Temperature measurement planning for thermal compensation of dimensional measurement in assembly environments

  • David Ross-Pinnock

Student thesis: Doctoral ThesisPhD


As more is demanded from dimensional measurement capability, more is demanded from the understanding of its main sources of uncertainty. At the large volume scale, thermal effects contribute significantly to dimensional uncertainty, particularly through thermal expansion and contraction of parts, tooling, and instruments. The problem was highlighted in aerospace assembly, while marine, and automotive assembly are other sectors affected by complex thermal environments.

This thesis focuses on the problem of thermal expansion compensation of objects being measured. Most of the current understanding of thermal expansion compensation has been gained at the instrument level, in which manufacturers have modelled the effects of ambient temperature on measurement error and provided a calibrated correction. Simulation based thermal-structural modelling is well established for several applications. A lot of temperature measurement research and standards have focused on sensors, and not as much on the practicalities of using the sensors to produce the best outcomes.

Experimentation on structures at the laboratory scale provided insights into how simulation could be used to compensate for thermal expansion. It became evident that the position of the sensors plays a significant role in accurately reproducing temperature distributions. Industrial measurements showed spatial and temporal thermal variation of several degrees, further highlighting the need for a tool to integrate dimensional and temperature measurement planning.
A computational tool was built to test the task specific performance of temperature sensor networks in the context of thermal expansion. The tool allows for temperature distributions to be generated and FEA simulations to be run to test specified sensor networks. Results for temperature measurement capability were calculated, and its ultimate impact on the simulation’s ability to determine thermal expansion can be assessed. The approach was first applied to the case of a large beam to develop the tool, and to understand how different factors affected the ability to reconstruct temperature distributions. Sensor positioning and models for reconstruction had a more significant impact on temperature distribution reproduction than individual sensor uncertainties for this task.

The final case study focused on a more complex assembly structure. Random search optimisation and sensor removal sensitivity studies of the network positions revealed most impactful sensors. Simulation of daily temperature variation using the tool demonstrated its ability to determine performance over time with varying temperature distributions. A polynomial interpolation model using a 16-sensor network with 0.1 °C (confidence interval, k = 2) uncertainty sensors could produce a consistent temperature reconstruction error of ~0.04 °C RMS, corresponding to a thermal expansion error of ~1.5 µm in aluminium over the 1.6 m-tall structure. Results such as this could impact how temperature measurement planning is valued and how resources are allocated to measurement activities.

The creation of this tool demonstrates a computational, low-risk approach to temperature measurement planning and uncertainty quantification for dimensional. It is anticipated that in the future this tool can be used for increasingly complex cases and further validated through detailed uncertainty studies at large scales.
Date of Award21 Jul 2021
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorPatrick Keogh (Supervisor) & Andrew Rees (Supervisor)


  • Metrology
  • Temperature measurement
  • Thermal compensation
  • large volume metrology
  • finite element analysis
  • measurement planning
  • sensor networks

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