small, and for most huge structures it is just ignored. However, load cells are comparatively highly stressed devices which deform less than 0.010″ at full applied load. Thus, to a load cell, an expansion of 0.060″ applied to the mounting flange can produce very high “shear” forces in the load cell itself. For this reason, multiple load cell installations which could experience differential thermal expansion must allow these expansions or else problems are indeed sure to take place.
Thermal expansion of the load cells also takes place with an increase in temperature. Assume that a load cell is 8″ high and produced from steel. At full applied load, the cell deflects 0.010″. If the load cell experiences a temperature change of 100 °F, it will expand 0.0048″ (.000006 x 8″ x 100 °F), which is practically half as much as it normally deflects under full load. Why doesn' t the signal change with this change in length due to temperature while it changes as a result of change in length brought about by load?
Temperature Correction Systems
A load cell under load contracts (or extends in tension) anywhere from 0.002″ to 0.010″ based on the internal design of the cell. A temperature rise of 100 °F on an 8″ long steel load cell may cause the cell to grow 0.005″. How can the cell differentiate between the two length changes brought about by force, while being insensitive to length changes brought about by temperature?
The answer to this question is that there are two main temperature correction systems within the load cell, which takes care of thermal expansion effect: the strain gage itself cancels expansion brought about by resistance changes, and the electrical circuit in which the strain gages are wired performs the remaining cancellation. To understand how this takes place, it is necessary to examine the electrical circuit in order to see how it usually functions.
Figure 1 displays the primary electrical circuit employed for strain gage transducers – the Wheatstone Bridge.
In the bridge shown, treat resistors R1, R2, R3, and R4 to be strain gages. If the resistance of all the strain gages is precisely equal, the bridge is believed to be “balanced” and no output voltage will appear at the signal leads. However, if one of the strain gages (say R1) happens to increase in value, the bridge is no longer balanced and a voltage proportional to the increase in resistance will appear across the signal leads (if R1 increases, voltage at point A will be lower than at point B. Likewise, if R1 decreases in value, the voltage at point A will be higher than at point B). With extremely little imagination, it is simple to extend this circuit by noting that the voltage at point B will be lower than that at point A if R1 and/or R3 decrease or if R4 and/or R2 increase. Understanding this paragraph will guarantee that one has successfully mastered most of the principles behind the Wheatstone Bridge.
Restating the previous paragraph, it can be stated that the Wheatstone Bridge will produce a signal which is considered to be proportional to the increase in resistance in arms 1 and 3 and the decrease in resistance in arms 2 and 4.
When a load is applied to a transducer, the strain gages (R1, R2, R3, and R4) are applied to the structure in such a way that causes gages 1 and 3 to stretch (undergo tension) and, therefore, increase in resistance, while gages 2 and 4 are compressed which causes them to decrease in resistance. All these load-caused resistance changes contribute to producing the same polarity signal at the output terminals (A and B) and, thus, the load cell gives a signal which is considered to be proportional to the applied load. The easiest structure for visualizing these tension and compression-induced resistance changes is the simple cantilever beam, as presented in Figure 2.
If, however, the transducer is subjected to an increase of temperature, all of the component parts to which the strain gages were fixed to would increase in length allowing all gage resistances to increase equally. (In this instance, the signal produced by the increase in resistance in arms 1 and 3 would be accurately canceled by the increase in resistance in arms 2 and 4 and the net bridge output would be zero).
Thus, in a Wheatstone Bridge, if it is possible to make each arm change identically with temperature, then it could indeed be possible to eliminate the “temperature effect on zero” for the transducer. Even better, if it is somehow possible to make the temperature-induced changes in resistance of the strain gages small or zero, the nulling effect of the Wheatstone Bridge would then be increasingly effective.
In 1858, a gentleman called Thompson (who later was named Lord Kelvin), presented a paper before the Royal Society in London entitled “On the Electrodynamic Qualities of Metals,” where he reported that particular electrical conductors displayed a “…change of electrical resistance with change in strain.” He also stated that the resistance change was so small that delicate instruments were needed for detecting it.
During the same meeting, Sir Charles Wheatstone reported on work carried out 23 years earlier by a Mr. S. Hunter Christie on an electrical bridge network which had the potential to detect extremely small resistance changes. Eventually, the network became linked with the reporter rather than the inventor, and today the network is called the “Wheatstone Bridge.”
Little use was made of Lord Kelvin’s discovery until 1937 when Professor Ruge of MIT unwound a wire wound resistor and used the wire for constructing the first bondable strain gage. Simultaneously, at Cal Tech University, a graduate lab assistant by the name of Ed Simmonds suggested doing the same thing to a researcher who published his research and also credited Simmonds for the first bonded resistance strain gage. Due to the simultaneity of discovery, a joint patent was issued to both inventors and the Simmonds Ruge (“SR-4”) strain gage was born.
It turns out that the choice of wire used by both of the inventors was rather fortuitous. In order to develop stable wire wound resistors of reasonable size, resistor manufacturers had developed distinct alloys which had extremely high resistance (so that reasonable lengths of wire would generate the required resistance values), and possessed extremely small temperature coefficients of resistivity (which means that the resistance of the wire would not change with differences in temperature). The metallurgy of these alloys is moderately complex, and if the resistor industry hadn't born the development cost, it could still not be possible to have the strain gage. The choice of alloys was so good in fact that basically the same ones are being used in modern strain gages 50 years later.
