Understanding the Problem. The first step in designing for accurate position measurement over big temperature ranges is to be clear about what is required. Obvious? Maybe, but there are plenty of engineers who still tell me “it has to be pretty accurate even when its fairly hot or quite cold – but not cost too much”. The main data requirements are:
- Max., typical & min. operating temperatures
- Max. & min. storage temperatures;
- Max. permissible error at the various operating temperatures.
In considering the technical solution to any requirement, there should be two realistic budgets – a cost budget and an error budget.
The Error Budget. The difference between actual and measured position will comprise several different errors. Together, this is referred to the error budget and typically comprises:-
- errors from the position sensor’s (less than perfect) measurement performance
- thermal drift in the sensor’s output
- mechanical effects from clearances in couplings or bearings, backlash in gears etc.
- thermal effects in the host mechanical structure – notably from differential thermal expansion.
Understanding Measurement Performance. In theory, all sensors have data-sheets that clearly state measurement performance. In practice, not so. Sensor manufacturers often use ‘specmanship’ to promote the strengths of their products and hide the weaknesses. So, let’s clarify the main parameters relating to a position sensor’s measurement performance:-
- Accuracy refers to its veracity or maximum deviation from actual position.
- Resolution refers to the smallest change in position that it can measure.
- Repeatability (or Precision) refers to its degree of reproducibility.
- Linearity refers to how well its output over a range matches a straight line. In many instances, Linearity and Accuracy are the same if there is no offset.
If position is to be measured during motion then the dynamic errors due to the time difference between the sensor’s output and reality should be included.
A common mistake in angle sensors, which are specified in cpr or ppr (counts or pulses per rev), is the assumption that a 1000cpr sensor is accurate to 1/1000th of a rev. Read – and understand – the small print of the sensor’s data sheet. You may be unpleasantly surprised. If you simply buy the most accurate sensor that you can find, it’s likely that you will be paying over the odds. In many instances, resolution and repeatability are the key factors – not necessarily accuracy. This can make a huge difference to the price you will pay for a sensor.
Temperature Coefficient. Whenever measurement performance parameters are stated they should be specified at a temperature along with a temperature coefficient. This refers to the change in the sensor’s output as temperature varies from that stated. A small temperature coefficient means a thermally stable device. Typically, temperature coefficients are stated in parts per million per Kelvin. This is an unfortunate unit as it is usually a tiny number and often ignored. The snag is that this tiny number has to be multiplied by the temperature differential. A seemingly ideal sensor at 20ºC may not good enough when the temperature reaches 120ºC.
Thermal & Mechanical Effects. Typically, it is not the sensor’s elements that are of interest but rather the position of the host’s elements such as the angle of a shaft or displacement of a piston. Of course, these will have their own contributions to the error budget caused by factors such as backlash, clearances and thermal expansion. Thermal expansion is a natural phenomenon and one which should not be ignored. More problematic is differential thermal expansion and this can lead to significant measurement errors if its effects are not minimized by appropriate mechanical arrangements or material selection.
If the sensor’s mounting structure expands or contracts by the same amount as the components being measured, the effect of differential thermal expansion can be negated. Ideally, the sensor’s thermal coefficient either matches or counteracts the effects of thermal expansion. In many instances the sensor’s mechanical arrangement relative to the host equipment means that differential thermal expansion has to be included in to the error budget. In instances where such an effect dominates the error budget, there is always the option for temperature compensation. This requires the local temperature to be measured and the output from the sensor to be compensated accordingly. This is undesirable as temperature will not be uniform; there will be thermal lags; there is an increase in cost and complexity and so a reduction in reliability. Nevertheless, in some instances it is unavoidable.
Choosing the right sensor. A position sensor’s fundamental physics generally determines how big its temperature coefficient is. A basic understanding helps in choosing the right sensor for the job. Some of the common principles used to measure position are:
Potentiometers – the basic physics measures the resistance of an electrically conductive material. Since conductivity varies with temperature, coefficients are likely to be large.
Optical – transmission of light is largely independent of temperature but the associated electronics suffer from thermal drift and most optical sensors have a narrow operating temperature range. Further, many optical sensors – notably ring & kit forms – rely on tight installation tolerances and so are likely to suffer additional thermal effects at extreme temperatures.
Magnetic (Hall) – Hall effect sensors measure field strength and magnetic properties vary with temperature so thermal coefficients may be significant. Precision magnetic sensors also need tight installation tolerances so additional thermal effects may be large.
Magnetic (Magnetostrictive) – These devices measure the propagation of an energy pulse along a magnetostrictive strip to/from a magnet. Typically, thermal coefficients are relatively large.
Capacitive – since capacitance changes a lot with temperature, many capacitive devices have large temperature coefficients which are further exacerbated by changes in humidity. In some instances, condensation or foreign matter on the sensing elements can have disastrous consequences.
Inductive – Inductance varies with temperature but most precision inductive sensors use a ratiometric technique based on the ratio of at least 2 inductances. Since the values of both will vary by similar amounts, thermal coefficients are typically low.
Traditional inductive sensors . Typically, these sensors use transformer techniques with precision wound spools and they have become the automatic choice in the aerospace, military, oil & gas sectors where there is often a big temperature range. The basic physics means that they are ideally suited to difficult operating environments but they are not widely used due to their high cost, weight and bulk.
New Generation Inductive Sensors. A new generation of inductive sensor has entered the market in recent years and has a growing reputation, not only in the traditional markets, but also in industrial, automotive, medical, utility and scientific sectors. The new generation sensors use the same basic physics as the traditional ones but rather than the bulky transformer constructions and complex analogue electronics, the new generation uses printed circuit boards and digital electronics. The approach is elegant and also opens up the range of applications for inductive sensors to include 2D & 3D sensors, short throw (<1mm) linear devices, curvilinear geometries and high precision angle encoders.
Zettlex technology is the forerunner of this new technology and has grown over recent years thanks to some high profile design wins. As well as compact, lightweight, non-contact designs a key factor is that they offer extremely stable measurement over wide temperature ranges. The example shown below is an Incoder (inductive encoder) which offers a cost effective and more accurate alternative to traditional pancake resolvers. As can be seen in the diagram such incoders offer remarkably small temperature coefficient of <0,25ppm/K which equates to less than one fifth of an arc-second per Celsius change.
Graph of change in output from a 75mm (18bit) Incoder at a static angle versus temperature