Conway, Benjamin (2021) Estimating positional thermal errors in a ballscrew feed-drive system from discrete ballscrew temperature measurements. Doctoral thesis, University of Huddersfield.

Accuracy of machine tool linear axes is affected by the thermal expansion of the ballscrew. Most research and industrial compensation estimates expansion based on duty-cycle (motion at a given feed rate for a given length of time) or a limited number of temperature readings, usually one, on a non-rotational part of the structure. These assumptions introduce model errors and compromise reproducibility under different machine operating conditions.

In this thesis, a non-contact temperature measurement system was created to directly generate a temperature profile of the rotating ballscrew to provide better estimation of the expansion. Infrared sensors were selected, but they are shown to be heavily affected by emissivity. This creates a significant challenge for use on ballscrews that, in operation, are often non-uniformly covered in lubricants which modify the effective emissivity. A new method of emissivity calibration was developed and optimised with a golden section search algorithm and parabolic interpolation to find and map an emissivity profile along the length of the ballscrew.

A further challenge was found to be that given its response time, the infra-red sensor has a reliable sample rate of 250ms. It cannot therefore be used for continuous measurement, due to the relative motion of the sensor to the ballscrew. This means that under normal machine operation reliable ballscrew temperature measurements can only be obtained at quasi-random, probably spatially sparse locations. The data is not sufficiently spatially dense to produce an accurate estimate of the resultant positional error. Thus, a temperature model is required to estimate the spatial temperature profile of the ballscrew. Linear interpolation was found to be too coarse a solution and did not account for thermal dissipation. A thermal field model provided better estimation of the thermal dissipation, but the only heat input was at the few locations with direct sensor measurement, ignoring those parts of the ballscrew that are not directly measured.

To overcome the interpolation problem, an online multi-parameter parametric thermal model was developed from a theoretical model previously created within the research group. The previous model used only simple movement with basic trapezoidal heating, in line with ISO230-3:2001 axis heating tests, as its inputs. The new model is adapted to take actual, random position data as the motion input, making it much more representative of a machine tool in use. Model parameters were updated with values, found either from calculation or experimentally, to tune it for the rig under test. Testing was carried out on a ballscrew to calculate the free-and forced-convection for specific temperature ranges and to find the ballscrew-nut contact conduction coefficient. New conduction coefficients values were found by utilising a Nelder-Mead simplex algorithm to reduce the output thermal profile error compared to the reference temperature profile.

The final deliverable from the project is anew parametric model that interpolates discrete, non-contact thermal measurement to measure estimate the thermal profile of the ballscrew before converting this to an estimate of thermal expansion. The parametric model splits the ballscrew into small elements and has block thermal parameters for components in the ballscrew feed drive system. The model’s heat generation calculation is updated with feedback from the infrared sensor whenever the axis is stationary to overcome limitations in the accuracy of the model parameters. For the machine and conditions tested, a thermal displacement error of up to 73.7μm was predicted with a model error of less than 6%achieved.This compares to 37% with the previous model on which it was based.

This model is suitable for any ballscrew-based feed axis, given knowledge of the physical geometry of the ballscrew and the known friction torque, thermal contact coefficients, which can both be found experimentally. The work proved the feasibility of this approach however, it has only been proven on the ballscrew feed drive detailed in this thesis. Development work is needed to industrialise the system to make it immune from oil ingress. Further research is recommended into methods of overcoming the slow response time of the infrared detector to further improve the accuracy of the estimation algorithm.

FINAL THESIS - Conway.pdf - Accepted Version
Restricted to Repository staff only until 17 May 2026.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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