Accurate position measurement at varying temperatures

The first step in designing for accurate position measurement over wide temperature ranges is to be clear about what is required. 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 as the error budget, which 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.

Tip #2 – prepare an error budget & ensure all contributing factors are considered.


Understanding Measurement Performance


In theory, all sensors have datasheets that clearly state measurement performance. In practice, this is not so. Sensor manufacturers often use ‘specmanship’ to promote the strengths of their products and to 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 also be included.

Tip #3 - understand what aspects of measurement performance are important in your application and ensure the sensing system aligns with these requirements.

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.

Tip #4 – make sure your error budget includes the sensor’s temperature coefficient.


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 mechanical tolerances, 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 minimised 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.

Tip #5 – Mechanical effects & differential thermal expansion must be included in any error budget. Wherever possible, these should be minimised through careful mechanical arrangement and material selection.

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. As 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. Furthermore, 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 two inductances. Since the values of both will vary by similar amounts, thermal coefficients are typically low.

Tip #7 – design the host system to minimise differential thermal expansion and select a sensor with a small thermal coefficient or one whose temperature coefficient matches the host system.


Traditional inductive sensors


Typically, these sensors use transformer techniques with precision wound spools and they have become the automatic choice in the oil & gas, aerospace and military sectors, where there is often a wide 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.

Tip #8 – it is no coincidence that inductive sensors are often an automatic choice for high-reliability, harsh environment applications.


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.

Tip #9 – if a traditional inductive sensor is too big, bulky, expensive or not sufficiently accurate, consider one of the new generation of inductive sensors.

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 these sensors offer extremely stable measurements over wide temperature ranges. The example shown below is an Incoder (inductive encoder) that 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 coefficients of <0,25ppm/K, which equates to less than one fifth of an arc-second per Celsius change.

Tip #10 – Inductive encoders offer especially low thermal coefficients.