An analytical solution to temperature field distribution in a thick rod subjected to periodic-motion heat sources and application in ball screws

ABSTRACT

In this work, an analytical solution to temperature field distribution in a finite cylinder body caused by constant-strength, periodic-motion heat sources is obtained. Two heat source models, i.e. single and multiple, are proposed. The analytical solution is applied in calculating the temperature rise of a Z-direction feeding ball screw. The plotted temperature rise curves show that the error of the two models is 0.5% and they are both reasonable for theoretical calculation as they show the same trend as a test value curve. The maximum error of surplus temperature in the steady state between the calculated values and test results of the single heat source model is 14.1%, which is acceptable in engineering applications.

KEYWORDS:

• Finite-length thick rod
• periodic-motion heat source
• Green’s function approach
• temperature rise

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Key R&D Plan [grant number 2019YFB2006402] and the Key Projects of Science and Technology Support in Jiangsu Province [grant number BE2014004-3].