Abstract
The use of strain gauge technology in industry is a common feature for determining mechanical stress in components. However, there is less understanding of the use of this technology in cryogenic applications. The current method of recording gas pressure in containment vessels used at cryogenic temperatures can be considered to be unreliable under certain conditions. A development project has been instigated to investigate the extreme temperature effects on strain gauges working at liquid helium (4 K) temperatures. A small, rectangular helium gas pressure containment vessel has been designed which operates at 20 bar. This will provide deflections to one of its faces onto which a suitable strain gauge can been fixed. The key temperature-dependent variables influencing the strain gauge’s parameters are discussed, with proposed methods to mitigate their effect.
Keywords
Strain gauge fundamentals
Strain gauges are devices used to measure the strain on loaded objects such as lifting beams and pressure containment vessels. Their construction is principally a metallic foil, which under deformation causes a change in the electrical resistance through the foil. This shift in resistance can be calibrated to represent strain values. Knowing the strain within these objects will by definition allow the stresses to be determined.
A Wheatstone bridge configuration is used to measure the change in resistance of the strain gauge. This is an electrical circuit used to measure any unknown resistance by balancing two legs of a bridge circuit. It is made up of two fixed resistors, one adjustable resistor and the variable resistor strain gauge. If the fixed resistors are known to a high accuracy, an extremely accurate measurement of the variable resistance can be determined to balance the bridge (Fig. 1).
Wheatstone bridge circuit.
Gas pressure measurement at the ISIS neutron source facility uses either a pressure gauge or a pressure transducer on the room temperature, gas inlet side of any circuit. Unless the circuit has a gas return line, there are no means of verifying the pressure inside sample containment vessels at any given point in time. Gas flow impedance and the possibility of gas-line blockages forming at liquid helium temperatures can result in the assumption that gas pressure exhaust has taken place when in fact the containment vessel is still pressurised. A method of measuring the deformation of the sample containment vessels by using strain gauges has therefore been developed. Ideally, the strain gauges will be fixed to parts of the containment vessel giving maximum deflection, but not within the neutron beam profile.
Temperature-dependent variables
Working at the proposed extreme cryogenic temperatures, certain temperature-dependent characteristics of the strain gauge and its adhesive will have to be considered and methods on how to mitigate their effects developed. The initial suitability of a particular gauge has been determined based on an existing application used on the 35 bar methane moderators on the ISIS target facility. Here they employed a fully encapsulated K-alloy gauge from Vishay Precision Group which is designed to operate down to 4 K [3]. The key temperature-dependent variables influencing the strain gauge’s parameters are as follows:
Material strain
This is the apparent strain (strain without load) which is a result of the contraction in size of the containment vessel due to the change in temperature. As the containment vessel’s dimensions are reduced because of the cryogenic temperature, this will create an associated reduction in the apparent strain. The expansion coefficient of any material is temperature-dependent which also changes as the temperature is decreased.
The practical way of compensating for this apparent strain is to choose a temperature-compensated strain gauge which has the same coefficient of contraction value as the containment vessel material of construction. The temperature response of the strain gauge is matched in such a way that they compensate for the apparent strain. They are however optimised for a particular temperature range and can be non-linear over larger temperature changes.
Electrical resistance
The change in resistance of the strain gauge is the measure used to determine accurate strain. The resistance of the strain gauge will change as temperature changes. The total variable resistance in the circuit is a combination of both the strain gauge resistance added to the feed wire resistance. For most applications supporting sample environment equipment, these feed wires would be of significant length. The feed wire resistance change due to temperature can therefore be a dominant factor in producing resistance shifts. In addition, the rate of change of both the strain gauge circuit and the feed wire changes as temperature is decreased. In most cases this is non-linear. The combination of these factors creates a resulting zero shift without the application of strain.
Compensation for this is done by the use of a half-bridge strain gauge circuit (Fig. 2). In this circuit, a second identical strain gauge is placed at an unstressed location at the working temperature. The change in electrical resistance of the working temperature parts will automatically balance the circuit. Also, the feed wires can be made from a material with a low temperature coefficient of resistance value, such as Manganin® (86% copper, 12% manganese and 2% nickel) [1].
Half-bridge strain gauge circuit.
This is a material-dependent property which by definition is the ratio of measured strain to mechanical stress. Typically, it will increase by about 20% between room temperature and liquid helium temperature [2]. This results in an increase in the strength and stiffness of the material of the containment vessel. Deformations due to any applied pressure will therefore be smaller at the cryogenic temperature compared to those for the equivalent loading at room temperature.
Compensating for this characteristic is difficult. However, force is direction-dependent and the change in the modulus of elasticity can be minimised by limiting deflections in the location where the strain gauge is employed. Typically, this factor is ignored as the actual deflection can be calibrated to reflect the force needed to produce it. Knowing the change in strength of the material of construction, both deformations and the associated forces can be calculated.
Other temperature-dependent factors
Other temperature-dependent factors which need to be considered during testing of the strain gauges are less obvious in what their effect will be on the overall results. These include:
Self-heating of the strain gauge.
Hysteresis errors produced on returning to zero.
The sensitivity changes of the strain gauge over a linear range.
The possible embrittlement of the adhesive.
The long-term effect of neutrons on the function of the strain gauge.
Design
A rectangular pressure containment vessel with circular end flanges has been designed to provide the means by which to test the suitability of the chosen strain gauge. The containment vessel is small enough to fit through the neck of a liquid helium Dewar and is compliant with relevant safety codes. One wall of the vessel has been designed thin enough to create maximum deflection at a working pressure of 20 bar, but strong enough not to yield during the requisite proof test. A shield guard has been added over this wall to protect against possible fatigue failure during the test programme. Provision is also made for an unstressed strain gauge on one of the end flanges.
The cryogenic centre-stick arrangement supporting the containment vessel has been designed to provide a helium gas feed, which is fully protected with a pressure relief valve. A pressure transducer to record the applied pressure is located on the room-temperature side of the pressure circuit. Electrical connectors to provide wiring for both an external and internal strain gauge are also part of the assembly.
Project schedule
As a development project, the manufacture and testing of the pressure containment vessel has priority. Testing of the selected strain gauge under cryogenic temperatures can then proceed, although a series of room temperature deflection tests will be undertaken prior to this. Calibration of the strain gauge can then be initiated.
Conclusion
Mitigation of the temperature-dependent variables is a key factor in the accurate measurement of strain at cryogenic temperatures, which can then be converted to the equivalent energising pressure within containment vessels. Many separate methods will have to be employed, some more critical than others. True and accurate pressure measurement under these conditions requires care in preparation of the strain-gauge and consideration of the long-term use of fixed strain-gauges.