Although the basic alloys used for making strain gages have not changed, the strain gage definitely has. The key change was when the gage started to be manufactured by using printed circuit techniques rather than just winding a wire into a grid configuration. The use of foil allowed the gage to be manufactured with great uniformity and also placed the gage closer to the surface of the part to which it was bonded, which allowed it to operate at basically the same temperature as the part. It was then identified that minor or subtle processing changes (chiefly heat treating of the foil), could generate strain gages with even more repeatable temperature coefficients of resistivity and even better, allowed the gage manufacturer to generate slight negative coefficients.
In order to see what effect this has on a strain gage, it is necessary to assume that a gage is mounted on a piece of steel which is heated 100 °F. With this heating, the steel part expands 0.0006″ per inch of length. Since the strain gage is fixed to the part, it would be stretched, thus increasing in resistance. However, if the gage alloy has been correctly heat-treated, as the temperature goes up, the base resistance of the gage goes down by precisely the same amount as it would have increased by the elongation of the part; thus developing a strain gage system that would not change in resistance with temperature.
This is the fundamental mechanism for developing self-temperature compensating strain gages, and is the reason why gages are specified by the temperature coefficient of expansion of the material to which the gage is to be mounted.
Self-temperature compensating strain gages, merged with the temperature cancellation effects of the Wheatstone Bridge are considered to be quite effective in decreasing temperature created “zero shifts” from transducers.
In commercially available transducers, it turns out that even these zero correction mechanisms are not quite good enough, and thus extra temperature compensation elements are at times added to even further decrease the effects of temperature on the zero output of a transducer.
So far, this article has discussed those factors which produce and also prevent an erroneous signal being delivered from a transducer, as the temperature changes, with no applied load. These “zero balance” effects are quite simple to detect, since any indicated load reading from an unloaded transducer is evidently incorrect. If, however, the transducer modifies its sensitivity, the only clue is to apply a well-known force or weight to the transducer and check its output. For installed scales, this checking procedure is inconvenient and in a number of cases, impossible to perform. Thus, the temperature effects on span or sensitivity of a transducer is usually measured and then corrected by the transducer manufacturer, and the end-user must trust that the manufacturer has carried out the job correctly, since it is unlikely that the scale will ever be calibrated at two varied temperatures unless it is suspected that the transducer is out of specification.
The reasons for the transducer’s temperature sensitivity with respect to span can be easily explained by analyzing a simple model of a transducer. A transducer can be considered as nothing more than a “spring-like” structure which deforms under load, and a sensor (such as a strain gage) which generates a signal proportional to this deformation. The deflection of the transducer structure relies on the shape of the structure, the magnitude of the applied load, and the properties of the material from which the structure is made. The material property which relates deflection to applied load is known as the “Modulus of Elasticity” or the “Elastic Modulus”. If the Modulus of Elasticity of a material would remain constant, the deformation caused by an applied load would also remain constant.
Unfortunately, the Modulus of Elasticity for most materials varies slightly with temperature, the end result being that a typical transducer becomes “softer” with increase in the temperature. If uncorrected, this “softening” effect would make the transducer more sensitive as the temperature increased. For most materials employed in transducers, the magnitude of this effect is about 1.5% per 100 °F.
A second effect which produces a change in sensitivity with temperature change, is linked with the strain gages employed for measuring the deformation of the transducer structure. Strain gages, based on which alloy is used in their construction, modify their sensitivity from +0.5%/100 °F (Karma and Platinum/Tungsten). A transducer using Constantan strain gages can be expected to increase its sensitivity by 2%/100 °F because of the combined effect of elastic modulus decrease and the strain gage sensitivity increase. In transducers, these two combined effects are frequently lumped together, and just referred to as the modulus effect.
Since Karma and Platinum alloys decrease in sensitivity by about the same amount as the increase in sensitivity of the structure itself. It should be emphasized that this correction network which is generally used by transducer manufacturers, will only work when the transducer is excited with constant VOLTAGE supplies. If constant CURRENT systems are employed, the compensated system is wholly nullified and a different compensation system must be used.
Manufacturers have developed sensors which possess self-modulus temperature compensation. In order for this self-compensation to occur, careful matching of the strain gage to the structure is needed, which suggests some rather intensive testing in order to assure a consistent match. For this reason, this technique has been restricted to sensors in comparatively high production where the initial evaluation costs can be amortized over the length of the production run.
Sensors developed with Constantan strain gages (even though they always need correction for their increase in sensitivity versus temperature), provide advantages in stability and cost that still make them desirable for most of the available transducers today. Furthermore, if a constant voltage excitation system is used with the sensor, it turns out that an extremely simple addition to the Wheatstone bridge circuit will correct the sensor for modulus variations.
The output of a transducer is a function of the excitation voltage and the applied load. If it is possible to somehow decrease the excitation voltage of a sensor at the same rate as it was increasing its sensitivity, the sensor would be efficiently modulus compensated. The method used for accomplishing this is simply to add a resistance in series with the Wheatstone bridge which increases with temperature.
The Wheatstone bridge, which is developed with strain gages that basically do not change resistance with temperature changes, can be considered just as another single resistor in series with the temperature sensitive one. If a constant voltage is applied across this circuit, the current will indeed decrease as the resistance increases in the temperature sensitive resistor. As this takes place, the effective voltage across the Wheatstone bridge decreases, because its resistance continues to be constant. In practice, this temperature sensitive resistor, which is known as the modulus resistor, is generally split into two resistors, with each resistor in series with each excitation lead going to the bridge circuit. (See Figure 3)
This information has been sourced, reviewed and adapted from materials provided by HITEC Sensor Developments, Inc.
For more information on this source, please visit HITEC Sensor Developments, Inc.